Page 104 - Solutions Manual to accompany Electric Machinery Fundamentals

f 60.5 Hz
f  nl,C   58.967 Hz
fl,C SD C  1 2.6  1
100 100
and the slopes of the power-frequency curves are:
100 MW
S   56.27 MW/Hz
PA

61 Hz 59.223 Hz
100 MW
S   49.46 MW/Hz
PB

61.5 Hz 59.478 Hz
100 MW
S   65.23 MW/Hz
PC

60.5 Hz 58.967 Hz
(a) The total load is 230 MW, so the system frequency is
P LOAD  s PA  f nlA  f sys  s PB  f nlB  f sys  s PC  f nlC  f sys 
230 MW  56.27 61.0   f sys  49.46 61.5   f sys  65.23 60.5   f sys 





230 MW 3433 56.27 f sys  3042 49.46 f sys  3946 65.23 f
sys
170.96 f sys  10191
f sys  59.61 Hz
The power supplied by each generator will be
P   f  f   s  56.27 MW/Hz 61.0 Hz 59.61 Hz   78.2 MW
A PA nlA sys
P   f  f   s  49.46 MW/Hz 61.5 Hz 59.61 Hz  93.5 MW
B PB nlB sys
P   f  f   s  65.23 MW/Hz 60.5 Hz 59.61 Hz  58.1 MW
C PC nlC sys
(b) The equation in part (a) can be re-written slightly to express system frequency as a function of load.

  P 56.27 61.0   f  49.46 61.5   f  65.23 60.5   f 
LOAD sys sys sys



P LOAD  3433 56.27 f sys  3042 49.46 f sys  3946 65.23 f sys

170.96 f sys  10421 P LOAD

10421 P
f  LOAD
sys
170.96
A MATLAB program that uses this equation to determine the power sharing among the generators as a
function of load is shown below:

% M-file: prob4_10b.m
% M-file to calculate and plot the power sharing among
% three generators as a function of load.

% Define values for this generator
fnlA = 61.0; % No-load freq of Gen A
fnlB = 61.5; % No-load freq of Gen B
fnlC = 60.5; % No-load freq of Gen C
spA = 56.27; % Slope of Gen A (MW/Hz)
spB = 49.46; % Slope of Gen B (MW/Hz)
spC = 65.23; % Slope of Gen C (MW/Hz)
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