0195136047.pdf

11.3 TRANSFORMER EQUIVALENT CIRCUITS 483

Note that phasor notation andrmsvalues for all voltages and currents are used.
It is generally more convenient to have the equivalent circuit entirely referred to either
primary or secondary by using the ideal-transformer relationships [Equations (11.3.2), (11.3.3),
and (11.3.7)], thereby eliminating the need for the ideal transformer to appear in the equivalent
circuit. Figure 11.3.4 shows such circuits, which are very useful for determining the transformer
characteristics.

a^2 ZL

+

−

V 1 RC^ jXm

IC Im

R 1 jX 1 ja^2 X 2 a^2 R 2

−

Io

aV 2

+

−

I 1 I 2 /a

(a)

ZL

+

−

V 1 /a RC /a^2 jXm /a^2

aIC aIm

jX (^2) R 2
aI 1
jX 1 /a^2
−
aIo
V 2

• −
  R 1 /a^2 I 2
  (b)
  Figure 11.3.4Equivalent circuits of a transformer.(a)Referred to primary.(b)Referred to secondary.
  EXAMPLE 11.3.1
  A single-phase, 50-kVA, 2400:240-V, 60-Hz distribution transformer has the following parame-
  ters:
  Resistance of the 2400-V windingR 1 = 0. 75
  Resistance of the 240-V windingR 2 = 0. 0075
  Leakage reactance of the 2400-V windingX 1 = 1 
  Leakage reactance of the 240-V windingX 2 = 0. 01 
  Exciting admittance on the 240-V side= 0. 003 −j 0 .02 S
  Draw the equivalent circuits referred to the high-voltage side and to the low-voltage side. Label
  the impedances numerically.
  Solution
  (a) The equivalent circuit referred to the high-voltage side is shown in Figure E11.3.1 (a). The
  quantities, referred to the high-voltage side from the low-voltage side, are calculated as