Electric Power Generation, Transmission, and Distribution

½Š¼At

1

nt

10  1

 110

0  11

2

6

4

3

7

5

½Š¼Bt

Zta 00

0 Ztb 0

00 Ztc

2

(^64)
3
(^75)
21.1.5.4.2 Ungrounded Wye–Delta
Power-flow equations:
Backward sweep:
½ŠVLNABC ¼½Šat½ŠVLNabcþ½Šbt½ŠIabc
½Š¼IABC ½Šct½ŠþVLNabc ½Šdt½ŠIabc
Forward sweep:
½Š¼VLNabc ½ŠAt½ŠVLNABC ½ŠBt½ŠIabc
Matrices used for the step-down connection are
½Š¼at nt
1  10
01  1
 101
2
(^64)
3
(^75)
½Š¼bt
nt
3
Ztab Ztab 0
Ztbc 2 Ztbc 0
 2 Ztca Ztca 0
2
6
4
3
7
5
½Š¼ct
000
000
000
2
6
4
3
7
5
½Š¼dt
1
3 nt
1  10
120
 2  10
2
(^64)
3
(^75)
½ŠAt ¼
1
3 nt
210
021
102
2
6
4
3
7
5
½Š¼Bt
1
9
2 ZtabþZtbc 2 Ztbc 2 Ztab 0
2 Ztbc 2 Ztca 4 ZtbcZtca 0
Ztab 4 Ztca Ztabþ 2 Ztca 0
2
6
4
3
7
5
whereZtab,Ztbc, andZtcaare the transformer impedances inside the delta secondary connection.