Electric Power Generation, Transmission, and Distribution

When the ‘‘ladder technique’’ or ‘‘sweep’’ iterative method is used, the ‘‘forward’’ sweep is assumed to
be from the source working toward the remote nodes. The ‘‘backward’’ sweep will be working from the
remote nodes toward the source node.

21.1.5.2 Common Variable and Matrices

All transformer models will use the following common variable and matrices:

.Transformer turns ratio

nt¼

Vratedsource

Vratedload

(21:139)

whereVratedsource¼transformer winding rating on the source side. Line-to-line voltage for delta

connections and line-to-neutral for wye connections.

Vratedload¼transformer winding rating on the load side. Line-to-line voltage for delta connections

and line-to-neutral for wye connections.

Note that the transformer ‘‘winding’’ ratings may be either line-to-line or line-to-neutral, depending
upon the connection. The winding ratings can be specified in actual volts or per-unit volts using the
appropriate base line-to-neutral voltages.

.Source to load matrix voltage relations:

½Š¼VABC ½ŠAV½ŠVabc (21:140)

The voltage matrices may be line-to-line or line-to-neutral voltages depending upon the connection.
.Load to source matrix current relations:

½Š¼Iabc ½ŠAI½ŠIABC (21:141)

The current matrices may be line currents or delta currents depending upon the connection.
.Transformer impedance matrix:

½ŠZtabc ¼

Zta 00

0 Ztb 0

00 Ztc

2

4

3

(^5) (21:142)
The impedance elements in the matrix will be the per-unit impedance of the transformer windings on
the load side of the transformer whether it is connected in wye or delta.
.Symmetrical component transformation matrix:
½Š¼As
11 1
1 a^2 s as
1 as a^2 s
2
4
3
(^5) (21:143)
whereas¼ 1 ff 120
.Phaseshift matrix
½Š¼Ts
100
0 ts* 0
00 ts
2
4
3
(^5) (21:144)