Synchronous Generator
Capability Curve
Generator Capability Curves (1)
(1) Stator Copper Loss (stator heating):
PSCL  3I R
2
A s
The maximum allowable heating of the stator sets a maximum
phase current IA for the machine. It’s equivalent to set a maximum
apparent power for the machine. (Power factor is irrelevant.)
(2) Rotor Copper Loss (rotor heating):
PRCL  IF2 RF
The maximum allowable heating of the rotor sets a maximum
field current IF for the machine. It’s equivalent to set a maximum
EA for the machine.
(3) Prime-mover’s Power Limit.
Generator Capability Curves (2)
E A  V  jX s I A
(rotor heating)
(stator heating)
rotor field current sets the rated power factor
Generator Capability Curves (3)
E A  V  jX s I A
Assume V keeps rated value. Multiply the above figure by
P
Q
3V 
X
S
Generator Capability Curves (4)
Q
P
P
Q
flip
capability curve
Generator Capability Curves (5)
Q
P
Add prime mover’s power limit (real power)
Example 3 (1)
A 480V, 50 Hz, Y connected, six pole synchronous generator is rated at 50 kVA at 0.8 PF lagging. It
has a synchronous reactance of 1.0  per phase. Assume that this generator is connected to a steam
turbine capable of supplying up to 45 kW. The friction and windage losses are 1.5 kW, and the core
losses are 1.0 kW.
(a)
(b)
(c)
(d)
Sketch the capability curve for this generator, including the prime-mover power limit.
Can this generator supply a line current of 56 A at 0.7 PF lagging? Why or why not?
What is the maximum amount of reactive power this generator can produce?
If the generator supplies 30 kW of real power, what is the maximum amount of reactive power that
can be simultaneously supplied?
sg3.m
Example 3 (2)