Handbook of Electrical Engineering

96 HANDBOOK OF ELECTRICAL ENGINEERING

Returning to (4.22) and substitutingu,

Vfd 3 −Vfd 2 =

(

u− 1

u

)

Vfd 3

And so,

B=

1

Vfd 3

(

u

u− 1

)

loge

(

S 3

S 2

)

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

u=

m+ 1

m

From which,

1

1 −u

=−m,

u

1 −u

=−m− 1 , and

u

u− 1

=m+ 1

Therefore,

A=

S 2 m+^1

S 3 m

And

B=

1

Vfd 3

(m+ 1 )loge

(

S 3

S 2

)

Table 4.2 shows the various coefficients and subscripts ofS 2 andS 3 for different choices of m.
For an exciter the customary choices ofS 2 andS 3 areSE 75 andSE 100 because the excursions
ofVaandVfdabove 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 ofm
is more suitable, e.g.m=4 or 5, which requiresS 2 to beSE 80 orSE 83.

Since computer programs usually require per unit data, the calculation ofS 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 integerm

mum+ 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