Page 114 - Handbook of Electrical Engineering
P. 114
AUTOMATIC VOLTAGE REGULATION 95
And,
V a31 − V a32 BVf d3
S 3 = u = Ae (4.21)
V a12 V fd3pu
Divide (4.21) by (4.20)
S 3 B(Vf d3−Vf d2)
= e
S 2
From which,
S 3
log e
S 2
B = (4.22)
V fd3 − V fd2
Also,
(V a31 − V a32 )
S 3
=
S 2 (V a21 − V a22 )u
Since
V fd3
u = by proportion from (4.18)
V fd2
S 3 = Ae Bu Vf d2
S 2 = Ae BVf d2
Hence,
log S 3 = log A + uBV fd2 (4.23)
e
e
And,
log S 2 = log A + BV fd2 (4.24)
e
e
Multiply (4.24) by u, and subtract from (4.23),
log S 3 − u log S 2 = log A − u log A
e e e e
= (1 − u) log A
e
Therefore,
A 1−u = S 3
u
S 2
Hence,
1/(1−u)
S 3
A =
u/(1−u)
S 2
