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React ive Power Cont rol of Autonomous Wind-DieselHybr id Power Systems Using Simul inkR. C. Bansal

a& T. S. Bhatti

b

aElect rical and Elect ronics Engineering Division, School of Engineering and Physics, The

Universi t y of t he South Paci f ic, Suva, Fi j ib

Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi,

IndiaVersion of r ecord f irst p ubli shed: 19 Sep 2007.

To cite this art icle: R. C. Bansal & T. S. Bhat t i (2007): React ive Power Cont rol of Autonom ous Wind-Diesel Hybri d PowerSyst ems Using Sim ulink , Elect ric Power Component s and Syst ems, 35:12, 1345-1366

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Electric Power Componen ts an d S ystems, 35:13451366, 2007

Copyright Taylor & Francis Group, LLC

ISSN: 1532-5008 print/1532-5016 online

DOI: 10.1080/15325000701426096

Reactive Power Control of AutonomousWind-Diesel Hybrid Power Systems Using Simulink

R. C. BANSAL

Electrical and Electronics Engineering Division

School of Engineering and Physics

The University of the South Pacific

Suva, Fiji

T. S. BHATTI

Centre for Energy Studies

Indian Institute of Technology, Delhi

Hauz Khas, New Delhi, India

Abstract This article presents reactive power control of autonomous wind-dieselhybrid power system for realistic load disturbance using Simulink. The simulationblock diagram of wind-diesel, multi-wind-diesel, and wind-multi-diesel hybrid systembased on Simulink is developed. Reactive power control performance is comparedusing three different types of static VAR compensator (SVC) models. Reactive power

performance is also compared for wind-diesel, multi-wind-diesel, and wind-multi-diesel hybrid power systems.

Keywords autonomous wind-diesel hybrid power system, diesel generator set, in-

duction generator, multi-wind-diesel, reactive power compensation, Simulink, staticvar compensator, wind-multi-diesel

1. Introduction

In recent years there has been continuous growth of power generation from non-conven-

tional energy sources. The main advantages of non-conventional sources of power gener-

ation are no fuel consumption in most cases, sustainable, and eco-friendly. The major dis-

advantage with these energy sources is that they are generally intermittent or fluctuating in

nature.

The non-conventional sources such as wind and micro/mini hydro, etc. are generally

integrated with diesel system to increase the reliability of the system to supply power to

the isolated loads. Such systems are called isolated/autonomous hybrid power systems.

In hybrid power systems, there may be more than one type of electrical generators [1,2]. In such circumstances it is normal, though not essential, for generator(s), usually on

Received 28 September 2006; accepted 13 March 2007.Address correspondence to Prof. R. Bansal, Electrical and Electronics Engineering Divi-

sion, School of Engineering and Physics, Laucala Campus, Private Mail Bag, Suva, Fiji. E-mail:[email protected]

1345


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1346 R. Bansal and T. Bhatti

Nomenclature

A, B , C system, control, and disturbance matrix, respectively

, thyristor firing angle and small deviation in thyristor firing angle,

respectively

power angle between terminal voltage and armature internal emf

BSVC, BSVC reactive susceptance of the SVC and small change in its value,

respectively

EM, EM electromagnetic energy stored in induction generator (IG) and

small deviation in energy stored, respectively

Efd 1, Eq1, E0

q1,

Efd 2 , Eq2, E0

q2

small change in voltages of exciter, internal armature emf under

steady state and transient conditions of synchronous generator

(SG) 1 and 2 respectively

KA, KE , KF, KR,

K , KV

amplifier, exciter, stabilizer, VAR regulator, thyristor firing, and

hybrid power system gain constants, respectively

KP, KI proportional and integral controller gain constants of the VAR

regulator, respectively

IG

efficiency of the IG

PI W, PIG , PS G real power input to the IG, real power generated by IG and SG,

respectively

PL, QL real and reactive power load demand, respectively

QI G, QI G 1, QI G 2 reactive power required by IG, IG 1, and IG 2, respectively

QS G, QS G 1, QS G 2 reactive power generated by SG, SG 1, and SG 2, respectively

