Page 124 - Solutions Manual to accompany Electric Machinery Fundamentals

(c) In what direction must the field current on each generator be adjusted in order for them to operate
at the same power factor?
SOLUTION

(a) The real and reactive powers are
P  1 3 V T cos   I L  3 1200 V 1200 A 0.9  2245 kW


Q  1 3 V T sin   I L  3 1200 V 1200 A sin cos  1 0.9     1087 kVAR


P  2 3 V T cos   I L   3 1200 V 900 A 0.75  1403 kW

Q  2 3 V T sin   I L   3 1200 V 900 A sin cos  1 0.75     1237 kVAR


(b) The overall power factor can be found from the total real and reactive power supplied to the load.

P TOT  P  1 P  2 2245 kW 1403 kW  3648 kW

Q TOT  Q  1 Q  2 1087 kVAR 1237 kVAR  2324 kVAR
The overall power factor is
 Q 

PF cos tan  1 TOT   0.843 lagging

 P TOT 
(c) The field current of generator 1 should be increased, and the field current of generator 2 should be
simultaneously decreased.
4-28. A generating station for a power system consists of four 300-MVA, 15-kV, 0.85-PF-lagging synchronous
generators with identical speed droop characteristics operating in parallel. The governors on the
generators’ prime movers are adjusted to produce a 3-Hz drop from no load to full load. Three of these
generators are each supplying a steady 200 MW at a frequency of 60 Hz, while the fourth generator
(called the swing generator) handles all incremental load changes on the system while maintaining the
system's frequency at 60 Hz.
(a) At a given instant, the total system loads are 650 MW at a frequency of 60 Hz. What are the no-
load frequencies of each of the system’s generators?
(b) If the system load rises to 725 MW and the generator’s governor set points do not change, what
will the new system frequency be?
(c) To what frequency must the no-load frequency of the swing generator be adjusted in order to
restore the system frequency to 60 Hz?
(d) If the system is operating at the conditions described in part (c), what would happen if the swing
generator were tripped off the line (disconnected from the power line)?

SOLUTION


(a) The full-load power of these generators is 300 MVA 0.85  255 MW and the droop from no-
load to full-load is 3 Hz. Therefore, the slope of the power-frequency curve for these four generators is
255 MW
s   85 MW/Hz
P
3 Hz
If generators 1, 2, and 3 are supplying 200 MW each, then generator 4 must be supplying 50 MW. The
no-load frequency of the first three generators is

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