Electric Power Generation, Transmission, and Distribution

Phases CA and BA

½Š¼aRVabc

aRB 00

aRB 0 aRC

00 aRC

2

4

3

(^5) (21:123)
½Š¼aRVABC
1
aRB
00

1
aRB
0 
1
aRC
00
1
aRC
2
6
(^66)
(^66)
6
4
3
7
(^77)
(^77)
7
5
(21:124)
½Š¼aRIabc
0 
1
aRB

1
aRC
0
1
aRB
0
00
1
aRC
2
6
6
(^66)
6
(^64)
3
7
7
(^77)
7
(^75)
(21:125)
½Š¼aRIABC
0 aRB aRC
0 aRB 0
00 aRC
2
4
3
(^5) (21:126)
21.1.4.9 Generalized Equations
The voltage regulator models used in power-flow studies are generalized for the various 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 is
½Š¼VABC ½Ša½ŠþVabc ½Šb½ŠIabc (21:127)
½Š¼IABC ½Šc½ŠþVabc ½Šd½ŠIabc (21:128)
½Š¼Vabc ½ŠA½ŠVABC ½ŠB½ŠIabc (21:129)
Depending upon the connection, the matrices [VABC] and [Vabc] can be either line-to-line or line-
to-ground. The current matrices represent the line currents regardless of the regulator connection. For all
voltage regulator connections, the generalized constants are defined as
½Ša¼½ŠaRVabc (21:130)
½Š¼b ½Š 0 (21:131)
½Š¼c ½Š 0 (21:132)
½Š¼d ½ŠaRIabc (21:133)
½Š¼A ½ŠaRVABC (21:134)
½ŠB¼½Š 0 (21:135)