QSVC reactive power generated by SVC

Qc rating of the SVC

QR system reactive power rating

r1, x1, r0

2, x0

2 stator resistance, stator reactance, rotor resistance and rotor re-

actance referred to primary side of IG, respectively

Req , Xeq , Xm equivalent resistance, equivalent reactance and magnetizing re-

actance of the IG, respectively

s slip of the IG

Td SVC average dead time of zero crossing in a three phase systemT thyristor firing delay time

T1, T2, T3, T4 time constants of the SVC regulator of lead-lag type

TE , TF, TR, TV exciter, stabilizer, regulator, and hybrid power system time con-

stants, respectively

T0do

direct axis open circuit transient time constant

V system terminal voltage

V, Vref small change in terminal and reference voltage, respectively

Va1, Va2,

Vf 1, Vf 2

small change in the amplifier output of amplified 1 and 2, and

exciter feedback voltages of exciter 1 and 2, respectively

xd, x0

ddirect axis reactance of SG under steady state and transient state

conditions, respectively

x, u, p state, control, and disturbance vector, respectively

the diesel, to be synchronous, and wind turbine generator(s) to be asynchronous (induc-

tion) [2]. An IG offers many advantages over a conventional SG, like reduced unit cost,

ruggedness, brushless (in squirrel cage construction), absence of separate DC source, ease

of maintenance, self-protection against severe overloads and short circuits, etc. [36]. A

major disadvantage of an IG is that it requires reactive power support for its operation.


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Reactive Power Control of Hybrid Power Systems 1347

In addition, most of the loads are also inductive in nature. The mismatch in generation

and consumption of reactive power can cause a serious problem of large voltage fluctu-

ations at generator terminals. A number of FACTS (flexible AC transmission systems)

devices have been developed to provide the reactive power to the system. SVC is one of

the FACTS device that has been used in conventional power systems, and can also beemployed in isolated power systems.

In recent times, there has been large number of application of Matlab/Simulink

developed by the Math Works Inc., for solving various power system problems [710].

With the addition of several toolboxes and Simulink, Matlab provides an interactive

environment with hundreds of reliable and accurate built in functions. Simulink is a

window-based package built in the Matlab software and consists of a library of basic

building blocks, which can be combined to form a dynamic model.

This article presents reactive power control of autonomous wind-diesel hybrid power

system for realistic (step plus stochastic) load disturbance using Simulink. In the con-

sidered wind-diesel hybrid system (transfer function block diagram shown in Figure 1),

SG along with an IEEE type-I excitation system is considered to be connected to diesel

generator (DG) set and IG on wind system. The DG set acts as a local grid for the

wind energy conversion system. The system has a SVC to provide the required reactive

power in addition to the reactive power generated by the SG. Simulink block diagrams

for autonomous wind-diesel, multi-wind-diesel (2 wind-1 diesel), and wind-multi-diesel

(1 wind-2 diesel) hybrid power systems have been developed as shown in Figures 2, 3,

and 4, respectively, to compare their reactive power requirement performance. Figures 3

and 4 can be developed by incorporating the components of multiplicity of wind and

diesel system, respectively.

Simulation block diagrams of three different types of SVC models have been used to

compare their performances. The basic difference in the transfer function block diagrams

is the type of VAR regulator used. In SVC type-I [11, 12] the VAR regulator is an

amplifier with a gain and time constant. The regulator in SVC type-II [13, 14] is a twin

lead-lag type for providing compensation for the time delays in the firing circuit and due

to phase sequence dead time delay of zero crossing. The VAR regulator is proportionalplus integral in SVC type-III [15, 16]. The Simulink block diagrams of IEEE type-I

excitation system and SVC type-I, -II, and -III have been shown in Figure 5(a), 5(b),

5(c), and 5(d), respectively. The advantage of simulation block diagram is that a block

diagram containing many elements can be replaced by a single block having input and

output terminals, e.g., SVC and excitation system in Figures 24 have been shown by

single block.

2. Mathematical Modeling of Wind-Diesel Hybrid System

Detailed mathematical modeling of autonomous wind-diesel hybrid power system based

on power equations has been presented in [1719]. System data considered are given

in Appendix 1. Small changes in real power are mainly dependent upon the frequency,

whereas small change in reactive power is mainly dependent on voltage [20]. The ex-citation time constant is much smaller than the prime mover time constant, its transient

decay much faster, and does not affect the load frequency control (LFC) dynamic. Thus,

cross coupling between LFC and AVR loop is negligible. The reactive power balance

equation of the system under steady state condition is

QS G C QSVC D QL C QI G (1)


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Figure 1. Transfer-function block diagram for reactive power control of wind-diesel autonomoushybrid power system.


