Page 60 - Solutions Manual to accompany Electric Machinery Fundamentals

(e) Compare the efficiencies of the transmission system with and without transformers.

SOLUTION
(a) In the case of the directly-connected load, the line current is

13.8 0 kV

 I  I  24.83  39.3 A




line load

60 60 500 36.87  
The load voltage is


V load  load Z load  I 24.83  39.3 A 500 36.87     12.42   2.43 kV
The resistance in the load is

R load  Z load cos  500cos  60  250
The power supplied to the load is
P load  line 2 R load   I 24.83 A 2   250   154 kW
The ratio of the load voltage to the generated voltage is 12.42/13.8 = 0.900. The resistance in the
transmission line is
R line  Z line cos  60cos 60  30  

so the transmission losses in the system are

P loss  line 2 R line   I 24.83 A 2  30    18.5 kW
(b) The efficiency of this power system is

P P 154 kW

  out  100%  out  100%   100% 89.3%

P in P  out P loss 154 kW 18.5 kW
(c) In this case, a 1:10 step-up transformer precedes the transmission line and a 10:1 step-down
transformer follows the transmission line. If the transformers are removed by referring the transmission
line to the voltage levels found on either end, then the impedance of the transmission line becomes

 1  2  1  2

Z line    line     Z  60 60   0.60 60 
 10   10 
The current in the referred transmission line and in the load becomes


 13.8 0 kV

line I load  I  27.57   36.9 A





0.60 60 500 36.87 
The load voltage is


V load  load Z load  I 27.57  36.9 A 500 36.87     13.785   0.03 kV
The resistance in the load is

R load  Z load cos  500cos  60  250
The power supplied to the load is
P  2 R   I 27.57 A 2   250   190 kW
load line load
The ratio of the load voltage to the generated voltage is 13.785/13.8 = 0.9989. Also, the transmission
losses in the system are reduced. The current in the transmission line is
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