Dpfc Thesis

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DISTRIBUTED POWER FLOW

CONTROLLER

Zhihui Yuan

苑苑苑苑

志志志志

辉辉辉辉

Electrical Power Processing (EPP) Unit

Electrical Sustainable Energy Department

Delft University of Technology



DISTRIBUTED POWER FLOW

CONTROLLER

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft;op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben;

voorzitter van het College voor Promoties

in het openbaar te verdedigen op maandag 18 oktober 2010 om 10.00 uur

door

Zhihui YUAN

Master of Science in Engineering, Charlmers University of Technology

geboren te Hei Long Jiang, China



Dit proefschrift is goedgekeurd door de promotor:

Prof. dr. J.A. Ferreira

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. dr. J.A. Ferreira, Delft University of Technology, promotor

Ir. S.W.H. de Haan, Delft University of Technology, copromotor

Prof. ir. L. van der Sluis, Delft University of Technology

Prof. dr. ir. M. Verhaegen, Delft University of Technology

Prof. dr. ir. P. Lataire, Vrije Universiteit Brussel

Prof. ir. W.L. Kling, Eindhoven University of Technology

ISBN: 978-90-8570-612-0

Printed by WOHRMANN PRINT SERVICE, Zutphen, the Netherlands.

Proofread by Veronica Pisorn

Copyright c 2010 by Zhihui Yuan

All rights reserved.



ACKNOWLEDGEMENT

The research presented in this thesis was carried out at the Delft University of Technology

in the Netherlands, in the research group of Electrical Power Processing (EPP), in where

I have spent unforgettable four years towards my Ph.D. During this period, many people

directly or indirectly involved in the research and this thesis would not complete without

them. I would like to take this opportunity to express my gratitude and appreciation to

these people.

First of all, I would like to thank to my promoter Professor Braham Ferreira for the

opportunity to do my Ph.D. in the Netherlands and for his guidance and brilliant ideas

that enlighten the research. I wish to express my sincere gratitude to my daily supervisor

Ir. Sjoerd W.H. de Haan, whose door was always open to me. Thanks for his guidance

and so many discussions on the research. I am also grateful for his patience on correcting

my papers and thesis. Without him, the thesis would not be possible.

I would also like to thank my doctoral examination committee, Prof. Philippe Lataire,

Prof. Lou van der Sluis, Prof. Michel Verhaegen and Prof. Wil Kling for spending a

large amount of time on reading on my draft thesis and giving valuable comments and

suggestions.

The research presented in this thesis was partially funded from the energy research

program ‘Energie Onderzoek Subsidie (EOS)’, supported by the Ministry of Economic

Affairs, the Netherlands. I wish to express my thanks for the support.

In addition, I would like to thank my colleagues and friends in the EPP group, espe-

cially Rob Schoevaars for his great help and assistance of my experiment, Bart Rooden-

burg for the translation of the summary into Dutch and Rick van Kessel for translating

the propositions into Dutch. Thanks to Aleksandar Borisavljevic, Anoop Jassal, Balazs

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Czech, Dalibor Cvoric and J. Marcelo Gutierrez-Alcaraz for the enjoyable sports and fun

activities. It was super fun to play tennis, snowboard and to do gym with you. I wouldalso like to thank to Deok-Je Bang, Dongshen Zhao, Ghanshyam Shrestha, Ivan Josifovic,

Johan Wolmarans, Yi Wang and Yi Zhou for making the time of my Ph.D. enjoyable.

Last but not least, I would like to thank my family; my mother Gao Ling, my father

Yuan QingGuo and my lovely wife Zhao Bo, to whom this thesis is dedicated for, for their

love, support and understanding.



To my family



SUMMARY

In modern power systems, there is a great demand to control the power flow actively.

Power flow controlling devices (PFCDs) are required for such purpose, because the power

flow over the lines is the nature result of the impedance of each line. Due to the control

capabilities of different types of PFCDs, the trend is that mechanical PFCDs are gradually

being replaced by Power Electronics (PE) PFCDs. Among all PE PFCDs, the Unified

Power Flow Controller (UPFC) is the most versatile device. However, the UPFC is not

widely applied in utility grids, because the cost of such device is much higher than the

rest of PFCDs and the reliability is relatively low due to its complexity.

The objective of this thesis is to develop a new PFCD that offers the same control

capability as the UPFC, at a reduced cost and with an increased reliability. The new

device, so-called Distributed Power Flow Controller (DPFC), is invented and presented

in this thesis. The DPFC is a further development of the UPFC. It has been shown that

the DPFC fulfills all three of the listed goals. This thesis starts with the review the state-

of-art of current PFCDs, followed by the research at the DPFC device level, including

the operation principle, the modeling and control, and experimental demonstrations. At

the end, the thesis presents the research at the system level, which includes the DPFC

applications to improve power system controllability and stability, and the feasibility of

the DPFC for real networks.

Device Level

The DPFC eliminates the common DC link within the UPFC, to enable the independent

operation of the shunt and the series converter. The D-FACTS concept is employed in

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the design of the series converter. Multiple low-rating single-phase converters replace the

high-rating three-phase series converter, which greatly reduces the cost and increases thereliability. The active power that used to exchange through the common DC link in the

UPFC, is now transferred through the transmission line at the 3rd harmonic frequency.

The DPFC has been modeled in a rotating dq -frame. Based on this model, the basic

control of the DPFC is developed. The basic control stabilizes the level of the capacitor

DC voltage of each converter and ensures that the converters inject the voltages into the

network according to the command from the central control. The shunt converter injects

a constant current at the 3rd harmonic frequency, while its DC voltage is stabilized by the

fundamental frequency component. For the series converter, the reference of the output

voltage at the fundamental frequency is obtained from the central controller and the DC

voltage level is maintained by the 3rd harmonic component.

To verify the dynamic model and the basic control, a DPFC demonstration setup is

built. The setup consists of a scaled network, one shunt converter and six series converters.

All DPFC converters are independently controlled by their own DSP controllers. It shows

that the shunt and series converters can exchange active power through the 3rd harmonic

component and that the DC voltages of the series converter can be maintained at a

constant level during different situations.

The fault tolerance of the DPFC is also investigated. The protection method of the

DPFC for different types of failures is addressed. In addition, the use of supplementary

controls to ensure the continuously operation of the DPFC during converter failures is

presented.

Power System Level

Two applications of the DPFC at the system level are investigated, namely utilizing the

DPFC to damp low-frequency power oscillation and to compensate asymmetrical voltages.

A maximum of three Power Oscillation Damping (POD) controllers can be applied to one

DPFC, which indicates that the DPFC can shift three critical oscillatory modes at the

same time. Within the thesis, the POD controller is designed using the residue method and

a two-area network is used in the case study. For asymmetry compensation, the DPFC can

compensate both active and reactive asymmetry at the fundamental frequency, because

of the active power exchange between the shunt and the series converters. In addition,



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since the series converter is single-phase converter, the DPFC can compensate for both

zero and negative sequence components. Accordingly, the DPFC currently is the mostversatile device for asymmetry compensation among all FACTS devices.

DPFC design procedures are introduced, which give the equations to determine the

major parameters of the DPFC. According to the procedure, a case study, which is to

use DPFC to replace the KEPCO UPFC in Korea, is investigated. It is found that in

order to achieve the same control capability as the UPFC, the DPFC requires much less

material and creates a smaller footprint. The application of the DPFC for power flow

control is discussed and a triangle network in the Netherlands is selected as the case. It

shows that the DPFC can dynamically control the power flow within the triangle network.In addition, the DPFC improves the voltage and angle stability of the network.



Samenvatting

Er is een grote vraag ontstaan om het energietransport in moderne elektriciteitsnetwerken

actief te kunnen regelen. Het energietransport over een lijn wordt bepaald door de aard

(impedantie) van elke lijn en voor actieve regeling zijn Power Flow Controlling Devices

(PFCDs) nodig. Door de beperkte mogelijkheden van de verschillende soorten PFCDs

is de trend dat mechanische PFCDs geleidelijk worden vervangen door varianten met

vermogenselektronica, zogenaamde PE PFCDs. Van alle PE PFCDs is de Unified PowerFlow Controller (UPFC) het meest veelzijdig. Deze worden echter niet op grote schaal

in elektriciteitsnetten toegepast omdat de kosten van dergelijke apparatuur veel hoger

ligt dan die van standaard PFCDs en tevens is door de complexiteit van de UPFC de

betrouwbaarheid relatief laag.

Het doel van dit proefschrift is om een nieuwe PFCD te ontwikkelen met dezelfde

controle mogelijkheden als de UPFC, maar dan tegen lagere kosten en met een hogere

betrouwbaarheid. Het ontwikkelde nieuwe apparaat, de zogenaamde Distributed PowerFlow Controller (DPFC) is beschreven in dit proefschrift. De DPFC is een verdere on-

twikkeling van de UPFC. Er wordt aangetoond dat de DPFC voldoet aan alle drie de

gestelde doelen. Dit proefschrift begint met een overzicht van de huidige PFCD tech-

nieken en vervolgens wordt het onderzoek aan de DPFC op apparaat niveau beschreven,

met inbegrip van het werkingsprincipe, de modellering, het regelgedrag, en experimentele

validatie. Als laatste presenteert het proefschrift het onderzoek op systeem niveau, in-

clusief de DPFC toepassingen voor het verbeteren van de stabiliteit en regelbaarheid van

netten en de haalbaarheid van de DPFC in het echte elektriciteitsnet.

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Apparaat Niveau

De DPFC elimineert de gemeenschappelijke DC tussenkring in de UPFC, om een on-

afhankelijke werking van de shunt- en de series converter mogelijk te maken. Bij het on-

twerpen van de series converter is gebruik gemaakt van het D-FACTS concept. Meerdere

laag vermogen enkelfase omvormers vervangen de hoog vermogen driefasen serie converter.

Dit reduceert de kosten en verhoogt de betrouwbaarheid sterk. Het actieve vermogen

dat uitgewisseld werd via de gemeenschappelijke DC tussenkring in de UPFC, wordt nu

overgebracht via de transmissie lijn op de 3e harmonische frequentie.

De DPFC is gemodelleerd in een roterend dq stelsel en de ontwikkelde regeling van deDPFC is gebaseerd op dit model. De regeling stabiliseert het niveau van de condensator

gelijkspanning van elke converter en zorgt ervoor dat de te injecteren spanning in het

netwerk in overeenstemming is met het commando vanuit de centrale regelaar. De shunt

converter injecteert een constante 3e harmonische stroom, terwijl de DC spanning wordt

gestabiliseerd door de fundamentele frequentie. Het referentiesignaal aan serie converter

voor de fundamentele frequentie van de uitgangsspanning wordt verkregen vanuit de cen-

trale regelaar en het DC spanningsniveau wordt gehandhaafd door de 3e harmonische

component.Om het dynamische model en de fundamentele werking van de regelaar te verifiren

is een DPFC demonstrator gebouwd. De opstelling bestaat uit een geschaald netwerk,

een shunt converter en zes serie converters. Alle DPFC converters worden onafhankelijk

geregeld door hun eigen DSP regelaar. Hieruit blijkt dat de shunt- en series converters

actief vermogen kunnen uit te wisselen via de 3e harmonische component en dat de DC

spanning van de serie converter op een constant niveau kan worden gehouden gedurende

verschillende situaties.

Eveneens is de fouttolerantie van de DPFC onderzocht, inclusief de beveiliging ten

gevolge van verschillende fouten en het gebruik van aanvullende regelingen om de sys-

teemeigenschappen te verbeteren tijdens converter fouten.

System Niveau

Twee toepassingen van de DPFC zijn op systeemniveau onderzocht, te weten het gebruik

van de DPFC om laagfrequente vermogensoscillaties te dempen en de mogelijkheid om



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asymmetrische spanningen te compenseren. Op een DPFC kunnen maximaal drie Power

Oscillatie Damping (POD) regelaars worden toegepast, waardoor de DPFC drie kritischeresonantie modes op hetzelfde moment kan verschuiven. De POD regelaar in dit proef-

schrift is ontworpen met behulp van de residue-method en in de case studie is een two-area

netwerk gebruikt. Tijdens asymmetrie compensatie kan de DPFC zowel actieve- als re-

actieve asymmetrie compenseren op de fundamentele frequentie. Dit is mogelijk omdat

actief vermogen uitgewisseld kan worden tussen de shunt- en de serie converters. Omdat

de serie converter een n fase converter is, kan de DPFC zowel de homopolaire component

als de negatieve component compenseren. Daardoor is de DPFC op dit moment het meest

veelzijdig van alle FACTS apparaten.Voor het bepalen van de systeemoverdracht en de belangrijkste parameters van de

DPFC is een ontwerp procedure ontwikkeld. Volgens deze procedure is een DPFC case

studie uitgevoerd, waarbij de KEPCO UPFC in Korea moest worden vervangen. Hieruit

kwam naar voren dat de DPFC bij gelijke regeleigenschappen veel minder materiaal en

ruimte nodig heeft. De toepassing om het energietransport te regelen met een DPFC

is besproken aan de hand van een driehoekig netwerk in Nederland. Hieruit blijkt dat

de DPFC in staat is het energietransport in dit netwerk dynamisch te kunnen regelen.

Bovendien verbetert de DPFC de spanning en de fase stabiliteit van het netwerk.



Contents

1 INTRODUCTION 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Power Flow Controlling Devices . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Objective and Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 OVERVIEW OF POWER FLOW CONTROLLING DEVICES 13

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Power Flow Control Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Categorization of PFCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Shunt Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.1 SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.2 STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Series Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.1 TSSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.2 TCSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.3 SSSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5.4 DSSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6 Combined Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6.1 PST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6.2 UPFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.7 IPFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 DISTRIBUTED POWER FLOW CONTROLLER 29

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Distributed Power Flow Controller (DPFC) . . . . . . . . . . . . . . . . . 30

3.2.1 DPFC Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.2 DPFC Operating Principle . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.3 DPFC Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.4 Variation of the Shunt Converter . . . . . . . . . . . . . . . . . . . 36

3.2.5 Advantages and Limitation of the DPFC . . . . . . . . . . . . . . . 373.3 DPFC Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 DPPF Simplification and Equivalent Circuit . . . . . . . . . . . . . 38

3.3.2 Fundamental Frequency Circuit . . . . . . . . . . . . . . . . . . . . 40

3.3.3 Third Harmonic Frequency Circuit . . . . . . . . . . . . . . . . . . 44

3.3.4 Control Range of the DPFC . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Distributed Interline Power Flow Controller . . . . . . . . . . . . . . . . . 47

3.4.1 DIPFC Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4.2 DIPFC Operating Principle . . . . . . . . . . . . . . . . . . . . . . 483.4.3 DIPFC Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.5 DIPFC Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.5.1 DIPPF Simplification and Equivalent Circuit . . . . . . . . . . . . . 51

3.5.2 Fundamental Frequency Circuit . . . . . . . . . . . . . . . . . . . . 53

3.5.3 Third Harmonic Frequency Circuit . . . . . . . . . . . . . . . . . . 53

3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 DPFC MODELING AND BASIC CONTROL 574.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2 DPFC Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2.1 DPFC Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2.2 Connection of Separated Models . . . . . . . . . . . . . . . . . . . . 60

4.2.3 Network Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.4 Series Converter Modeling . . . . . . . . . . . . . . . . . . . . . . . 64

4.2.5 Shunt Converter Modeling . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 DPFC Basic Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69



CONTENTS xv

4.3.1 Series Converter Control . . . . . . . . . . . . . . . . . . . . . . . . 69

4.3.2 Shunt Converter Control . . . . . . . . . . . . . . . . . . . . . . . . 724.4 Simulation Results of the DPFC Modeling and Control . . . . . . . . . . . 78

4.5 Communication Between the Central Control and Series Converters . . . . 80

4.5.1 Principle of the Method . . . . . . . . . . . . . . . . . . . . . . . . 81

4.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5 DPFC EXPERIMENTAL DEMONSTRATOR 87

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.1 Scaled Network Specifications . . . . . . . . . . . . . . . . . . . . . 88

5.2.2 DPFC Converter Specifications . . . . . . . . . . . . . . . . . . . . 89

5.3 DPFC Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.1 Scaled Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.2 Series Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.3 Shunt Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.4 Overall Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 935.4 DPFC Control Realization . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.5 Results of the Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 95

5.5.1 Steady-state Results . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.5.2 Step-response Results . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6 DPFC FAULT TOLERANCE 101

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.2 Possible Faults in the DPFC . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.3 Shunt Converter Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.2 Principle of the Control . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.3 Transient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.3.4 Simulation and Experiments Results . . . . . . . . . . . . . . . . . 109

6.4 Series Converter Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111



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6.4.2 Principle of the Control . . . . . . . . . . . . . . . . . . . . . . . . 111

6.4.3 Compensation Controller Design . . . . . . . . . . . . . . . . . . . . 1136.4.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7 DPFC AUXILIARY SERVICES 119

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2 Power Oscillation Damping (POD) . . . . . . . . . . . . . . . . . . . . . . 120

7.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.2.2 POD Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.2.3 DPFC Current Injection Model . . . . . . . . . . . . . . . . . . . . 121

7.2.4 DPFC POD Controller Design . . . . . . . . . . . . . . . . . . . . . 123

7.2.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.3 Asymmetrical Component Compensation . . . . . . . . . . . . . . . . . . . 129

7.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.3.2 Principle of Compensating the Asymmetrical Voltage . . . . . . . . 130

7.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.3.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8 DPFC APPLICATION IN UTILITY GRIDS 137

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

8.2 DPFC Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

8.2.1 System Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1388.2.2 DPFC Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

8.2.3 Converter Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

8.3 Case Study 1: Two-Port Network . . . . . . . . . . . . . . . . . . . . . . . 144

8.3.1 Case Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8.3.2 DPFC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

8.3.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.4 Case Study 2: Triangle Network . . . . . . . . . . . . . . . . . . . . . . . . 149

8.4.1 Case Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 149



CONTENTS xvii

8.4.2 DPFC Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.4.3 Control Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1518.4.4 Advantages of the DPFC solution . . . . . . . . . . . . . . . . . . . 152

8.4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

9 CONCLUSIONS AND RECOMMENDATIONS 157

9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

9.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

A PARK’S TRANSFORMATION 163

A.1 3-Phase Park’s Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 163

A.2 Single-phase Park’s Transformation . . . . . . . . . . . . . . . . . . . . . . 164

B SINGLE-PHASE PHASE LOCK LOOP 167

C NETWORK SIMPLFICATION 169

C.1 Network Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.2 Network Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

C.3 PU Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

C.4 Experimental Setup Specifications . . . . . . . . . . . . . . . . . . . . . . . 171

D LIST OF SYMBOLS 173

REFERENCES 185

LIST OF PUBLICATIONS 187

CURRICULUM VITAE 189



Chapter 1INTRODUCTION

1.1 Background

S INCE Thomas Edison and his company, the Edison Electric Light Company, devel-

oped the first steam-powered electric power station on Pearl Street in New York City,

electricity has played an increasingly important role in our daily lives, with a dramatic

increase in consumption as well as the generation of electricity over the past hundred

years. In the year 2008, the world’s electricity consumption reached 17.48 tera kWh1 and

this number continuously advances.

The electrical power system serves to deliver electrical energy to consumers. An elec-

trical power system deals with electrical generation, transmission, distribution and con-

sumption. In a traditional power system, the electrical energy is generated by centralized

power plants and flows to customers via the transmission and distribution network. The

rate of the transported electrical energy within the lines of the power system is referred

to as ‘Power Flow’ [Park 09], to be more specific, it is the active and reactive power that

flows in the transmission lines.

During the last twenty years, the operation of power systems has changed due to

growing consumption, the development of new technology, the behavior of the electricity

market and the development of renewable energies. In addition to existing changes, in

the future, new devices, such as electrical vehicles, distributed generation and smart grid

concepts, will be employed in the power system, making the system extremely complex.

Figure 1-1 shows the representation of a future power system, where the clouds in the fig-

1

DATA SOURCE: CIA World Factbook

1



2 1.1 Background

ure indicate the mentioned developments. According to the time line, these developments

are happening in the sequence from bottom to top of Figure 1-1.

transmission

network

substation

transformer

step up

transformer

power

generation

distribution

network

industry

consumers

private

consumers

inter-area

connection

commercial

consumers

distributed

generation

solar cell

wind

turbines

growing

consumption

electrical

vehicles

system

control

center

electricity

marketing

smart grid

T I M

E

Figure 1-1: Simple diagram of an electric power system and scenario trends

The above-mentioned developments and growth will have a great impact on the power

system, especially on power flow. Conventionally, the power flow in power systems has

a fixed direction; it always flows from the point of generation through the transmission

network to the distribution network. In these systems, changes in power flow are sched-

uled based on hours, not more frequently. However, due to the trends listed above, newer

systems with greater capabilities are already being put to use; power flow can be bidi-

rectional and variations can occur in minutes or even seconds. Figure 1-2 illustrates theimpact of these new trends on the power flow.

Distributed Generation (DG) takes place at small and medium power generators that

are connected to the distribution side of the power system [Bark 00]. Many DG units

are based on renewable energy sources such as solar and wind [ Putt 03]. Driven by

government policies aimed at reducing greenhouse gas emissions and conserving fossil

fuels, as agreed by the Kyoto protocol [Morr 06], the number of grid-connected DG units

is increasing. Introducing a number of generators on the distribution side leads to big

changes of the power flow in networks. First, the direction of the power flow is different



1 INTRODUCTION 3

distributed

generation

growing

consumption

smart grid

electricity

marketing

inter-area

connection

bidirectional

power flow

inverse power

flow

fast variation

power flow

d e v e l o p m e n t s

i m p a c t s o n p o w e r f l o w

Figure 1-2: Relation chart of the trends and their impact on the power flow

from the traditional direction. When DG units in one area feed loads in other areas, there

will be reverse power flow from the distribution to the transmission side. Second, the

output energy of renewable sources depends on weather conditions. With the increasing

percentage of renewable energy sources in use, a large amount of power has to be controlled

to enable the power system to quickly switch between the renewable sources and stand-by

power generation. Therefore, stand-by power, which can be provided by near-by power

plants or energy storages, should be available when renewable energy is insufficient to

supply the load. This leads to an increased need for power flow control methods.

Growing consumption requires transmission networks and generation plants to support

this grow. However, the increase of the transmission capacity cannot follow the increased

demand due to the high cost, right-of-way issues and environmental problems. A possible

solution is to optimize the utilization of the network and to boost the transmitted power

to the thermal limit of the network. However, within a meshed network, several parallelpaths may exist from the generation plants to the loads. As power tends to flow along the

path with the lowest impedance, this results in overloaded lines. Overloaded lines make it

difficult to utilize the full transmission capacity of the network. Consequently, to increase

the transmission capacity of the whole network, there is a need to shift the power from

the overloaded line to other parallel paths.

To enable the trading of electricity between different zones, power systems in different

locations are inter-connected [Bomp 08]. During an emergency, the inter-connection can

reroute power to support the loads, thereby increasing the stability of the system. How-



4 1.2 Power Flow Controlling Devices

ever, inter-area connections result in multiple parallel paths between power plants and

consumers, which give rise to loop flow [Choo 06] and cause congestions. To reduce theloop flow, there is a need for bidirectional power flow control between zones [Wei 03].

The electricity market is a system for effecting the purchase and sale of electricity,

using supply and demand to set the price [Song 03]. With the emerging liberalization of

the electricity market, power prefers to flow ‘from the source with the lowest price in the

direction of the highest price’ [Grai 94]. To ensure that the power flows according to the

economic law, rather than Ohm’s law, the power should be controlled to flow within the

transmission network with the desired direction and quantity.

A smart grid is a concept that integrates IT technology into the electricity network to

control appliances at consumer locations to save energy, reduce cost and increase reliability

and transparency [Farh 09, Sloo 09]. The idea of a smart grid is to monitor conditions

anywhere in the power generation, transmission, distribution and demand chain. Any

change in conditions, in the environment, in the power supply market, locally in the

distribution grid or at home, will be reported to the system central controller to change

the power flows accordingly.

As a consequence of the above-mentioned developments, the future power system

will be a meshed network and the power flow within this network, both the direction and

quantity, will be controlled. To keep the system stable during faults or weather variations,

the response time of the power flow control should be within several cycles to minutes.

Without proper controls, the power cannot flow as required, because it follows the path

determined by the parameters of generation, consumption and transmission [Van 05]. To

fulfill the power flow requirements for the future network, power flow controlling devices

are needed.

1.2 Power Flow Controlling Devices

Power flow is controlled by adjusting the parameters of a system, such as voltage magni-

tude, line impedance and transmission angle. The device that attempts to vary system

parameters to control the power flow can be described as a Power Flow Controlling Device

(PFCD).

Depending on how devices are connected in systems, PFCDs can be divided into shunt

devices, series devices, and combined devices (both in shunt and series with the system),



1 INTRODUCTION 5

as shown in Figure 1-3.

PFC

PFC

PFC

grid grid grid

transmission

linetransmission

line

transmission

line

shunt PFC series PFC combined PFC

Figure 1-3: Simplified diagram of shunt, series and combined devices

A shunt device is a device that connects between the grid and the ground. Shunt

devices generate or absorb reactive power at the point of connection thereby controlling

the voltage magnitude. Because the bus voltage magnitude can only be varied within

certain limits, controlling the power flow in this way is limited and shunt devices mainly

serve other purposes. For example, the voltage support provided by a shunt device at the

midpoint of a long transmission line can boost the power transmission capacity [Hing 00].

Another application of shunt devices is to provide reactive power locally, thereby reduc-

ing unwanted reactive power flow through the line and reducing network losses. Also,

consumer-side shunt devices can improve power quality, especially during large demand

fluctuations [Zhan 06]. The operating principle of shunt devices can be found in chapter 2.

A device that is connected in series with the transmission line is referred to as a ‘series

device’. Series devices influence the impedance of transmission lines. The principle is to

change (reduce or increase) the line impedance by inserting a reactor or capacitor. To

compensate for the inductive voltage drop, a capacitor can be inserted in the line to reduce

the line impedance. By increasing the inductive impedance of the line, series devices are

also used to limit the current flowing through certain lines to prevent overheating. Theprinciple of series devices is explained in more detail in chapter 2.

A combined device is a two-port device that is connected to the grid, both as a

shunt and in a series, to enable active power exchange between the shunt and series parts.

Combined devices are suitable for power flow control because they can simultaneously vary

multiple system parameters, such as the transmission angle, the bus voltage magnitude

and the line impedance.

Based on the implemented technology, PFCDs can be categorized into mechanical-

based devices and power electronics (PE)-based devices.



6 1.2 Power Flow Controlling Devices

Mechanical PFCDs consist of fixed or mechanical interchangeable passive components,

such as inductors or capacitors, together with transformers. Typically, mechanical PFCDshave relatively low cost and high reliability. However, because of their relatively low

switching speed (from several seconds to minutes) and step-wise adjustments of mechan-

ical PFCDs [Baum 65, Pill 03], they have relatively poor control capability and are not

suitable for complex networks of the future.

PE PFCDs also contain passive components, but include additional PE switches to

achieve smaller steps and faster adjustments [Song 99]. There is another term - Flexible

AC Transmission System (FACTS) - that overlaps with the PE PFCDs. According to

the IEEE, FACTS is defined as an ‘alternating current transmission system incorporating

power electronic based and other static controllers to enhance controllability and increase

power transfer capability’ [Edri 97]. Normally, the High Voltage DC transmission (HVDC)

and PE devices that are applied at the distribution network, such as a Dynamic Voltage

Restorer (DVR), are also considered as FACTS controllers [Moor 95]. Most of the FACTS

controllers can be used for power flow control. However, the HVDC and the DVR are out

of the scope of the PFCD. The relationship between the PFCDs, FACTS controllers and

mechanical controller is shown in Figure 1-4.

power flow

controlling devices

FACTS

controller

mechanical

controller

Figure 1-4: Relationship between the PFCDs, FACTS controllers and mechanical controller

PE PFCD devices can be further subcategorized into two types according to the ap-

plied switch technologies: thyristor-based devices and Voltage Source Converter (VSC)

[Moha 03]-based devices.

Thyristor PFCDs use inverse-parallel thyristors in series or in parallel with passive

components. By controlling the firing angle of the thyristors, the impedance of the device

can be adjusted. A thyristor can be controlled to turn on but not to turn off. It will turn



1 INTRODUCTION 7

off automatically when the current goes negative. Consequently, the thyristor can only be

turned on once within one cycle. The switching frequency of thyristor PFCDs is thereforelimited to the system frequency (50/60Hz), resulting in low switching losses. Because

thyristors can handle larger voltages and currents than other power semiconductors, the

power level of thyristor PFCDs are also higher. The thyristor PFCDs are simpler than

VSC PFCDs, allowing them higher reliability. However, the waveforms of voltages and

currents generated by thyristor PFCDs contain a large amount of harmonics, thereby

requiring large filters.

VSC PFCDs employ advanced switch technologies, such as Insulated Gate Bipolar

Transistors (IGBT), Insulated Gate Commutated Thyristors (IGCT), or Metal Oxide

Semiconductor Field Effect Transistors (MOSFET) to build converters. Because these

switches have turn-on and turn-off capability, the output voltage of a VSC is independent

from the current. Consequently, it is possible to turn the switches on and off within the

VSC multiple times within one cycle. Several types of VSCs have been developed, such

as multi-pulse converters, multi-level converters, square-wave converters, etc [Moha 03].

These VSCs proved a free controllable voltage in both magnitude and phase. Due to their

relatively high switching frequency, VSC PFCDs make practically instant control (less

than one cycle) possible. High switching frequencies also reduce low frequency harmon-

ics of the outputs and even enable PFCDs to compensate disturbances from networks.

Therefore, VSC PFCDs are the most suitable devices for future power systems.

On the other hand, there are some challenges facing VSC PFCDs. Firstly, because

large amounts of switches are connected in series or in parallel to allow the high voltage

and high current through, the VSC PFCDs are expensive. In addition, due to their

higher switching frequency and higher on-state voltage in comparison with thyristors,

VSC PFCD losses are higher as well. However, with developments in power electronics

(such as Silicon-carbide, Gallium-Nitride and synthetic diamond) [Davi 09], VSC PFCDs

can become more feasible and cost-effective in the future.

According to the above considerations of different types of PFCDs, it can be concluded

that PE combined PFCDs (also referred to as combined FACTS) have the best control

capability among all PFCDs. They inherit the advantages of PE PFCDs and combined

PFCDs, which is the fast adjustment of multiple system parameters. The Unified Power

Flow Controller (UPFC) and Interline Power Flow Controller (IPFC) [Gyug 92, Gyug 99]

are currently the most powerful PFCDs; they can adjust all system parameters: line



8 1.3 Problem Definition

impedance, transmission angle, and bus voltage. The operating principle of the UPFC

and the IPFC will be introduced in chapter 2.

