Page 86 - Handbook of Electrical Engineering

66 HANDBOOK OF ELECTRICAL ENGINEERING

Quadrative axis:

X q = X a + X mq (3.4)
X mq X kd

X = X a + (3.5)
q X a + X kd
X mq + X kd
Where X md and X mq are much larger than any of the other reactances.

These equations can be transposed to find X f , X kd and X kq in terms of X , X and X in
d d q
particular. The purchaser may require certain limits to X and X because of constraints on fault

d d
currents and volt drop. Consequently the machine designer is faced with finding physical dimensions
to satisfy the resulting X md , X f and X kd . The purchaser is not usually too concerned about the
quadrature parameters. Transposing (3.1), (3.2) and (3.3) gives the designer the following:-
(3.6)
X md = X d − X a

X md (X − X a )
d
X f = (3.7)

X md − X + X a
d

X md X f (X − X a )
d
X kd = (3.8)

X md (X f + X a ) + X a X f − X (X md + X f )
d
Where X a is kept as small as is practically reasonable.
Figures 3.2 and 3.3 show the variations of X and X with X f for a family of X md and

d d
X kd values.

Figure 3.2 D-axis transient reactance versus field leakage reactance.