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Figure 2. Simulation block diagram of wind-diesel autonomous hybrid power system for step plus

stochastic disturbance.


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Figure 3. Simulation block diagram of multi-wind-diesel autonomous hybrid power system for

step plus stochastic disturbance.


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Figure 4. Simulation block diagram of wind-multi-diesel autonomous hybrid power system for

step plus stochastic disturbance.


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Figure 5. Simulation block diagram of (a) IEEE type-I exciter, (b) SVC type-I, (c) SVC type-II,

and (d) SVC type-III.


10/23


For the small incremental reactive power balance analysis of the hybrid system, (1) in

Laplace form can be written as

V.s/ D fKV=.1 C sTV/gfQS G .s/ C QSVC.s/ QL.s/ QI G .s/g (2)

KV D1

DV(3)

TV D2HR

DVV0(4)

where V0 is the nominal value of system voltage, HR is a constant of the system and its

unit is s and its value depends upon the constant Kr (considering that system reactive

power rating is Kr times the rated magnetizing reactive power of the IG), DV is the small

increase in reactive power loads with small increase voltage, i.e., DV D @QL=@V p.u.

kVAR/p.u. kV. The parameter DV can be found empirically. KV =.1 C sTV/ is transfer

function of hybrid power system. The values of KV and TV can be computed using

(3) and (4), respectively, with the data given in Appendix 1, and their values have been

shown in Figures 2, 3, and 4. The values of KV and TV remain the same with SVC

type-I, type-II, and type-III for wind-diesel hybrid power system. The following section

presents the mathematical modeling of various components of hybrid systems.

2.1. The Flux Linkage Equations

The flux linkage equation of the round rotor synchronous machine for small perturbation

is [21]

d

dtE0q D

Efd Eq

T0do

(5)

In (5), Eq is given by

Eq Dxd

x0d

E0q .xd x

0

d/

x0d

cos V (6)

For small changes (5), using (6) in Laplace transform form can be written as

.1 C sTG/E0

q .s/ D K1Efd .s/ C K2V.s/ (7)

where

TG Dx0

dT0

do

xd(8)

K1 D x0d=xd (9)

K2 D f.xd x0d/ cos g=xd (10)

The values of K1 (K11 and K12 in case of wind-multi-diesel system) and K2 (K21

and K22 in case of wind-multi-diesel system) can be computed using (9) and (10),

respectively, with the data given in Appendix 1, and their values have been shown in

Figures 2, 3, and 4. The values of K1 and K2 remain the same with SVC type-I, type-II,

and type-III for wind-diesel hybrid power system.


11/23


2.2. The Synchronous Generator Equations

Under transient condition QSG is given by [20]

QS G D E0

qV cos V2

x0d

(11)

For small perturbation (11) can be written as

QS G DV cos

x0d

E0q CE 0q cos 2V

x0d

V (12)

In Laplace transform (12) can be written as

QS G .s/ D K3E0

q.s/ C K4V.s/ (13)

where

K3 D .V cos /=X0d (14)

and

K4 D .E0q cos 2V /=x0

d (15)

The values of K3 (K31 and K32 in wind-multi-diesel system) and K4 (K41 and

K42 in wind-multi-diesel system) can be computed using (14) and (15), respectively,

with the data given in Appendix 1, and their values have been shown in Figures 2, 3,

and 4. The values of K3 and K4 remain the same with SVC type-I, type-II, and type-III

for wind-diesel hybrid power system.

2.3. IEEE Type-1 Excitation System Equations

IEEE type-1 excitation system [22], as shown in Figure 5(a), is considered for the syn-

chronous generator of the hybrid system. From the block diagram, the transfer function

equations neglecting saturation function (SF) can be written as

Efd.s/ D1

KE C sTEVa.s/ (16)

Va.s/ DKA

1 C sTA V.s/

KF

TFEfd .s/ C Vref.s/

(17)

Vf .s/ DKF=TF

1 C sTFEfd.s/ (18)

The values of transfer functions of amplifier, exciter, and stabilizing circuit, as shown

in Figure 5(a), are obtained using the data of Appendix 1. This excitation system has

been represented by a single block in Figures 24.


