Page 62 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

TRANSFORMERS

TRANSFORMERS 3.19

I S
I P R eq j X eq a aI P R j X I S
P P eq S eq S

V X
V P R c j X m aV S P R c j m V S
a a 2 a 2

R eq = R + a R S R P
2
P
P R eq = a 2 + R S
2
(a) X eq = X + a X S (b) S
P
P X
X eq = P + X S
I S S a 2
I P R X a aI P R X I S
eq
P j eq P eq S j eq S
V P
V P aV S a V S

(c) (d)
FIGURE 3.14 Approximate transformer models: (a) Referred to the primary side; (b) referred to the secondary
side; (c) with no excitation branch, referred to the primary side; (d) with no excitation branch, referred to the
secondary side.

where a is the turns ratio of the transformer, then

V P /a V S,fl
VR 100%
V S,fl
Most transformer applications limit the VR to a small value. In an ideal transformer VR
0 percent.

The Transformer Phasor Diagram
Figure 3.13 illustrates a simplified equivalent circuit for a transformer. The excitation
branch (R and X ) has a negligible effect on the voltage regulation of the transformer. The
c
m
secondary voltage of the transformer depends on the magnitude of the series impedances
within it and on the phase angle of the current flowing through it.
The primary voltage of the transformer is given by
V R I jX I
V P
a S eq S eq S

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