1.3 Problem Definition

Although the UPFC and the IPFC have superior capability to control power flow, there

is no commercial application currently. The main reasons are:

• The first concern with a combined FACTS is cost. Typically, a FACTS cost around

120-150 $ per kVA, compared to 15-20 $ per kVA for static capacitors [ Diva 07]. Oneof the reasons for the high cost is that the ratings of FACTS devices are normally

in 100 MVA, with the system voltage from 100 kV to 500 kV. This requires a large

number of power electronic switches in series and parallel connection. To provide

voltage isolation, 3-phase high-voltage transformers are essential; furthermore, the

series-connected transformers require an even higher rating to handle fault voltages

and currents. Secondly, as the FACTS devices are installed at different locations for

different purposes, each of them is unique. As a result, each FACTS device requires

custom design and manufacturing, which leads to a long building cycle and highcost. Lastly, a FACTS is a complex system, and requires a large area for installation

and also well-trained engineers for maintenance.

• The second concern is possible failures in the combined FACTS. Two issues are

considered: the reliability of the device itself and its influence on power system se-

curity. The combined FACTS is a complex system, which contains a large number of

active and passive components. The large component number results that, without

proper precautions, the combined FACTS have a bigger chance of failure than other

PFCDs. To gain the desired reliability, complex protections (bypass circuit) andredundant backups (backup transformers and capacitor banks) are always provided

for the combined FACTS device, further raising the cost, an already concerning

factor. Also, a failure in the combined FACTS is more critical to the power system

than in other devices. For a shunt FACTS, device failure results in a disconnection

of the device from the grid which prevents it from providing reactive compensation.

Because the series converter of the combined FACTS is directly inserted into trans-

mission lines, not only the device, but also the transmission lines will be disengaged

from the system during the failure [Verm 04].



1 INTRODUCTION 9

Due to these two major drawbacks, the UPFC and IPFC are not widely applied in

practice. Even when there is a large demand of power flow control within the network, theUPFC and IPFC are not currently the industry’s first choice. Normally, a phase shifting

transformer, which has less control capability [Bres 04], is selected for economic reasons.

Accordingly, a low-cost, reliable combined FACTS device has great market potential.

1.4 Objective and Approaches

There is a great demand of power flow control in power systems of the future and combined

FACTS devices are the most suitable devices. However, due to the cost and the reliability

issues given above, there are many hurdles to the widespread application of combined

FACTS devices. Accordingly, the main objectives of this thesis can be summarized as:

To develop a new power flow controlling device that has the following characteristics:

• Comparable performance as the combined FACTS device - the UPFC or IPFC.

• Acceptable cost to electric utilities.

• Acceptable reliability for power systems.

The approach to develop such a device consists of the following steps:

• Review the fundamentals of power-flow-control theory and the state-of-art of PFCDs

with respect to operating principles, advantages and limitations.

• Analyze the UPFC and IPFC to determine their performance of power flow control.

• Find ways to reduce the cost and increase the reliability of combined FACTS devices.

• Generate a new concept of a power flow controlling device according to these points.

The new concept presented in this thesis is called ‘Distributed Power Flow Controller

(DPFC)’. It is a combined FACTS device, which has taken a UFPC as its starting point.The DPFC has the same control capability as the UPFC; independent adjustment of

the line impedance, the transmission angle and the bus voltage. The DPFC eliminates

the common DC link that is used to connect the shunt and series converter back-to-

back within the UPFC. By employing the Distributed FACTS concept [ Diva 07] as the

series converter of the DPFC, the cost is greatly reduced due to the small rating of the

components in the series converters. Also, the reliability of the DPFC is improved because

of the redundancy provided by the multiple series converters.

Once the DPFC concept is presented, the research follows the listed steps:



10 1.5 Thesis Layout

• Analyze and evaluate the proposed concept with respects to the control capability

and the rating of the DPFC.• Find the mathematical model of the DPFC.

• According to the DPFC model, design the control schemes of the DPFC.

• Verify the DPFC concept, both in the simulation and in experimental setup.

• Investigate the reliability of the DPFC during the failure of a single converter.

The above research focuses on the level of the DPFC device, and the following studies

consider the DPFC application at the power system level:

• Investigate the capability of the DPFC to damp low-frequency power oscillation.

• Utilize the DPFC to balance asymmetrical components within the network.

• Study the feasibility of the DPFC in a real transmission network.

1.5 Thesis Layout

The layout of the thesis is illustrated in Figure 1-5.

Chapter 2 gives an overview of the status of PFCDs. This chapter begins with the

principle of power flow control. Various PFCDs are introduced, categorized and compared.A new FACTS device, called Distributed Power Flow Controller (DPFC), is presented

in chapter 3. The DPFC is developed based on the UPFC and employs the Distributed

FACTS concept [Diva 05] for the series converters. Once the principle of the DPFC is

presented, the steady-state of the DPFC is analyzed. In the last part of this chapter, a

concept that is derived from the DPFC, the so-called Distributed Interline Power Flow

Controller (DIPFC) is introduced.

Chapter 4 addresses the modeling and control of the DPFC. The chapter begins with

modeling the DPFC in the dq -frame. Once the modeling of the DPFC is examined, thedesign of the DPFC primary control is given. The primary control is the basic control

layer for the DPFC, responsible for maintaining DC voltages of converters and generating

the AC voltages required by the central control. Further, the communication between the

DPFC series converters and the central control is considered. A low-cost and high-reliable

synchronization method for series converters is presented.

Chapter 5 considers the DPFC verification in a scaled experimental setup. The chapter

begins by presenting the specification of the setup, and continues with the design of major

components and control implementation. The chapter is concluded with the experimental



1 INTRODUCTION 11

Chapter 3: Distributed

Power Flow Controller

Chapter 4: DPFC

Modeling and Basic

Control

Chapter 6: DPFC FaultTolerance

Chapter 9: Conclusions

and Recommendations

Chapter 1: Introduction

Chapter 2: Overview of

Power Flow Controlling

Devices

Chapter 7: DPFC

Auxiliary Services

Chapter 8: DPFC

Application in Utility Grid

Chapter 5: DPFC

ExperimentalDemostrator

power system

level

DPFC device

level

DPFC

elementary

component &

control

DPFC

supplementary

control

Figure 1-5: Layout of the thesis



12 1.5 Thesis Layout

results of the DPFC.

The reliability of the DPFC is considered in chapter 6. Two types of converter failuresin the DPFC, namely a shunt converter failure and a series converter failure, are discussed.

In this chapter, the supplementary controllers that deal with different converter failures are

separately introduced. The principle, analysis and design of the controller are presented,

and the results achieved in both simulation and experimental setups are shown.

Chapter 7 considers the DPFC application at the power system level and focuses

on the outer loop within the central control. Two issues are discussed in this chapter:

utilizing DPFC to damp low-frequency power oscillation and methods of compensating

asymmetrical components.In chapter 8, the realization of the DPFC in real networks is examined. First, DPFC

design procedures are introduced, which give the equations to determine the major pa-

rameters of the DPFC. Two cases are studied for different purposes. Case 1 aims to find

the feasibility of the DPFC in a real transmission line and a two-port network is taken

as an example. The physical and electrical sizing of the DPFC converters is considered.

In Case 2, the application of the DPFC for power flow control is discussed and a triangle

network in the Netherlands is selected as the case.

This thesis concludes with chapter 9, which summarizes the major contributions of

the research. Recommendations for future research on the subject are also given.



Chapter 2OVERVIEW OF POWER FLOW

CONTROLLING DEVICES

2.1 Introduction

I

T is shown in the previous chapter that there is a growing demand for fast, reliable

and multi-directional power flow control. To achieve this, special devices are needed.

This chapter gives an overview of the state-of-art of PFCDs, considering the operating

principles and the advantages and limitations of each device.

First the theory of power flow control is discussed and the parameters that can be

used to control power flow are investigated. Later, several PFCDs are categorized and

introduced.

2.2 Power Flow Control Theory

To study the power flow through a transmission line, a mathematical representation of

a transmission line is required. A transmission line can be characterized by four param-

eters: resistance, inductance, capacitance and conductance. Conductance accounts for

the leakage current at the insulators of overhead lines. However, for a short and medium

length line (less than 240 km), the capacitance and conductance are so small that they

can be neglected with little loss of accuracy [Grai 94]. Accordingly, a transmission line

can be simplified as shown in Figure 2-1, where V s and V r are the sending and receiving

end line-to-ground phasor voltages, I is the phasor current through the line, and R and

13



14 2.2 Power Flow Control Theory

L are the series resistance and inductance of the line, respectively.

area 1 area 2

R L

sV

r V I

,r r P Q

Figure 2-1: Simplified one-line representation of a transmission line

From the diagram, the power flow S r through the line at the receiving end is given by:

S r = V r · I ∗ = V r ·

V r − V sR + jωL

∗

= P r + jQr (2.1)

where ∗ means the conjugation of a complex number, and ω is the angular frequency of

the power system [Grai 94]. The line impedance can be written as Z and it is equal to

R + jωL. The real part of S r is the active power P r and the imaginary part is the reactive

power Qr. According to (2.1), the active and reactive power flows at the receiving end

are given by:

P r = |V r|2|Z | cos δ +

|V r||V s||Z | cos(θ − δ )

Qr = |V r|2|Z | sin δ − |V r||V s|

|Z | sin(θ − δ )

(2.2)

where θ is the angle between the sending and receiving ends’ voltages, referred to as the

transmission angle, and δ is defined as tan−1(ωL/R). In a typical high-voltage or medium-

voltage transmission line, the reactance is normally much larger (over 10 times) than the

resistance [Kund 94]. Therefore, the resistance can be neglected during the power flow

calculation with little loss of accuracy, and the active and reactive power flow through alossless line can be simplified to the following:

P r = |V r||V s|

X sin θ

Qr = |V r||V s|

X cos θ − |V r|2

X

(2.3)

where X = ωL is the inductive impedance of the line. Equation (2.3) shows that three

system parameters can by utilized to vary the power flow; transmission angle θ, line

impedance X and bus voltage magnitudes |V r| and |V s|. Because power systems are




operated in a unified voltage mode (voltages are close to 1 per unit (pu)) [Grai 94],

power flows can only be adjusted in a small range by varying the bus voltage magnitude.Therefore, the bus voltage magnitude is not suitable for controlling the power flow over

a large range. By assuming that the bus voltages at the sending and receiving ends have

the same magnitude |V |, the power flow equations can be further simplified to:

P r = |V |2

X sin θ

Qr = |V |2

X (cos θ − 1)

(2.4)

As shown, the active and reactive power flows are coupled. By varying one parameter,both active and reactive power flow will change accordingly. From (2.4), the locus of

(P r, Qr) with X and θ as the control parameter is achieved and shown in Figure 2-2.

r P

r Q

θ

2

(0, )V

X −

control range

of varying θ

with fixed X

control range

of varying X

with fixed θ

Figure 2-2: Control range of active and reactive power flows with vary θ and X

By adjusting the transmission angle, both the magnitude and direction of the active

power flow can be controlled; but for the reactive power flow, only the magnitude, but

not the direction can be controlled, as shown in Figure 2-2. The variation range of θ is (−90, 90), because the trigonometric functions are periodic functions. The line

impedance X can be changed to inductive or capacitive (although the capacitive line

impedance is not common). Accordingly, by varying X , the magnitude and the direction

of both the active and reactive power flow can be widely controlled. Theoretically, both

active and reactive power flow can be adjusted from zero to infinity by changing the line

impedance.

By varying single parameter, there is only one degree of freedom for controlling the

power flow. Normally the active power flow control has priority because the reactive



16 2.3 Categorization of PFCDs

power can be generated at the load side though capacitor banks. If the active and reac-

tive power flows need to be controlled independently, two or more parameters should besimultaneously controlled by the PFCD.

2.3 Categorization of PFCDs

As has already been explained in chapter 1, the main categories of PFCDs are mechanical-

and power electronic-based regarding incorporated technology and shunt, series and com-

bined devices based on their placement in the network. Figure 2-3 gives most of the

important PFCDs and their categorization.

thyristor

MECHANICAL

PFCDs

voltage source

converter (VSC)

Static VarCompensator (SVC)

Static SynchronousCompensator (SVC)

Thyristor Controlled

Series Compensator

(TCSC)

Static Synchronous

Series Compensator

(SSSC)

Unified / Interline

Power Flow Controller

(UPFC / IPFC)

switched shuntcompensation (L, C)

switched series

compensation (L, C)

phase shifting

transformer

shuntdevices

series

devices

combined

devices

Power Electronics PFCDs

FACTS controllers

others:

HVDC,

DVR...

Figure 2-3: Categorization of PFCDs

2.4 Shunt Devices

The basic principle of a shunt device is shown in Figure 2-4. The idea is to supply the

reactive power locally that is required by the load. By varying the impedance of the shunt

device, the injected reactive current I sh can be adjusted, thereby indirectly controlling




the line current I . According to Ohm’s law, the voltage drop across the transmission line

V s − V r is correlated to the line current I . As the voltage at the sending end V s can beassumed a constant value, the magnitude of the receiving end voltage |V r| can then be

controlled by the shunt devices.

R L

load

shunt

device

I

sh I

r I sV

r V

Figure 2-4: Shunt device operating principle

This indirect relationship between the current injected by the shunt device I sh and

the voltage V r can be found in the following equation:

V r = V s − IZ

= V s−

(I r−

I sh)Z (2.5)

where Z = R + jωL. As shown in (2.5), the shunt current I sh can partly compensate for

the large load current I r, thereby reducing the line current I in heavy load conditions and

leading to a small voltage drop. Accordingly, the shunt device can control the voltage

magnitude by varying its impedance.

Three types of shunt devices can be distinguished: switched shunt inductor and capaci-

tor devices, Static Var Compensation (SVC) devices and Static Synchronous Compensator

(STATCOM) devices. The configuration of the switched shunt inductor and capacitor de-

vice is shown in Figure 2-5. As the switched shunt inductor and capacitor device only hastwo statuses (on and off), its operation and principles are relatively simple and will not

be discussed here. The SVC and STATCOM devices will be introduced in the following

sections.

2.4.1 SVC

A Static Var Compensator (SVC) is an electrical device used to provide fast-acting reactive

power on high-voltage electricity transmission networks [De K 04]. It is a shunt-connected



18 2.4 Shunt Devices

grid

transmission line

grid

transmission line

(a) (b)

Figure 2-5: Switched shunt inductor and capacitor configuration: (a) inductor; (b) capacitor

device whose output is adjusted to exchange capacitive or inductive current so as to main-

tain or control specific parameters of the electrical power system (typically bus voltage).

The first commercial SVC was installed in 1972. Since then, it has been widely used and

represents the most accepted FACTS device [Edri 97].

Typically, a SVC is comprised of a bank of Thyristor-Switched Capacitors (TSC) in

conjunction with a Thyristor-Controlled Reactor (TCR), as shown in Figure 2-6.

TSC TSC TCR harmonic

filter

grid

transmission line

Figure 2-6: Typical SVC configuration

The TSC and TCR consist of an inverse-parallel thyristor in series with a capacitor

or inductor. TSC utilizes inverse-parallel thyristors instead of mechanical connectors to

allow capacitors to be quickly switched on and off. A small inductor in series is used to

limit inrush currents on the occasions when severe transience occurs, for instance during




the initial charging of a capacitor [Song 99]. TCR employs the firing angle control to

the thyristors to vary the current thereby controlling the shunt reactance of the TCR[Hing 00]. The firing angle varies from a 90 delay, for continuous conduction, to 180

delay, for minimum conduction [Song 99], as shown in Figure 2-7. A TCR combined with

TSCs is able to provide continuously variable Var injection or absorption [Than 79].

voltage

current

partconduction

minimumconduction

continuousconduction

Figure 2-7: Voltage and current waveforms of a TCR for different firing angles

The SVC acts as a controllable reactor (or capacitor), and the supplied reactive power

is proportional to the square of the bus voltage [Gyug 00]. Accordingly, the SVC isless effective in providing reactive power when the bus voltage is low. In addition, the

current provided by the SVC contains large amounts of harmonics as shown in Figure 2-7,

therefore a filter with low cutoff frequency is required to improve the waveform quality.

2.4.2 STATCOM

A static synchronous compensator (STATCOM) is basically a VSC that is connected

between a grid and the ground through a coupling inductance, as shown in Figure 2-8[Gyug 94].

The STATCOM acts as an AC voltage source and has characteristics similar to a

synchronous condenser (a synchronous generator that is running idle and used for reactive

compensation) [Song 99]. The STATCOM injects an AC current in quadrature (leading or

lagging) with the grid voltage, and emulates capacitive or inductive impedance at the point

of connection. If the voltage generated by the STATCOM is less than the grid voltage, it

will act as an inductive load and withdraw reactive powers from the system. Conversely,

when the STATCOM voltage is higher than the grid voltage, it will act as a capacitive



20 2.4 Shunt Devices

grid

coupling

inductance

AC

DC

transmission line

Figure 2-8: STATCOM configuration

load and provide reactive power to the grid [Sing 09]. Compared to the synchronous

condenser, the STATCOM is a PE-based device without inertia and therefore has a faster

dynamic response.

The DC VSC is the most common type of converter that used for the STATCOM

[Qing 04] and the DC voltage source can be a capacitor. By using a multi-level, multi-

phase, or Pulse-Width Modulated (PWM) converter, the current distortion of the STAT-

COM outputs can be sufficiently reduced and the STATCOM may even require no filter-

ing. Figure 2-9 shows the waveforms of a voltage generated by a five-level STATCOM

and the corresponding current.

voltagecurrent

Figure 2-9: Voltage and current waveforms generated by a five-level STATCOM

As shown, the STATCOM has better characteristics than the SVC, because the out-

put contains fewer harmonics. Also the reactive power provision of the STATCOM is

independent from actual grid voltage magnitude [Gyug 00]. However, the STATCOM is

more complex than the SVC due to the inclusion of a VSC. Accordingly, the STATCOM




is more expensive than the SVC, especially for the high-voltage transmission lines.

2.5 Series Devices

Series devices have been successfully used for many years in order to enhance the stability

and loadability of transmission networks. The approach of series devices is to install

variable impedance in series with the transmission line, as shown in Figure 2-10.

R L

I

sV

r V

series device

Figure 2-10: Series device operating principle

The series device can be inductive or capacitive, thereby varying the line impedance

to control the power flow according to the equation:

P r = |V r||V s|

X sin θ

Qr = |V r||V s|

X

cos θ

−

|V r|2

X

(2.6)

In the case of a capacitive device, a fraction of the reactance of the transmission line

is balanced, which increases the power flow. When the series device acts as inductive, the

reactance will be increased thereby limiting the power flow. Besides controlling the power

flow, series devices can also be used to improve angular stability and voltage stability

[Huan 02, Kund 94, Pill 03]. However, these applications are out of the scope of this

thesis.

Series devices have been developed, including fixed or mechanical switched compen-

sators to thyristor controlled series compensators and VSC-based devices. The configura-

tions of the fixed and mechanical switched compensators are shown in Figure 2-11. Due

to their relatively simple operation, slow response and stepwise adjustment, they will not

be discussed in this section.

(a) transmission line (b) transmission line

Figure 2-11: Configurations of mechanical switched series devices: (a) capacitor; (b) inductor



22 2.5 Series Devices

2.5.1 TSSC

A Thyristor Switched Series Capacitor (TSSC) uses inverse-parallel thyristors in parallel

with a segment of the series capacitor bank to rapidly insert or remove portions of the bank

in discrete steps, as shown in Figure 2-12. Because the TSSC employs thyristors to switch

the capacitor banks, it has a faster response than mechanically switched compensators.

However, as the TSSC also has stepwise adjustment, it is not widely used in applications.

In addition, the TSSC can only insert capacitance into lines and cannot limit line currents.

transmission line

Figure 2-12: TSSC configuration

2.5.2 TCSC

According to IEEE, the Thyristor Controlled Series Capacitor (TCSC) is defined as ‘a

capacitive reactance compensator which consists of a series capacitor bank shunted by

a thyristor controlled reactor in order to provide a smoothly variable series capacitive

reactance [Edri 97].’ The configuration of a TCSC is shown in Figure 2-13.

TCSC transmissionline

Figure 2-13: TCSC configuration

The idea behind TCSC is to use inverse-parallel thyristors to control the reactance of

the TCR branch. Together with the fixed capacitor, the total impedance of the TCSC is

adjusted [McDo 94, Song 99]. The line impedance adjustment of the TCSC can be done

within one cycle [Maha 06], thereby providing a faster power flow control than mechanical

switched devices.




As shown in Figure 2-7, the branch within the TCR will cause low frequency harmonic

currents. The capacitor bank provides a low impedance path for the harmonics current;therefore, most of the harmonic currents will circulate within the TCR and the capacitor

branches. However, there will still be a small amount of harmonics leaking into the

transmission line. Also, as the voltage injected by the TSSC and TCSC is proportional

to the line current, during low loading conditions, TSSC and TCSC are not effective

[Zhan 06].

2.5.3 SSSC

The Static Synchronous Series Compensator (SSSC) consists of a converter that is con-

nected in series with the transmission line, as shown in Figure 2-14. The SSSC operates

without an external energy source as a series compensator whose output voltage is in

quadratic with, and controllable independently of, the line current. The purpose of this is

to increase or decrease the overall reactive voltage drop across the line, thereby controlling

the power flow [Edri 97]. A small part of the injected voltage, which is in phase with the

line current, compensates for losses in the converter.

transmission line

AC

DC

Figure 2-14: SSSC configuration

Because the voltage that is injected by the VSC within the SSSC is not related to the

line current and can be controlled independently, the SSSC is effective for both low and

high load conditions [Sen 98]. Similar to the STATCOM, the output of the SSSC contains

fewer harmonics than thyristor-based devices [Moha 03]. Although the configuration of

SSSC is similar to a STATCOM, the SSSC is more complicated in reality. It requires

platform mounting for high-voltage isolations and complex bypass protection in case of

failures [Zhan 06].



24 2.5 Series Devices

2.5.4 DSSC

The Distributed Static Series Compensator (DSSC), recently presented by Prof. Deepak

Divan [Diva 07, Diva 05], is a distributed SSSC, which keeps the functionality of the SSSC

with a much lower cost and higher reliability. The concept of DSSC uses a large number

of units with low power ratings instead of one controller with a large power rating, as

shown in Figure 2-15.

DSSC unit

transmission line

Figure 2-15: Transmission line with the DSSC units

A DSSC unit consists of multiple low-rated, single-phase VSCs that are attached to

the transmission line by single-turn transformers. The single-turn transformer uses the

transmission line as its secondary winding and injects a controllable voltage directly into

the line. Most of the voltage injected by a DSSC unit is in quadrature with the line

current, to emulate inductive or capacitive impedance. A small part of the voltage is

in phase with the line current and serves to self-power the DSSC unit and cover losses.

The DSSC is remotely controlled via wireless communication or a PLC [ Ferr 96]. The

configuration of a DSSC unit is shown in Figure 2-16.

The unique character of the DSSC results in relatively low cost and high reliability.

As DSSC units are single-phase devices floating on lines, high-voltage isolation between

the phases are avoided. The units can easily be applied at any transmission voltage level

because they do not require supporting phase-ground isolation. The power and voltage

rating of each unit is small. Further, the units are clamped on transmission lines, requiring

no additional land, thereby eliminating their footprint. The redundancy of DSSC provides

uninterrupted operation during a single module failure, thereby giving reliability at lower

cost than with other FACTS devices.




AC

DC controller

power

supply

communicationmodule

current

feedback

single-turn

transformer

transmissionline

Figure 2-16: DSSC module configuration

2.6 Combined Devices

In this section, three combined devices will be introduced: the Phase Shifting Trans-

former (PST), the Unified Power Flow Controller (UPFC) and the Interline Power FlowController (IPFC).

2.6.1 PST

The Phase Shifting Transformer (PST) is a specialized form of transformer used to control

the active power flow of transmission networks. A PST typically consists of a shunt

transformer with a tap changer and a series transformer. The principle of PST is that

the series transformer inserts a voltage, which is obtained from the other phases of theshunt transformer [Verb 05]. The injected voltage is in quadrature with the phase voltage

and causes a phase angle shift across the transformer, thereby varying the transmission

angle. By changing the taps of the shunt transformer, the magnitude of the quadrature

voltage can be controlled and thus the voltage phase shifts across the PST. Figure 2-17

illustrates the configuration of a simple PST.

The major drawbacks associated with PSTs are slow response due to the inherent

inertia of the mechanical tap changer, its limited lifetime and the frequent maintenance

required due to mechanical wear and oil deterioration [Arsh 04]. There are also PSTs



26 2.6 Combined Devices

transmission linea

b

c

Figure 2-17: Configuration of a simple PST

based on PE, but no such PST is in service, mainly due to the complex short circuit

current protection that is required [Verm 04].

2.6.2 UPFC

The Unified Power Flow Controller (UPFC) is comprised of a STATCOM and a SSSC,

coupled via a common DC link to allow bi-directional flow of active power between the

series output terminals of the SSSC and the shunt output terminals of the STATCOM

[Edri 97]. Each converter can independently generate (or) absorb reactive power at its

own AC terminal. The two converters are operated from a DC link provided by a DC

storage capacitor. The configuration of a UPFC is shown in Figure 2-18.

grid

AC

DC

transmission line

DC

AC

Figure 2-18: UPFC configuration

The series converter executes the main function of the UPFC by injecting a voltage,

with controllable magnitude and phase angle, in series with the transmission line. It




is controlled to provide concurrent active and reactive series compensation without an

external energy source. By means of the series voltage injection without angular con-straint, the UPFC is able to control, concurrently or selectively, the transmission angle,

impedance and line voltage or, alternatively, active and reactive power flow through the

line [Gyug 92]. The voltage injected by the series converter results in active and reac-

tive power exchange between the series converter and the transmission line. The reactive

power is generated internally by the series converter (like SSSC), and the active power is

supplied by the shunt converter that is transported through the common DC link.

The basic function of the shunt converter is to supply or absorb the active power

demanded by the series converter. The shunt converter controls the voltage of the DCcapacitor by absorbing or generating active power from the bus, therefore it acts as a

synchronous source in parallel with the system. Similar to the STATCOM, the shunt

converter can also provide independently controllable reactive compensation for the bus

[Gyug 95, Kann 04]. Considering its control capability, the UPFC can have the functions:

• Voltage regulation by continuously varying in-phase/anti-phase voltage injection

that is similar to a tap-change transformer.

• Series reactive compensation by injecting a voltage that is in quadrature to the line

current. Functionally, this is similar to an SSSC that can provide a controllable

inductive and capacitive series compensation.

• Phase shifting by injecting a voltage with an angular relationship with respect to

the bus voltage. By varying the magnitude of this voltage, the phase shift can be

controlled.

The listed functions of the UPFC can be executed simultaneously, which makes the

UPFC the most powerful PFCD. However, due to high voltage VSCs and corresponding

protection requirements, UPFC is quite expensive, which limits its practical application.

2.7 IPFC

The Interline Power Flow Controller (IPFC) consists of the two (or more) series converters

in different transmission lines that are inter-connected via a common DC link, as shown

in Figure 2-19. Unlike other FACTS devices that aim to control the parameter of a single

transmission line, the IPFC is conceived for the compensation and control of power flow

in a multi-line transmission system [Gyug 99].



28 2.8 Conclusions

AC

DC

transmission line 1

DC

AC

transmission line 2

Figure 2-19: IPFC configuration

Each converter can provide series reactive compensation of its own line, just as anSSSC can. As the converters can exchange active power through their common DC link,

the IPFC can also provide active compensation. This allows the IPFC to provide both

active and reactive compensation for some of the lines and thereby optimize the utilization

of the overall transmission system. Note that the active power supplied to one line is taken

from the other lines. If required, the IPFC can be complemented with an additional shunt

converter to provide active power from a suitable shunt bus [Gyug 99, Vasq 08].

2.8 Conclusions

This chapter reviewed the theory of power flow control and PFCDs. The DSSC have

relatively low cost and high reliability. However, the control capability of the DSSC is

limited because it can only inject reactive power. It is found that the combined PFCDs

based on VSCs have the best capability of power flow control, and are therefore the most

suitable device for the future network. However, their high cost and complexity become

the bottleneck for their application in practice.



Chapter 3DISTRIBUTED POWER FLOW

CONTROLLER

3.1 Introduction

I

N the previous chapter, an overview was given of mechanical- and PE-based PFCDs.

Because of high control capability, the PE-based combined PFCs, specifically UPFCand IPFC are suitable for the future power system. However, the UPFC and IPFC are

not widely applied in practice, due to their high cost and the susceptibility to failures.

Generally, the reliability can be improved by reducing the number of components; however,

this is not possible due to the complex topology of the UPFC and IPFC. To reduce

the failure rate of the components by selecting components with higher ratings than

necessary or employing redundancy at the component or system levels are also options.

Unfortunately, these solutions increase the initial investment necessary, negating any cost-

related advantages. Accordingly, new approaches are needed in order to increase reliabilityand reduce cost of the UPFC and IPFC at the same time.

After studying the failure mode of the combined FACTS devices, it is found that a

common DC link between converters reduces the reliability of a device, because a failure

in one converter will pervade the whole device though the DC link. By eliminating this

DC link, the converters within the FACTS devices are operated independently, thereby

increasing their reliability.

The elimination of the common DC link also allows the DSSC concept to be applied

to series converters. In that case, the reliability of the new device is further improved

29



30 3.2 Distributed Power Flow Controller (DPFC)

due to the redundancy provided by the distributed series converters. In addition, series

converter distribution reduces cost because no high-voltage isolation and high power ratingcomponents are required at the series part. By applying the two approaches -eliminating

the common DC link and distributing the series converter, the UPFC is further developed

into a new combined FACTS device: the Distributed Power Flow Controller (DPFC), as


AC

DC

DC

AC

AC

DC DC

AC

ACDC

ACDC

ACDC

AC

DC

UPFC

DPFC

eliminate the

common dc link

distribute

series converter

Figure 3-1: Flowchart from UPFC to DPFC

In this chapter, the principle of the DPFC is presented, followed by a steady-state

analysis of the DPFC. During the analysis, the control capability and the influence of

the DPFC on the network are investigated. The principle and analysis of another device

that emerges from the IPFC, the so-called Distributed Interline Power Flow Controller

(DIPFC), is also introduced.

3.2 Distributed Power Flow Controller (DPFC)

In this section, DPFC topology and operating principle are introduced.




3.2.1 DPFC Topology

By introducing the two approaches outlined in the previous section (elimination of the

common DC link and distribution of the series converter) into the UPFC, the DPFC

is achieved. Similar as the UPFC, the DPFC consists of shunt and series connected

converters. The shunt converter is similar as a STATCOM, while the series converter

employs the DSSC concept, which is to use multiple single-phase converters instead of

one three-phase converter. Each converter within the DPFC is independent and has its

own DC capacitor to provide the required DC voltage. The configuration of the DPFC is


AC

DC

transmission line

AC

DC

AC

DC

AC

DC high-

pass

filter

snt

onerter

seres onerters

Figure 3-2: DPFC configuration

As shown, besides the key components - shunt and series converters, a DPFC also

requires a high pass filter that is shunt connected to the other side of the transmission

line and a Y-∆ transformer on each side of the line. The reason for these extra components

will be explained later.

The unique control capability of the UPFC is given by the back-to-back connection

between the shunt and series converters, which allows the active power to freely exchange.

