Electric Power Generation, Transmission, and Distribution

wherets¼

1

ffiffiffi

3

p ff 30

.Matrix to convert line-to-line voltages to equivalent line-to-neutral voltages:

½ŠW ¼½ŠAs½ŠTs½ŠAs^1 ¼

1

3

210

021

102

2

4

3

(^5) (21:145)
Example: [VLN]¼[W][VLL]
.Matrix to convert delta currents into line currents:
½Š¼DI
10  1
 110
0  11
2
4
3
(^5) (21:146)
Example: [Iabc]¼[DI][IDabc]
.Matrix to convert line-to-ground or line-to-neutral voltages to line-to-line voltages:
½Š¼D
1  10
01  1
 101
2
4
3
(^5) (21:147)
Example: [VLLabc]¼[D][VLNabc]
21.1.5.3 Per-Unit System
All transformer models were developed so that they can be applied using either ‘‘actual’’ or ‘‘per-unit’’
values of voltages, currents, and impedances. When the per-unit system is used, all per-unit voltages
(line-to-line and line-to-neutral) use the line-to-neutral base as the base voltage. In other words, for a
balanced set of three-phase voltages, the per-unit line-to-neutral voltage magnitude will be 1.0 at rated
voltage and the per-unit line-to-line voltage magnitude will be the
ffiffiffi
3
p

. In a similar fashion, all currents
(line currents and delta currents) are based on the base line current. Again,

ffiffiffi

3

p
relationship will exist
between the line and delta currents under balanced conditions. The base line impedance will be used for
all line impedances and for wye and delta connected transformer impedances. There will be different
base values on the two sides of the transformer bank.
Base values are computed following the steps listed below:

.Select a base three-phasekVAbaseand the rated line-to-line voltage,kVLLsource, on the source side

as the base line-to-line voltage.

.Based upon the voltage ratings of the transformer bank, determine the rated line-to-line voltage,

kVLLload, on the load side.

.Determine the transformer ratio,ax,as

ax¼

kVLLsource

kVLLload

(21:148)

.The source side base values are computed as

kVLNS¼

kVLLS

ffiffiffi

3

p (21:149)