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2.4. The Induction Generator Equations

The small deviation in reactive power absorbed by the IG by neglecting the effect of

variation in reactive power with the variation of slip/speed (constant slip/speed model)

and by considering the effect of variation in reactive power with variation in slip/speed(variable slip/speed model) can be written as [1719]

QIG .s/ D K5V.s/ (19)

where

K5 D2V Xeq

R2Y C X2eq

(20)

QIG .s/ D K6PI W.s/ C K7V.s/ (21)

where

K6 C

Xeq

RP .R2Y C X2eq /=2RY (22)

K7 D2V

R2Y

C X2eq

"Xeq

RPXeq

fRP .R2Y

C X2eq/=2RYg

#(23)

where

RP Dr 02s

.1 s/ (24)

RY D RP Req (25)

Req D r1 C r0

2 (26)

Xeq D x1 C x0

2 (27)

This article considers the variable slip model of IG. The values of K6 (K61 and K62

in multi-wind-diesel system) and K7 (K71 and K72 in multi-wind-diesel system) can

be computed using (22) and (23), respectively, with the data given in Appendix 1, and

their values have been shown in Figures 2, 3, and 4. The values of K6 and K7 remainthe same with SVC type-I, type-II, and type-III for wind-diesel hybrid power system.

2.5. SVC Equations

The reactive power supplied by the SVC is given by [23]

QSVC D V2BSVC (28)

For small perturbation, (28) can be written in Laplace transform form as

QSVC.s/ D K8V.s/ C K9BSVC.s/ (29)

where

K8 D 2VBSVC (30)


13/23


and

K9 D V2 (31)

The state equations of a SVC type-I in Laplace transform can be written as

BSVC.s/ D1

1 C sTdB0SVC.s/ (32)

B0SVC.s/ DK

1 C sT.s/ (33)

.s/ DKR

1 C sTR.Vref.s/ V.s// (34)

The state equations of a SVC type-II in Laplace transform can be written as

01.s/ D1 T2=T4

1 C sT4

0.s/ (35)

02.s/ DKR.1 T1=T3/

1 C sT3.Vref.s/ V.s// (36)

where

0.s/ D 02.s/ C KRT1

T3.Vref.s/ V.s// (37)

.s/ D 01.s/ CT2

T4.0.s// (38)

The state equations of a SVC type-III in Laplace transform can be written as

0.s/ D KIs

fVref.s/ V.s/g (39)

where

.s/ D 0.s/ C KPfVref.s/ V.s/g (40)

Equations (32) and (33) remain the same in SVC type-II and type-III.

The values of K8 and K9 can be computed using (30) and (31), respectively, with

the data given in Appendix 1, and their values have been shown in Figures 24. The

values of K8 and K9 remain the same with SVC type-I, type-II, and type-III for wind-

diesel hybrid power system. VAR gain KR in SVC type-I and type-II; and KP and KIin SVC type-III have been optimized and their values have been shown in Figures 5(b),

5(c), and 5(d), respectively. Dynamic responses of hybrid system have been shown in

Figures 610 using optimum settings of the gain parameters of the SVC.Based on the above mathematical equations, Simulink block diagram of wind-diesel,

2 wind-1 diesel, 1 wind-2 diesel isolated hybrid power system have been developed as

shown in Figures 2, 3, and 4, respectively. The state space equations can be written in a

standard form for load voltage control system as

Px D Ax C Bu C Cp (41)


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Figure 6. Dynamic responses of the wind-diesel autonomous hybrid power system with SVC

type-I for 1% realistic increase in reactive power load plus 1% step increase in input wind power.


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Figure 7. Dynamic responses of the wind-diesel autonomous hybrid power system with SVC

type-II for 1% realistic increase in reactive power load plus 1% step increase in input wind power.


16/23


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Figure 9. Dynamic responses of the multi-wind-diesel autonomous hybrid power system with SVC

type-II for 1% realistic increase in reactive power load plus 1% step increase in input wind power

of both wind machines.


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Figure 10. Dynamic responses of the wind-multi-diesel autonomous hybrid power system with

SVC type-II for 1% realistic increase in reactive power load plus 1% step increase in input wind

power.


