Electric Power Generation, Transmission, and Distribution

21.1.5 Transformer Bank Connections

Unique models of three-phase transformer banks applicable to radial distribution feeders have been
developed (Kersting, 1999). Models for the following three-phase connections are included in this
document:

.Delta–grounded wye

.Grounded wye–delta

.Ungrounded wye–delta

.Grounded wye–grounded wye

.Delta–delta

Figure 21.21 defines the various voltages and currents for the transformer bank models. The models can
represent a step-down (source side to load side) or a step-up (source side to load side) transformer bank.
The notation is such that the capital letters A,B,C,N will always refer to the source side of the bank and
the lower case letters a,b,c,n will always refer to the load side of the bank. It is assumed that all variations
of the wye–delta connections are connected in the ‘‘American Standard Thirty Degree’’ connection. The
standard is such that:
Step-down connection

VABleadsVabby 30 8

IAleadsIaby 30 8

Step-up connection

VableadsVABby 30 8

IaleadsIAby 30 8

21.1.5.1 Generalized Equations

The models to be used in power-flow studies are generalized for the connections in a form similar to the
ABCD parameters that are used in transmission line analysis. The general form of the power-flow
models in matrix form are

½Š¼VLNABC ½Šat½ŠþVLNabc ½Šbt½ŠIabc (21:136)

½Š¼IABC ½Šct½ŠþVabc ½Šdt½ŠIabc (21:137)

½Š¼VLNabc ½ŠAt½ŠVLNABC ½ŠBt½ŠIabc (21:138)

In Eqs. (21.136) through (21.138), the matrices [VLNABC] and [VLNabc] will be the equivalent line-to-
neutral voltages on delta and ungrounded wye connections and the line-to-ground voltages for
grounded wye connections.

IA Ia

Vab Van

Vbn

Vcn

Vca V

bc

Ib

In

Ic

vAN

vBN

vCN

vAB

vBC vCA

IB

IC

IN

+

−−

−−

−

−−−

− −

−

−

+

++

+

++

+

+

+

+

+

Source Side Load Side

Three-Phase

Transformer

Bank

FIGURE 21.21 General transformer bank.