The values of the source side Thevenin equivalent
circuit will be the same regardless of the type of
connection of the feeder transformer. For each
three-phase transformer connection, unique values
of the matrices [Ethabc] and [Zthabc] are defined as
functions of the source side Thevenin equivalent
circuit. These definitions are shown for each trans-
former connection below.21.1.5.6 Center Tapped Transformers
The typical single-phase service to a customer is 120=240 V. This is provided from a center tapped
single-phase transformer through the three-wire secondary and service drop to the customer’s meter.
The center tapped single-phase transformer with the three-wire secondary and 120=240 V loads can be
modeled as shown in Fig. 21.24.
Notice in Fig. 21.24 that three impedance values are required for the center tapped transformer. These
three impedances typically will not be known. In fact, usually only the magnitude of the transformer
impedance will be known as found on the nameplate. In order to perform a reasonable analysis, some
assumptions have to be made regarding the impedances. It is necessary to know both the per-unitRA
and theXAcomponents of the transformer impedance. References Gonen (1986) and Hopkinson (1977)
are two sources for typical values. From Hopkinson (1977) the center tapped transformer impedances as
a function of the transformer impedance are given. For interlaced transformers the three impedances are
given by
Z 0 ¼ 0 : 5 RAþj 0 : 8 XA
Z 1 ¼RAþj 0 : 4 XA
Z 2 ¼RAþj 0 : 4 XA (21:157)The equations for the noninterlaced design are
Z 0 ¼ 0 : 25 RAj 0 : 6 XA
Z 1 ¼ 1 : 5 RAþj 3 : 3 XA
Z 2 ¼ 1 : 5 RAþj 3 : 1 XA (21:158)[Iabc][VLNabc][Ethabc] [Zthabc]FIGURE 21.23 Three-phase Thevenin equivalent
circuit.
+VsZ 0E 0 Vt 2Z 1I 1InZ 2I 2Zs 11V (^1) Zs 12
V 2
Zs 22
VL 1
VL 2
S 1
S 2
IL 1
IL 2
S 12 VL 12
IL 12 −
- −
−
−
−
Vt 1
−
−
−
- I 0
−
FIGURE 21.24 Center tapped single-phase transformer with secondary.