Page 115 - Handbook of Electrical Engineering

96 HANDBOOK OF ELECTRICAL ENGINEERING

Returning to (4.22) and substituting u,

u − 1

V fd3 − V fd2 = V fd3
u
And so,
1 u S 3
B = log e
V fd3 u − 1 S 2

If u is chosen as a quotient of integer numbers, one greater than the other, such that the result
is greater than unity, then the quotient is,

m + 1
u =
m
From which,
1 u u
=−m, =−m − 1, and = m + 1
1 − u 1 − u u − 1

Therefore,
m+1
S 2
A =
m
S 3
And
1 S 3
B = (m + 1) log
e
V fd3 S 2
Table 4.2 shows the various coefficients and subscripts of S 2 and S 3 for different choices of m.
For an exciter the customary choices of S 2 and S 3 are S E75 and S E100 because the excursions
of V a and V fd above their full-load values are large. However, such excursions in a main generator
are smaller and the data given covers a smaller range of values. In this situation a larger value of m
is more suitable, e.g. m = 4 or 5, which requires S 2 to be S E80 or S E83 .
Since computer programs usually require per unit data, the calculation of S 2 , S 3 ,AandB
should be carried out after the open-circuit data has been converted into per unit values.

Table 4.2. Saturation function S 2 and S 3 as
functions of integer m
m u m + 1 S 2 S 3
1 2.0 2 SE50 SE100
2 1.5 3 SE67 SE100
3 1.333 4 SE75 SE100
4 1.25 5 SE80 SE100
5 1.20 6 SE83 SE100