To ensure the DPFC has the same control capability as the UPFC, a method that allowsactive power exchange between converters with an eliminated DC link is required.

3.2.2 DPFC Operating Principle

Active power exchange with eliminated DC link

Within the DPFC, the transmission line presents a common connection between the AC

ports of the shunt and the series converters. Therefore, it is possible to exchange active

power through the AC ports. The method is based on power theory of non-sinusoidal




components. According to the Fourier analysis, non-sinusoidal voltage and current can

be expressed as the sum of sinusoidal functions in different frequencies with differentamplitudes. The active power resulting from this non-sinusoidal voltage and current is

defined as the mean value of the product of voltage and current. Since the integrals of

all the cross product of terms with different frequencies are zero, the active power can be

expressed by:

P =∞

i=1

V iI i cos φi (3.1)

where V i and I i are the voltage and current at the ith harmonic frequency respectively, and

φi is the corresponding angle between the voltage and current. Equation (3.1) shows that

the active powers at different frequencies are independent from each other and the voltage

or current at one frequency has no influence on the active power at other frequencies.

The independence of the active power at different frequencies gives the possibility that a

converter without a power source can generate active power at one frequency and absorb

this power from other frequencies.

By applying this method to the DPFC, the shunt converter can absorb active power

from the grid at the fundamental frequency and inject the power back at a harmonic

frequency. This harmonic active power flows through a transmission line equipped with

series converters. According to the amount of required active power at the fundamental

frequency, the DPFC series converters generate a voltage at the harmonic frequency,

thereby absorbing the active power from harmonic components. Neglecting losses, the

active power generated at the fundamental frequency is equal to the power absorbed at

the harmonic frequency. For a better understanding, Figure 3-3 indicates how the active

power is exchanged between the shunt and the series converters in the DPFC system.

The high-pass filter within the DPFC blocks the fundamental frequency components

and allows the harmonic components to pass, thereby providing a return path for the

harmonic components. The shunt and series converters, the high pass filter and the

ground form a closed loop for the harmonic current.

Using third harmonic components

Due to the unique features of 3rd harmonic frequency components in a three-phase sys-

tem, the 3rd harmonic is selected for active power exchange in the DPFC. In a three-phase




AC

DC

AC

DC

AC

DC

AC

DC high

pass

filter

shunt

converter

series converters

active power at the fundamental frequency

active power at the harmonic frequency

Figure 3-3: Active power exchange between DPFC converters

system, the 3rd harmonic in each phase is identical, which means they are ‘zero-sequence’

components. Because the zero-sequence harmonic can be naturally blocked by Y-∆ trans-

formers and these are widely incorporated in power systems (as a means of changing

voltage), there is no extra filter required to prevent harmonic leakage.

As introduced above, a high-pass filter is required to make a closed loop for the har-

monic current and the cutoff frequency of this filter is approximately the fundamentalfrequency. Because the voltage isolation is high and the harmonic frequency is close to

the cutoff frequency, the filter will be costly. By using the zero-sequence harmonic, the

costly filter can be replaced by a cable that connects the neutral point of the Y-∆ trans-

former on the right side in Figure 3-2 with the ground. Because the ∆-winding appears

open-circuit to the 3rd harmonic current, all harmonic current will flow through the Y-

winding and concentrate to the grounding cable as shown in Figure 3-4. Therefore, the

large high-pass filter is eliminated.

+

+

+

Y-∆ transformer

Figure 3-4: Utilize grounded Y-∆ transformer to filter zero-sequence harmonic




Another advantage of using the 3rd harmonic to exchange active power is that the

grounding of the Y-∆ transformers can be used to route the harmonic current in a meshednetwork. If the network requires the harmonic current to flow through a specific branch,

the neutral point of the Y-∆ transformer in that branch, at the side opposite to the shunt

converter, will be grounded and vice versa. Figure 3-5 shows a simple example of routing

the harmonic current by using the grounding of the Y-∆ transformer. Because the floating

neutral point is located on the transformer of the line without the series converter, it is

an open-circuit for 3rd harmonic components and therefore no 3rd harmonic current will

flow through this line.

shunt

converter +

+

series converters

Figure 3-5: Route the harmonic current by using the grounding of the Y-∆ transformer

The harmonic at the frequencies like 3rd, 6th, 9th... are all zero-sequence and all can

be used to exchange active power in the DPFC. However, the 3rd harmonic is selected,

because it is the lowest frequency among all zero-sequence harmonics. The relationship

between the exchanged active power at the ith harmonic frequency P i and the voltages

generated by the converters is expressed by the well known the power flow equation and

given as:

P i = |V sh,i||V se,i|

X isin(θsh,i − θse,i) (3.2)

where X i is the line impedance at ith frequency, |V sh,i| and |V se,i| are the voltage magni-

tudes of the ith harmonic of the shunt and series converters, and θsh,i − θse,i is the angle

difference between the two voltages. As shown, the impedance of the line limits the active

power exchange capacity. To exchange the same amount of active power, the line with high

impedance requires higher voltages. Because the transmission line impedance is mostly

inductive and proportional to frequency, high transmission frequencies will cause high




impedance and result in high voltage within converters. Consequently, the zero-sequence

harmonic with the lowest frequency - the 3rd harmonic - has been selected.

3.2.3 DPFC Control

To control multiple converters, a DPFC consists of three types of controllers: central

control, shunt control and series control, as shown in Figure 3-6.

AC

DC

transmission line

AC

DC

AC

DC

AC

DC high-

pass

filter

snt

onerter

seres

onerters

snt

ontrol

seres

ontrol

seres

ontrol

seres

ontrol

entral

ontrol

Figure 3-6: DPFC control block diagram

The shunt and series control are localized controllers and are responsible for main-

taining their own converters’ parameters. The central control takes care of the DPFC

functions at the power system level. The function of each controller is listed:

• Central control: The central control generates the reference signals for both

the shunt and series converters of the DPFC. Its control function depends on the

specifics of the DPFC application at the power system level, such as power flow

control, low frequency power oscillation damping and balancing of asymmetricalcomponents. According to the system requirements, the central control gives cor-

responding voltage reference signals for the series converters and reactive current

signal for the shunt converter. All the reference signals generated by the central

control concern the fundamental frequency components.

• Series control: Each series converter has its own series control. The controller

is used to maintain the capacitor DC voltage of its own converter, by using 3 rd

harmonic frequency components, in addition to generating series voltage at the

fundamental frequency as required by the central control.




• Shunt control: The objective of the shunt control is to inject a constant 3 rd

harmonic current into the line to supply active power for the series converters.At the same time, it maintains the capacitor DC voltage of the shunt converter

at a constant value by absorbing active power from the grid at the fundamental

frequency and injecting the required reactive current at the fundamental frequency

into the grid.

The detailed schematics and designs of the DPFC control will be introduced in fol-

lowing chapters.

3.2.4 Variation of the Shunt Converter

In the DPFC, the shunt converter should be a relatively large three-phase converter that

generates the voltage at the fundamental and 3rd harmonic frequency simultaneously. A

conventional choice would be a three-leg, three-wire converter. However, the converter is

an open circuit for the 3rd harmonic components and is therefore incapable of generating

a 3rd harmonic component. Because of this, the shunt converter in a DPFC will require

a different type of 3-phase converter. There are several 3-phase converter topologies that

can generate 3rd

harmonic frequency components, such as multi-leg, multi-wire convert-ers or three single-phase converters [Juli 99]. These solutions normally introduce more

components, thereby increasing total cost.

A new topology for the DPFC shunt converter is proposed. The topology utilizes

the existing Y-∆ transformer to inject the 3rd harmonic current into the grid. A single-

phase converter is connected between the transformer’s neutral point and the ground,

and injects a 3rd harmonic current into the neutral point of the transformer. This current

evenly spreads into the 3-phase line through the transformer. The converter can be

powered by an additional back-to-back converter connected to the low-voltage side of thetransformer. The circuit scheme of this topology is shown in Figure 3-7.

For a symmetrical system, the voltage potential at the neutral point and fundamental

frequency is zero. Accordingly, the single-phase converter only handles the 3rd harmonic

voltages, which are much lower than the voltage at the fundamental frequency. As the

single-phase converter is only used to provide active power for the series converter, the

voltage and power rating are small. In addition, the single-phase converter uses the

already present Y-∆ transformer as a grid connection. The single-phase converter is

powered by another converter through a common DC link. In the case of the system with




+

+

+

Y-∆ transformer

AC

DC

AC

DCsingle phase

converter

STATCOM

Figure 3-7: DPFC shunt converter configuration

a STATCOM, the single-phase converter can be directly connected back-to-back to the

DC side of the STATCOM, as shown in Figure 3-7.

3.2.5 Advantages and Limitation of the DPFC

The DPFC can be considered a UPFC that employs the D-FACTS concept and the

concept of exchanging power through the 3rd harmonic. In this way, the DPFC inherits

all their advantages:

• High controllability: the DPFC can simultaneously control all the parameters of

the transmission network: line impedance, transmission angle and bus voltage.

• High reliability: the redundancy of the series converter gives high reliability with-

out increasing cost. In addition, the shunt and series converters are independent

and failure of one will not influence the other converters.

• Low cost: there is no phase-to-phase voltage isolation required between the series

converters of different phases. The power rating of each converter is also low.

Because of the large number of the series converters, they can be manufactured in

series production. If the power system is already equipped with the STATCOM,

the system can be updated to the DPFC with only low additional costs.

However, there is a drawback to using the DPFC:

• Extra currents: Because the exchange of power between the converters takes

place through the same transmission line as the main power, extra currents at

the 3rd harmonic frequency are introduced. These currents reduce the capacity of



38 3.3 DPFC Steady-State Analysis

the transmission line and result in extra losses within the line and the two Y-∆

transformers. However, because this extra current is at the 3rd harmonic frequency,the increase in the RMS value of the line current is not large and through the design

process can be limited to less than 5% of the nominal current.

3.3 DPFC Steady-State Analysis

In this section, the steady-state behavior of the DPFC is analyzed and the control capa-

bility of the DPFC is expressed in the parameters of both the network and DPFC itself.

This section begins with the simplification of the DPFC, followed by the analysis of the

circuit at the fundamental frequency. The 3rd harmonic circuit is examined with regards

to the active power required by the fundamental frequency components. The section

ends by considering the relationship between the ratings of the DPFC converters and the

corresponding capability of power flow control.

3.3.1 DPPF Simplification and Equivalent Circuit

To simplify the DPFC, the converters are replaced by controllable voltage sources in serieswith impedance. Since each converter generates voltages at two different frequencies, they

are represented by two series connected controllable voltage sources, one at the fundamen-

tal frequency and the other at the 3rd harmonic frequency. Assuming the converters and

the transmission line have no loss, the total active power generated by the two voltage

sources will be zero. The multiple series converters are simplified as one large converter

with a voltage that is equal to the voltages of all series converters. Consequently, a

simplified representation of the DPFC is shown in Figure 3-8.

The DPFC is placed in a two-bus system with the sending end and the receiving endvoltages V s and V r. The transmission line is represented by an inductance L with the line

current I . The voltage injected by all the DPFC series converters is V se,1 and V se,3 at the

fundamental and 3rd harmonic frequencies, respectively. The shunt converter is connected

to the sending bus through the inductor Lsh and generates the voltage V sh,1 and V sh,3, and

the current injected by the shunt converter is I sh. The active and reactive power flows at

the receiving end are P r and Qr. Arrow A represents the active power exchange within

the converter itself and arrow B indicates the power exchange between the shunt and the

series converter through the 3rd harmonic.




,1seV ,3seV

,1shV

,3shV

sh L

L

r V s

V ,1 ,3se seP P= −

, 1

, 3

s h

s h

P

P

=

−

,3 ,3se shP P= −

,r r P Q

high-

pass

filter

I

sh I

A

A

B

Figure 3-8: DPFC simplified representation

This representation consists of both the fundamental frequency and 3rd harmonic

frequency components. For an easier analysis, based on the superposition theorem, the

circuit in Figure 3-8 can be further simplified by splitting it into two circuits at different

frequencies. The two circuits are isolated from each other, and the link between these

circuits is the active power balance of each converter, as shown in Figure 3-9.

,1seV

,1shV

,1sh X

1 X

r V sV

,1 ,3se seP P= −

,1 ,3sh shP P= −

1 I

,1sh I

,3seV

,3shV

,3sh X

3 X

3 I

,3sh I

(a) (b)

Figure 3-9: DPFC equivalent circuit: (a) the fundamental frequency; (b) the 3rd harmonic

frequency

These two circuits are linear circuits and can be analyzed separately, where each circuit

contains only single-frequency components.




3.3.2 Fundamental Frequency Circuit

In this section, the DPFC circuit is analyzed at the fundamental frequency. The control

capability of the DPFC is examined and the relationship between the exchanged active

power and control range is found.

Power flow control capability

The power flow control capability of the DPFC can be illustrated by the active power P r

and reactive power Qr at the receiving end, shown in Figure 3-9(a). With reference to

this figure, the active and reactive power flow can be expressed as follows:

P r + jQr = V rI ∗1

= V r

V s − V r − V se,1

jX 1

∗ (3.3)

where the phasor values are used for voltages and currents, ∗ means the conjugate of a

complex number and X 1 = ω1L is the line impedance at the fundamental frequency. The

power flow (P r, Qr) consists of two parts: the power flow without DPFC compensation(P r0, Qr0) and the part that is varied by the DPFC (P r,c, Qr,c). The power flow without

DPFC compensation (P r0, Qr0) is given by:

P r0 + jQr0 = V r

V s − V r

jX 1

∗

(3.4)

Accordingly, by substituting (3.4) into (3.3), the DPFC control range on the power

flow can be expressed as:

P r,c + jQr,c =V rV ∗se,1

jX 1(3.5)

As the voltage at the receiving end and the line impedance are fixed, the power flow

control range of the DPFC is proportional to the maximum voltage of the series converter.

Because the voltage V ∗se,1 can be rotated 360, the control range of the DPFC is a circle

in the complex P Q-plane, whose center is the uncompensated power flow (P r0, Qr0) and

whose radius is equal to |V r||V se,1|/X 1. By assuming that the voltage magnitude at the

sending and receiving ends are both V , the control capability of the DPFC is given by




the following formula:

(P r − P r0)2 + (Qr −Qr0)2 =

V |V se,1|

X 1

2

(3.6)

In the complex P Q-plane, the locus of the power flow without the DPFC compensation

f (P r0, Qr0) is a circle with radius |V |2/|X 1| around its center (defined by coordinates

P = 0 and Q = |V |2/|X 1|). Each point of this circle gives P r0 and Qr0 values of the

uncompensated system at the corresponding transmission angle θ. The boundary of the

attainable control range for P r and Qr is obtained from a complete rotation of the voltage

V se,1 with its maximum magnitude. Figure 3-10 shows the power flow control range of theDPFC with the transmission angle θ.

r P

r Q

θ 2

1

(0, )V

X −

DPFC control

range with θ

,1

1

| |seV V

X

Figure 3-10: DPFC active and reactive power control range with the transmission angle θ

Active power required by the series converters

To inject a 360 rotatable voltage, an active and reactive power at the fundamental

frequency has to be supplied to the series converter, which is given as:

P se,1 + jQse,1 = V se,1I ∗1

= V se,1

S r

V r

(3.7)




The voltage injected by the series converter V se,1 can be solved from (3.3), which is

given as:

V se,1 =

(S r − S r0) jX 1

V r

∗

(3.8)

By substituting (3.8) into (3.7), the power requirement can be written as:

P se,1 + jQse,1 =

(S r − S r0) jX 1

V r

∗

S rV r

= jX 1

|V r|2

(S rS r0− |

S r|2)

(3.9)

The reactive power is provided by the series converter locally and the active power

is indirectly supplied by the shunt converter through the 3rd harmonic component. This

active power requirement is given by:

P se,1 = Re

jX 1|V r|2 (S rS r0 − |S r|2)

= X 1

|V r

|2|S r||S r0| sin(ϕr0 − ϕr)

(3.10)

where ϕr0 is the power angle at the receiving end of the uncompensated system, which is

equal to tan−1(P r0/Qr0) while ϕr is the power angle at the receiving end of the system

with DPFC compensation. The line impedance X 1 and the voltage magnitude |V r| are

constant, therefore the required active power is proportional to |S r||S r0| sin(ϕr0 − ϕr).

This can also be expressed as two times the area of the triangle that is constructed by

the two vectors S r0 and S r. Figure 3-11 illustrates the relationship between P se,1 and the

power flow at the receiving end at a certain power angle θ.

Consequently, the required active power by the series converter can be written as:

P se,1 = C A(o,r0,r) (3.11)

where the coefficient C = 2X 1/|V r|2, and A(0,r0,r) is the area of the triangle (0, S r0, S r).

The angle difference ϕr0−ϕr can be positive or negative, and the sign gives the direction

of the active power through the DPFC series converters. A positive sign means that the

DPFC series converters generate active power at the fundamental frequency. The active

power requirement varies with controlled power flow, and reaches its maximum when the

vector S r − S r0 is perpendicular to the vector S r0, as shown in Figure 3-12.




r P

r Q

2

1

(0, )V

X −

DPFC control

range with θ

0r S

r S

0r r ϕ ϕ −

,1seP C

Figure 3-11: Relationship between P se,1 and the power flow at the receiving end

r P

r Q

2

1

(0, )V

X −

DPFC control

range with θ

0r S

r S

0r r ϕ ϕ −

Figure 3-12: Maximum active power requirement for the series converters




The control range of the DPFC is limited by this maximum value. According to the

figure, the relationship between the power flow control range and the maximum activepower requirement can be represented with the following equation:

P se,1,max = |X 1||S r0||V r|2 |S r,c| (3.12)

where |S r,c| is the control range of the DPFC and given by:

|S r,c

|= max

|P r,c + jQr,c

| (3.13)

For a transmission line, the line impedance and the bus voltage can be assumed con-

stant values. Accordingly, the control range is proportional to the maximum of the ex-

changed active power. The line impedance |X 1| is normally around 0.05 pu. By assum-

ing that the bus voltage |V r| and uncompensated power flow |S r0| is 1 pu, the value of

exchanged active power can be determined as approximately 0.05 pu by using (3.12),

allowing the DPFC to control 1 pu power flow.

3.3.3 Third Harmonic Frequency Circuit

The 3rd harmonic component within the DPFC system is used to exchange active and

reactive power between the shunt and series converters. Therefore, the voltages and

currents at the 3rd harmonic frequency are related to the required active power at the

fundamental frequency. For the series converters, there is:

Re (V se,3I ∗3 ) = −P se,1 (3.14)

From Figure 3-9(b), the power that is absorbed by the series converters at the 3rd harmonic

frequency is given by:

P se,3 + jQse,3 = V se,3I ∗3

= V se,3

V sh,3

−V se,3

X ′3∗ (3.15)




where X ′3 = X 3 + X sh,3. By separating the real and imaginary parts, the absorbed active

and reactive power at 3rd harmonic frequency can be expressed as:

P se,3 = |V se,3||V sh,3|

X ′3sin θ3

Qse,3 = |V se,3|

X ′3(|V sh,3| cos θ3 − |V se,3|)

(3.16)

where θ3 is the phase angle difference between the voltages V sh,3 and V se,3. For the series

converters, any reactive power at the 3rd harmonic frequency results in unnecessary extra

voltages and currents. Therefore, the reactive power flowing through the series converters

at the 3rd harmonic frequency is controlled to be zero, which is Qse,3 = 0. It follows that

the relationship between the voltages V sh,3 and V se,3 is:

|V se,3| = |V sh,3| cos θ3 (3.17)

By including (3.17) to (3.16),

P se,3 = |V sh,3|2

X ′3cos θ3 sin θ3 (3.18)

When the angle θ3 is 45, the maximum value of cos θ3 sin θ3 is equal to 1/2. Therefore,to efficiently supply the active power requirement P se,1,max, the voltage injected by the

shunt converter at the 3rd harmonic frequency should be:

|V sh,3,max| ≥

2|P se,1,max|X ′3 (3.19)

Equation (3.17) shows that the maximum voltage of the series converters at the 3rd

harmonic frequency should comply with:

|V se,3,max| ≤ |V sh,3,max| (3.20)

To transmit the same amount of active power, different combinations of voltage and

current can be selected for different cases. If the DPFC is employed to boost the power

flow through the transmission line, the DPFC can be designed to inject a small 3 rd har-

monic current, since the transmission line is likely to operate close to its thermal limits.

As compensation, more voltage at the 3rd harmonic frequency will be required, thereby

involving more series converters. In the case where the DPFC is used to limit the line cur-

rent, more losses at the 3rd harmonic frequency can be tolerated. Therefore, the DPFC




can be designed to inject a high 3rd harmonic current and low voltage to reduce the

number of series converters.

3.3.4 Control Range of the DPFC

Each converter in the DPFC generates two voltage components at different frequencies,

simultaneously. Because both voltage phasors are free with respect to their phase angles,

the voltage rating of the each converter should be the sum of the maximum voltage of the

two frequency components.

V se,max = |V se,1,max|+ |V se,3,max| (3.21)

During the operation, the active power requirement of the series converter varies with

the voltage injected at the fundamental frequency. When the requirement is low, the

series voltage at the 3rd harmonic frequency will be smaller than |V se,3,max|. The potential

voltage that is between V se,3 and |V se,3,max| can be used to generate more voltage at the

fundamental frequency, thereby increasing the control region of the power flow of the

DPFC. When S r,c is perpendicular to the uncompensated power S r0, the series converters

require maximum active power, and the radius of the DPFC control region is given by:

|S r,c| = |V r||V se,1,max|

X 1(3.22)

If S r,c is in the same line as S r0, the series converters only provide the reactive compen-

sation, and the boundary of the DPFC control region will extend to:

|S r,c| = |V r|(|V se,1,max|+ |V se,3,max|)

X 1= |V r||V se,max|

X 1(3.23)

Consequently, the control region of the DPFC can be extended to an ellipse, as shown in

Figure 3-13.

As shown, the control range of the DPFC is extended from a circle to an ellipse. When

the series converters of the DPFC require less active power, the converter can generate

more voltages at the fundamental frequency, thereby increasing control range.




r P

r Q

2

1

(0, )V

X −

DPFC control

range with θ

,r cS

r S

Figure 3-13: DPFC power flow control range

3.4 Distributed Interline Power Flow Controller

The DPFC is a solution to control the power flow in a single transmission line. By

eliminating the common DC link and distributing the series converters of the IPFC, a

new concept of the Distributed Interline Power Flow Controller (DIPFC) is achieved. The

DIPFC is a concept for control power flow through multiple transmission lines. It inherits

the advantages of the IPFC and the DFACTS concept, which allow power flow control

for multi-line systems with relatively low cost and high reliability without additional

investment.

3.4.1 DIPFC Topology

The Interline Power Flow Controller (IPFC) is comprised of a number of SSSCs with

the common link at their DC sides. The IPFC provides series compensation for multiple

lines. This compensation can be both active and reactive. The reactive power required

for the series compensation is generated by the series converter itself and the required

active power is exchanged from other converters [Gyug 99].

Similar to the DPFC, the DIPFC consists of multiple single-phase series converters,

which are independent from each other. As the DIPFC is a power flow control solution

for multiple transmission lines, the series converters are installed in different lines. The



48 3.4 Distributed Interline Power Flow Controller

DIPFC can also include shunt converters, but these are not compulsory. The single line

diagram of a DIPFC is shown in Figure 3-14.

AC

DC

transmission line i

AC

DC

AC

DC

AC

DC

sunt

converter

seres converters

transmsson lne

AC

DC

AC

DC

AC

DC

seres converters

Figure 3-14: DIPFC configuration

There is an exchange of active power between the DIPFC converters and this active

power is exchanged in the same transmission line at the 3rd harmonic frequency. If the

DIPFC is without a shunt converter, the series converters in one transmission line will

exchange active power with the converters in the other lines. If there is a shunt converter

in the DIPFC, the shunt converter will supply the active power for each series converter.

As described before, the converters in the DIPFC use the AC transmission lines to

exchange active power at the 3rd harmonic frequency. Accordingly, 3rd harmonic currents

should flow through the lines with the DIPFC converters. To make a closed loop for the

3rd harmonic current, the branches with DIPFC series converters should have common

connections. This can be a direct connection or go through other transmission lines. In

order to prevent 3rd harmonic leakage to other parts of the network, transmission lines

with the DIPFC converters should be closed by Y-∆ transformers, as shown in Figure 3-15.

3.4.2 DIPFC Operating Principle

In the same way as with the DPFC, the DIPFC utilizes the 3rd harmonic current to

exchange active power between converters. The operating principle of the DIPFC can be

distinguished in two cases: with and without the shunt converter.




transmission line i

AC

DC

AC

DC

AC

DC

transmission line ii

ACDC

ACDC

ACDC

transmissionnetwork with the

DIPFC

Figure 3-15: DIPFC within a meshed network

With shunt converter

If the DIPFC contains a shunt converter, the shunt converter will supply the required

active power for all series converters. Accordingly, each series converter has the capability

of injecting both active and reactive power into the transmission line. In this case, the

DIPFC acts like multiple DPFCs that are installed in different transmission lines. The

line with the series converters can be fully controlled to adjust the line impedance, the

transmission angle and the bus voltage magnitude. As the DIPFC with a shunt converter

is identical to a DPFC, that has already been examined, it will not be discussed here.

Without shunt converter

In a DIPFC without a shunt converter, the series converters in different lines will exchange

active power with each other. The sum of the active power that is injected by all series

converters is zero at the fundamental frequency. It is assumed that the converters in

one (or more) of the lines inject both active and reactive power and they are referred

to as ‘master converters’. Neglecting losses, the active power required by these master

converters is supplied by converters in other lines, which can be referred to as ‘slave



50 3.4 Distributed Interline Power Flow Controller

converters’. The master converters can generate a 360 rotatable voltage. However,

the slave converters can only provide controlled reactive power to the line, because theactive power injection of the slave converters depends on the requirement from the master

converters and does not have control freedom. In this section, the DIPFC without the

shunt converter will be considered.

3.4.3 DIPFC Control

The control of the DIPFC with a shunt converter is the same as the DPFC, and consists

of central control, shunt control and series control. Within a DIPFC without a shunt

converter, active power is exchanged between the series converters. Therefore, the control

is different and consists of three different controllers; central control, master control and

slave control, as shown in Figure 3-16.

transmission line ii

AC

DC

AC

DC

AC

DC

series

converters

slave

control

slave

control

slave

control

centralcontrol

transmission line i

AC

DC

AC

DC

AC

DC

series

converters

master

control

master

control

master

control

Figure 3-16: Control the DIPFC without a shunt converter

Each series converter has its own localized controller to maintain DC capacitor voltage.

The central controller generates the setting points for the fundamental frequency voltage

that will be injected by the series converter.




• Central control: The central control generates reference signals for both the mas-

ter and slave converters. Reference signals are the voltages at the fundamentalfrequency. For the master converters, the reference voltage consists of both active

and reactive components. However, for the slave converters the reference voltage

contains only the reactive component. The central control for the DPFC and DIPFC

are similar and both focus on the applications in the power system level. However,

the DIPFC central control generates reference signals for the series converter in

multiple transmission lines.

• Master control: The master controller is used to maintain the capacitor DC

voltage of its own converter at a constant value by using the 3rd harmonic frequencycomponents. It also generates a series voltage at the fundamental frequency that is

prescribed by the central control.

• Slave control: The task of the slave control is similar to the task of a shunt control

within the DPFC. The slave converter injects a constant 3rd harmonic current into

the line to supply active power for the master converters. It also maintains the

capacitor DC voltage of the slave converters at a constant value by absorbing active

power from the grid at the fundamental frequency and injecting the required reactive

voltage at the fundamental frequency.

3.5 DIPFC Steady-State Analysis

This section presents the steady-state analysis of the DIPFC without a shunt converter.

The simplest DIPFC system, as shown in Figure 3-16, is used as an example. The DIPFC

is installed in two parallel transmission lines between two buses. These lines are closed by

two Y-∆ transformers with floating neutral points. Accordingly, the 3rd harmonic current

will flow only inside the parallel transmission lines.

3.5.1 DIPPF Simplification and Equivalent Circuit

For analysis, the DIPFC converters can be replaced by two controlled voltage sources. One

represents the fundamental frequency and the other represents the 3rd harmonic frequency.

Assuming a lossless converter, the active power exchange in a single converter between

the different frequencies is zero. The transmission line i and ii are represented by inductor

Li and Lii respectively. The phasor voltage at the sending-end of the transmission lines



52 3.5 DIPFC Steady-State Analysis

is V s and at the receiving-end is V r. The equivalent circuit of the basic DIPFC is shown

in Figure 3-17. The converters in line i are controlled to be the ‘master converter’ andsupported by the converter in line ii.

,1mV ,3m

V i L

r V s

V ,1 ,3m m

P P= −

, ,,

m r m r P Q

m I

,1slV ,3sl

V ii L

,1 ,3sl slP P= −

sl I

, 3

, 3

s

m

P

P

=

−

line i

line ii

, ,,

sl r sl r P Q

Figure 3-17: DIPFC simplified circuit

The voltages injected by the DIPFC converter are V m,1 and V m,3 for the master con-

verter, and V sl,1 and V sl,3 for the slave converter. The currents through the two lines are

I m and I sl respectively. By applying the super position theorem in the simplified DIPFC

circuit, Figure 3-17 can be split into two circuits according to frequencies, as shown in

Figure 3-18.

,1slV

,1i X

r V sV

,1 ,3m mP P= −

,1 ,3sl slP P= −

,1sl I

,3mV ,3i X

,3m I

(a) (b)

,1mV

,1ii X

,3slV ,3ii X

,3sl I

, ,,

m r m r P Q

, ,,

sl r sl r P Q

,1m I

Figure 3-18: DIPFC equivalent circuit: (a) the fundamental frequency; (b) the 3rd harmonic

frequency

The two circuits are isolated with each other and the components in one circuit are only

at one frequency. This arrangement simplifies the steady-state analysis of the DIPFC,

which allows each circuit to be analyzed separately.




3.5.2 Fundamental Frequency Circuit

In the fundamental frequency circuit of the DIPFC, there are two transmission lines: the

line with the master converters and with the slave converters. The master converters

have the same capability as the series converters within the DPFC, which is to inject

a voltage with controllable active and reactive components. For a description of the

control capability of the DIPFC master converter refer to the analysis of the DPFC series

converter in previous section.

The slave converters can also inject a fundamental frequency voltage that contains both

active and reactive components. As the active power absorbed or generated by the slave

converters is related to the master converter, the slave converters can only independently

control the reactive voltage at the fundamental frequency. Accordingly, the control range

of the DIPFC slave converters depends on the active power requirement of the master

converters.

Assuming the active power required by master converters at the fundamental frequency

is Pm,1, the active power supplied by the slave converter is:

P sl,1 =−

P m,1 (3.24)

The active power injected by the converters is related to the triangle that is constructed

by the uncompensated and compensated power flow, as described above. Therefore, to

supply the active power P sl,1, the control range of the slave converters should have the

character that the area of triangle (0, S sl,r0, S sl,r) is P sl,1. Accordingly, the control range

of the slave converter is a straight line that is parallel with S sl,r0, as shown in Figure 3-19.

