Page 52 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

TRANSFORMERS

TRANSFORMERS 3.9

Working back through T gives
2
N I N I
P 2 line S 2 load
N
P 2
I load I line
N
S 2
10
(9.594 36.88° A)
1
95.94 36.88° A
It is now possible to answer the questions originally asked. The load voltage is given by
V load I load Z load
(95.94 36.88° A)(5 36.87° )
479.7 0.01° V

and the losses are given by
2
P (I ) R
loss line line
2
(9.594 A) (0.18 )
16.7 W
Notice that by stepping up the transmission voltage of the power system, the trans-
mission losses have been reduced by a factor of 90. Also, the voltage at the load
dropped significantly in the system with transformers compared to the system without
transformers.

THEORY OF OPERATION OF REAL SINGLE-PHASE
TRANSFORMERS

Figure 3.6 illustrates a transformer consisting of two conductors wrapped around a trans-
former core. Faraday’s law describes the basis of transformer operation:
d
e
ind
dt
where is the flux linkage in the coil across which the voltage is being induced. Flux link-
age is the sum of the flux passing through each turn in the coil added over all coil
turns:
n
i
i 1
The total flux linkage through a coil is not N (N is the number of turns). This is so
because the flux passing through each turn of a coil is slightly different from the flux in the

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