Page 295 - Solutions Manual to accompany Electric Machinery Fundamentals

Therefore, the line voltage at the loads is V 3 V  439 V .
L 
(b) The voltage drop in the transmission lines is


 line V  ,gen  V  ,load  V 277 0 V 253.2   7.3   41.3 52 V




(c) The real and reactive power of each load is
V 2  253.2 V 2
P  1 3 Z  cos  3 2.5  cos 36.87  61.6 kW
V 2  253.2 V 2
Q  1 3 Z  sin  3 2.5  sin 36.87  46.2 kvar

V 2  253.2 V 2
P  3  cos  3  cos  20   108.4 kW
2
Z 1.67 
V 2  253.2 V 2
Q  3  sin  3  sin  20    39.5 kvar
2
Z 1.67 
(d) The line current is


 41.3 52 V
V

I line  line   225   8.6 A
Z line 0.09  j 0.16 
Therefore, the loses in the transmission line are
P line  3I line 2 line  3 225 A  2 0.09   13.7 kW
 R
Q line  3I line 2 line  3  X 225 A 2 0.16    24.3 kvar

(e) The real and reactive power supplied by the generator is



P gen  P  line P  1 P  2 13.7 kW 61.6 kW 108.4 kW 183.7 kW


Q gen  Q line  Q  1 Q  2 24.3 kvar 46.2 kvar 39.5 kvar  31 kvar
The power factor of the generator is
 Q   31 kvar 
PF  cos tan -1 gen   cos tan  1   0.986 lagging


P gen      183.7 kW 
A-3. Figure PA-2 shows a one-line diagram of a simple power system containing a single 480 V generator and
three loads. Assume that the transmission lines in this power system are lossless, and answer the
following questions.
(a) Assume that Load 1 is Y-connected. What are the phase voltage and currents in that load?

(b) Assume that Load 2 is -connected. What are the phase voltage and currents in that load?
(c) What real, reactive, and apparent power does the generator supply when the switch is open?
(d) What is the total line current I L when the switch is open?

(e) What real, reactive, and apparent power does the generator supply when the switch is closed?

(f) What is the total line current I L when the switch is closed?
(g) How does the total line current I L compare to the sum of the three individual currents I  I  I ? If
2
3
1
they are not equal, why not?

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