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For the autonomous wind-diesel system with SVC type-I, II, and III, 2 wind-1 diesel

with SVC type-II, and 1 wind-2 diesel with SVC type-II hybrid power system state space

equations can be written as

2.6. Wind-diesel System

State space equations with SVC type-I

Px D Efd Va Vf E0

q BSVC B0

SVC V T

u D Vref

p D QL PI WT (42)

State space equations with SVC type-II

Px D Efd Va Vf E0

q BSVC B0

SVC 0

1 0

2 V T

u D Vref

p D QL PI WT (43)

State space equations with SVC type-III

Px D Efd Va Vf E0

q BSVC B0

SVC 0 V T

u D Vref

p D QL PI WT (44)

2 Wind-1 diesel system with SVC type-II

Px D Efd Va Vf E0

q BSVC B0

SVC 0

1 0

2 V T

u D Vref

p D QL PI W 1 PI W 2T (45)

1 Wind-2 diesel system with SVC type-II

Px D Efd 1 Va1 Vf 1 E0

q1 Efd 2 Va2 Vf 2 E0

q2

BSVC B0

SVC 0

1 0

2 V T

u D Vref

p D QL PI W T (46)

Elements of matrices A, B, and C can be obtained from above mathematical model-

ing/simulation block diagrams of Figures 15.


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3. Simulation Results and Discussions

In this section, dynamic responses of wind-diesel hybrid power systems are presented.

In practical situation variation in reactive power load is not in step, but the variation

is realistic (step plus stochastic) in nature. There are number of realistic disturbancesavailable in Matlab/Simulink toolbox to simulate the realistic situation. In the present

case, step plus stochastic load disturbances, i.e., step plus normally (Gaussian) distributed

random signal, has been considered for the simulation of different configurations of

autonomous hybrid power systems and stochastic disturbance is properly adjusted by

multiplying suitable value of constant K10, as shown in Figures 24. The dynamic

responses of some of the system variables are shown for the optimum gain settings for

the autonomous hybrid power systems and are compared in terms of first swing amplitude

and settling time, etc.

The dynamic responses for 1% realistic increase in reactive power load plus 1%

step increase in input wind power with SVC type-I, type-II, and type-III are shown

in Figures 6, 7, and 8, respectively. Figures 9 and 10 show the dynamic responses

for 1% realistic increase in reactive power load plus 1% step increase in input wind

power with SVC type-II for multi-wind-diesel and wind-multi-diesel hybrid power systemrespectively. Figures 68 show the small deviations in terminal voltage ( V), reactive

power supplied by SVC (QSVC), reactive power supplied by synchronous generator

(QSG ), and reactive power absorbed by induction generator (QI G), in parts (a), (b),

(c), and (d), respectively. Figure 9 shows the small deviations in V, QSVC, QS G , and

power absorbed by induction generators (QI G 1 and QIG 2); and Figure 10 shows

the small deviations in V, QSVC, small deviations in power supplied by synchronous

generators (QSG 1, QS G 2) and QI G in parts (a), (b), (c), (d), and (e), respectively.

To get the dynamic responses with SVC type-II and type-III, SVC type-I in the simulation

block diagram can be replaced by SVC type-II and type-III of Figures 5(c) and 5(d),

respectively, in Figures 24. The maximum peak deviations of different parameters of

hybrid power systems have been presented in Table 1.

From Figures 610, it is observed that initially the synchronous generator provides

the reactive power required by the load, but substantially it is met by the SVC alone, andtherefore the steady state values of V and QS G become zero. It is also found from

Table 1 that the respective peak deviations are less with SVC type-II and SVC type-

III as compared with SVC type-I. The settling time is about 0.015 sec. for the system

responses with SVC type-II, and SVC type-III, but with SVC type-I it is about 0.15 sec.

Table 1

The peak deviations of different parameters of wind-diesel hybrid system

System and

SVC type V QSVC QSG QIG

Wind-diesel, I 0.00187 0.02592 0.01374 0.00321

Wind-diesel, II 0.00184 0.02089 0.01356 0.00320

Wind-diesel, III 0.00184 0.02102 0.01356 0.00320

2 Wind-1 diesel, II 0.00203 0.02183 0.01438 0.00322 (IG 1)0.00071 (IG 2)

1 Wind-2 diesel, II 0.00087 0.01947 0.00618 (SG 1) 0.00308

0.00724 (SG 2)


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Performance of SVC type-II and type-III is better than SVC type-I in terms of first peak

deviations and settling time.