As shown, the control line of the slave converters is parallel with the vector S sl,r0 in

the complex P Q-plane. From (3.11), the distance S d,sl between the two parallel lines is

given by:

S d,sl = P sl,1

C |S sl,r0| (3.25)

where the coefficient C = 2X ii,1/|V r|2.

3.5.3 Third Harmonic Frequency Circuit

The structure of the 3rd harmonic frequency circuit of the DIPFC is similar as the one of

the DPFC. The slave converters correspond to the shunt converters of the DPFC and the



54 3.6 Conclusions

,sl r P

,sl r Q

2

,1

(0, )sl

V

X −

DIPFC slave

converters

control range

, 0sl r S

,sl r S ,d sl

S

Figure 3-19: Control range of the DIPFC slave converters

master converters correspond to the series converters. Accordingly, the analysis of the

DIPFC 3rd harmonic frequency circuit can be found in the aboved section.

3.6 Conclusions

In this chapter, two new concepts within the combined FACTS family are presented,

namely a Distributed Power Flow Controller (DPFC) and a Distributed Interline Power

Flow Controller (DIPFC). The DPFC and DIPFC are derived from the UPFC and IPFC.

Two new approaches are employed; eliminating the common DC links and distributing

the series converters.

By the elimination of the common DC link, the converters within the UPFC and IPFC

are independent. The active power exchange between the converters that used to throughthe common DC link in the UPFC and IPFC, is now through the transmission line at

the 3rd harmonic frequency. By employing the D-FACT concept, the series converters of

the UPFC and IPFC are distributed. Compared to the UPFC and IPFC, the cost of the

DPFC and DIPFC is reduced, due to the small rating of the components and the low

voltage isolation. Also, because of the redundancy of the series converters, the reliability

of the DPFC and DIPFC is increased without additional backup components. To reduce

the investment, the shunt converter can be adapted from a STATCOM. A single-phase

AC-DC converter can be connected back-to-back to the DC side of the STATCOM, and




its AC terminals are connected between the Y-∆ transformer’s neutral point and the

ground.A steady-state analysis is also presented in this chapter. It is found that the DPFC

and DIPFC have the same control capability as the DPFC and IPFC. The DPFC can

simultaneously adjust the line impedance, the transmission angle and the bus voltage.

The DIPFC is capable of controlling multiple transmission lines. If DIPFCs include a

shunt converter, it acts like multiple DPFCs. If made without a shunt converter, the

DIPFC will exchange active power between the converters in different lines. In this case,

the DIPFC converters can be distinguished: master and slave converters. The master

converter can inject a voltage that contains independent controllable active and reactivecomponents, while the slave converter supplies active power to the master converter and

provides reactive compensation for its own line.

To obtain the same control capability as the UPFC and IPFC, the rating of the DPFC

and DIPFC converters at the fundamental frequency should be the same as the one for

the UPFC. Because the voltages and currents at the 3rd harmonic frequency have to be

added, the rating of the DPFC converter is slightly larger than the UPFC and IPFC. The

increased rating is related with the active power exchanged at the 3 rd harmonic frequency

and can limited within 5% of the nominal rating.



Chapter 4DPFC MODELING AND BASIC

CONTROL

4.1 Introduction

I

N the previous chapter, the new FACTS device, a DPFC, as well as its operating

principle were introduced, followed by an analysis of the DPFC in steady-state. To

enable the control of the DPFC, controllers for individual DPFC converters are needed.

This chapter addresses the basic control system of the DPFC, which is composed of shunt

control and series control that are highlighted in Figure 4-1.

AC

DC

transmission line

AC

DC

AC

DC

AC

DC hgh-

pass

filter

snt

onerter

seres

onerters

snt

ontrol

seres

ontrol

seres

ontrol

seres

ontrol

entral

ontrol

Figure 4-1: DPFC basic control

The functions of the series control can be summarized as:

• Maintain the capacitor DC voltage of its own converter by using the 3 rd harmonic

57



58 4.2 DPFC Modeling

frequency components.

• Generate the series voltage at the fundamental frequency that is prescribed by thecentral control.

The functions of the shunt control are:

• Inject a constant 3rd harmonic current into the line to supply active power for series

converters.

• Maintain the capacitor DC voltage of the shunt converter by absorbing active power

from the grid at the fundamental frequency.

• Inject reactive voltage at the fundamental frequency to the grid as prescribed bythe central control.

This chapter begins with the modeling of the DPFC in the dq -frame [Fitz 03]. The

AC components of the DPFC are transformed to DC components by using Park’s ( dq )

transformation. The transformed DC components of the DPFC can be controlled by

traditional PI controllers.

Once the modeling of the DPFC is introduced, the design of the DPFC basic control

is given in section 4.3. The basic control is responsible for maintaining the DC voltages of the DPFC converters and generating the AC voltages as prescribed by the central control.

Further, the communication between the DPFC series converters and the central con-

trol is considered in section 4.4. A relatively low cost and reliable synchronization method

for series converters is proposed. This method involves transmitting the control signals in

DC-quantity, thereby only requiring low-bandwidth communication. In addition, during

communication failure the series converters can continue synchronization.

4.2 DPFC Modeling

To design a DPFC control scheme, the DPFC must first be modeled. This section presents

such modeling of the DPFC. As the DPFC serves the power system, the model should

describe the behavior of the DPFC at the system level, which is at the fundamental and

the 3rd harmonic frequency. The modeling of the switching behavior of converters is not

required.



4 DPFC MODELING AND BASIC CONTROL 59

4.2.1 DPFC Model Overview

The modeling of the DPFC consists of the converter modeling and the network modeling.

Due to the use of single-phase series converters, they are modeled as a single-phase system.

To ensure that the single-phase series converter model is compatible with the three-phase

network model, the network is modeled as three single-phase networks with 120 phase

shift. Figure 4-2 gives the flow chart of the DPFC modeling process, which leads to six

separated models.

DPFC

network converter

1st freq. 3

rd freq.

s.p.

dq dq

1st

freq.network

model

3rd

freq.network

model

shunt

converter

ac sideshunt

model

dc sideshunt

model

series

converter

ac side dc side

s.p.

dqdq

ac sideseries

model

dc sideseries

model

ac side dc side

s.p.

dqdq

Figure 4-2: DPFC modeling process flow chat

Two tools are employed for the DPFC modeling: the superposition theorem and Park’s

transformation [Fitz 03, Soo 98]. As is well known, the transmission network is a lin-

ear system and the superposition theorem can therefore be applied. However, for the

converter, certain approximations are needed for the application of the superposition the-orem. Within the flow chart, the diamond shapes with ‘s.p.’ indicate the process of

applying the superposition theorem, and the shapes with ‘dq’ represent the process of

Park’s transformation.

Because Park’s transformation is designed for analysis of signals at a single frequency

and the DPFC signal consists of two frequency components, the superposition theorem is

first used to separate the components. Then, the component at different frequencies are

subjected to Park’s transformation and analyzed separately. Park’s transformation, which

is widely used in electrical machinery analysis, transforms AC components into DC. The




principle of Park’s transformation is to project the AC signal in vector representation on

to a rotating reference frame, referred to as the ‘dq -frame’. The frequency of the rotationis chosen to be the same as the frequency of the AC signal. As a result, the voltages and

the current in the dq -reference are constant in steady-state.

The components at different frequencies are transformed into two independent rotating

reference frames at different frequencies. The components at the fundamental frequency

are 3-phase components, so Park’s transformation can be applied directly. However, as

Park’s transformation is designed for a 3-phase system, a variation is required before its

application to a single-phase system [Sala 04, Zhan 02]. The reason for this is that the 3rd

harmonic component of a three phase system can be considered a single-phase component,

as its components are all in phase (‘zero-sequence’). A detailed description of single-phase

Park’s transformation can be found in Appendix A.

In this section, the network modeling is introduced, followed by the modeling of the

DPFC converter. Once the separated models are presented, the correlation between the

different models is given.

4.2.2 Connection of Separated Models

The DPFC is modeled in separated parts. In this subsection, the connection between the

models of separated parts is presented, as shown in Figure 4-3.

As shown, the DPFC model consists of the fundamental frequency network model, the

3rd harmonic frequency network model, the series converter model and the shunt converter

model. The fundamental frequency network model calculates the current through the line

I 1 based on sending end, receiving end and series converter voltages. This current feeds

back to the shunt and series converter models for the DC voltage calculation and to the

central control for applications at the power system level. The 3rd harmonic frequencynetwork model calculates the current I 3 from the voltages injected by the shunt and the

series converters. The 3rd harmonic current is used for the calculation of the converter’s

DC voltages and it is also one of the control objects of the shunt control.

4.2.3 Network Modeling

This section presents the mathematical representation of a network with a DPFC at both

the fundamental and the 3rd harmonic frequencies. As the circuits at the two frequen-




DC

se

1st

se

3rd

se

1st

network

model

3rd

network

model

DC

sh 1stsh

3rd

sh

series

control

shunt

control

,se ref V

1 I

3 I

series converter model

,sh ref V

1 I

3 I

shunt converter model

1 I

3

I

central

control

,1seV

,3seV

,3shV

,1shV

sV

r V

to converter

models

to converter

models

,1,se ref V

,1, ,s h q r ef I

for reactive

compensation

Figure 4-3: Connection of the separated models of the DPFC

cies have been separated by the superposition theorem, the modeling of each circuit is

presented separately.

Fundamental frequency network modeling

During the process of the network modeling, the DPFC converters can be considered

controllable voltage sources [Song 99]. In a practical transmission system, perfect balance

between phases is often assumed because the effect of the asymmetry is usually small,

especially if the lines are transposed along their lengths. Most overhead transmission

lines have at least two overhead conductors called ground wires, which are grounded at

uniform intervals along the length of the lines. Therefore, the grounding can be treatedas an ideal conductor with zero impedance and the mutual impedances between phases

can be neglected [Grai 94]. With these assumptions, the network with the DPFC series

converters at the fundamental frequency can be simplified as shown in Figure 4-4.

With the equivalent circuit, the voltages at the fundamental frequency injected by the

series converters is Vse,1, the line impedance is Z 1, and the voltages at the sending and

receiving ends are Vr and Vs, respectively. The voltages Vse,1, Vr, Vs and the current I1

are column vectors, which consist of information for the three phases. At the fundamental

frequency, the network is modeled as three single-phase systems whose phases are shifted




+ -1 Z ,1,se aV

,s aV ,r aV 1,a

I

+ -1 Z ,1,se b

V ,s bV ,r b

V 1,b I

+ -1 Z ,1,se c

V ,s cV ,r c

V 1,c I

Figure 4-4: Fundamental frequency network equivalent circuit

by 120. According to the equivalent circuit, the relationship between the line current I1

and the series voltage is given by:

V s,a

V s,b

V s,c

−

V r,a

V r,b

V r,c

−

V se,1,a

V se,1,b

V se,1,c

=

Z 1 0 0

0 Z 1 0

0 0 Z 1

i1,a

i1,b

i1,c

(4.1)

The model of the DPFC fundamental frequency represents how DPFC series converters

affect the current through the transmission line by varying the injected voltages. Accord-

ingly, the input of the model is the voltage injected by the series converters Vse,1, and

the output is the line current I1. The voltage at the sending and the receiving ends can

be considered constant in the two-port network. While for the meshed network modeling,

these two voltages can also be treated as the inputs. A block diagram of the fundamental

network model is shown in Figure 4-5.

1st network

model

1I

sV

rV

se,1V

Figure 4-5: Input and output of the fundamental frequency network model

Third harmonic frequency network modeling

Within the DPFC, the shunt converter injects 3rd harmonic current at the neutral point

of the Y-∆ transformer, as shown in Figure 3-7. This current distributes over the three

phases and makes a closed-loop through the grounded neutral point of the other Y-∆




transformer. By representing the converters with voltage sources, the equivalent circuit

for the 3rd harmonic frequency network can be simplified as shown in Figure 4-6.

+ -3 Z ,3,se aV

3,a I

+ -3 Z ,3,se bV

3,b I

+ -3 Z ,3,se cV

3,c I

,3shV

+

-

transformer

winding

transformer

winding

Figure 4-6: 3rd harmonic network equivalent circuit

The zero sequence reactance of the two transformer windings and the line impedance

can be combined. This total impedance at the 3rd harmonic frequency is represented by

Z 3. As described before, the neutral impedance is assumed to be zero. Therefore, the

relationship between the voltages and the currents at the 3rd harmonic frequency is:

V sh,3 − V se,3,a

V sh,3 − V se,3,b

V sh,3 − V se,3,c

=

Z 3 0 0

0 Z 3 0

0 0 Z 3

I 3,a

I 3,b

I 3,c

(4.2)

The 3rd harmonic network model represents the 3rd harmonic current within each

phase, which is caused by the 3rd harmonic voltage injected by the shunt and the series

DPFC converters. The inputs of the model are the voltages V sh3 and Vse,3, which come

from the converter models, while the output of the model is the 3rd harmonic current of

each phase I3, as shown in Figure 4-7.

3rd network

model

3I

,3shV

se,3V

Figure 4-7: Input and output of the 3rd harmonic frequency network model




4.2.4 Series Converter Modeling

The DPFC series converters are identical, as are their models. The series converter is

PWM control single-phase converter. Its simplified configuration is shown in Figure 4-8.

As mentioned before, the switching behavior of the converter is not considered. To simplify

the analysis, the loss of the converter is neglected.

AC

DC

+ se

V I

,V seref

,se dc I

,se dcV

seC

transmission line

series

control

,1,s e r ef V from

central

control

Figure 4-8: Simplified diagram of a series converter

Due to the identity of the series converters, Figure 4-8 depicts a converter that is availed

in all three phases. To distinguish the converter in different phases, a subscript of phase

could be added to the voltages and currents in Figure 4-8 if necessary. The AC side and

the DC side voltages of the series converter are V se and V se,DC respectively and ref V,sef is

the modulation amplitude of the reference AC signal in pu, which is generated by the series

control. Note that the AC voltages and currents in Figure 4-8 consist of two components at

different frequencies, namely the fundamental and the 3rd harmonic frequency components

that are denoted by subscripts 1 and 3 respectively. Their relationship can be illustrated

as follows:

V se = V se,1 + V se,3 (4.3)

AC side modeling

The series converter is a PWM converter. The AC side voltage of the converter can be

approximated with the product of the AC reference signal and the DC voltage as V se:

V se = ref V,se · V se,dc (4.4)




The reference signal is pu value with the range from -1 to 1. By applying the super-

position theorem to the equation, equation (4.4) can be separated into: V se,1

V se,3

=

ref V,se,1

ref V,se,3

· V se,dc (4.5)

The input signals of the AC side model of the series converter is ref V,se and V se,dc and the

output is the AC voltage V se, which comes from the DC side model.

DC side modeling

The DC voltage of the series converter V dc,se is related with the DC current I dc,se and therelationship is given by:

C sedV dc,se

dt = I dc,se (4.6)

Two frequency components exist in both the reference voltage and the AC current.

The DC side current of the series converter is approximated to:

I dc,se = ref V,se

·I = (ref V,se,1 + ref V,se,3)(I 1 + I 3) (4.7)

and the DC voltage can be written as:

C sedV dc,se

dt = (ref V,se,1 + ref V,se,3)(I 1 + I 3) (4.8)

By applying the inverse single-phase Park’s transformation, explained in Appendix A, we

obtain:

C sedV dc,se

dt = (ref V,se,1,d sin θ + ref V,se,1,q cos θ + ref V,se,3,d sin 3θ + ref V,se,3,q cos 3θ)

· (I 1,d sin θ + I 1,q cos θ + I 3,d sin 3θ + I 3,q cos 3θ)

(4.9)

where θ is the angle of the rotation reference frame for Park’s transformation. On the right

side of (4.9), there are cross terms of different frequency components, which appear as

zero-average ripples superimposed with the DC voltage. As this ripple has no contribution

to the DC voltage magnitude, the terms that cause the ripple are neglected during the

modeling. Therefore, the DC voltage can be approximated to:

C se

dV dc,se

dt =

1

2 (ref V,se,1,dI 1,d + ref V,se,1,qI 1,q) +

1

2 (ref V,se,3,dI 3,d + ref V,se,3,qI 3,q) (4.10)




Accordingly, the input signals for the DC side model are ref V,se,1, ref V,se,1, I 1 and

I 3, and the output is the DC voltage V se,dc. Equation (4.9) can accurately represent thecapacitor DC voltage of the series converter, which consists of the mean-value and the

ripple, while equation (4.10) neglects the ripple. During the design of the DPFC, the

capacitance of the series converter is selected to limit the ripple within a 5% error of the

nominal DC voltage. Therefore, the model given in (4.10) is sufficiently accurate for the

DC voltage calculation.

Series converter model

By combining the models of the AC side and the DC side, the series converter model is


dc side

model

,se dcV

, ,1V seref

, ,3V seref

1st ac side

model

3rd

ac side

model

1 I

3 I

,1seV

,3seV

Figure 4-9: Block diagram of the series converter model

The input signals for the series converter model are the reference voltage from the

series control and the line current, taken at both frequencies. The output signal of the

model is the AC voltage generated by the series converter.

4.2.5 Shunt Converter Modeling

The shunt converter consists of a three-phase converter that is back-to-back connected to

a single-phase converter. Similar as a STATCOM, the three-phase converter is connected

to the low-voltage side of the Y-∆ transformer to absorb active power from the grid. The

single-phase converter is connected between the ground and the neutral point of the Y-∆

transformer to inject 3rd harmonic current. The simplified diagram of the shunt converter

is shown in Figure 4-10.




AC

DC AC

DC

Y∆ tanfoms

V

sh,1V

sh,1I

sh Z

,sh dcV

shC

, ,1sh dc I , ,3sh dc I

V,sh,1ref , ,3V shref

,3shV

,3sh I

,1, ,s h q r ef I

hunt

contol

fom

cntal

contol

tanmon ln

Figure 4-10: Simplified diagram of the shunt converter

Due to no 3rd harmonic component at the ∆ side of the transformer, the converter

at the left side contains only the components at the fundamental frequency, namely the

voltage Vsh,1 and the current Ish,1. The voltage V sh,3 and current I sh,3 at the 3rd harmonic

frequency are single-phase components.

AC side modeling

Similar to the series converter modeling, the AC voltage can be approximately written as

follows:

Vsh,1 = ref V,sh,1 · V sh,dc

V sh,3 = ref V,sh,3 · V sh,dc

(4.11)

where the modulation amplitudes ref V,sh,1 and ref V,sh,3 are pu values with the range from-1 to 1.

DC side modeling

The capacitor DC voltage of the shunt converter is given with the following equation:

C sh

dV sh,dc

dt = I sh,dc,1 − I sh,dc.3 (4.12)




By applying Park’s transformation to the fundamental frequency components, the DC

current at the three-phase side can be found:

I sh,dc,1 = 3

2(ref V,sh,1,dI sh,1,d + ref V,sh,1,qI sh,1,q) (4.13)

If the three-phase components are symmetrical, the DC current I sh,dc,1 is a constant with

no ripple.

By substituting single-phase Park’s transformation into the 3rd harmonic components,

the 3rd DC current is:

I sh,dc,3 = (ref V,sh,3,d sin 3θ + ref V,sh,3,q cos 3θ) · (I sh,3,d sin 3θ + I sh,3,q cos 3θ) (4.14)

As previously discussed concerning series converter modeling, terms with zero-average

values will not contribute to the capacitor DC voltage while appearing as ripples of the DC

voltage. By neglecting these terms, the shunt converter DC voltage can be approximated

by:

C sh dV sh,dc

dt =3

2 (ref V,sh,1,dI sh,1,d + ref V,sh,1,qI sh,1,q)

− 1

2 (ref V,sh,3,dI sh,3,d + ref V,sh,3,qI sh,3,q)

(4.15)

Shunt converter model

The overall shunt converter model, created by connecting the AC and DC sides of the

shunt converter model, is shown in Figure 4-11.

dc side

model

,sh dcV

V,sh,1ref

, ,3V shref

1st ac side

model

3rd

ac side

model

sh,1I

,3sh I

sh,1V

,3shV

Figure 4-11: Block diagram of the series converter model




The input signals for the model are reference voltage signals and current, at both

frequencies, while the outputs are the fundamental and 3rd harmonic frequency voltages,generated by the shunt converter.

4.3 DPFC Basic Control

Based on the DPFC model presented previously, the control can now be further developed.

The DPFC basic control consists of the series control and the shunt control. In this section,

the control schemes and their corresponding design are addressed. Because of its simple

implementation, the vector control method [Kann 04, Papi 97] is employed to control the

DPFC converter. The calculation of the controller parameter is based on the Internal

Model Control (IMC) method [Garc 82, Harn 98].

4.3.1 Series Converter Control

Each DPFC series converter is locally controlled by its own controller, and the scheme for

each series control is identical. To control the series converter, separate control loops are

employed for the two frequency components. The 3rd harmonic control loop is used for

DC voltage control. The block diagram of the DPFC series converter control is shown in

Figure 4-12.

1-ph PLL3rd passfilter

dc control

1-ph

inverse

dq

0

PWM

gen.

signal

process AC

DC

+ -seV

I

,V seref ,se dc

V

transmission line

, ,1V seref

3θ 3 I

, , 3,V se qref

, , 3,V se d ref , ,se dc ref

V

, ,3V seref

C

I

from central

control

+

+

,se dcV

series control

,1,s e r ef V

Figure 4-12: Control scheme of the series converter



70 4.3 DPFC Basic Control

Control of the fundamental frequency component

The reference voltage at the fundamental frequency for the series converters is gener-

ated by the central control and transmitted to each converter through a communication

channel. The signal-process block is utilized to transform the ‘communication voltage’ to

the AC reference voltage at the fundamental frequency. This block will be introduced in

section 4.5. This AC signal, superimposed with the signal generated by the 3rd harmonic

control, is sent to the PWM generator to drive the switches of the series converter.

Control of the third harmonic frequency component

As shown in Figure 4-12, the 3rd harmonic frequency control is the major control loop

with the DPFC series converter control. Its task is to maintain the DC capacitor voltage.

The principle of vector control is used here for DC voltage control. Normally, the

voltage is used as the rotation reference frame for Park’s transformation, but here the 3rd

harmonic current through the line is selected because it is easily measured by the series

converter. As the line current contains two frequency components, a 3rd band pass filter

is needed to extract the 3rd harmonic current. The single-phase Phase-Lock-Loop (PLL),

as described in Appendix B, creates a rotation reference frame from the 3rd harmonic

current. The d component of the 3rd harmonic voltage is the parameter used to control

the DC voltage. The control signal is generated by the DC voltage control loop. Because

the q component of the 3rd harmonic voltage will only cause reactive power injection to

the AC network, the q component is kept at zero during the operation.

- DC voltage control design

The DC voltage control loop is used for maintaining the DC voltage of the series converter.

Within the series converter control, both frequency component currents are taken astheir rotating reference frame for Park’s transformation. By projecting the currents to

themselves, the q components I 1,q and I 3,q that are perpendicular to the current, will be

zero and (4.10) can be written as:

C sedV se,dc

dt =

1

2 (ref V,se,1,dI 1,d + ref V,se,3,dI 3,d) (4.16)

As shown, the DC capacitor voltage is affected by both the fundamental and the

3rd harmonic frequency components. The components at the fundamental frequency




ref V,se,1,dI 1,d can be treated as a disturbance. Because the 3rd harmonic current within

the line is a constant value, the current I 3,d is considered constant.To design the controller, (4.16) is transformed from the time-domain to the frequency

domain (s-domain) using the Laplace Transform. By selecting ref V,se,3,d as the control

parameter and V se,dc as the control object, the transfer function from ref V,se,3,d to V se,dc

is found:

G(s) = V se,dc(s)

ref V,se,3,d(s) =

I 3,d

2C ses (4.17)

As shown, the pole of the transfer function is at the origin. To improve disturbancerejection, an inner feedback loop is introduced for active damping [Pete 05] as a part of

the DC voltage control loop. The scheme of the DC voltage control is shown in Figure 4

13.

F ( s)

R

+

-

+

-

G( s), , 3,V se d

ref ,se dc

V , ,se dc ref

V

G’( s)

dc control

Figure 4-13: Scheme of the DC voltage control loop of the series converter

Within the DC control, F (s) is the control function and R is the active damping taken

as feedback in the controller. The active damping and G(s) results in a new virtual system

G′(s). The transfer function of G′(s) is given by:

G′(s) = G(s)1 + RG(s)

= I 3,d

2sC se + RI 3,d

(4.18)

The virtual system G′(s) is a first order system and according to the IMC method,

the control function for a first order system is given by:

F (s) = αd

s G′(s)−1 (4.19)

where αd is a design parameter, and means the desired bandwidth of the closed-loop

system here. The relationship between the bandwidth and the rise time trise (from 10%




to 90% of the final value) is [Otte 03]:

αd = ln 9

trise

(4.20)

Consequently, F (s) is a PI controller and can be described by:

F (s) = 2Cαd

I 3,d

+ Rαd

s (4.21)

To calculate the active damping R, a suitable choice is to make the inner feedback loop

as fast as the closed-loop system. This means placing the pole of G′(s) at −αd, thereby

obtaining the active damping R:

RI 3,d

2C = αd ⇒ R =

2Cαd

I 3,d

(4.22)

Accordingly, the parameters of PI controllers k p and ki and the active damping R

within the DC voltage control can be calculated from the following equations:

k p = 2Cαd

I 3,d, ki =

2Cα2d

I 3,d, R =

2Cαd

I 3,d(4.23)

4.3.2 Shunt Converter Control

The shunt converter contains two converters as described in Figure 4-10. The single-

phase converter injects the constant 3rd harmonic current into the grid. The three-phase

converter maintains the DC voltage at a constant value and generates reactive power to

the grid. The control of each converter is independent. A block diagram of the shunt

converter control is shown in Figure 4-14.

Control of the third harmonic frequency component

The converter that is connected between the neutral point of the Y-∆ transformer and the

ground is a single-phase converter. It is responsible for injecting a constant 3rd harmonic

current into the grid, therefore requiring a current controller. The 3rd harmonic current is

locked with the bus voltage at the fundamental frequency. A PLL is used to capture the

bus voltage frequency, and the output signal of the PLL θ1 is multiplied by 3 to create a

virtual rotation reference frame for the 3rd harmonic component.




, ,1V shref from central

control

PLL

dc

control

inverse

dqcurrent

control

, ,1,V sh d ref

, ,1,V sh qref

,1, ,s h d re f I

,1, ,s h q r ef I

AC

DC

Y-∆ transformer

s

V

,1shV

,1sh I

sh Z

,sh dcV

PWM

gen., ,sh dc ref V C

1

θ

,sh dcV

shunt control

1st frequency

(a)

AC

DC

Y∆ tanfom

sV

, ,3V shref

,3shV

1p

inverse

dqcurrent

control

P

, , 3,V sh d ref

, , 3,V sh qref

3

PWM

gen.

,3,s h r ef I C

,3sh I

1θ 3

θ shunt control

3rd

hrmonic

(b)

Figure 4-14: Control scheme of the shunt converter: (a) for the fundamental frequency

components; (b) for the 3rd harmonic frequency components




- Current control design

The current control loop is the major loop within the shunt converter’s 3rd harmoniccontrol. In order to design the current control, the relationship between the 3rd harmonic

current and the shunt voltage should be determined. Assuming that the DC voltage of the

back-to-back converter is constant, the shunt and series converters can be represented by

voltage sources. From Figure 4-7, the 3rd harmonic circuit can be further simplified into

two voltage sources series connected to an inductor and resistor, as shown in Figure 4-15.

+ -

,3shV

,3sh I 3 R 3

L ,3seV

+

-

Figure 4-15: Simplified 3rd harmonic circuit

The resistor R3 and L3 are the equivalent resistance and inductance of the network

at the 3rd harmonic frequency. The circuit shows that the current and voltage have the

following relationship:

V sh,3 = L3dI sh,3

dt + R3I sh,3 + V se,3 (4.24)

By applying Park’s transformation to (4.24), the relationship between the voltage and

the current in the dq -frame can be determined:

V sh,3,d = R3I sh,3,d + L3dI sh,3,d

dt − ω3L3I sh,3,q + V se,3,d

V sh,3,q = R3I sh,3,q + L3dI sh,3,q

dt + ω3L3I sh,3,d + V se,3,q

(4.25)

where ω3

is the 3rd harmonic angular velocity. The terms with ω3

in both equations cause

a coupling of the two equations. To decouple the control of the d and q components, the

coupling terms can be cross added with the signal generated by the PI controller [Milo 06].

The voltage injected by series converter V se,3 and the coupling terms within (4.25) can be

considered disturbances. By transforming (4.25) into the frequency-domain, the transfer

functions from the voltage V sh,3 to the current I sh,3 for both d and q components are the

same and can be expressed as:

G(s) =

1

R3 + sL3 (4.26)




As concerns the shunt converter, the voltage injected by the series converter is unpre-

dictable. To minimize this disturbance, additional active damping is added as the innerfeedback loop for each current control loop. Consequently, the scheme of the current

control is shown in Figure 4-16.

G( s) F d ( s)

+

-

+ +

-

+-

+

-

ω3 L3

+

-

Rd

-

-

,3,se d V

, , 3,V sh d ref

G( s)

ω3 L3

Rq

F q( s)+

,3,se qV

, , 3,V sh qref

,3,sh q I

,3,sh d I

, 3, ,s h d r ef I

, 3, ,s h q r ef I

current

control

Figure 4-16: Scheme of the 3rd harmonic current control within the shunt converter

By using the IMC method, as introduced above, to design the current control, the

parameters of the control functions F (s) can be calculated as:

F d(s) = αdL3 + αd(R3 + Rd)

s

F q(s) = αqL3 + αq(R3 + Rq)

s

(4.27)

where αd and αq are the bandwidths for the d and q components respectively, and the

reactive damping R is given by:

Rd = αdL3 −R3

Rq = αqL3 −R3

(4.28)

Control of the fundamental frequency component

The control of the shunt converter at the fundamental frequency aims to inject a con-

trollable reactive current into the grid and to keep the DC voltage of the capacitor at a

constant level. As shown in Figure 4-14, this control consists of two major blocks: the

current control and the DC control. The current control is the inner control loop, which




controls the current Ish,1. The reference of the q component of the current is from the

central control and the reference signal of the d component is generated by the DC con-trol. For Park’s transformation, the rotation reference frame is created by the PLL using

the bus voltage as input.

- Current control design

This control scheme is similar to the current control scheme for 3rd harmonic components.

As the grid voltage V s is available for the control, there is theoretically no disturbance of

the system, and it is not necessary to add active damping for the control. The scheme of

the current control is shown in Figure 4-17.

