2016 2017

Hogere Zeevaartschool Antwerpen

Maritime Electricity and Electronics

0.1 Prerequisites

The courses Marine Electrotechnics part1, Marine Electronics Analoge part1and Marine Electronics digital part1 will pursue, Marine Electrotechnics part1 , General Electricity as well as the basics on Thermodynamics and Mechan-ics. The comprehension of these preliminary courses is a premise for successthis year. To test yourself: Electrical Machines, Drives, And Power Systems.Theodore WildiISBN 0-13-196918-8

1. Units

2. Fundamentals of Electricity, Magnetism, and Circuits

3. Fundamentals of Mechanics and Heat

4. Three-Phase Induction Machines

5. Selection and Application of three Phase Induction Machines

6. Equivalent Circuit of the Induction Motor

7. Synchronous Generators

8. Synchronous Motors

• Solve the excersises of aforementioned chapters.These chapters are considered an integral part of the courses MarineElectrotechnics part 2.

• Marine Electronics Analoge part 1 is considered an integral part ofMarine Electronics Analoge part 2.

• Marine Electronics digital part 1 is considered an integral part of Ma-rine Electronics Digital part 2.

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0.2 Conventions

0.2.1 Units

Values and numbers can have a maximum of two lagging zero’s, and can’thave any leading zeros.

10Ω = OK

100Ω = OK

1000Ω = NOK → 1KΩ

0, 1A = NOK → 100mA

0.2.2 Earth ⇔ Ground

Earth

Figure 1: earth symbol

Earth is a direct connection to the earth’s potential. As long as a ship isat sea the hull can be considered as the earth, when the ship is moored theschip’s hull can no longer be considered as earth as it will propably have adifferent potential unless the hull is earthed ,fysically connected to the earth.

0.2.3 Ground

Figure 2: ground symbol

The ground of an electrical circuit is the reference we chose and againstwhich we make our measurements, its our 0 volts or the place where we putthe black lead of our voltmeter.

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0.2.4 Earth Ground

In some cases the chassis or metal case of our appliance is connected to boththe earth and the ground. In this special case we refer to this connection asearth ground. (osciloscopes and power supply’s in the electronics lab).

0.3 Review

0.3.1 Ohm’s law

Figure 3: ohm’s law

i =v1− v2

R

−i =v2− v1

R

Unloaded Voltage Divider

i1 = i2 = i =v1− v2

R1 +R2

vo = v1−R1.i1 = v1−R1.v1− v2

R1 +R2

= v1− R1

R1 +R2.(v1− v2)

= v1− (v1.R1

R1 +R2− v2.

R1

R1 +R2)

vo = v1.R2

R1 +R2+ v2.

R1

R1 +R2

3

Figure 4: Unloaded Voltage Divider

Figure 5: Loaded Voltage Divider

Loaded Voltage Divider

i1 = i2 + i(1)

i1 =v1− voR1

(2)

i2 =vo− v2

R2(3)

With (1),(2) and (3)v1− voR1

=vo− v2

R2+ i

v1

R1− vo

R1=vo

R2− v2

R2+ i

vo

R1+vo

R2=v1

R1+v2

R2− i

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R1.R2

R1.vo+

R1.R2

R2.vo =

R1.R2

R1.v1 +

R1.R2

R2.v2−R1.R2.i

vo = v1.R2

R1 +R2+ v2.

R1

R1 +R2− i. R1.R2

R1 +R2

0.3.2 Capacitor

Figure 6: capacitor i,v relationship

Unit of capacitance C is expressed in Farad.

i = C.dv

dt

v =1

C

∫ t

0i.dt

with S = ddtand 1

S=

∫ t0 dt

i = S.C.v or i = S.C.(v1− v2)

v =1

S.C.i or (v1− v2) =

1

S.C.i

• v can not change instantaneously (initial value)

• i = 0 for DC (perfect insulator) (final value)

• every change of voltage over a capacitor takes time

Reactance

The reactance of a capacitor is its resistance towards AC currents and isexpressed in ohms.

Zc =v1− v2

i=

1

S.C

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Special Case: pure sinusoidal voltage

Zc =1

S.C=

1

ω.C=

1

2.π.f.C

What if f =0 ?

0.3.3 Inductor

Figure 7: inductor i,v relationship

Unit of inductance L is expressed in Henri.

v = L.di

dt

i =1

L

∫ t

0i.dt

with S = ddtand 1

S=

∫ t0 dt

v = v1− v2 = S.L.i

i =1

S.L..(v1− v2)

• i can not change instantaneously (initial value)

• v = 0 for DC (short circuit) (final value)

• every change of current through a capacitor takes time

Reactance

The reactance of an inductor is its resistance towards AC currents and isexpressed in ohms.

ZL =v1− v2

i= S.L

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Special Case: pure sinusoidal voltage

d

dt= ω = S

ZL = ω.L = 2.π.f.L

What if f = 0 ?

0.3.4 Stepresponse

Figure 8: exponential function

• The voltage over a capacitor will change exponentially in response toa unity step function.

• The current through an inductor will change exponentially in responseto a unity step function.

Whe can write an exponential function as:

x = A+B.e−tτ

with:

• A and B are constants

• t =time in seconds

• τ is the time constant in seconds

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startvalue at a time t = 0

x = xo = A+B

final value at a time t = ∞

x = x∞ = A

Then we can write:B = xo− A = xo− x∞

So:x = x∞+ (xo− x∞).e−

tτ

Or:x = x∞− (x∞− xo).e−

tτ

Voltage over a capacitor in response to a step function

Figure 9: Voltage over a capacitor in response to a step function

x = x∞− (x∞− xo).e−tτ

vc = v2− (v2− v1).e−t

R.C

We can prove that R.C is a time constant in seconds:

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• 1volt = 1ampere.1ohm

• 1coulomb = 1farad.1volt

• 1ampere = 1coulomb1seconde

τ = C.R = Farad.ohm =coulomb

volt.volt

ampere=coulomb

ampere= coulomb.

seconds

coulomb= seconds

Current through an induction in response to a step function

Figure 10: Current through an induction in response to a step function

io = 0

i

∞=v

R

x = x∞− (x∞− xo).e−tτ

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iL =v

R− v

R.e

− tLR

We can prove that LR

is a time function in seconds: With:

H =m2.kg

C2=m2.kg

s2.A2=

J

A2=T.m2

A=Wb

A=V.s

A=s2

F= Ω.s

with:

• A= ampere

• C = Coulomb

• F = Farad

• J = Joule

• kg = kilogram

• m = meter

• s = second

• Wb = Weber

• T = tesla

• V = volt

• Ω=ohm

So:L

R= τ =

Henri

Ω=

Ω.seconds

Ω= seconds

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