Page 117 - Solutions Manual to accompany Electric Machinery Fundamentals

4-25. Assume that the generator’s field current is adjusted so that the generator supplies rated voltage at the
rated load current and power factor. If the field current and the magnitude of the load current are held
constant, how will the terminal voltage change as the load power factor varies from 0.9 PF lagging to 0.9
PF leading? Make a plot of the terminal voltage versus the load impedance angle.
SOLUTION If the field current is held constant, then the magnitude of E A will be constant, although its
angle  will vary. Also, the magnitude of the armature current is constant. Since we also know R A , X S ,

and the current angle , we know enough to find the phase voltage V  , and therefore the terminal voltage
V T . At lagging power factors, V  can be found from the following relationships:
E
A




 V  jX I
S A

I R I
A
A
A
By the Pythagorean Theorem,
2
E A 2    R A I A cos  X S I A sin  V  2  X S I A cos  R A I S sin 
V  E A 2   S I A cos   R A I S sin  X 2  R A I A cos   X S I A sin 


At unity power factor, V  can be found from the following relationships:
E
A

jX I
S A

I V R I
A  A A
By the Pythagorean Theorem,
E A 2   2 V  S A 2  X I

V  A 2   E S I A X 2


At leading power factors, V  can be found from the following relationships:
E
A

jX I
S A 
I
A R I
  A A 

V

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