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POWER FLOWS

EQUATIONS for

ALTERNATOR & MOTOR

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Fig A shows the circuit model of a phase cylindrical rotor

synchronous generator.Let, V = terminal voltage per phase,

Ef= excitation voltage per phase,

Ia

= armature current,

= phase angle between Efand V

The phasor diagram at lagging power factor is shown in

fig B.

The synchronous impedance is given by Zs = Ra +j XS =Zs

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Fig. A Fig. B

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Fig C shows the impedance

triangle.

Let the subscripts i, o, g and m

denote input, output, generator and

motor respectively.

By KVL in Fig. A,

S

a

ZZ

a

S

Z

X

R

R

X

1

1

tan90

tan

s

f

a

asf

Z

VEI

IZVE

Fig. C

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Complex Power Output Of The Generator

Per Phase (Sog )

Zs

Z

s

Z

s

f

Z

s

f

ogog

Z

s

Z

s

f

og

Z

s

Z

s

f

og

Zs

f

s

f

aogogog

Z

VjZ

V

Z

VE

jZ

VE

jQP

Z

V

Z

VES

Z

V

Z

EVS

Z

VEV

Z

VEVVIjQPS

sincossincos

0

00

22

2

*

**

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Real Power Output Of The Generator Per Phase

(Pog ) = Electrical Power Developed by the

Generator

RZ

V

Z

VEorP

RZ

V

Z

VEP

butR

Z

V

Z

VEP

ZZ

V

Z

VEP

S

Z

s

f

og

S

Z

s

f

og

ZZ

S

Z

s

f

og

s

ZZ

s

Z

s

f

og

2

2

2

2

2

2

2

sin

)(90cos

90cos

Rcossincecoscos

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Reactive Power Output Of The Generator Per

Phase (Qog )

s22

s2

2

s2

2

s

2

Xcos

X)(90sin

90Xsin

Xsinsincesinsin

S

Z

s

fog

S

Z

s

f

og

ZZ

S

Z

s

f

og

s

ZZ

s

Z

s

f

og

Z

V

Z

VEQor

Z

V

Z

VEQ

but

Z

V

Z

VEQ

ZZV

ZVEQ

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Complex Power Input Of The Generator

Per Phase (Sig )

Z

s

fZ

s

fZ

s

fZ

s

figig

Z

s

f

Z

s

f

ig

Z

s

Z

s

f

fig

Zs

f

f

s

f

fafigigig

Z

VEj

Z

VE

Z

Ej

Z

EjQP

Z

VE

Z

ES

Z

V

Z

EES

Z

VEE

Z

VEEIEjQPS

sincossincos

)(

0

22

2

**

*

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Real Power Input Of The Generator Per

Phase (Pig)

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Reactive Power Input Of The Generator

Per Phase (Qig )

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Prove difference between input output must be equalto ohmic loss.

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Maximum Power Output Of The Generator Per

Phase (Pog)(max)

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Maximum Power Input Of The Generator Per

Phase (Pig)(max)

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Power Flow Equations For A Generator With

Armature Resistance Neglected