G( s) F d ( s)

+

-

+

-

+-

+

-

ω1 L1

+

-

,s d V

, ,1,V sh d ref

G( s)

ω1 L1

F q( s)

,s qV

, ,1,V sh qref

,1,sh q I

,1,sh d I

,1, ,s h d re f I

,1, ,s h q r ef I

current

control

Figure 4-17: Scheme of the fundamental current control within the shunt converter

Within the scheme, ω1 is the angular velocity of the system; L1 and R1 are equivalent

to the inductance and resistance of the shunt converter at the fundamental frequency. This

control is designed in the same way as the current control for 3 rd harmonic components

and the control function is given by:

F d(s) = αdL1 + αdR1s

F q(s) = αqL1 + αqR1

s

(4.29)

- DC control design

As presented in the section on the DPFC modeling at the beginning of this chapter, the

DC voltage of the shunt converter is given as:

C se

dV dc,se

dt =

1


1





For Park’s transformation at the fundamental frequency, the rotation reference frame

is derived from the bus voltage Vs. Neither the d nor the q component of the voltageref V,sh,1 is zero. Therefore, all the terms with ref V,sh,1 have an influence on the DC

voltage, which makes the control difficult.

The DC voltage control of the shunt converter is based on another approach that treats

the DC capacitor as an energy storage device. Neglecting losses, the time derivative of

the stored energy equals the sum of instantaneous power at both frequencies:

1

2

C sh

dV 2dc,sh

dt

= P 1

−P 3 (4.31)

Since the equation is nonlinear with respect to V dc,sh, a new variable W = V 2dc,sh is

introduced to overcome the nonlinearity. For the active calculation, because the resistance

between the grid and the shunt converter is small, the active power is approximately the

same at both ends. Within Park’s transformation, the voltage Vs is the rotation reference

frame. By projecting Vs to itself, the q component of Vs is zero, and (4.31) can be written

as:

12

C sh dW dt

= 32

V s,dI sh,1,d − P 3 (4.32)

The grid voltage Vs is constant and P 3 is considered a disturbance. By applying the

Laplace transform, the transfer function from I sh,1,d to W is found as:

G(s) = W (s)

I sh,1,d(s) =

3V s,d

sC sh

(4.33)

Similarly to the DC voltage control of the series converter, an inner feedback loop is

also added for damping the pole at the origin. A scheme of the DC voltage control of theshunt converter is shown in 4-18.

F ( s)

R

+

-

+

-

G( s),1, ,s h d re f I 2

,se dcW V =ref

W

G’( s)

dc control

Figure 4-18: Scheme of the DC voltage control of the shunt converter



78 4.4 Simulation Results of the DPFC Modeling and Control

By using the IMC method, the control function and the active damping R can be

calculated as:

R = αC

3vs,d

, K p = αC

3vs,d

, K i = α2C

3vs,d

(4.34)

4.4 Simulation Results of the DPFC Modeling and

Control

The DPFC modeling and control are simulated in the Matlab Simulink. The schematic of the DPFC system in the simulation is shown in Figure 4-19. To simplify the calculation,

one set of series converters is used to represent the distributed converters.

AC

DC

series

control

central

control

AC

DC AC

DC

sV

sh,1V

sh,1I

,sh dcV

shC

V,sh,1ref , ,3V shref

,3shV

,3sh

I

shunt

control

R L

seC

1se, ,ref V

rV1se,

V ,r r P Q

Figure 4-19: DPFC system in the simulation

The specifications of the system are shown in Table 4-1.

Parameter Value Parameter Value

V s (pu) 1 I 3,ref (pu) 0.166

V r (pu) 1 V se,dc,ref (pu) 0.087

θ () 1.5 V sh,dc,ref (pu) 0.174

R (pu) 0.095 C se (µF) 2200

X (pu) 0.178 C sh (µ F) 6600

Table 4-1: Specifications of the DPFC in the simulation




The capability of injecting a controllable 360 series voltage is signified by the inde-

pendent control of the active and reactive power flows at the receiving end. A step changeof the reference of the active and reactive power flows is made for the DPFC as shown in

Figure 4-20.

0.2

0.4

0.6

0.8

1

P r ( p u )

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

0

0.2

0.4

0.6

Q r ( p u )

reactive power flow

reference

active power flow

reference

Figure 4-20: Active and reactive power flow at the receiving end

As shown, the active and reactive power can be independently controlled, which in-

dicates that the DPFC is capable of injecting the 360 controllable voltage at the funda-

mental frequency. The transients are caused by the variation in the DC voltages of the

series converters. The DC voltages of the DPFC converters are shown in the following

figures:

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60.06

0.07

0.08

0.09

V s e , d c ( p u )

(a)



80 4.5 Communication Between the Central Control and Series Converters

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60.16

0.165

0.17

0.175

0.18

V s h , d c ( p u )

(b)

Figure 4-21: DC voltages of the DPFC converters (a) series converter; (b) shunt converter

The DC voltages of both the series and the shunt converters are well maintained during

operation. More results, based on specific cases, will be included later.

4.5 Communication Between the Central Control and

Series Converters

As introduced in previous sections, the reference signals generated by the central control

are sent to the series converters remotely. In principle, these signals are AC quantities. In

the UPFC, the shunt converter, series converter and central control are all close to each

other. Therefore, communication between the control and converters is not an issue. The

reference signals in AC quantity can be directly sent to the converters via signal cables.

Within the DPFC, the series converters are distributed along the transmission line, and

several issues about the communication should be considered:

• Communication method: It is possible to use signal cables to transmit the ref-erence signals. However, the required length of the signal cable (as long as the

transmission line) increases costs. In addition, because the series converters are

electrically floating and different converters have different voltage potentials - ex-

tra isolation is required between the signal cable and each converter. Therefore,

wire-communication is not a good option for the DPFC. Methods such as wireless-

communication and Power Line Communication (PLC), are more suitable for the

DPFC.

• Disturbance and failure of the communication: As the reference signals for




the series converters are AC quantities, a high bandwidth communication method is

required. Communication quality has a huge influence on the reliability of a DPFC.In the case of a disturbance or communication failure, the series converters would

lose their synchronization with the grid, leading to transmission failure.

Accordingly, it is important to find a new method of determining a reliable means of

communication between the central control and the distributed series converters.

4.5.1 Principle of the Method

The principle of the proposed method is to transform the control signal from AC quantities

into DC quantities by using Park’s transformation at the sending end and convert the

received DC control signals back to AC locally, at each series converter. For the inverse

transformation at the receiving end, the line current is used as the rotation reference

frame, instead of the line-to-line voltage that is commonly used. The line current can

easily be measured by the series converter locally without extra cost. A Single-phase

Phase Lock Loop (PLL) [Sant 08, Shin 08] is employed in each DPFC floating series

converter to achieve the phase and frequency information of the grid. In this case, only

the d and q information in DC quantities is transmitted to the converters. Together withthe phase and frequency information from the line current, the signals in DC quantities

can be transformed back into AC by the inverse Park’s transformation. Because DC

quantities are transmitted, the series converter can continue operation at the last received

setting if the communication is lost. A block diagram of the new method is illustrated in

Figure 4-22.

1-ph PLL1st

passfilter 1-ph

inverse

q

seV I

transmission line

,1,s e r ef

V 1

θ 1 I

,1, , ,1, ,&se d ref se q ref V V

I

series onverter

ACDCentral

ontrol

referene

onversion

,1,s e r ef V

I to other series converters

Figure 4-22: Block diagram of the new method

As said within the new method, the line currents are selected as the rotation reference



82 4.5 Communication Between the Central Control and Series Converters

frame of the inverse Park’s transformation. However, normally within the central control,

the bus voltage V s is used to as the reference frame for the Park’s transformation. Toachieve the same control result, a conversion of the rotation reference frame is required.

The objective of this conversion is to keep the AC voltage, injected by the series converters,

the same as the voltage prescribed by the central control. This conversion is given as:

[V se,1,dq,ref ]I = [T dq(θI )][V se,1,ref ]

= [T dq(θI )][T dq(θV s)]−1[V se,1,dq,ref ]V s

(4.35)

where [V se,1,dq,ref ]I and [V se,1,dq,ref ]V s are the series voltages in I and V s rotation reference

frames respectively, while [T dq(θI )] and [T dq(θV s)] form the corresponding Park’s transfor-mation matrix. The phasor diagram of the conversion of the rotation reference frame is

illustrated in Figure 4-23.

d_V s

q_V s

V se,1,r ef

d_I

q_I

V se,1,q,ref

φ

V se,1,d,ref

V se,1,d ,ref_Vs

V se,1,q ,ref_Vs

Figure 4-23: Phasor diagram of the rotation reference frame conversion

The angle ϕ between voltage V s and current I can be measured at the shunt converter

part, the rotation reference frame can therefore be written as:

V se,1,d,ref = V se,1,d,ref V s cos ϕ + V se,1,q,ref V s sin ϕ

V se,1,q,ref = −V se,1,d,ref V s sin ϕ + V se,1,q,ref V s cos ϕ(4.36)

Concerning the communication, this method greatly increases the reliability of the

system. A buffer can be used to store received data. During communication failures, the




last received information can be used, together with the phase and frequency information

from the line current, as the floating converter will maintain synchronization.

4.5.2 Simulation Results

This method has been tested in Matlab Simulink using the DPFC system in Figure 4-19.

To demonstrate the improvement of the system’s reliability during communication failure,

large noise is injected, as shown in Figure 4-24, between 2 s and 3 s.

centralcontrol

seriescontrol

,1, ,s e r ef a bcV

noise

++

central

control

series

control

,1, ,s e r ef d qV

noise

++

Park

Trans.

inverse

Park

(a)

(b)

Figure 4-24: Place where the noise is added; (a) reference signals in AC quantities; (b) in DC

quantities

The DC voltages of the series converter are shown in two different cases: the reference

signals in AC and DC quantities. The communication noise and the DC voltages in both

cases are shown in Figure 4-25.

1 1.5 2 2.5 3 3.5 4 4.5 5−3

−2

−1

0

1

2

3

c o m m u n i c a

t i o n n o i s e

(a)



84 4.6 Conclusions

1 1.5 2 2.5 3 3.5 4 4.5 5

−0.15

−0.075

0

0.075

0.15

V s e , d c ( p u )

(b)

1 1.5 2 2.5 3 3.5 4 4.5 50

0.04

0.08

0.12

V d c ( p u )

(c)

Figure 4-25: Comparison between the two communication methods: (a) communicationnoise; (b) in AC quantity; (c) in DC quantity

In the steady-state, the communication methods in AC and DC quantity have the same

control results. During communication failure, the system totally loses stability in the case

of using communication in AC quantity. While using the DC quantity communication, the

series converters do not lose synchronization with the grid and the DC capacitor voltage

is well maintained. After a failure, the system recovers much faster by using this method.

4.6 Conclusions

In this chapter, the modeling and the basic control of the DPFC are presented. The DPFC

is modeled in the dq -frame by using Park’s transformation. The components of the DPFC

in AC quantity are transformed into DC quantity. The components in different frequencies

are then separately modeled. This model is a good representation of the behavior of the

DPFC at the system level and can be used to design the parameters of the DPFC control.

Based on the DPFC model, the shunt control and the series control are developed.




The functions of these controls are to maintain the DC capacitor voltages of the converters

and to ensure the required voltages and currents are injected from the central control.The IMC method is employed to calculate the control parameters. The DPFC basic

control and model are simulated in Matlab Simulink. The simulation results show that

the DPFC is able to control the active and reactive power flows independently and that

during operation, the DC voltages of the converters are well maintained.

Communication between the central control and the series converters is also consid-

ered. To increase the reliability of the DPFC during communication failure, the reference

signals in DC quantities are used instead of in AC quantities. The line current is selected

as the rotation reference frame because it can be easily measured by the series converterswithout extra cost. During communication failure, the series converter can use the last

received setting to continue operation, thereby increasing the system’s reliability. This

communication method is also tested in Matlab Simulink. It shows that in steady-state,

communication in DC quantities has the same result as in AC quantities. During com-

munication failure, the series converter of the DPFC can maintain synchronization with

the system.



Chapter 5DPFC EXPERIMENTAL

DEMONSTRATOR

5.1 Introduction

I

N the previous two chapters, a new concept of a DPFC and corresponding modeling

and control were presented. The DPFC has been simulated in Matlab, Simulink.

However, during the simulation, several issues were neglected, such as switching behaviors,

converter losses and measurement delays. Accordingly, to show the neglected effects and

to test the basic control whose design is based on the model, the DPFC is tested in

an experimental setup. The setup consists of two main parts: the network and DPFC

converters.

The chapter begins by presenting the specifications of the DPFC experimental setup.

Once the specifications are introduced, the design of the DPFC experimental setup is

given. The design concerns the electrical part of the experimental setup. The control

of the DPFC converters is done using the Texas Instrument DSP controller F2808. The

real-time programming of the converter is introduced after the electrical design. The last

section of this chapter presents the results of the DPFC experiments.

5.2 Specifications

As has been stated, the DPFC experimental setup consists of a scaled network part and

a converter part. In principle, the DPFC is used in transmission networks. However,

87



88 5.2 Specifications

to reduce the cost of the setup, the experiment is carried out on a scaled network with

low voltages. The DPFC converters within the setup consist of one shunt converterand six single-phase series converters. The circuit of the experimental setup is shown in

Figure 5-1. Two isolated buses with different voltage angles are connected by lines. Two

sets of series converters are applied in this setup. Within the experimental setup, the

shunt converter is a single-phase inverter that is connected between the neutral point of

the Y-∆ transformer and the ground. The inverter is powered by a constant DC voltage

source.

AC

DC

AC

DC

AC

DC

L

ACDC

ACDC

L

ACDC

ACDC

L

a

b

cDC

supply

gi gi

seies

onvete

shunt

onvete

sV

r V

Figure 5-1: Circuit of the DPFC experimental setup

5.2.1 Scaled Network Specifications

The voltage and power rates of the network are scaled down, consistent with the pu values

of a real network. The real network that the setup is based on is part of the Netherlands

transmission network, which requires power flow control because of its overload problem1.

The DPFC converters are consequently designed based on the required control range of

the power flow in the scaled network.

Due to the availability of a 380 V supply within the lab, this has been selected as

1

DATA source: NUON, network in Nijmegen area




the base voltage of the setup. The procedure used to scale down the network is shown

in Appendix C. The electrical specifications of the experimental network are shown inTable 5-1.

Symbol Value Description

V s (V) 380 Sending end’s voltage

V r (V) 380 Receiving end’s voltage

θ () 1.2 Transmission angle

L (mH) 6 Line reactance

|S max| (VA) 6000 Transmission capacity|S r| (VA) 1400 Power flow limit

Table 5-1: Specification of the scaled network

5.2.2 DPFC Converter Specifications

As introduced in previous chapters, the voltage and current ratings of the shunt and

series converters depend on the control range of the DPFC. Referring to chapter 3, for

the network without the DPFC compensation, the power flow through the line will be:

|S r0| = |P r0 + jQr0| = |4010.9 + j35.0| ≈ 4100 VA (5.1)

The objective of the DPFC is to limit this power to under 1400 VA. Accordingly, the

control range of the DPFC is given as:

|S range| = |S r − S r0| = |4100− 1400| = 2700 VA (5.2)

Specifications of the converter at the fundamental frequency

Once the control range of the DPFC is known, the total voltage injected by series con-

verters can be calculated according to equations in chapter 3:

|V se,1| = |S range

|X 1

|V r| =

2700

×2π

×50

×6

×10−3

380 ≈ 5 V (5.3)



90 5.2 Specifications

The current that flows through the series converters is the same as the line current.

Therefore, the maximum current at the fundamental frequency of the series converters isgiven as:

|I 1| = |S r0|+ |S range|√

3|V r|=

4100 + 2700

380√

3≈ 11 A (5.4)

Specifications of the converter at the third harmonic frequency

To find the specifications of the converters at the 3rd harmonic frequency, the maximum

active power that is exchanged between the converters is given by:

P se,MAX = |X 1||S r0||V r|2 |S range| =

0.63 × 4011 × 2674

3802 = 46.7 W (5.5)

The 3rd harmonic current is chosen to be one third of the nominal line current at the

fundamental frequency, which gives a constant value of I 3 = 3 A per phase. Consequently,

the maximum voltage of the series converter at the 3rd harmonic will be:

|V se,3,max| = |P se,MAX

|3|I 3| =

46.7

3 × 3 = 5.2 V ≈ 6 V (5.6)

The 3rd harmonic current though the shunt converter is:

|I sh,3| = 3|I 3| = 9 A (5.7)

and the voltage of the shunt converter is given by:

|V sh,3| = |V se,3 + jX 3|ise,3|| = 7.7 V ≈ 10 V (5.8)

By adding the components at both frequencies, the specifications of the DPFC con-

verters are shown in Table 5-2.

series converter shunt converter

voltage rating (V) 10 10

current rating (A) 13 9

Table 5-2: Specifications of the DPFC converters




5.3 DPFC Experimental Setup

This section introduces the electrical part of both the network and the DPFC converters.

Three major parts are taken into consideration in the DPFC experimental setup: the

scaled network, sets of series converters and one shunt converter.

5.3.1 Scaled Network

The scaled network consists of 3-phase transmission lines and power transformers. The 3-

phase transmission line is represented by three inductors while two three-phase transform-

ers represent the sending and receiving buses. The primary sides of the two transformers

are connected to the same grid. To generate a difference in the phase angle between the

voltages of the buses, a zig-zag transformer is employed. Besides the main transformer

that handles the power, an additional small, three-phase transformer is used. The primary

sides of the main and additional transformers are connected in parallel and the secondary

sides are connected in series, but with transposed phases as shown in Figure 5-2(a). The

phase angle of the power transformer can be adjusted by selecting different voltage ra-tios of the additional transformer. The principle of the phase shift transformer and the

transformer that is employed in the experimental setup are shown in Figure 5-2.

primary

winding

secondary

winding

main

transformer

additional

transformer

main

transformer

additional

transformer sockets

(a) (b)

Figure 5-2: Transformer in the experimental setup: (a) connection of transformer windings;

(b) picture



92 5.3 DPFC Experimental Setup

5.3.2 Series Converter

The series converter is the key component of the DPFC experimental setup. To verify the

concept of the distributed series converter, two sets of single-phase converters are required

with each set consisting of three converters for different phases. The series converter is

connected to the line by a transformer. To reduce the RMS currents on the converter

side, the ratio of the transformer winding is 5:25 V.

The series converter is a full-bridge single-phase converter with a capacitor acting as

short-term energy storage on the DC side. The technology used to control the series

converter is PWM with unipolar voltage switching with a 6 kHz switching frequency

[Moha 03]. The capacitors in the series converter are implemented with a combination of

an aluminum electrolytic capacitor in parallel with two ceramic capacitors. The aluminum

electrolytic capacitor is used to provide DC voltage as energy storage, while the ceramic

capacitors provide decoupling for the high-frequency switching components.

All inputs and outputs of the series converter are galvanically isolated from the outside.

The series device, consisting of the series converter, the control circuit (DSP board) and

auxiliaries, floats on the voltage potential of the transmission line. The central control

that gives a set point for voltage to be injected, operates at ground potential. Therefore,in practice the control signals have to be transmitted over a high voltage barrier, via

a wireless communication or through power line communication for instance. In the

experimental setup, communication between the central controller and series converters

takes place through USB cables to reduce its complexity. Therefore, voltage isolation is

required between the DSP board and the power circuit. This isolation is provided by the

gate drives and the measurement device that gives feedback signals for the DSP. Figure 5-3

shows a simplified diagram of the series converter and a photo of a series converter in the

experimental setup.

5.3.3 Shunt Converter

The basic structure of the shunt converter is similar to the series converter, which is a

single-phase full-bridge VSC with unipolar PWM control. To simplify the experimental

setup, the DC voltage is supplied by a DC voltage source instead of a back-to-back

connected AC/DC converter. The AC output terminals of the shunt converter are directly

connected to the neutral points of the Y-∆ transformers to inject 3rd harmonic current.




power modules DSP board

series transformer measurements

MOSFET

drive

MOSFET &

capacitors

ac

output

AC

DC

measurement

voltage

isolation

DSP

board

t r a n s m i s s i o n

l i n e

power

circuit

gate drive

(a) (b)

Figure 5-3: Series converter in the experimental setup: (a) simplified diagram; (b) picture

For control, the 3rd harmonic current is locked to the same phase as the bus voltage at the

fundamental frequency, as described in chapter 4, thereby requiring a voltage transducer

to measure the bus voltage for synchronization. Figure 5-4 shows the shunt converter

within the experimental setup that is made on a prototype board.

3rd

harmonic

output

DSP board

measurements

dc

source

MOSFET

drive

MOSFET &

capacitor

synchronization

voltage

Figure 5-4: Photo of the shunt converter within the setup

5.3.4 Overall Experimental Setup

The experimental setup is powered by the grid at 380 V and the overall setup is shown

in Figure 5-5. The connection of the setup is based on the DPFC test circuit shown in



94 5.4 DPFC Control Realization

Figure 5-1. The waveforms of voltages and current are captured by an oscilloscope.

series

converterscentral controller

shunt

converters

Y-∆

transformers

scaled

network

Figure 5-5: DPFC experimental setup

5.4 DPFC Control RealizationThe DPFC converters are controlled by eZdsp F2808 Kits, which use the microcon-

troller C2000 F2808 from Texas Instruments as their processor. The DSP F2808 is a

programmable high performance digital processor with system clock 100MHz and with

integrated PWM signal generators and an A/D converter. The F2808 can be programmed

using C++ or an assembling language. For programming the DPFC control, the toolbox

in Matlab Simulink - Target for TI C2000 (TC2000) is utilized as the program environ-

ment, which provides a friendly graphic interface for DSP programming. The TC2000generates a C language real-time implementation from the Simulink model by using Real-

Time Workshop and TI development tools. Therefore, the DSP programming is as easy

as simulations in Matlab Simulink.

The control schemes of the converters are developed according to the DPFC basic

control that is presented in chapter 4. The control algorithms are firstly programmed in

Matlab and copied to the Flash memory of the DSP board. The control algorithms for

both the shunt and series converters, which can directly be downloaded into the DSP, are





measurements

single −phase

Park ’s transformation

current control

Alpha

Beta

Angle

Ds

Qs

Park

DMC

PWM generator

In1

PLL

PLLPID Controller 1

ref

fdb

out

PID

DMC

PID Controller

ref

fdb

out

PID

DMC

Inverse Park

Transformation

Ds

Qs

Angle

Alpha

Beta

IPark

DMC

−K−

−K−

F2808 eZdsp

Stand alone code

using Flash Memory

Delay

−10

Z

0.6

0A/D converter

Iac

Vac

(a)

fundamental frequency control

third harmonic frequency control

DC voltage control

vdc,ref

30

single −phase

PLL

single −phase

PLLA Y

Sin

IQmath

Saturate

A Y

IQsat

IQmath

PWM generator

In1

PI

In1 Out1

Ds

Qs

Angle

Alpha

BetaIPark

DMC

A

B

Y

mpy

IQmath

R

F2808 eZdsp

Stand alone code

using Flash MemoryA/D converter

Vdc

Iac

vd

vq

50Hz pass

Digital

Filter

150Hz pass

Digital

Filter

(b)

Figure 5-6: Control in Simulink for DSP F2808: (a) shunt converter ; (b) series converter

5.5 Results of the Experimental Setup

To verify the DPFC principle, two situations are demonstrated: the DPFC behavior in

steady-state and the step response. For easier viewing, only the waveforms of one phase

are shown.

5.5.1 Steady-state Results

In steady-state, the series converter is controlled to insert a voltage vector with both d

and q components, which are V se,d,ref = 0.3 V and V se,q,ref = −0.1 V. Figure 5-7 shows



96 5.5 Results of the Experimental Setup

the voltage injected by the series converter, the current through the line and the voltage

and current at the ∆ side of the transformer.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−4

−2

0

2

4

c u r r e n t t h r o u g h t h e l i n e ( A )

(a)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−5

0

5

s e

r i e s c o n v e r t e r v o l t a g e ( v )

(b)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−5

0

5

b u s v o l t a g e ( V * 1 0 0 )

c u r r e n t ( A )

voltagecurrent

(c)

Figure 5-7: DPFC operation in steady-state; (a) line current; (b) series converter voltage; (c)

bus voltage and current at the ∆ side of the transformer

The constant 3rd harmonic current injected by the shunt converter is evenly dispersed




to the 3 phases and is superimposed on the fundamental current, as shown in Figure 5-7(a).

The voltage injected by the series converter also contains two frequency components inFigure 5-7(b). The amplitude of the PWM waveform represents the DC capacitor voltage,

which is well-maintained by the 3rd harmonic component in steady-state. As shown,

the DC voltage has a small oscillation, however does not influence the DPFC control.

Figure 5-7(c) demonstrates the 3rd harmonic filtering by Y-∆ transformers. As shown,

there is barely any 3rd harmonic current or voltage leaking to the ∆ side of the transformer.

5.5.2 Step-response Results

The aim of this test is to verify if the series converter can inject both active and reactive

power at the fundamental frequency. A step change of the fundamental reference voltage

of the series converter is made, which consists of both active and reactive steps as shown

in Figure 5-7(a). Figure 5-7 shows the behavior of the DPFC during this step.

0.2 0.25 0.3 0.35 0.4 0.45 0.5−2

0

2

V q , r e f ( V )

−2

0

2

V d , r e f ( V )

(a)

0.2 0.25 0.3 0.35 0.4 0.45 0.5−5

0

5

s e r i e s c o n v e r t e r v o l t a g e

( V )

before step after step

(b)



98 5.5 Results of the Experimental Setup

0.2 0.25 0.3 0.35 0.4 0.45 0.5−4

−2

0

2

4

l i n e c u r r e n t ( A )

after stepbefore step

(c)

−1

0

1

a c t i v e ( W )

0.2 0.25 0.3 0.35 0.4 0.45 0.5

−2

0

2

r e a c t i v e ( V a r )

calculated

measured

measured

calculated

(d)

0.25 0.3 0.35 0.4 0.45 0.5−3

−2

−1

0

1

2

3

b u s v o l t a g e ( V * 1 0 0 )

c u r r e n t ( A )

currentbus voltage

after stepbefore step

(e)

Figure 5-7: Step response of the DPFC; (a) reference voltage for the series converters; (b)

series converter voltage; (c) line current; (d) active and reactive power injected

by the series converter at the fundamental frequency; (e) bus voltage and current

at the ∆ side of the transformer




As shown, the DC voltage of the series converter is stabilized before and after the step

change. To verify whether the series converter can inject or absorb active and reactivepower from the grid at the fundamental frequency, the power is calculated from the

measured voltage and current plotted in Figure 5-7(b&c). The measured data in one

phase is processed in the computer by using Matlab. To analyze the voltage and current

at the fundamental frequency, the measured data that contains harmonic distortion is

filtered by a low-pass digital filter with the 50Hz cut-off frequency. Because of this filter,

the calculated voltage and current at the fundamental frequency have a 1.5 cycle delay

compared to the actual values, thereby causing a delay of the measured active and reactive

power. Figure 5-7(d) illustrates the active and reactive power injected by the seriesconverter. A comparison is made between the measured power and the calculated power.

We can see that the series converters are able to absorb and inject both active and reactive

power to the grid at the fundamental frequency.

5.6 Conclusions

This chapter presents the experimental setup and test results of the DPFC. The electrical

design and the implementation of real-time control are considered and briefly introduced.

The DPFC is tested in a scaled two-bus network with fixed voltages at the sending and

receiving ends. Due to the phase shift between the voltages, there is a power flow between

the buses through the line. The DPFC series converters are in series with the line to

control the power flow. The DPFC converters employ the DSP board from TI for real-

time control. The control schemes were programmed in Matlab Simlink and downloaded

in the Flash memory of the DSP for the control. Two cases were tested: the steady-state

and the step response. During both tests, the shunt converter and the series converter

could exchange active power through the 3rd harmonic component and the DC voltages

of the series converters were-well maintained. The series converter can inject and absorb

both active and reactive power, which proves the DPFC principle and verifies the control

schemes that are presented in previous chapters.



Chapter 6DPFC FAULT TOLERANCE

6.1 Introduction

THE concept of the DPFC was presented and analyzed in previous chapters. The

basic control of the DPFC was designed and verified both in the simulation and

in the experimental setup. When the DPFC is applied to power systems, reliability is

one of the most important issues that should be taken into consideration. This chapter

addresses the fault tolerance of the DPFC.

The chapter begins by listing possible faults that can occur in the DPFC and their

corresponding effects on the network. Three types of faults are categorized: shunt con-

verter failure, series converter failure and control failure. In this chapter, the DPFC fault

tolerance of the shunt and series converter failures is examined. Several supplementary

controllers are added to ensure the continuously operation of the DPFC during converter

failure. The supplementary controllers that deal with the shunt and series converter fail-

ures are separately introduced. The principle, analysis, and design of the controller are

presented. The results of both the simulation and the experimental setup are shown.

6.2 Possible Faults in the DPFC

Several possible faults may occur in the DPFC, as shown in Figure 6-1. They are fault in

the central control 1, in communication 2, in the shunt control 3, in the shunt converter

4, in the series control 5 and in the series converter 6.

Faults in the central control and communication are categorized as ‘control failure’.

101



102 6.2 Possible Faults in the DPFC

AC

DC

transmission line

AC

DC

AC

DC

AC

DC hgh-

pass

filter

snt

onerter

seres

onerters

snt

ontrol

seres

ontrol

seres

ontrol

seres

ontrol

entral

ontrol

1

2

3

4

5

6CB

Figure 6-1: Locations of possible faults in the DPFC

During this type of failure, the shunt and series converters will not receive any reference

signals from the central control. As mentioned in chapter 4, these reference signals are in

DC quantities. Losing signals will not lead to system corruption and the converters can

continue operating by using the last received data. Accordingly, the DPFC is tolerant of

control failure.

Faults in the shunt converter and shunt control are referred as to ‘shunt converterfailure’. A fault (such as an isolation failure of a transformer, switch failures or currents

that exceed the limits) will appear as a short circuit or low impedance to the network and

the shunt converter will trip by opening a circuit breaker. Consequently, the two major

functions of the shunt converter, which are to inject reactive current at the fundamental

frequency and to inject the constant 3rd harmonic current, will stop. At the fundamen-

tal frequency, the shunt converter stops providing reactive compensation. As a faulty

shunt converter does not change the network topology, the system can continue operation

without serious damage. However, at the 3rd

harmonic frequency, the zero 3rd

harmoniccurrent prevents the exchange of active power between converters. Fortunately, this side

effect can be compensated by control schemes that supplement the basic control as will

be introduced in section 6.3.

A ‘Series converter failure’ is a fault that happens to the series converter or the series

control. When the transformer has isolation failure, the switch is short-circuited or the

series control gives wrong signals that leave the switches on, the series converter short-

circuits the network. The short circuit for the series converters is not a problem because

it will not interrupt the transmission line. However, when the series converters have an




open circuit, such as disconnection of components or wrong signals that turn off switches,

large impedance will be inserted into the transmission line, thereby influencing the wholenetwork. To prevent an open circuit from being created, a bypass circuit is provided for

each series converter. The bypass circuit parallels the output terminals of the series con-

verter. Once the series converter has an open circuit, the bypass circuit will be connected

and short circuit the series converter with respect to the transmission line.

