Electric Power Generation, Transmission, and Distribution

The transformer turns ratio is defined as

nt¼

high side rated voltage

low side half winding rated voltage (21:159)

Example:nt¼

7200

120

¼ 60

With reference to Fig. 21.24, note that the secondary currentI 1 flows out of the dot of the secondary half
winding whereas the currentI 2 flows out of the undotted terminal. This is done in order to simplify the
voltage drop calculations down the secondary. The basic transformer equations that must apply at all
times are

E 0 ¼ntVt 1 ¼ntVt 2

I 0 ¼

1

nt

ðÞI 1 I 2 (21:160)

General matrix equations similar to those of the three-phase transformer connections are used in the
analysis. For the backward sweep (working from the load toward the source), the equations are

½Š¼Vss ½Šact½ŠþV 12 ½Šbct½ŠI 12

½Š¼I 00 ½Šdct½ŠI 12 (21:161)

where

½Š¼Vss

Vs

Vs



½Š¼I 00

I 0

I 0



½Š¼I 12

I 1

I 2



½Š¼act

nt 0

0 nt

"#

½Š¼bct

nt Z 1 þ

Z 0

n^2 t





Z 0

nt

Z 0

nt

nt Z 2 þ

Z 0

n^2 t



2

(^66)
(^64)
3
(^77)
(^75)
½Š¼dct
1
nt
1  1
1  1

(21:162)
For the forward sweep (working from the source toward the loads) the equations are
½Š¼V 12 ½ŠAct½ŠVss ½ŠBct½ŠI 12 (21:163)
where
½Š¼Act
1
nt
10
01

½Š¼Bct
Z 1 þ
Z 0
n^2 t

Z 0
n^2 t
Z 0
n^2 t
 Z 2 þ
Z 0
n^2 t

2
6
(^66)
4
3
7
(^77)
5
(21:164)