Page 136 - Handbook of Electrical Engineering

118 HANDBOOK OF ELECTRICAL ENGINEERING

requires stabilising with a ‘deceleration’ factor. Equation (5.7) for slip = 1 can be expanded to yield
the following equation,

j(D 1 E 1 − C 1 F 1 )
C 1 E 1 + D 1 F 1
Z 231 = R 231 + jX 231 = + (5.9)
G 1 G 1
Similarly (5.8) for slip = s can be expanded to yield the following equation,

j(D 0 E 0 − C 0 F 0 )
C 0 E 0 + D 0 F 0
Z 230 = R 230 + jX 230 = + (5.10)
G 0 G 0
From (5.9) a new value of R 22 can be found as R 22N ,

G 1 R 231 − D 1 F 1 X 22 X 33
R 22N = + (5.11)
E 1 R 33 R 33
Also from (5.9) a new value of X 22 can found be as X 22N ,

G 1 X 231 + C 1 F 1 R 22 X 33
X 22N = − (5.12)
E 1 R 33 R 33
From (5.10) a new value of R 33 can be found as R 33N ,

G 0 R 230 − D 0 F 0 X 22 X 33
R 33N = + (5.11)
2 2
U E 0 R 22 U R 22
Also from (5.10) a new value of X 33 can be found as X 33N ,

G 0 X 230 + C 0 F 0 X 22 R 33
X 33N = − (5.12)
UE 0 R 22 R 22
Where U = 1/slip = 1/s
C 1 = R 22 R 33 − X 22 X 33
D 1 = R 22 X 33 + X 22 R 33
E 1 = R 22 + R 33
F 1 = X 22 + X 33
2 2
G 1 = E 1 + F 1
2
and C 0 = U R 22 R 33 − X 22 X 33
D 0 = UR 22 X 33 + X 22 R 33
E 0 = U(R 22 + R 33 )
F 0 = X 22 + X 33
2 2 2
G 0 = U E 0 + F 0
The calculation process is simple and convergent provided some deceleration ‘k’ is applied.
An initial guess is required for R 22 , X 22 , R 33 and X 33 , which may require a little trial and error
experimentation to find suitable values. These values are used in the equations to yield a new set of