As mentioned previously, the converters within the DPFC operates independently and

a failure of one converter cannot percolate to other converters. Although the failures have

several negative effects on the system depending on the type of failure, these effects can

be compensated for by supplementary controllers that will be introduced in the followingsections.

6.3 Shunt Converter Failure

This section addresses the supplementary control of the DPFC, which handles converter

control during shunt converter failure. The effect of shunt converter failure is introduced

first. Next, the principle and the design of the supplementary control are presented. After

the analysis of this control, the results achieved in both the simulation and experiments

are shown.

6.3.1 Introduction

As said, the shunt converter failure results in no 3rd harmonic current injection to the

network. As mentioned, the DC voltages of the series converters are maintained by the 3rd

harmonic current injected by the shunt converter. This DC voltage cannot be maintained

during shunt converter failure, since there is no 3rd harmonic injected. Therefore, asupplementary control is added to the series control within each series converter and aims

to provide a stable DC voltage in all situations, as highlighted in Figure 6-2.

6.3.2 Principle of the Control

Two operation modes are defined for the series converter control:

• Full-control mode: In this mode, the DPFC operates in normal conditions. The

series converters inject both controllable active and reactive components into the



104 6.3 Shunt Converter Failure

AC

DC

transmission line

AC

DC

AC

DC

AC

DC hgh-

pass

filter

snt

onerter

seres

onerters

snt

ontrol

seres

ontrol

seres

ontrol

seres

ontrol

entral

ontrol

Figure 6-2: Location of the supplementary control for shunt converter failure

grid at the fundamental frequency and the DC voltage is stabilized by absorbing

active power from the 3rd harmonic frequency components.

• Limited-control mode: The DPFC operates in this mode when there is a shunt

converter failure. Due to incapability of exchanging active power between con-

verters, the series converters can only provide reactive compensation to the line,

which means that they can only control line impedance(similarly to an SSSC)

[Gyug 00, Pill 03]. The DC voltage of the series converter is stabilized by the active

power at the fundamental frequency instead of the 3rd harmonic frequency. In this

mode, there is no component injected at the 3rd harmonic frequency by the series

converters. Because the series converters lose the capability of active compensation,

the DPFC can only control the active power flow through the line by the injection

of reactive power.

The principle of the supplementary control for the shunt converter failure is to use a

different frequency current to maintain the DC voltage of the series converters in different

conditions.The signal for switching the series converters between the two operation modes is the

magnitude of the 3rd harmonic current through the line, which can easily be measured

by the series converters without extra cost. The presence of a 3rd harmonic current

clearly signifies the status of the shunt converter. A threshold is predefined for each

series converter. When the magnitude 3rd harmonic current is lower than this threshold,

indicating a shunt converter failure, the series converters are switched from the full-control

mode to the limited-control mode. A flow chart of the supplementary control is shown in

Figure 6-3.




measurement

3| | threshold I ≤

3| | I

full-control

mode

limited-

control mode

YESNO

Figure 6-3: Flow chart of the adapted shunt converter control

To enable the DPFC to switch between the two operation-modes, two controllers

should be adapted, namely the series control and the central control. For the series

control, the supplementary scheme should be able to use the components at different

frequencies to maintain the DC voltage of the series converter according to the operation

mode. For the central control, certain adaption is required due to the loss of the capability

of series active compensation.

Series control adaption

The supplementary scheme is implemented in the DSP control of each series converter.

In principle, two DC voltage control loops are required to enable the series converter to

operate in the two modes. In the full-control mode, the DC control loop that uses the 3rd

harmonic components is active and in the limited-control mode, the loop that uses the

fundamental frequency components is active. This solution increases the computational

effort required from the DSP because two loops need to be processed simultaneously

although only one loop is active. To reduce computation, a control scheme with only oneDC control loop is proposed and its structure is shown in Figure 6-4.

The control scheme for the series converter with the supplementary control is adapted

from the series control presented in chapter 4. As shown, there is only one DC control

within the series control at the left lower corner of Figure 6-4. Two signal selectors are

employed to route the output of the DC control to either the inverse Park’s transformation

block that generates V se,1,d,ref or the block that generates V se,3,d,ref .

In the full-control mode, the active component V se,1,d,ref is obtained from the signal

that is supplied by the central control. In the limited-control mode, this signal is obtained




3rd

pass

filter

dc

control

1-ph

inverse

dq

0

PWM

gen.

ACDC

+ -seV

,V seref

,se dcV

transmission line

, ,1V seref

3θ

3 I

, 3, ,s e q r ef V

, ,se dc ref V

, ,3V seref

C

I

from

central

control+

+

,se dcV series control

, ,se d ref V

I

1-ph PLL1st passfilter

1-ph

inverse

dq

1θ 1 I

,1, ,s e q ref V

,1, ,s e d ref V signal

selector

| |u

signal

selector

1-ph PLL

3| | I

| |u

Figure 6-4: Supplementary control scheme of the series converter

from the DC controller. The proposed control scheme only possesses one DC control loop

and consequently does not increase computation complexity.

Central Control Adaption

The power flow controller of DPFC within the central controller is designed for controlling

both active and reactive power flow independently. However, during shunt converter

failure the DPFC is operated in limited-control mode. Because the series converters

can only inject reactive power while in limit-control mode, it is impossible to control

active and reactive power flow independently. Therefore, one of the controllers must bedisabled during the shunt converter failure. As active power flow control has priority in a

normal power system, the remaining control freedom, namely to vary the line impedance,

is utilized for controlling the active power flow through the line. The simplest way of

adapting the central control is to disable the control loop of the reactive power flow

during shunt converter failure, as shown in Figure 6-5.

The output of the reactive power flow control loop is disabled by the signal selector

according to the magnitude of 3rd harmonic current. As the design of the power flow

control is outside the scope of this chapter, its details will not be discussed here.




active power

flow control

reactive power

flow control

signal

selector

reference

conversion

| |u

,r ref P

r P

,r ref Q

r P

3 I

,1, ,s e q r ef V

,1, ,s e d ref V

to series

converters

Figure 6-5: Adapted power flow control within the central control

6.3.3 Transient Analysis

Because the same DC control loop generates the reference signal for the components at

the fundamental and 3rd harmonic frequencies, it is important to study whether the DC

control can maintain the DC voltage in all conditions as well as the transition from the

full-control mode to the limited-control mode and back.

To investigate the transient behavior, first the controller is modeled. The parameters

for the DC control are calculated according to the system parameters in full-control mode.

The scheme of the DC control is shown in Figure 6-6. As the design of the DC controlwas introduced in chapter 4, it will not be repeated here.

F ( s)

R

+

-

+

-

G( s), , 3,V se d

ref ,se dcV

, ,se dc ref V

G’( s)

dc control

Figure 6-6: Scheme of the DC voltage control loop of the series converter

The function G(s) is the transfer function from ref V,se,3,d to V se,dc where F (s) is a PI

controller and R is active damping feedback within the DC control. The parameters of

the DC control are:

k p = 2Cαd

I 3,d

, ki = 2Cα2

d

I 3,d

, R = 2Cαd

I 3,d

(6.1)

where αd is a design parameter that determines the desired bandwidth of the closed-loop

system.




During shunt converter failure, the DC control loop is the same as the one in the

full-control mode, but the transfer function of the system changes. The transfer functionin the limited-control mode can be calculated from the equations that are presented in

chapter 4:

C sedV dc,se

dt =

1


1


As the 3rd harmonic current is zero during shunt converter failure, equation (6.2) can

be written as:

C sedV dc,se

dt =

1


Similarly as in the control loop for 3rd harmonic component, the rotation reference

frame for the Park’s transformation at the fundamental frequency is also generated from

the current through the line. Therefore, by projecting the current to itself, the q com-

ponent I 1,q is zero. The DC capacitor voltage is stabilized by the d component at the

fundamental frequency. By applying the Laplace transform to (6.3), the transfer functionfrom ref V,se,1,d to V se,dc is given as:

G1(s) = V se,dc(s)

V se,1,d,ref (s) =

I 1,d

2sC se

(6.4)

Comparing the two transfer functions for the full and limited control model G(s) in

(3.17) and G1(s) in (6.4) respectively, shows that the structures of the transfer functions

are identical only with different ratios. In the limited-control mode, the open-loop transfer

function is:

Gop(s) = F (s) G1(s)

1 + RG1(s) (6.5)

By substituting the parameters from (6.1) to (6.5), the open-loop transfer function can

be given as:

Gop

(s) = αdI 1,d(2C ses + RI 3,d)

sI 3,d(2C ses + RI 1,d) (6.6)




To assess the stability of the system, the characteristic equation of the closed-loop system

is determined:

D1(s) = 2C seI 3,ds2 + (RI 1,d + αdI 1,d2C se)s + αdRI 1,dI 3,d (6.7)

As the current magnitudes, active damping and capacitance are positive values, all

terms in (6.7) are positive. Based on the Routh-Hurwitz stability criterion in control

systems [Para 02], the closed-loop system is stable. However, because the zero and pole

in (6.6) increase the damping of the closed-loop system, the controlled DC voltage is over-

damped in the limited-control mode. Therefore, it can be concluded that the DC control

that is designed for the full-control mode will work in the limited-control mode also, but

with a different transience.

6.3.4 Simulation and Experiments Results

The supplementary control for the shunt converter failure has been tested both in Simulink

and in the experimental setup.

Simulation

The DPFC system for simulation has been introduced in chapter 4. To simulate shunt

converter failure, the shunt converter is shut down at the time t = 2 s and the DC voltages

of the series converters are shown in Figure 6-7.

1.9 2 2.1 2.2 2.3 2.4 2.5 2.60.084

0.086

0.088

V d c , s e

( p u )

Figure 6-7: DC voltages of the series converters after the shunt converter failure at t = 2 s

The DC voltages of the series converters in all three phases are well maintained after

the failure of the shunt converter. The ripple of the DC voltage is less than 1% during




operation.

Experimental Setup

The experimental setup is presented in chapter 5. In this setup, to represent the circuit

breaker tripping the shunt converter, the shunt converter is manually turned off at the

time t = 0.08 s. The reference signals of the series converters at the fundamental frequency

are fixed during operation. The line current and voltage injected by one series converter

are shown in Figure 6-8. For easier viewing, only the waveforms of one series converter

are shown.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−3

−2

−1

0

1

2

3

C u r r e n t ( A )

3rd current magnitude

Line current

full−control mode limited−control mode

(a)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−4

−2

0

2

4

V o l t a g e ( V )

converter ac voltage

converter dc voltage

full−control mode limited−control mode

(b)

Figure 6-8: DPFC behaviors during the shunt converter failure: (a) line current; (b)

converter voltages at both AC and DC sides

As shown, the voltage injected by the series converter is in PWM format. Preceding

the shunt converter failure, the voltage contains both the fundamental and 3rd harmonic

frequency components. After the failure, no current at 3rd harmonic frequency exists in




the system and the series converter successfully stabilized the DC voltage at a constant

value.

6.4 Series Converter Failure

This section addresses the supplementary control that improves DPFC performance dur-

ing the failure of a single series converter. The series converter failure’s influence on the

network is first introduced, which is followed by the operating principle and design of the

supplementary control. This section ends with the simulation results of this supplemen-

tary control.

6.4.1 Introduction

As mentioned in section 6.2, the failed series converter always appears as a short circuit

in the transmission line and stops providing desired voltages. Therefore, the total voltage

injected by series converters in different phases becomes asymmetrical. This asymmetrical

series voltage leads to asymmetrical current in the line, thereby decreasing the powerquality of the network. Series converter failure will not only influence the current at

the fundamental frequency, but also at the 3rd harmonic frequency. Since a faulty series

converter does not absorb any active power, the total active power absorbed in this phase

will be different from the amount of active power absorbed in other phases (without faulty

converters). This results in a change of the 3rd harmonic current. This 3rd harmonic

current will contain positive and negative components, which can not be blocked by the

Y-∆ transformers.

To eliminate the asymmetry at the fundamental frequency and the leakage at the 3rd

harmonic frequency, a supplementary control is needed to boost the injected voltages in

the faulted phase.

6.4.2 Principle of the Control

The principle of the supplementary control is to let the remaining converters in the phase

with the faulty converter inject higher voltages to maintain the voltage symmetry be-

tween phases at the fundamental frequency. Because the series converters are centrally



112 6.4 Series Converter Failure

controlled, this supplementary control is within the central control, as highlighted in

Figure 6-9.

AC

DC

transmission line

AC

DC

AC

DC

AC

DC hgh-

pass

filter

snt

onerter

seres

onerters

snt

ontrol

seres

ontrol

seres

ontrol

seres

ontrol

entral

ontrol

Figure 6-9: Location of the supplementary control for the series converter failure

There are two requirements for the supplementary control:

• The controller should be able to distinguish the phase with the faulty converter and

should adapt voltage reference signals for the remaining converters in the faulty

phase.

• The reference signals for the converters in different phases should be independent

to enable the series converters in one phase to generate a different voltage than the

other phases.

One approach to compensate for converter failure is to let series converters report

their status of operation (active/inactive) back to the central control. The controller

generates corresponding reference signals for each phase according to the number of active

converters. However, there are two major drawbacks to this method. First, this methodhighly relies on the communication between the converters and the central control. Any

false report will lead to incorrect compensation. Second, the failed series converter is

not a pure short circuit and there will be a small unpredictable inductance inserted by

the single-turn transformer, and this inductance cannot be compensated for using this

method.

The proposed method measures the fundamental-frequency voltages at the sending

and the receiving ends (Vs and Vr) and the current through the line I. According to the

measured information, the total voltage injected by all series converters Vse,1,cal can be




calculated by the following equation:

Vse,1,cal= Vs−Vr−I ·X (6.8)

where X is the line impedance at the fundamental frequency, the voltages and current

are column vectors that consist of the information of three phases. By comparing this

calculated voltage with the total reference voltage generated by the central control, the

operation status of the series converters is known. When the calculated voltage is lower

than the reference in one phase, it indicates one or more faulty converters in that phase.

To compensate for this missing voltage resulted by the faulty converter, a controller is

applied between the central control that gives the total reference voltage and the signal-

transmitting device that sending the reference to each series converter. This controller

generates a modified voltage reference for each series converter according to the calculated

operation status of the series converters. Because the series converters in different phases

are controlled independently, three supplementary controllers are needed, as shown in

Figure 6-10.

seriesvoltage

calculation

faulty converter

compensation

I

rV

sV

f r o m

m e a s u r e m e n t s

faulty converter

compensation

faulty converter

compensation f r o m c

e n t r a l

c o n t r o l

,1, ,s e a calV

,1, ,s e b c alV

,1, ,s e c c alV

,1, ,s e a r ef

V

,1, ,s e b r ef V

,1, ,s e c r ef V

signal

transmitting

to series

converters

,1, , ,s e a r ef a d pV

,1, , ,s e b r ef a d pV

,1, , ,s e c ref a dpV

Figure 6-10: Supplementary control scheme for compensating series converter failures

6.4.3 Compensation Controller Design

The objective of the compensation controller is to generate the adapted reference signal

according to the operation status of series converters. The input signals of the controller

are the reference voltage V se,1,ref and the calculated voltage V se,1,cal. The output signal is

the reference voltage of a single series converter V se,1,ref,adp. Because the reference voltages




for series converters are in DC quantities as discussed in chapter 4, two independent

controllers are required for one phase, responsible for the d and q components respectively.Totally, six controllers are needed for faulty series converter compensation. Due to the

identity of each controller, the design of one controller will be introduced only.

The compensation controller is a close-loop control, with V se,1,ref as the reference,

V se,1,cal as the feedback and V se,1,ref,adp as the output, as shown in Figure 6-11. A saturation

block is added to limit the output of the controller. For simplicity, the subscript se,1 are

omitted within the symbols of this subsection.

G( s) F ( s)+

-

compensation controlref

V ,ref calV

,ref adpV

Figure 6-11: Scheme of the controller for faulty series converter compensation

To design the controller, the open loop transfer function G(s) from V ref,adp to V ref,cal

should be found first. Theoretically, the calculated voltage V ref,cal equals to the multi-

plication of the number of series converters per phase and the adapted reference V ref,adp.

However, due to the measurement and the response time of series converter control, there

will be a delay between the two components. For simplification, this delay is assumed to

be a first order system, then the transfer function from V ref,adp to V ref,cal can be written

as:

G(s) = V ref,cal

V ref,adp= n

1

sT r + 1 (6.9)

where n is the number of active series converters and T r is the rise time of the delay.

Within the transfer function, n is a variable value and can be considered as a disturbance.

According to the delay of the measurements and the control of series converter, 0.01 s is

recommended for the constant T r.

According to the internal model control (IMC) method [Namh 01, Otte 03], the pa-

rameters of the controller function are calculated by:

F (s) =

α

s G(s)−1

(6.10)




where α is the design parameter that gives the bandwidth of the control. Since G(s) is a

first order system, the control is a PI regular with the parameters:

K i = α

n, K p =

αT rn

(6.11)

Within the parameters, n is the number of installed series converters per phase.


The supplementary control that compensates for the failure of a series converter is sim-

ulated in Matlab Simulink. The system that is used to verify the supplementary controlwas introduced in Chapter 4. Two sets of series converters are used. To simulate failure,

one series converter in phase a is short-circuited. To demonstrate the performance of

the supplementary control, the compensation controls are off before t=1.1 s. Figure 6-12

shows the system behavior during the failure of the series converter, in where x-axis is

time with the unit second.

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4−4

−2

0

2

4

c u r r e n t ( A )

phase aphase b

phase c

with controlwithoout controlbefore fault

(a)




0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.41.5

2

2.5

3

3.5

4

s e r i e s v o l t a g e ( V )

phase a

phase b

phase c


(b)

Figure 6-12: DPFC behaviors during a series converter failure: (a) Three-phase current at

the delta side of a transformer; (b) magnitude of the voltage injected by all

series converters

As shown, without the controller, the 3-phase current through the line becomes asym-

metrical during the converter failure. The supplementary controller successfully com-

pensates the phase difference caused by the series converter failure. As said, two seriesconverters exist in one phase. One converter has a fault in phase a, therefore the control

signal for phase a should be twice larger than without the fault, while the control signals

for the other phases should be unchanged. The reference signals of the series voltage are


0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

1.5

2

2.5

3

r e f e r e n c e v o l t a g e ( V )

phase a

phase b

phase c


Figure 6-13: Reference signals for the series converters in three phases




6.5 Conclusions

In this chapter, the DPFC’s operation during a failure is considered. It shows that the

DPFC is tolerant of control failure, shunt converter failure and series converter failure.

Two supplementary controllers are presented, used to compensate during shunt converter

and series converter failures.

For the shunt converter failure, the supplementary control is applied to each of the

series converters. This control automatically switches the series converters between the

full-control mode and the limited-control mode, according to the magnitude of the 3 rd

harmonic current. When the magnitude is lower than a threshold defined for this pur-pose, the series converters are switched to the limited-control mode that uses the active

component at the fundamental frequency to stabilize their DC voltages. Both a simulation

and practical experiment are done to verify the supplementary control and to prove that

the adapted control can successfully switch the DPFC between the two control modes,

thereby increasing the whole DPFC system reliability.

The series converters have over-voltage protection at the secondary side of the single-

turn transformer. When the series converter has a fault, the failed series converter appears

short-circuit to the transmission line and the voltage injected by all the series convertersbecomes asymmetrical. To improve the DPFC performance during the series converter

failure, a supplementary control scheme is added at the DPFC central control. The control

scheme has been simulated in Matlab and it proved that the asymmetry caused by the

failure could be compensated completely.



Chapter 7DPFC AUXILIARY SERVICES

7.1 Introduction

IN previous chapters, the control of the DPFC was presented. According to the control

objects, the DPFC control can be distinguished as the control at device level and

at system level. The control at the device level aims to maintain the capacitor DC

voltage of each converter. It also ensures that the DPFC generates the series voltages

and shunt reactive current, at the fundamental frequency, that is required by the system

operator. Consequently, the control at device level consists of the following controls that

were presented earlier:

• Shunt control (in chapter 4)

• Series control (in chapter 4)

• Supplementary controls that ensure the DPFC to keep operating during converter

failures (in chapter 6)

The control that is to use the DPFC for the network applications can be consideredthe control at system level. Such controls generate reference signals for the converters

of the DPFC and are normally on the central control side. The control at system level

discussed previously is:

• Power flow control

Because the DPFC can simultaneously adjust multiple network parameters, namely

the line impedance, the transmission angle and the bus voltage, it implies a great potential

of the DPFC for more auxiliary services at system level. In this chapter two auxiliary

services are discussed; they utilize the DPFC to damp low frequency power oscillation

119



120 7.2 Power Oscillation Damping (POD)

and compensate for asymmetrical components.

7.2 Power Oscillation Damping (POD)

In this section, the DPFC application of low frequency power oscillation damping is

introduced. The section begins by describing the background of the power oscillation and

continues with the modeling of the DPFC that is used for POD controller design (based

on the so-called current injection model). Next, the parameters of the POD controller are

designed using the Residue method [Ghai 05] and finally a case study of using DPFC for

POD is presented.

7.2.1 Background

In the current power industry, networks tend to be interconnected to allow the use of a

market-oriented business model and improve system stability. However, the capability

of long, inter-regional power transmission is usually limited and one of its limitations is

caused by low-frequency power oscillations. Damping these oscillations is a prerequisite

for secure system operation because an undamped oscillation can lead to a blackout of the power network.

One type of oscillation, known as ‘local mode’, is associated with a single generator or

a very closely connected group of units at a generating plant. Local modes normally have

frequencies in the range of 0.7 to 2.0 Hz [Klei 91]. The characteristics of these oscillations

are well understood and can be damped by the use of Power System Stabilizers (PSSs)

in generator excitation control systems [Roge 00a]. The principle of PSS is to increase

the damping of the oscillation mode by regulating the voltage of the excitation system

of a synchronous generator, to generate an electrical damping torque that counters theoscillation [Pal 05].

Oscillations, which are observed when a group of generators in one region swings

against the group in another region [Kund 94], are known as ‘inter-area modes’. Inter-

area modes have frequencies in the range of 0.1 to 0.8 Hz. Because PSSs are usually

designed for local oscillation damping, they are not effective in damping inter-area modes.

However, recent research has proven FACTS devices can be used for inter-area power

oscillation damping (POD) [Cai 05, Mhas 06, Sadi 05]. Similar to PSSs, the principle

of using FACTS devices for POD is to vary one or multiple parameters of the network




that counter the oscillation. For instance, TCSCs adjust line impedance while SVC varies

shunt capacitance.Since the DPFC can simultaneously control three parameters of a network, namely

the line impedance, transmission angle and bus voltage magnitude, it implies a great

potential for power oscillation damping.

7.2.2 POD Controller

To damp oscillations, POD controllers should be attached to DPFC control. The structure

of a DPFC POD controller, as shown in Figure 7-1, is similar to PSS controllers [Cai 05].

It involves an amplification block, a wash-out block and two lead-lag blocks [Roge 00b].

K 1

w

w

sT

sT +

1

1

lead

lag

sT

sT

+

+

1

1

lead

lag

sT

sT

+

+

max

min

input

wash-out lead-lag lead-lag

output

Figure 7-1: POD controller

The washout block is intended to eliminate the DC component of a POD controller

input signal and has a large time constant, usually from 5 s to 10 s, since the oscillation

is low frequency (less than 2 Hz normally) [Kund 94]. The lead-lag blocks provide phase

shifting characteristics to compensate for the difference between the oscillation input

signal and the DPFC output variables. The time constants of lead-lag blocks T lead, T lag

and the amplification gain K are taken as the POD design parameters.

Any signals with oscillations, such as line current, power flow and bus voltage, can be

selected as the input of the POD controller. The output of the POD controller is added

to the reference signals that are generated by the DPFC central control. As the central

control generates three reference signals for the series and shunt converters, a maximum

of three POD controllers can be employed. They can be added to I sh,q,ref , V se,d,ref and

V se,q,ref , which are the q component of the shunt current and the d and q components of

the series voltage, respectively, as shown in Figure 7-2.

7.2.3 DPFC Current Injection Model

To design a POD controller, the network with the DPFC should first be modeled. Nor-

mally, a network can be described by the equation that gives the relationship between the




central control

POD

1

+POD

2

POD

3

, ,se q ref V

, ,se d ref V

, ,sh q ref I

+ +

++

+

to shunt

converter

to series

converter

to series

converter

Figure 7-2: Location of the POD controller in the DPFC

voltage V and current I:

V = Z−1I (7.1)

where V and I are vectors of the bus voltage and the line current, respectively, and Z−1 is

the admittance matrix of the network. Within this representation, the admittance matrix

of the network is constant. However, during the operation of the DPFC, the voltage

injected by the series converters changes the admittance matrix. To make the DPFC

model compatible with the network model, the current injection model, which does not

change the admittance matrix, is employed instead of the voltage injection model. The

idea of the current injection model is to use current sources, which are shunt connected

to buses, instead of the voltage sources in series with the line, as shown in Figure 7-3.

+ V se -

I sh

Z = R + XjV r V s

I sh

Z = R + XjV r V s

I se

I r

Z = R + XjV r V s

I s I sh

Z = R + XjV r V s

I se I se

(a)(b)

(c)(d)

Figure 7-3: Transformation from the voltage source to the current injection model

In Figure 7-3(a), the series converter of the DPFC is represented by the voltage source

V se. In Figure 7-3(b), the series connected voltage V se is replaced by a current source I se




in parallel with the transmission line. The current is given as:

I se = V se

Z (7.2)

By replacing the parallel current source I se by two shunt connected current sources

in Figure 7-3(c), the current injection model of the DPFC is achieved as shown in

Figure 7-3(d), where:

I r = −I sh − I se, I s = I se (7.3)

Since the currents injected into buses can be treated as loads, the DPFC current

injection model will not change the network admittance matrix.

7.2.4 DPFC POD Controller Design

The purpose of the POD controller design is to find the parameters K , T lead and T lag.

The process consists of the following steps.

Oscillatory modes

The first step in designing a POD controller is to identify the oscillatory modes. To do so,

the power system with the DPFC is represented in state-space format that is linearized

around the operation point [Kund 94]:

∆x = A∆x + B∆u

∆y = C∆x(7.4)

where A is the state matrix, ∆x is the state vector, ∆u is a single input, ∆y is a single

output, C is a row vector and B is a column vector. To find the oscillation mode, it

depends on the eigenvalues analysis of the system state matrix A. Let λi = σi + jωi be

the ith eigenvalue of the state matrix A. The real part of the eigenvalue gives the damping

and the imaginary part gives the angular velocity of the oscillation. The relative damping

ratio is given by:

ζ i = −σ√

σ2 + ω2(7.5)

The eigenvalues which have a damping ratio of less than 3% are considered the critical

oscillatory modes [Sadi 06].




POD controller design using residue method

To design the POD controller, the system without the POD controller can be considered

a single input - single output (SISO) system. By applying the Laplace transform to ( 7.4),

the open-loop transfer function is given as:

G(s) = ∆y(s)

∆u(s)

= C(sI − A)−1B

(7.6)

The transfer function G(s) can also be represented in partial fractions:

G(s) =N

i=1

Ri

s − λi(7.7)

The term in the numerator Ri of the summation is called residue [Kund 94]. If feedback

is applied between the output y and the input u of the SISO system, the residue of a

particular mode gives the feedback sensitivity of that mode’s eigenvalue. By applying a

POD controller as feedback to the SISO system, as shown in Figure 7-4, the eigenvalues

of the whole system are changed.

G( s)

KH ( s)

+

-

uref y

∆u

u

Figure 7-4: Closed-loop system with POD controller

Here the transfer function of the POD controller is KH(s), the change of the eigenvalue

because of the POD controller is given as [Abou 96]:

∆λi = RiKH (λi) (7.8)

It can be seen from (7.8) that the change of the eigenvalue that is caused by the

POD controller is proportional to the magnitude of the residue. Therefore, the input

signal of the POD controller is selected according to the residue magnitude. To damp a

particularly oscillatory mode λi, the signal with the largest residue Ri is chosen as the

most appropriate feedback signal of the POD controller. In the DPFC, it is easy to use




local signals as the POD input signal, such as the active and reactive power flow through

the line, the current, or the bus voltage magnitude.To damp the oscillation, the shift of the eigenvalue should be towards the left half

complex plane, as shown in Figure 7-5.

σ

jω

direction of Ri

ang(Ri )φcomp

λi(0) λi(POD)

direction

of POD ∆λi

Figure 7-5: Shift of eigenvalue by the POD controller

The angle between the directions of the residue and the POD is the so-called compen-

sation angle ϕcomp, which is achieved by the lead-lag blocks. If the two lead-lag blocks in

the POD controller are identical, then the parameters T lead and T lag are determined by

[Abou 96]:

ϕcomp = 180 − ang(Ri)

T lag = 1

ωi√

αc

T lead = αcT lag

(7.9)

where mc is the number of the lead-lag blocks, ωi is the frequency in rad/sec of the

oscillation and αc is given by:

αc = T lead

T lag

=1 − sin( ϕcomp

mc

)

1 + sin( ϕcompmc

)

(7.10)

The amplification gain K can be calculated from the desired eigenvalue location λi,des

according to (7.8):

K = λi,des − λi

RiH (λi) (7.11)




Design procedure of the DPFC POD controller

As described above, there are a maximum of three POD controllers that can be applied in

the DPFC. Since the POD controllers can influence each other, it is not easy to calculate

all three sets of POD parameters at one time by using the residue method. The process

for designing POD controller parameters for a DPFC is described in the following steps:

• Find the most critical eigenvalue of the system as the damping object of the first

POD controller.

• Calculate the residue for the possible POD locations and place the first POD con-

troller at the location with the biggest residue.• Compute the first POD controller parameters.

• Calculate the new eigenvalues of the system with the first POD controller, and find

the most critical one as the second POD controller damping objects.

• Repeat the procedures above to calculate the remaining POD controller parameters

in an iterative process.

7.2.5 Case Study

The POD capability of the DPFC is simulated in a simple two-area system [Kund 94]

shown in Figure 7-6. The system consists of two areas connected by a weak tie and each

area contains two coupled generators. The generators are self-excited by DC exciters and

without PSSs. After the linearization of the system without DPFC, a pair of eigenvalues

is found on a positive plane with an oscillation frequency of approximately 0.4 Hz. The

DPFC series converters are placed at the lines between bus 8 and 9 to control the power

flow through the tie and to damp the oscillation at the same time. Bus 8 is obviously a

suitable location for the shunt converter, because voltage swings are the greatest at bus8.

The placement of only a DPFC without a POD controller causes the unstable eigen-

values to be shifted slightly leftward; however, the eigenvalues are still on the right half of

the plane signifying that the system remains unstable. By increasing the DPFC control

dynamic, the eigenvalue can be further shifted to the left, however the shift is not large.

The critical oscillatory mode is characterized by eigenvalue λ1 = 0.034 + j3.004 with the

damping ratio ζ 1 = −1.12%. It is found that the DPFC control parameter V se,d,ref has

the largest residue R1 = 11.206 and therefore it would be most effective to apply the POD




G1

G2 G3

G41

2

3

4

5 6 7 8 9 10 11

L7 L9

DPFC series converter

DPFC shunt converter

Figure 7-6: A simple two-area system with the DPFC

controller to that variable.The input signal of the POD controller is the active power flow from bus 8 to bus 9.