It is also observed from Figures 9 and 10 that the settling time remains almost same

as in previous cases. It is also seen that multiplicity in the wind power generation reduces

the reactive power performance of the system whereas multiplicity in the diesel generatorsystem improves the same. It is further observed from Figures 9 and 10 that performance

of SVC type-II and type-III is better than SVC type-I.

4. Conclusions

This article has presented the effectiveness of the application of Simulink tool for reactive

power control of autonomous wind-diesel hybrid power systems. Simulink is very effec-

tive and easy for studying and comparing the performance of the systems with different

types components, e.g., various types of SVCs and different types of disturbances, etc.

A reactive power control study of sample wind-diesel isolated hybrid power system with

three types of SVCs and multi-wind-diesel, wind-multi-diesel hybrid systems with SVC

type-II have been presented in this article. It is seen that performance of SVC type-II and

type-III is better than SVC type-I in terms of first peak deviations and settling time. It is

also observed that multiplicity in the wind power generation reduces the reactive power

performance of the system whereas multiplicity in the diesel generator system improves

the same.

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Appendix 1

The data of the wind-diesel, multi-wind-diesel, wind-multi-diesel hybrid power system,

system capacity/load, reactive power, synchronous generator, induction generator, exci-

tation system, and the SVCs under consideration are as follows in Table 2.

Table 2

Parameters of hybrid systems

Multi-wind-diesel

system

Wind-multi-diesel

system

System parameter

Wind-diesel

system IG 1 IG 2 SG 1 SG 2

System capacity/load

Wind capacity (kW) 150 150 50 150

Diesel capacity (kW) 150 150 150 75

Load (kW) 250 300 300

Base power (kVA) 250 300 300

(continued)


23/23


Table 2

(Continued)

Multi-wind-diesel

system

Wind-multi-diesel

system

System parameter

Wind-diesel

system IG 1 IG 2 SG 1 SG 2

Synchronous generator

PS G (p.u. kW) 0.4 0.333 0.333 0.1667

QSG (p.u. kVAR) 0.2 0.162 0.162 0.081

Eq (p.u.) 1.1136 1.1242 1.1242 1.1083 () 21.05 17.2483 17.2483 6.91

E 0q (p.u.) 0.9603 0.9804 0.9804 1.01

V (p.u.) 1.0 1.0 1.0 1.0

xd (p.u.) 1.0 1.0 1.0 0.8

x0d

(p.u.) 0.15 0.15 0.15 0.12

T0do

(s) 5.0 5.0 5.0 5.0

Induction generator

PI G (p.u. kW) 0.6 0.5 0.1667 0.5

QIG (p.u. kVAR) 0.189 0.1343 0.0426 0.1343

PI W (p.u. kW) 0.75 0.63 0.21 0.63

IG (%) 80 80 80 80

r1 D r0

2 (p.u.) 0.19 0.19 0.55 0.19

x1 D x0

2 (p.u.) 0.56 0.56 1.6 0.56

s (%) 4.1 3.49 3.37 3.49

Load

PL (p.u. kW) 1.0 1.0 1.0

QL (p.u. kVAR) 0.75 0.75 0.75

pf (lag) 0.8 0.8 0.8

Reactive power data

QSVC (p.u. kVAR) 0.498 0.7649 0.6413

Qc (p.u. kVAR) 0.5727 0.87961 0.7375

(rad.) 2.4440 2.4452 2.45568IEEE type-I excitation system

KA 40 40 40

TA (s) 0.05 0.05 0.05

KF 0.5 0.5 0.5

TF (s) 0.715 0.715 0.715KE 1.0 1.0 1.0

SF (s) 0.0 0.0 0.0

TE (s) 0.55 0.55 0.55

SVC data

SVC type-I

T (s) 0.005 0.005 0.005Td (s) 0.00167 0.00167 0.00167

TR (s) 0.715 0.715 0.715

SVC type-IIT (s) 0.005 0.005 0.005

Td (s) 0.00167 0.00167 0.00167

T1 D T2 D T3 D T4 (s) 0.715 0.715 0.715

SVC type-III

T (s) 0.005 0.005 0.005

Td (s) 0.00167 0.00167 0.00167

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