Page 103 - Solutions Manual to accompany Electric Machinery Fundamentals


300 kW   9125 kW  0.15 MW/Hz f sys  19140 kW  0.319 MW/Hz f
sys
 0.469 MW/Hz f sys  9125 kW 19140 kW 300 kW


27,965 kW
f   59.627 Hz
sys
0.469 MW/Hz
(c) The power supplied by generator 1 is
P  1 s P 1  f nl1  f sys    0.15 MW/Hz 60.833 Hz 59.627 Hz  181 kW

The power supplied by generator 2 is

P  2 P 2  f nl2  f sys   s  0.319 MW/Hz 60.0 Hz 59.627 Hz  119 kW

(d) The get the system frequency to 60 Hz, the operators of the generators must increase the no-load
frequency setpoints of both generators simultaneously. That action will increase thefrequency of the
system without changing the power sharing between the generators.

(e) If the terminal voltage is 460 V, the operators of the generators must increase the field currents on
both generators simultaneously. That action will increase the terminal voltages of the system without
changing the reactive power sharing between the generators.
4-10. Three physically identical synchronous generators are operating in parallel. They are all rated for a full
load of 100 MW at 0.8 PF lagging. The no-load frequency of generator A is 61 Hz, and its speed droop is
3 percent. The no-load frequency of generator B is 61.5 Hz, and its speed droop is 3.4 percent. The no-
load frequency of generator C is 60.5 Hz, and its speed droop is 2.6 percent.
(a) If a total load consisting of 230 MW is being supplied by this power system, what will the system
frequency be and how will the power be shared among the three generators?

(b) Create a plot showing the power supplied by each generator as a function of the total power
supplied to all loads (you may use MATLAB to create this plot). At what load does one of the
generators exceed its ratings? Which generator exceeds its ratings first?
(c) Is this power sharing in (a) acceptable? Why or why not?

(d) What actions could an operator take to improve the real power sharing among these generators?
SOLUTION

(a) Speed droop is defined as
n  n f  f
SD  nl fl  100%  nl fl  100%
n fl f fl

f
so f  SD nl
fl
100  1
Thus, the full-load frequencies of generators A, B, and C are
f 61 Hz
f  nl,A   59.223 Hz
fl,A SD A  1 3.0  1
100 100
f 61.5 Hz
f  nl,B   59.478 Hz
fl,B SD B  1 3.4  1
100 100

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