Using the method above, the transfer function of the first POD controller is calculated

as:

H 1(s) = 0.283 5s

1 + 5s

1 + 0.137s

1 + 0.810s

2

(7.12)

By applying the first POD controller, the critical eigenvalue is shifted to a more stable

position. However, as a side effect, the controller also brings a stable eigenvalue towards

the critical damping. Figure 7-7 illustrated the eigenvalues of the system, where only the

eigenvalues close to the critical damping are shown. Three cases are presented: without

POD, with single and with double POD controllers. To compensate for the side effect,

the second POD controller is employed to damp the oscillatory mode λ2 = 0.089+ j0.968.

The DPFC control parameter V se,q,ref is selected for the application of the second POD

controller, using reactive power flow as the POD input signal. The second POD controller

transfer function is calculated as:

H 2(s) = 0.003 5s1 + 5s

1 + 0.158s1 + 2.342s

2

(7.13)

As shown, after applying two POD controllers, none of the eigenvalues is near the critical

damping line; therefore, it is not necessary to use the third POD controller in this case.




−1.2 −1 −0.8 −0.6 −0.4 −0.2 00

0.5

1

1.5

2

2.5

3

3.5

damping

f r e q u e n c y ( r a d / s )

with double POD

with single PODwithout POD

critical damping

Figure 7-7: Eigenvalues of the two-area system in three cases

The power oscillation phenomenon can be observed when a fault occurs. To test the

DPFC POD capability, a fault is applied in the line 7-8 at t = 1 s, which is then cleared

after 0.1 s. Figure 7-8 shows the active power flow from bus 8 to bus 9 in the three cases.

0 5 10 15 20 25 30 35 40 45 50−2

0

2

4

6

A c t i v e p o w e

r F l o w ( p u )

Without POD

Single POD

Double POD

Figure 7-8: Active power flow bus 8 and 9 without POD, with single and double POD

Without a POD controller, the system is unstable. By applying the POD controllers,

the 0.4 Hz oscillation is damped significantly. The difference between using one and two




POD controllers is not significant in this case because the damping object of the second

POD controller is still under the critical damping line. In this simple two-area system, onlytwo POD controllers are necessary to achieve the required stability. If all three possible

POD controllers are employed, the DPFC can further stabilize a complex system, which

has multiple critical eigenvalues.

7.2.6 Summary

This section studies the capability of the DPFC to damp low frequency power oscillation.

The POD controller parameters are calculated by using the residue method. It is shownthat the DPFC has the capability of damping multiple frequency oscillations at the same

time. Since the DPFC has three degrees of freedoms, the potential for the POD is larger

than other devices, like SVC, TCSC, or SSSC.

7.3 Asymmetrical Component Compensation

This section presents another DPFC auxiliary service at the system level, namely the

compensation of asymmetrical components.

7.3.1 Background

Power Quality is becoming an important issue for both electric utilities and end users

[Duga 03]. Asymmetrical voltages and currents in a network are one of the concerns un-

der the power quality issue. The asymmetry is mainly produced by single phase faults

within the network [Chin 07] or a large amount of single-phase loads. The asymmetrical

voltages can cause extra losses in components of the network, such as generators, motors,transmission lines and transformers [Pedr 05]. Active filters, dynamic voltage restorers

(DVR) and power factor correctors can be used to compensate the asymmetry at the load

side, however their contributions to the transmission system is not large because they are

focused on the load side [Noha 07, Soar 00]. FACTS devices can be employed to compen-

sate the asymmetrical currents and voltages in transmission systems. Unfortunately, it is

found that the capability of most FACTS devices to compensating asymmetry is limited.

Series and shunt FACTS device can only provide compensation of asymmetrical reactive

component [Kuan 07, Nune 01], and the most powerful device, i.e. the UPFC [Gyug 92],



130 7.3 Asymmetrical Component Compensation

cannot compensate the asymmetry at zero sequence, because of the converter topology

[Iked 05].Because the series converters of the DPFC are single-phase converters, they can inject

active and reactive voltage at all sequences. Accordingly, the DPFC can be utilized to

balance the asymmetrical voltage with the system. In this section, the principle is intro-

duced first and then the behavior of the DPFC during the asymmetrical compensation is

discussed. In the end, a case study is presented.

7.3.2 Principle of Compensating the Asymmetrical Voltage

To compensate the asymmetrical voltage, a voltage measurement is put at the receiving

end to sense the voltage at the zero sequence and negative sequence. This asymmetrical

voltage is compensated by an opposing voltage injected by the series converters. The

control for the asymmetry compensation is at the central control. During the case of

asymmetrical voltages, the control generates compensating voltage signals at the zero

and negative sequence for the series converters; these signals are transmitted together

with the positive voltage signals to the series converters. The scheme of the asymmetry

compensation of the DPFC is shown in Figure 7-9.

sequence

analyzer

+

+r

V 0,

r V −

seV +

,0

seV −

,1,s e r ef V

from central control

from

measurement

to series

convertersasymmetry

compensator

Figure 7-9: Control scheme of the asymmetry compensation

The opposing voltage signals are generated by the asymmetry compensator. The

asymmetry compensator is a PI regulator, with asymmetrical components V 0,−r as the

feedback and the voltages at the zero and negative sequence V 0,−se as the control signal.

The reference of the regulator is zero. To find proper parameters for the PI regulator,

the open-loop transfer function of the system from V 0,−se to V 0,−

r should be found. This

transfer function is calculated according to the network. The network with a DPFC and

an asymmetrical load can be simplified as shown in Figure 7-10, in where Z is the line

impedance and the Z L is the load impedance.




+ V se - Z V r V s

Z L

Figure 7-10: A simplified network with asymmetrical load

According to the figure, the bus voltage at the receiving end can be expressed as:

V r = Z LZ + Z L(V s − V se) (7.14)

Then, the zero sequence component of the voltage V 0r can be calculated by:

V 0r = Z L,a

Z + Z L,a

(V s,a − V se,a) + Z L,b

Z + Z L,b

(V s,b − V se,b) + Z L,c

Z + Z L,c

(V s,c − V se,c) (7.15)

In power systems, the load impedance is much larger than the line impedance (over

10 times) [Grai 94]. Accordingly, the line impedance Z in can be neglected without losing

large accuracy:

V 0r = (V s,a + V s,b + V s,c) + (V se,a + V se,b + V se,c) + err

= V 0s + V 0se + err(7.16)

For control, the zero sequence component of the sending voltage V 0s and the small

error err can be considered as disturbances. By applying the Laplace transformation to

(7.16), the transfer function from V 0se to V 0r can be found as:

G(s) = V 0

r (s)

V 0se(s) = 1 + H (s) (7.17)

where H (s) is the disturbance. The scheme of the asymmetry compensator is shown in

Figure 7 11.

The control function F (s) is designed according to the IMC method [Juli 99] and it is

given by:

F (s) = α

sG(s)−1 (7.18)

where α is the required bandwidth of the controller.




G( s) F ( s)+-

asymmetry compensator

0

0,

r V −0,

seV −

H ( s)

+

+

Figure 7-11: The scheme of the asymmetry compensator

7.3.3 Analysis

In order to compensate asymmetrical voltages, the series converters of each phase gen-

erate different voltages, thereby requiring different active power between phases. As theDPFC uses 3rd harmonic current to exchange active power between the shunt and series

converters, this compensation will have an influence to the 3rd harmonic current. This

section studies the behavior of a simple network with the DPFC under the asymmetrical

situation, by using the method of symmetrical components introduced by C.L. Fortescue

[Grai 94].

Figure 7-12 shows a simple network with the DPFC that has asymmetrical voltages.

The total voltage generated by the multiple series converters V se, grid s is in symmetry

with voltage V s and grid r is asymmetrical with the voltage V r + V u where V r is thesymmetrical part and V u represents the asymmetry.

AC

DC

AC

DC

AC

DC

AC

DC high

pss

filter

shunt

converter

series converters

sV

r uV V +

I

s r

Figure 7-12: DPFC network with asymmetrical voltages

To simplify the analysis, it is assumed that V u consists of negative and zero sequence

components only and V +u = 0. To compensate the asymmetrical voltage, the DPFC series

converter will generate a negative and zero sequence voltage that is opposite to V u:

V se = V +

se − V u (7.19)




The active power at the fundamental frequency required by each phase is given by:

P se,a

P se,b

P se,c

= Re

−V se,a · I ∗a

−V se,b · I ∗b

−V se,c · I ∗c

(7.20)

When the DPFC completely compensates the asymmetrical voltage, the series injected

voltage is asymmetrical and the current might be asymmetrical, too. Accordingly, the

active power requirement for the series converters of each phase is different. This results

in positive and negative components within the 3rd harmonic current, which can not be

blocked by the Y-∆ transformers. To find out whether the magnitudes of the leakage 3rd

harmonic current are acceptable for the network from the viewpoint of the power quality,

the equivalent network of the DPFC at the 3rd harmonic should be found, as shown in

Figure 7-13.

3 Z

,3a I ,se aP

3 I

3 Z

3 Z

,3b I

,3c I

,se bP

,se cP

Figure 7-13: Equivalent network of the DPFC at the 3rd harmonic

As introduced in chapter 4, to reduce the magnitude of the 3rd harmonic current

through the line, the series converter only generate active power at the 3rd frequency.

Therefore the series converters can be considered as resistances at the 3 rd frequency, and

the power consumed by the ‘resistors’ are P se. The shunt converter is controlled as a

current source, which injects a constant current I 3 to the neutral point. Consequently,the 3rd harmonic frequency circuit can be expressed by the following equations:

I a,3 + I b,3 + I c.3 = I 3

Z 3 · I a,3 + P se,a

I ∗a,3

= V 3

Z 3 · I b,3 + P se,b

I ∗b,3

= V 3

Z 3·

I c,3 + P se,c

I ∗

c,3

= V 3

(7.21)




where V 3 is the voltage across the transmission line. As equation (7.21) is not linear, it is

difficult to achieve analytical solutions for the 3rd harmonic current. However, by applyingsome typical DPFC parameters and solving the equations numerically, it is found that

the non-zero sequence 3rd current is less than 10% of the nominal line current, typically

around 4%.

7.3.4 Case Study

The simulation of application of the DPFC to compensate asymmetry has been done in

Matlab, Simulink. The system shown in Figure 7-12 is used as a test example. The

magnitudes of the voltages at grid are 1 pu, and V s leads V r 1.5. The transmission line

is represented by a 0.06 pu inductor and the resistance is neglected. The DPFC uses

constant 0.4 pu 3rd harmonic current to exchange active powers between the shunt and

series converters.

To simulate the asymmetrical condition, the load in phase a increases 100% at the

moment t = 1 s and the load at the rest two phases remains. The control for compensating

asymmetrical voltage is switched off before t = 1.2 s. Figure 7-14 illustrates the voltage

magnitude at the receiving end at the fundamental frequency.

0.9 1 1.1 1.2 1.3 1.4 1.50.9

0.91

0.92

0.93

0.94

0.95

0.96

V r ( p u )

phase a

phase b

phase c

w ou asymme ry compensa on w asymme ry compensa on

Figure 7-14: Voltage magnitude at the receiving end at the fundamental frequency

As shown, the asymmetrical load results in an asymmetrical voltage at the receiv-

ing end, with the magnitude approximately 2%. With the asymmetry compensation,

the asymmetrical voltage is totally compensated by the series converters. The voltages

injected by the series converter are shown in Figure 7-15.




0.9 1 1.1 1.2 1.3 1.4 1.5−0.04

−0.02

0

0.02

0.04

V e 1 ( p u )

phase a

phase b

phase c


Figure 7-15: Voltage injected by the series converter at the fundamental frequency

The 3rd harmonic currents which are used to supply the active power will contain

non-zero sequence components. The magnitude and angle of the 3rd harmonic current in

all three phases are shown in Figure 7-16(a). The 3rd harmonic currents that leaks to the

∆ side of the transformer are illustrated in Figure 7-16(b).

As shown, in the situation of asymmetrical voltage, around 0.01 pu non-zero sequence

3rd

harmonic is generated by the DPFC system.

7.3.5 Summary

This section investigates the capability of the DPFC to compensate for the asymmetrical

voltage of a network. It is found that the DPFC can compensate both negative and zero

sequence voltage, consequently the DPFC is more powerful than other FACTS devices for

compensation for the asymmetry. As a side effect, the DPFC generates non-zero sequence

3rd current during the situation of asymmetrical voltage, which cannot be blocked by the

Y-∆ transformer. However, the magnitude of the non-zero sequence 3rd current is much

smaller than the nominal current at the fundamental frequency, typically less than 4%.

7.4 Conclusions

This chapter addresses two applications of the DPFC at the system level, namely low-

frequency power oscillation damping and asymmetrical voltage compensating. Comparing

to other FACTS devices, such as TCSCs, SVC and STATCOM, the DPFC can simulta-



136 7.4 Conclusions

0.136

0.138

0.14

I 3 ( p u )

0.9 1 1.1 1.2 1.3 1.4 1.5−5

0

5

10

a n g l e ( d e g r e e )


(a)

0.9 1 1.1 1.2 1.3 1.4 1.5

−0.02

−0.01

0

0.01

0.02

I 3 ( p u )

phase a

phase bphase c


(b)

Figure 7-16: 3rd harmonic current for the DPFC asymmetry compensation: (a) magnitude

and angle of the current in each phase; (b) leakage

neously damp three critical oscillatory modes, which is as powerful as the UPFC. For

compensating asymmetrical voltage, the DPFC is more effective than the UPFC because

it can balance both zero and negative sequence asymmetrical voltages.



Chapter 8

DPFC APPLICATION IN UTILITY GRIDS

8.1 Introduction

THE concept of the DPFC is introduced previously. The presented issues, including

the modeling, control, fault tolerances and network applications, were focused on

the DPFC’s basic properties. As the DPFC intend to be applied in real power transmissionnetworks, it is important to study its feasibility.

In this chapter, the realization of the DPFC in real networks is examined. The DPFC

design procedures are introduced and the equations needed to determine the major pa-

rameters of the DPFC are given. Two case studies are presented. Case Study 1 aims to

analyze the feasibility of the DPFC on a real transmission line within a two-port network.

The DPFC will be considered from a physical, electrical and financial point of view. In

Case Study 2, the application of a DPFC for power flow control is discussed, in the case

of the Dodewaard triangle network in the Netherlands.

8.2 DPFC Design Procedure

The DPFC design can be divided into three major levels: system level, DPFC level and

converter level, as shown in Figure 8-1.

137



138 8.2 DPFC Design Procedure

find the voltage and

current ratings of

the DPFC

system

DPFC level

converter level

find the location

and control rangeof the DPFC

design the series

and shunt

converter

Figure 8-1: DPFC design levels

8.2.1 System LevelTo design a DPFC, the first concern is the location of the DPFC within a network. Fol-

lowed by, what is required of the DPFC from the power system’s point of view, namely

the voltage level and requisite control range of power flow S range. These issues fall under

the scope of power system engineering. They are related to the network topology, system

operation and system planning, and will not therefore be discussed here. The determina-

tion of the DPFC location and control range is similar to the one for the UPFC and can

be cited from [Gamm 98, Gerb 01, Rahm 97, Wei 03].

8.2.2 DPFC Level

Once the requirements of the DPFC at the system level are known, the design at the

DPFC level begins, which includes:

• Determining the 3rd harmonic frequency components.

• Finding the total voltage and current that must be injected by the series converter.

• Find the voltage and current rating of the shunt converter.

Third harmonic components

To calculate the 3rd harmonic components, the maximum active power that should be

transmitted between the DPFC shunt and series converters must first be determined.

According to chapter 3, this maximum active power is based on the uncompensated

power flow S r0 of the line and the DPFC control range S range, and can be estimated as:

P se,max = |X 1

||S r0

|V 2 |S range| (8.1)




where X 1 is the line impedance at the fundamental frequency and V is the nominal bus

voltage.Because the only purpose of the 3rd harmonic component is to exchange active power,

the selection of the 3rd harmonic voltage and current is flexible. However, as part of

the 3rd harmonic current will flow through the neutral wire, the thermal capacity of the

neutral wire should be taken into consideration. The 3rd harmonic current in the neutral

wire should be lower than its thermal capacity.

The 3rd harmonic current within the DPFC uses both the earth and the ground wire

as the return path, as shown in Figure 8-2. Accordingly, it is important to find the

percentage of the current flowing through the ground wire. Currently, the study on 3rd

harmonic distribution between the earth and ground wire is limited, and the study on the

distribution of zero-sequence current at the fundamental frequency is used as a reference.

Normally, the ground wire has around 40% capacity of a single conductor. According to

[Nahm 93, Sebo 69], if the distance between the zero sequence current feeding point and

the return path is large, 20% of the zero sequence current will flow through the ground

wire, with the remainder flowing into the ground.

stationstation

DPFC shunt converter DPFC series converter

Figure 8-2: 3rd harmonic current flow in a DPFC

Once the thermal capacity of the neutral wire is known, the maximum 3 rd harmonic

current can be determined. A relatively high 3rd harmonic current results in less series

converter units, however increases higher losses. With selected 3rd harmonic current I 3,

the 3rd harmonic voltage of the series converters |V se,3,max| can be calculated and this

voltage is given as:

|V se,3,max| = P se,max/|I 3| (8.2)




The maximum voltage |V sh,3,max| and current |I sh,3,max| for the shunt converter at the

3rd harmonic frequency can be calculated from:

|I sh,3,max| = 3I 3

|V sh,3,max| =

(X 3I 3)2 + V 2se,3,max

(8.3)

Within the equation, X 3 is the total zero sequence impedance at the 3rd harmonic

frequency. This impedance includes the self-impedance of the lines and the mutual

impedance between the lines and the ground wire and the ground [Grai 94, Thap 90].

As the zero-sequence impedance is related with the ground, the ground wire and the

geometry of the line, it is difficult to calculate accurately. According to the data from

Kerite, the zero sequence impedance is normally 2 to 4 times larger than the positive

sequence impedance1.

Voltage and current rating of the series converters

The voltage and current of the series converter consist of a fundamental frequency compo-

nent and 3rd harmonic frequency component. The 3rd harmonic component of the series

converter has been given previously and the fundamental frequency component can becalculated from:

|V se,1,max| = |S range| · |V |

X 1(8.4)

The voltage and current rating of the DPFC converters is the sum of the components at

both the fundamental and 3rd harmonic frequencies:

V se,max = V se,1,max + V se,3,max

I se,max = I 1,max + I 3(8.5)

where I 1,max is the maximum line current at the fundamental frequency.

Voltage and current rating of the shunt converter

The shunt converter of the DPFC consists of a three-phase converter with a back-to-

back connected single-phase converter. The three-phase converter supports the capacitor

voltage and provides reactive power for the network. The voltage and power ratings of

1

Date Source: http://www.kerite.com/catalog/catalogfiles/impedance data power.htm




the three-phase converter can be calculated according to the reactive compensation range,

similarly to the calculations used in a STATCOM, which can be found in [Lee 03].The single-phase converter is connected between the neutral point of the Y-∆ trans-

former and the ground. Since the transformer blocks the voltage and current at the

fundamental frequency, the single-phase converter only needs to handle the component at

the 3rd harmonic frequency, which is shown in (8.3).

8.2.3 Converter Level

Due to the similarity between the shunt converter and a STATCOM, design of the shuntconverter will not be discussed here in detail. The converter level design within the thesis

is focused on the series converter design. Because the units of the DPFC series converter

are hung on the transmission line, their weight is a major design factor, to ensure that

the towers can hold the units. Accordingly, the DPFC series converter design consists of

the following steps:

• AC-DC converter design

• single-turn transformer design

• unit weight calculation

AC-DC converter design

The total voltage and power of all series converters has been given above. The selection

of the size and number of units is flexible. The units with small voltage and power ratings

result in lightweight per unit; however, in this case, more units are required.

Due to the relatively low rating of the series converter units, MOSFET or IGBT can

be selected as switching devices. It is possible to find, the maximum RMS voltage V s,

current I s and DC voltage V dc of the series converter unit based on the parameters of the

selected semiconductors. The capacitor is used to maintain the DC voltages, accordingly

its capacitance depends on the allowed DC ripple V dc,ripple and the capacitance is given

as:

C dc = I s

4πf V dc,ripple

(8.6)

where V dc,ripple is the maximum ripple that is allowed on the DC side, f is the network

fundamental frequency and I s is the maximum RMS current on the AC side of the unit.




A choice can be made to use an electrolytic or film capacitor. Film capacitors have a

longer lifetime than electrolytic capacitors. However, they are much bigger, heavier andmore expensive. Even though, film capacitors are recommended, because they can handle

much larger RMS current than electrolytic capacitors.

Single-turn transformer design

The design of the single-turn transformer should determine the turns of the winding, core

material and core dimensions.

- Number of turns

The transformer uses the transmission line as its primary winding. The turns of the

secondary winding can be calculated according to maximum current flow through the

transmission line and maximum current allowed by the semiconductors:

N s = I max

I s(8.7)

where I max is the maximum RMS current through the line and I s is the maximum RMS

current of the selected semiconductor.

- Core dimensions

The core of the transformer is a ring core and the transmission line runs through the

core’s central opening, as shown in Figure 8-3.

core

transmission line

core

window

gross corearea

d

L

r

Figure 8-3: single-turn transformer core of the DPFC series converter

To find the gross core area of the core, the maximum voltage induced by the trans-

former Et should be found:

E t =

V s

N s (8.8)




According to the induced voltage per turn, maximum flux in the core is given as:

Φm = E t4.44f

(8.9)

To ensure the core not be saturated, the cross-section area of the core Agi should be:

Agi = Φm

0.9Bm(8.10)

where Bm is the saturation flux density of the core material. Normally, grain-oriented

silicon steel is used as the core material with maximum operation flux density 17000 gauss.

Once the cross-section is determined, the selection of the length L and the thickness d

of the core can be traded. A longer core requires less core material, but needs more

copper for the secondary winding. As most of the weight of the series converter unit is

contributed by the core, a longer core is recommended.

The transmission line and secondary winding run through the core window, which can

be calculated from:

Aw = 2Al

K w

(8.11)

where Al is the cross-section of the transmission line and K w is a design factor, so-called

window space factor, that gives extra space for voltage isolation. As the series converter

is electrically floated on the line, the single-turn transformer does not need high voltage

isolation. A window space factor of K w = 0.6 is recommended for a DPFC single-turn

transformer.

Weight calculation

The weight of the series converter unit is mainly contributed by the transformer and the

converter. According to the selected components, the converter weight can be roughly

calculated from data sheets. The weight of the transformer core is given as:

W c = ρcLπ[(d + r)2 + r2] (8.12)

where ρc is the density of the core. The weight of the secondary winding is given as:

W s = 2AsN s(L + d) (8.13)



144 8.3 Case Study 1: Two-Port Network

where As is the cross-section of the secondary winding and N s is the number of turns.

Once the weight per unit is known, the total weight of the series converter can becalculated by multiplying it by the number of the units. The number of the series converter

units depends on the required series voltage and the maximum voltage of a single series

converter unit, which is given as:

N se =√

3V se,maxN s

V s(8.14)

Note that V se,max is line-to-line voltage. If the extra weight of the series converter cannot

be hold by towers, the converter level design should be repeated.

8.3 Case Study 1: Two-Port Network

This case study investigates the feasibility of the DPFC in a real network and focuses on

the electrical parameters, the physical parameters (including the size, weight of a single

unit) and the approximate cost.

In this section, the specifications of the studied case are introduced. The UPFC

that is applied in the KEPCO transmission system in Korea is used as the case. Oncethe specifications of the KEPCO UPFC are presented, the design of the DPFC, which

replaces the KEPCO UPFC, is discussed. This section ends with a comparison between

the two solutions.

8.3.1 Case Specifications

As mentioned before, because of reliability and economical issues, UPFC is not widely

applied and there have been two UPFC projects undertaken as of 2010, the AEP UPFCproject in the USA operating at 60 Hz and the KEPCO UPFC project in Korea operating

at 50 Hz [Chan 03, Kim 05, Rahm 97, Renz 99, Scha 98, Yoon 03]. As the studies of the

DPFC are based on a 50 Hz fundamental frequency in this thesis, the KEPCO UPFC is

selected.

The KEPCO UPFC is installed on the Kangjin - Jangheung transmission line at 154

kV. The shunt and series converters have 40 MVA capacity each and are connected to the

network through two main transformers. The converters of the UPFC have 3-level switch

technology and 24 pulses per period. GTOs are selected as the switches. The UPFC uses




Kangjin Jangheung

shunt converter series converter

shunt TR

series TR

intermediate TRintermediate TR

thyristor bypass

Figure 8-4: Electrical configuration of KEPCO UPFC

intermediate transformers to magnetically couple two 6-pulse converter modules. The

configuration of the KEPCO UPFC is illustrated Figure 8-4.

The major specifications are deduced from published materials and listed in Table 8-1.

Voltage (kV) Capacity (MVA) Remarks

shunt TR 154/14.845 40 Y-∆series TR 6.061/14.845 40 open Y-∆

intermediate TR 4.757/8.239 22 open Y-∆

(a)

Resistance (Ω) Reactance (Ω) Capacity (kA)

0.382 3.001 2.2

(b)

Table 8-1: Major specifications of the KEPCO UPFC: (a) UPFC; (b) transmission line

According to the specifications, the control range of the KEPCO UPFC can be calcu-

lated:

S range = V V se

X L=

154 × 6.061

3.00837 ≈310 MVA (8.15)




8.3.2 DPFC Design

To replace the KEPCO UPFC with the DPFC solution, the shunt and series converters of

the DPFC should have the same voltage injection and capacity as the UPFC. Therefore,

the DPFC design begins at the DPFC level.

Several changes are made to the KEPCO UPFC. Firstly, the common DC link between

the shunt and series converters is eliminated. The shunt converter remains and the series

converters are replaced by multiple DPFC series converter units. The constant 3rd har-

monic current is injected by a single-phase converter that lies between the neutral point

of Y-∆ transformer and the ground. The DC side of this converter is connected back-to-

back to the shunt converter in order to absorb active power. The electrical configuration

of the DPFC solution in the KEPCO network is shown in Figure 8-5.

Kangjin

Jangheung

shunt converter

shunt TR

intermediate

TR single-phase

converter

ACDC

ACDC

DPFC series

converter units

Figure 8-5: DPFC solution in the KEPCO network

According to the DPFC design procedure, the major specifications of the KEPCO

DPFC are listed in Table 8-2.

Shunt converter(single-phase) Series converter (total)

V sh,max (kV) 2.5 V se,max ph-ph (kV) 7

I sh,max (kA) 1.5 I se,max (kA) 3.8

Table 8-2: Specifications of the DPFC converters

For the DPFC series converter unit, the IGBT with 70 A and 600 V is the first

selection to be tested. Consequently, the specification of the unit can be and they are

listed in Table 8-3.




Single-turn transformer Core

turn ratio 1/55 core thickness (m) 0.11

gross core area (m2) 0.022 window area (m2) 0.0032

core length (m) 0.2 window diameter (m) 0.064

Series converters

Capacitance (mF) 2.2 weight per unit (kg) 36.5

Table 8-3: Specification of DPFC series converter unit

The number of series converter units per phase is:

N unit = 524/phase (8.16)

The KPECO UPFC is installed between Gangjin and Jangheung, however the series

converter units can be attached to the line from Gangjin to Suncheon according to network

topology. The length of the line where the DPFC series converter has been installed is

approximately 100km, so the number of the units per phase per km is:

N unit/km = 5.24 /phase (8.17)

For the transmission line, aluminum conductors reinforced with steel (known as AC-

SRs) are used for the KEPCO network. According to the current flowing through, the

overhead line with a cross-section area of 800 mm2 is used in the KEPCO network, with

the density of 2991 kg/km. Therefore, the extra weight added to the transmission line by

the DPFC series converter unit is given as:

W ex/km = 191 kg/km (8.18)

Accordingly, the extra weight of the transmission line caused by the DPFC series

converter represents around 6% of the line’s own weight. For the purpose of this research,

it is assumed that the tower can hold the extra weight of the series converter units.

8.3.3 Comparison

A comparison between the DPFC solution and the original UPFC solution is listed in

Table 8-4.




DPFC solution UPFC solution

shunt 3-ph TR 2 2

series 3-ph TR 0 2

shunt converter 2 (one 3-phase for reactive

compensation; one single-

phase for 3rd harmonic in-

jection)

1 (3-phase for reactive com-

pensation)

series converter 1572 (single-phase, 600 V,

30 kW)

1 (3-phase, 6 kV, 40 MW)

Table 8-4: Comparison between the DPFC solution and the original UPFC solution

As shown, within the DPFC, the shunt converter of the UPFC remains and the series

converters are distributed along the transmission line. Therefore, two high-power 3-phase

transformers, a 3-level converter and one 40 MVA capacitor bank that are used for the

UPFC series converter are eliminated. Consequently, the DPFC’s footprint is only half

the size of the UPFC solution’s footprint.

Concerning the cost, the shunt converter of the DPFC is slightly more expensive than

the shunt converter of the UPFC, due to the single-phase converter that is required for

generating a 3rd harmonic current. Since the voltage and power rating of the single-phase

converter are relatively low and no extra transformer is needed, the expense difference is

not large. With regards to the series converter, the DPFC is much cheaper than the UPFC

because the high-power three-phase converter, two transformers and capacitor bank are

eliminated. Due to the low rating of the series converter unit, less copper and core-

material will be used for the series converters. In addition, the cost of semiconductors for

the DPFC series converter is much lower than for those in the UPFC, because a single

component can handle the voltage and current and there is no need for a large amount of

switches to connect in parallel or in series.

According to [Kim 05], the KEPCO UPFC had at least 18 faults within one year,

concerning controllers, transformers, gate drives, switches, cooling, etc. Most of these

faults led to the tripping of the UPFC. By using the DPFC solution, the faults on the

series converter side will not influence the network. Even when the shunt converter has

a failure, the DPFC can be switched from the full-control mode to limited-control mode.




In the limited-control mode, the DPFC series converters can continue providing reactive

compensation.

8.4 Case Study 2: Triangle Network

In this section, a case study is presented that shows how the DPFC can be used to solve

power congestion in a ring network. The triangle network in Nijmegen, the Netherlands

is selected as the case. In this case, the management of the 3rd harmonic current loop

and the design of the control loops for power flow are considered.

8.4.1 Case Specifications

The structure of the object network is illustrated in Figure 8-6. The network consists of

five buses that are operated at 156 kV. The power lines between the bus KBG and DOD

have a congestion problem because their impedance is lower than the rest of network. To

limit the power flow between KBG and DOD, several series inductors with fixed reactance

are inserted into the lines, as shown in Figure 8-6.

KBG

ELT

NMDOD

RK

1. 4 4 + j 3.

1 7 0. 9

3 + j 1.

9 5 0 .5 + j 2 .7

1.04+j6.35

0 . 4

7 + j 0 . 9

0 . 6

2 + j 3 . 5

8

extra series

inductor

Figure 8-6: Structure of the object network

The voltage magnitudes, voltages angle and the power consumption or generation of

the five buses are listed in Table 8-52.

Using an air core coil to limit the line current has several disadvantages:

• The impedance of the air core coil is fixed and can only be switched on or off.

2

Data source: NUON



150 8.4 Case Study 2: Triangle Network

DOD ELT KBG NM RK

bus voltage (kV) 158.886 159.43 159.342 158.619 159.257

angle () -6.97 -7.607 -7.977 - 6.764 -7.889

active power (MW) 121.1 -70.6 -184.3 168.2 -26.3

reactive power (MVA) 126.1 73.6 -42.8 -59.1 -56.0

Table 8-5: Voltage magnitudes, angles and power consumption or generation of the buses

• This solution will increase the line voltage drop, thereby resulting in a large reactive

loss.

8.4.2 DPFC Solution

By using the DPFC solution, the disadvantages listed above can be avoided. The location

of the DPFC is the first issue that should be determined. Two elements are considered

during the DPFC location determination: the power flow and the 3rd harmonic current

path.

To restrain the current that exceeds the line’s limit, one approach is to insert the

DPFC in the lines DOD-KBG to increase line impedance, the same approach as the fixed

coil solution. However, this results in large reactive losses. Another approach is to reduce

the line impedance of the other two lines, thereby leading the current flow through other

paths. This solution decreases the line impedance of the whole network, thereby reducing

reactive losses. The DPFC series converters will be installed in the line DOD-NM and

NM-KBG, as shown in Figure 8-7.

The location of the shunt converter is determined so the 3rd harmonic current flows only

within the lines with the series converters. In this triangle network, the shunt converter

is placed at the bus NM and the neutral points of the transformers at the node DOD and

KBG are grounded, as shown in Figure 8-7. In this case, the 3rd harmonic current will

be injected at the node NM and divided over the lines DOD-NM and NM-KBG. Because

of the neutral point grounded Y-∆ transformer, the 3rd harmonic current cannot flow to

the line DOD-KGB which is without a DPFC series converter.




KBG

ELT

NMDOD

RK

1. 4 4 + j 3.

1 7 0. 9

3 + j 1.

9 50 .5 + j 2 .7

1.04+j6.35

0 . 4

7 + j 0 . 9

0 . 6

2 + j 3 . 5

8

DPFC ont

DPFC hunt ont

Figure 8-7: DPFC converter arrangement in the triangle network

8.4.3 Control Scheme

To control the DPFC, it monitors the current in the line DOD-KBG. When the current

is under the limit, the DPFC will not be active. However, when the current is over the

limit, the DPFC series converter will reduce the impedance of the lines DOD-NM andNM-KBG, thereby leading more current to flow through these two lines. The control

scheme for limiting the current through the line DOD-KBG is shown in Figure 8-8.

+

-lim| | I

| | DK I

0

P & Q

cal.

K V

power

flow

control

,ex exP Q+

+

, DN DN P Q

, NK NK P Q

, ,se ref DN V

, ,se ref NK V

Figure 8-8: Control scheme for limiting the current through the line DOD-KBG

The subscripts D, N and K in the figure represent the buses DOD, NM and KBG

respectively. First, the magnitude of the current |I DK | is measured and compared with

the predefined current limitation. A saturation block is applied to ensure the DPFC

reduce the line impedance only when the current is over limit. Next, according to the

DOD bus voltages, the extra power flow that should be transmitted in the lines DOD-




NM and NM-KBG can be calculated. Then, the reference for the power flow control is

determined by adding the extra power flow to the original power flow signal. Finally, thepower control calculates the reference voltage of the series converters at these lines.

8.4.4 Advantages of the DPFC solution

Compared to the fixed inductor solution, the DPFC solution has the following advantages:

• Dynamic control: the DPFC has a smooth control range and can dynamically

adjust the line parameters according to different conditions.

• Independent active and reactive power flow control: due to the capabilityof the DPFC, the active and reactive power flow through the line DOD-NM and

NM-KBG can be independently controlled.

• Improved system stability: the DPFC reduces the total line impedance; there-

fore, the voltage drop across the line is also reduced, improving the voltage stability.

In addition to this, in order to transmit the same amount of power, the transmis-

sion angle is decreased because of the low line impedance. This also improves angle

stability.


This network is simulated in Matlab Simulink. The five buses are simplified to three buses

by shifting the load at RK and ELT buses to the nearby buses according to line impedances

[Grai 94]. Two cases are simulated, namely with fix series inductor in line DOD-KBG

and with the DPFC in the line DOD-NM and NM-KBG, as shown in Figure 8-9.

DOD

NM

KBG

load

extra

inductor DOD

NM

KBG

load

(a) (b)

Figure 8-9: Simplified Network of the case study: (a) with fix inductor; (b) with DPFC

With the voltage base and the power base V base = 156 kV and S base = 250 MVA, the

specifications of the network in pu is shown in Table 8-6, where the minus sign in the




column of the power consumption means that the bus is the load bus and a positive sign

means the generation bus.

Power consumption or generation

DOD KBG NM

active power (pu) 0.455 -0.975 0.552

reactive power (pu) 0.471 -0.195 0.109

Line impedance

DOD-KBG KBG-NM NM-DOD

resistance (10−

3pu) 5.24 6.22 5.78reactance (10−3pu) 10.93 34.89 35.28

Table 8-6: Network characters in pu

To test the DPFC, the active and reactive power consumption at the bus KBG is step

increased as shown in Figure 8-10.

0.5 1 1.5 2 2.5 3 3.5 40

1

2

3

P , Q ( p u )

active power

reactive power

Figure 8-10: Active and reactive power consumption at the bus KBG

Assuming that the thermal capacity of the line is 0.5 pu, the DPFC measures the

current of the line DOD-KBG and controls the RMS value of the current which falls

below the limit. The current flow through the line DOD-KBG, with and without the

DPFC, is shown in Figure 8-11.

As shown, the DPFC can successfully keep the current flowing through the line below

the limit. According to the load, the DPFC dynamically varies the voltages injected

by the series converters to distribute the current in the parallel lines evenly. When the

current though the DOD-KBG is not over the limit, the DPFC is not operating. When the




0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

I ( p u )

with DPFCwithout DPFC

Figure 8-11: RMS value of the current through the line DOD-KBG

line is overloaded, the DPFC reduces the impedance of the other lines, thereby limiting

the overload. The overshot of the current with the DPFC is caused by the power flow

controller. The ratio of the RMS valve of the current through the parallel line is shown

in Figure 8-12.

0.5 1 1.5 2 2.5 3 3.5 4

0.2

0.4

0.6

0.8

1

r a t i o b e t e e n t h e c u r r e n t

t h r o u g h t h e p a r a l l e l l i n e s

Figure 8-12: Ratio of the RMS valve of the current through the parallel line

Before the current goes over the limit, the current is distributed over the parallel linesaccording to their line impedances. By using the DPFC, the transmission capacity of

both lines can be boosted to the thermal limit, optimizing the usage of the network.

As said, the DPFC can improve the voltage and angle stability of the network. Within

this network, the transmission angle between the buses DOD and KBG is not large at

around 1, therefore the improvement of the angle stability is not clear. However, the

DPFC greatly improves the voltage stability and the voltage magnitude of the bus KBG

as shown in Figure 8-13.

As shown, without the DPFC and with the use of a fixed inductor, the load bus incurs




0.5 1 1.5 2 2.5 3 3.5 40.95

0.96

0.97

0.98

0.99

1

K B G b u s v o l t a g e ( a )

with DPFC

without DPFC

Figure 8-13: Voltage magnitude of the load bus KBG

an approximately 2.5% drop in voltage at heavy load condition. By using the DPFC, the

voltage drop is around 0.7% with the same load.

8.5 Conclusions

This chapter addresses the realization of the DPFC in real networks. The design procedure

of the DPFC is first presented, followed by two cases that have been examined from

different perspectives.

Case 1 uses the KEPCO UPFC as the example to investigate the feasibility of the

DPFC. The size, weight and cost issues of the DPFC are considered. By calculating the

parameters of the DPFC according to the design procedure, it is found that to gain the

same control capability as the UPFC, the DPFC requires much less material and creates

a smaller footprint. The total weight of the series converter units is 6% of the line weight,

which was assumed acceptable for the purposes of this research.

Case 2 concerns the power flow capability of the DPFC and the triangle network

between the buses NM, DOD and KBG in the Netherlands. Currently, this triangle

network has a congestion problem and a fixed inductor is connected in series with the

line that is overloaded. By using the DPFC to replace the fixed inductor, the power flow

through the network can be dynamically controlled. Besides limiting the current that

exceeds the line’s limit, it shows that the DPFC also improves the voltage and angle

stability of the network.



Chapter 9CONCLUSIONS AND

RECOMMENDATIONS

9.1 Conclusions

A

S mentioned in chapter 1, there is a large demand for power flow control in modern

power systems. The trend is that mechanical Power Flow Controlling Devices

(PFCDs) are gradually being replaced by Power Electronics (PE) PFCDs. Among all PE

PFCDs, the Unified Power Flow Controller (UPFC) is the most versatile device. However,

the UPFC is not widely applied in the utility grid due to its high cost and relatively low

reliability.

The aim of this thesis is to develop a new type of power flow controlling device that

offers the same control capability as the UPFC, at a reduced cost and with increased

reliability. The new device, the so-called Distributed Power Flow Controller (DPFC), is

a further development of the UPFC. It has been shown that the DPFC fulfills all three of

the listed goals. To ensure the feasibility of the DPFC, the detailed research in this thesis

addresses the following topics:

• Operating principle

The DPFC eliminates the common DC link within the UPFC to enable the independent

operation of the shunt and series converters. The D-FACTS concept is employed in

the design of the series converter. Multiple low-rating single-phase converters replace the

high-rating three-phase converter, which greatly reduces its cost, due to no requirement of

high-voltage isolation, and increases its reliability, due to redundancy. The active power

157



158 9.1 Conclusions

that used to exchange through the common DC link in the UPFC, is now transferred

through the transmission line at the 3rd harmonic frequency. The reason to select the3rd harmonic is that it is a zero-sequence component and can be naturally blocked by

a Y-∆ transformer. The steady-state analysis shows that the DPFC can simultaneously

adjust the voltage magnitude, the line impedance and the transmission angle, thereby

independently controlling the active and reactive power flow through lines.

• Dynamic model

A dynamic model of the DPFC in the dq rotation reference is developed. This model is

used for the design of a DPFC control algorithm and can be used in computer simulations

of future research. Within the model, the DPFC operation at the system level, which is

at the fundamental and the 3rd harmonic frequency, is described. The switching behavior

of converters is neglected in the model.

• DPFC basic control

The DPFC basic control is developed based on the dynamic model. The basic control

stabilizes the level of the capacitor DC voltage of each converter and ensures that the

converters inject the voltages into the network according to the command from the central

control. The shunt converter injects a constant current at the 3rd harmonic frequency,

while its DC voltage is stabilized by the fundamental frequency component. For the series

converter, the reference of the output voltage at the fundamental frequency is obtained

from the central control and the DC voltage level is maintained by the 3rd harmonic

components. The control parameters of the basic control are determined. Both the model

and the basic control are verified in Matlab Simulink.

• DPFC laboratory demonstrator

To verify the dynamic model and the basic control, a DPFC demonstration setup is built.

The setup consists of a scaled network, one shunt converter and six series converters.The scaled network contains two buses with fixed voltage, where the buses are connected

through inductors. The voltages of two buses have a phase shift and the series converters

are meant to control the power that flows between the buses. All the DPFC converters

are independently controlled by their own DSP controllers that are preprogrammed in

Matlab Simulink. Two cases are tested: the steady state and the step response. It is

demonstrated that the shunt and series converters can exchange active power through

the 3rd harmonic component and that the DC voltages of the series converter can be

maintained at a constant level during both situations.




• Fault tolerance

When the DPFC is applied in power systems, the reliability issue is important. The fault

tolerance of the DPFC is investigated, including the protection method for different types

of failures and the use of supplementary controls, to improve system performance during

converter failures.

Two control modes are predefined for each series converter, namely full-control mode

and limited-control mode. In normal situations, the series converters operate in the full-

control mode, which uses the 3rd harmonic component to maintain the DC voltage. When

the shunt converter has a failure, the 3rd harmonic current cannot be injected and the

series converter will operate in the limited-control mode. In the limited-control mode, the

series converter uses the active power at the fundamental frequency to stabilize the DC

voltage. It is also capable of controlling the reactive power injection at the fundamental

frequency.

Due to the over-voltage protection, during a failure, the series converter appears as a

short-circuit to transmission lines. Accordingly, the network becomes asymmetric during

the failure of a series converter because of the asymmetrical voltage injection. To compen-

sate for this asymmetry, a supplementary control is applied to the central controller. The

controller monitors the voltages at the sending and receiving ends and the line current, to

calculate the total voltage injected by all series converters. By comparing this calculated

voltage and the reference voltage generated by the central control, the operation status

of the series converters is known. According to the operation status, the controller can

automatically adjust the reference for each series converter.

The two supplementary controls are verified both in Matlab Simulink and in the ex-

perimental setup. This proves that the supplementary controls can improve DPFC perfor-

mance during converter failures and therefore, the DPFC have relatively high reliability.

• Power oscillation damping

Utilizing the DPFC to damp low-frequency power oscillation is investigated. The DPFC

is used to damp the inter-area oscillatory modes. Because the DPFC can simultaneously

adjust three system parameters, namely the bus voltage, the line impedance and the

transmission angle, a maximum of three POD controllers can be applied to one DPFC.

Within the thesis, the POD controller is designed using the residue method and a two-area

network is used in the case study. From the simulation, it can be seen that the DPFC

can shift three critical oscillatory modes at the same time. Therefore, it can be concluded



160 9.2 Recommendations

that the DPFC has the same capability as the UPFC for power oscillation damping.

• Asymmetrical components compensation

Employing the DPFC for asymmetry compensation is studied. Because of the active

power exchange between the shunt and the series converters, the DPFC can compensate

both active and reactive asymmetry at the fundamental frequency. In addition, since the

series converter is single-phase converter, the DPFC can compensate for both zero and

negative sequence components. Accordingly, the DPFC currently is the most versatile

device for asymmetry compensation among all FACTS devices.

• DPFC feasibility

To explore the feasibility of the DPFC, the design procedure of the DPFC is decided.

According to the procedure, a case study, which is to use DPFC to replace the KEPCO

UPFC in Korea, is investigated. It is found that in order to achieve the same control

capability as the UPFC, the DPFC requires much less material and creates a smaller

footprint. The total weight of the series converter units is approximately 6% of the

transmission line weight. In addition, the reliability of the DPFC is higher than that of

the UPFC.

• DPFC application in a triangle network

The application of the DPFC for power flow control in a real network is studied. The

triangle network between the buses NM, DOD and KBG in the Netherlands is selected.

Due to the existing congestion problem, fixed inductors are connected in series to the

transmission line to limit the current, which exceeds the line’s limit. By using the DPFC

instead of inductors, it is found that the DPFC can dynamically control the power flow

within the triangle network. In addition, the DPFC improves the voltage and angle

stability of the network.

9.2 Recommendations

The thesis shows that the DPFC has a lower cost and should be more reliable than the

UPFC. However, the DPFC also brings about some new problems. The issues that should

be addressed by future research are:

• Communications: Because the series converters operate outdoors, the communi-

cation (wireless or PLC) between the central control and series converters is sus-

ceptible to disturbances, such as lighting or a geomagnetic storm. Accordingly, the




communication should be reliable enough to continue operating in spite of these

disturbances.• Weight reduction of the series converter: Since the series converters are hung

on transmission lines, they result in extra pressure for towers. A lightweight series

converter unit is desirable.

The problem created by the DPFC, which cannot be avoided but can be minimized by

future research is:

• 3rd harmonic current management: The 3rd harmonic components within the

DPFC lead to extra losses in transmission lines and transformers. In this thesis, the

3rd harmonic current within the DPFC is set at a constant value. The magnitude

of the 3rd harmonic current can be managed in a way that it is adjusted according

to the requirement for active power. Consequently, the loss of the DPFC can be

reduced.

Besides the above concerns, additional DPFC applications for utility grid are also inter-

esting for future research:

• Centralized control for multiple DPFC: As the DPFC series converter can

be easily applied to multiple lines, the centralized control of multiple DPFCs is an

interesting potential application.

• Other applications: Besides the two presented applications to utilities, namely

power oscillation damping and asymmetry compensation, the DPFC can be used

for more applications, such as deicing, active filtering or voltage restoration.



164 A.2 Single-phase Park’s Transformation

of [T dq0(θ)] is given by:

[T dq0]−1 =

cos θ − sin θ 1

cos(θ − 2π3

) − sin(θ − 2π3

) 1

cos(θ + 2π3

) − sin(θ + 2π3

) 1

(A.4)

In a symmetical power system, the zero-axis component is 0 and can be neglected.

The power in dq -frame can be calculated as:

S (t) = [vabc]T [iabc]

= [[T dq−abc][vdq]]T [T dq−abc][idq]

= [vdq]T [T dq−abc]T [T dq−abc][idq]

= 3

2[vdq]T [idq]

(A.5)

The factor 3/2 can simply be explained because the amplitude invariant Park’s trans-

formation converts 3-phase to 2-phase where vectors have the same amplitude in both

domains. Therefore, the power in one phase is missing after the transformation. The

factor 3/2 corrects this missing power.

A.2 Single-phase Park’s Transformation

The Park’s transformation is designed for 3-phase system. For single-phase system, vari-

ations are needed. Two single-phase Park’s transformation methods have been proposed

[Sala 04]. The method, which creates a αβ -frame by delaying the single-phase signal by

π/2, is employed here, because it is easy to be implemented [ Zhan 02].With this method, a virtual two-phase system (αβ system) is created from the single-

phase signal. The α signal is the original input signal x and the β signal is created by

applying a π/2 transport delay to x, as shown in Figure A-1. As the α-axis is leading

β -axis by π/2, the delayed signal is the minus of the β -axis.

The transformation from the stationary αβ -frame to rotating dq -frame is is given by:

xd

xq = sin θ cos θ

cos θ − sin θ xα

xβ (A.6)



A PARK’S TRANSFORMATION 165

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

−1

−0.5

0

0.5

1

S i g n a l a m p l i t u d e

X = Xalfa

Xbeta

Xdelay = −Xbeta

Figure A-1: Relationship between x, xαβ , and xdelay

The inverse single-phase transformation is from [xdq] to the single-phase signal x and is

given by:

x = [ sin θ cos θ ][xdq] (A.7)

Components in the β -axis have the same amplitude as in the α-axis, so the power in

single-phase frame is half of the power in αβ -frame. The single-phase power in dq -frame

is given by:

S (t) = v(t) · i(t) = 1

2[vαβ ]

T [iαβ ]

= 1

2

[T αβ −dq]−1[vdq]

T [T αβ −dq]−1[idq]

= 1

2[vdq]T [T αβ −dq][T αβ −dq]−1[idq]

= 1

2[vdq]T [idq]

(A.8)

Note that in both 3-phase and single-phase dq -transformation, the length of the vector

xd + jxq is equals to the amplitude of vector x, but not the RMS value. For the phasor

x =√

2X RMS sin ωt, the length is:

x2

d + x2q =

√ 2X RMS (A.9)



Appendix BSINGLE-PHASE PHASE LOCK LOOP

Single-phase Phase Lock Loop (PLL) plays a important role within the DPFC control.

The topology of the PLL employed in the DPFC is shown in Figure B-1.

single-

phase

dq PI 1/s

x

xd

xq PLL ∆ω ∆θ

1/s

+

+ω0θ 0

θ

Figure B-1: Topology of the single-phase PLL

In the figure, x is the input signal in AC quantity and θ is the frequency and phase

information where θ = t0

ωdt + ϕ. The symbol ω is the angular frequency and ϕ is the

phase angle.

The single-phase PLL is based on the Park’s transformation. If a phasor is projected toitself, its q component will be zero. A rotated phasor is created, whose rotation frequency

is obtained from the q component of the input signal. A PI controller is used to force the

phase created by the PLL to approach the input signal. When the q component xP LLq is

zero, the PLL output is locked with input signal.

xP LLq = sin(ωt + ϕ)cos(ωt + ϕP LL) + sin[(ωt − π

4) + ϕ]sin(ωt + ϕP LL)

= sin(ϕ − ϕP LL)

(B.1)

167



168

To analyze the PLL, the phase angle ϕ of the input AC signal is selected as the PLL

input and ϕP LL is the output of the PLL. According to (B.1), the PLL can be representedby a single-input-single-output system as shown in Figure B-2.

PI 1/s+

-

sin PLLϕ

ϕ PLL

q x

Figure B-2: PLL representation by using phase angles as the input and output

As the difference between ϕ and ϕP LL is small, the sinusoid function in the PLL can

be linearized as sin x = x. Consequently, by applying the Laplace Transformation, the

open-loop transfer-function between ϕ and ϕP LL can be written as:

G(s) =

K is

+ K p

1

s =

K i + sK ps2

(B.2)

Then, the close-loop transfer function of the PLL is:

ϕP LL

ϕ =

G(s)

1 + G(s)

= sK P + K is2 + sK P + K i

(B.3)

As shown, the input and output of the PLL have the same value in steady-state.

However, there is difference during transients and the difference depends on the parameters

of the PLL.



Appendix CNETWORK SIMPLFICATION

C.1 Network Specifications

The structure of the object network is illustrated in Figure C-1. The network consists of

five buses that are operated at 156 kV. The power lines between the bus KBG and DOD

have a congestion problem because their impedance is lower than the rest of network. To

limit the power flow between KBG and DOD, several series inductors with fixed reactance

are inserted into the lines, as shown in Figure C-1.

KBG

RKELT

NMDOD

0 . 5 + j 2

. 7

0 . 6 2

+ j 3 . 5 8

1.04+j6.35

0 . 9 3

+ j 1 . 9 5

1. 4 4 + j 3.

1 7

0. 4 7 + j 0. 9

Extra impedance

j9Ω

Figure C-1: Structure of the object network

The voltage magnitudes, voltages angle and the power consumption or generation of

the five buses are listed in Table C-1, in where the buses with positive power are generation

buses.

169



170 C.2 Network Simplification

DOD ELT KBG NM RK

bus voltage (kV) 158.886 159.43 159.342 158.619 159.257

angle () -6.97 -7.607 -7.977 - 6.764 -7.889

active power (MW) 121.1 -70.6 -184.3 168.2 -26.3

reactive power (MVA) 126.1 73.6 -42.8 -59.1 -56.0

Table C-1: Voltage magnitudes, angles and power consumption or generation of the buses

C.2 Network Simplification

The load buses RK and ELT in the network increase the complexity of the lab realization.

To simplify the network, the loads at these two buses are shifted to the nearby buses

according to line impedances without changing the rest of the network [Grai 94]. Taking

the bus RK for example, the addition load at the bus DOD, which is shifted from RK, is

given by:

S DOD,RK = Z RK,KBG

Z Rk,KBG + Z DOD,RK

S RK (C.1)

where Z RK,KBG and Z DOD,RK are the line impedance between buses in complex number.

Therefore, by shifting the load at bus RK and ELT, the object network is represented by

a triangle network as shown in Figure C-2.

KBG

NMDOD0.52+j3.175

0 . 5 6 + j 3

. 1 4

0 . 4 7 1 5 +

j 0 . 9 8

3 3

j3Ω SKBG+SKBG,RK+SKBG,ELT

SDOD,RK

SDOD SNM,ELT

SNM

Figure C-2: Simplified network

The adapted power consumption and generation of the three buses is listed in Ta-

ble C-2.



C NETWORK SIMPLFICATION 171

DOD KBG NM

active power (MW) 113.8 -243.7 138.0

reactive power (MVA) 117.7 -48.8 -27.3

Table C-2: Power consumption and generation of the simplified network

C.3 PU Values

The object network is scaled to low voltage and power ratings for the experimental setup.

During the scaling, pu values of the network are kept. Table C-3 lists the pu values of the

network, with the voltage base and the power base V base = 156 kV and S base = 250 MVA

respectively.


DOD KBG NM

active power (pu) 0.455 -0.975 0.552

reactive power (pu) 0.471 -0.195 0.109

Line impedance


resistance (10−3pu) 5.24 6.22 5.78

reactance (10−3pu) 10-93 34.89 35.28

Table C-3: Network characters in pu

C.4 Experimental Setup Specifications

Within the experimental setup, the new voltage and power base are V base = 380 V and

S base = 2500 VA. Accordingly, the characters of the scaled network can be recalculated

and listed in Table C-4.

To reduce the complexity of the experimental setup, several approximation of the

scaled network has been made:

• The resistance of the line are neglected.

• The reactance of the line KBG-NM and NM-DOD are the same.



172 C.4 Experimental Setup Specifications


DOD KBG NM

active power (W) 1138 -2437 1380

reactive power (VA) 1177 -488 -273

Line impedance


resistance (Ω) 0.302 0.359 0.334

reactance (Ω) 0.631 2.015 2.038

Table C-4: Scaled network characters

• Bus DOD is selected as the swing bus.

• Voltage magnitude of each bus is the same.

Consequently, the electrical specifications of the experimental network are presented

as shown in Table C-5.

Bus voltage

DOD KBG NMvoltage magnitude (V) 380 380 380

voltage angle () 0 1.2 -0.2

Line impedance


inductance (mH) 2 6 6

Table C-5: Experimental setup network specifications



Appendix D

LIST OF SYMBOLS

Latin Letters

A State matrix -

A Area m2

B Flux density telsa

C Coefficient factor -

C Capacitance F

d Thickness m

E Induced voltage V

f Frequency of power system Hz

I Current A

I Current in row vector A j Imaginary unit -

k Controller parameter -

L Reactance H

L length m

mc Number of the lead-lag blocks -

N Number of turns -

P Active power W

Q Reactive power Var

173



174

R Resistance Ω

R Active damping in the IMC method -ref Reference signal -

ref Reference signal in row vector -

s Complex argument in Laplace transformation -

S Apparent power VA

t Time s

T dq Park’s transformation matrix -

∆u Single input -

V Voltage in phasor value V

V Voltage in row vector V

W Introduced variable in voltage control loop -

X Inductive impedance Ω

∆x State vector -

∆y Single output -

Z Impedance Ω

Greek Letters

α Desired bandwidth of the closed-loop -

θ Transmission angle

θ Angle of the rotation reference frame for Park’s transformation

ω Angular velocity rad/sϕ Power angle

ϕcomp Compensation angle of the POD controller

δ Phase angle of the impedance

λ Eigenvalue of the state matrix -

σ Damping of the oscillation mode -

ξ Relative damping ratio of the oscillation mode -

ρ Density kg/m3

Φ Flux weber



D LIST OF SYMBOLS 175

Superscript

0 Zero sequence component

+ Positive sequence component

− Negative sequence component

P LL Phase lock loop component

Subscript

0 Initial value

1 The fundamental frequency component

3 The 3rd harmonic frequency component

a Phase a

abc abc domain

b Phase b

base Base for pu calculation

c Phase cc Magnetic core

c Control range

d d component in Park’s Transformation

D DOD bus

dc DC side

dq dq domain

gi Cross-section of a core

i ith harmonic frequency componenti Transmission line i

i Integral value for PID control

ii Transmission line ii

I Using current as rotation reference frame

K KBG bus

l Transmission line

lag Lagging time constant for POD controller

lead Leading time constant for POD controller



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LIST OF PUBLICATIONS

Patent

1. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “Power Flow Controller”, Patent, WO

2008/153376 A1.

Journal Papers

1. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “A FACTS Device - Distributed Power

Flow Controller (DPFC)”, Power Electronics, IEEE Transactions on, 2010.

2. Cvoric, D.; de Haan, S.W.H.; Ferreira, B.; Yuan, Z.; “New Three-Phase Inductive

FCL with Common Core and Trifilar Windings”, Power Delivery, IEEE Transac-

tions on, 2010.

Conference Papers

1. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “UPFC with Eliminated Common DC

Link Connection between Shunt and Series Part”, IEEE Power Engineering SocietyGeneral Meeting (PESGM) 2007, Tampa, USA.

2. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “A New FACTS Component - Distributed

Power Flow Controller (DPFC)”, European Conference on Power Electronics and

Applications (EPE) 2007, Aalborg, Denmark.

3. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “A Method of Transmitting Active Power

Between Converters with Eliminated Common DC Link”, IEEE Benelux Young

Research Symposium in Electrical Power Engineering 2008, Eindhoven, the Nether-

lands.

187



188

4. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “A New Concept of Exchanging Active

Power without Common DC Link for Interline Power Flow Controller (S-IPFC)” ,IEEE Power and Energy Society General Meeting (PESGM) 2008, Pittsburgh,

USA.

5. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “A Method to Synchronize Single-phase

Floating with Grid without High Voltage Measurement or High Bandwidth Commu-

nication”, IEEE Power and Energy Society PowerTech 2009, Bucharest, Romania.

6. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “Utilizing Distributed Power Flow Con-

troller (DPFC) for Power Oscillation Damping”, IEEE Power and Energy Society

General Meeting (PESGM) 2009, Calgary, Canada.7. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “Construction and First Result of a Scaled

Transmission System with the Distributed Power Flow Controller (DPFC)”, Euro-

pean Conference on Power Electronics and Applications (EPE) 2009, Barcelona,

Spain.

8. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “DPFC Control during Shunt Converter

Failure”, IEEE Energy Conversion Congress and Exposition (ECCE) 2009, San

Jose, USA.

9. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.; Cvoric, D.: “Utilize Distributed Power

Flow Controller (DPFC) to Compensate Unbalanced 3-phase Currents in Trans-

missions Systems”, Electric Power and Energy Conversion Systems (EPECS) 2009,

Sharjah, United Arab Emirates.

10. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “DPFC design Procedure - a Case Study

Using the KEPCO UPFC as an Example”, International Power Electronics Con-

ference (IPEC) 2010, Sapporo, Japan.

11. Yuan, Z.; de Haan, S.W.H.; Ferreira, B.: “Control Scheme to Improve DPFC

Performance during Series Converter Failures”, IEEE Power and Energy Society

General Meeting (PESGM) 2010, Minneapolis, USA.



CURRICULUM VITAE

ZHIHUI YUAN was born in Hei Long Jiang, China, on 24 Nov 1981. In 2004, he

got his Bachelor of Science degree from Harbin Institute of Technology, majored inElectrical Engineering and Automation.

At the same year, he went to Sweden for the master degree in Chalmers Technology

University. He did his master final thesis in the Power System Group, ETH, Zurich. In

2006, he received the Master of Science degree in Electrical Power Engineering.

Since 2006, he began to work toward his PhD degree in the Electrical Power Processing

(EPP) group, in Delft University of Technology, in the Netherlands. The title of his PhD

project is ‘Active power control in utility grid’, which aims at the development of new,

relatively low-cost methods for power flow control without sacrificing system reliability.This research has been granted a WO patent.

His research interests include Flexible AC Transmission Systems, power system oper-

ation and the grid integration of renewable energy.

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