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,
Z 231 =R 231 +jX 231 =C 1 E 1 +D 1 F 1
G 1
+
j(D 1 E 1 −C 1 F 1 )
G 1( 5. 9 )
Similarly (5.8) for slip=scan be expanded to yield the following equation,
Z 230 =R 230 +jX 230 =C 0 E 0 +D 0 F 0
G 0
+
j(D 0 E 0 −C 0 F 0 )
G 0( 5. 10 )
From (5.9) a new value ofR 22 can be found asR 22 N,
R 22 N=
G 1 R 231 −D 1 F 1
E 1 R 33
+
X 22 X 33
R 33
( 5. 11 )
Also from (5.9) a new value ofX 22 can found be asX 22 N,
X 22 N=
G 1 X 231 +C 1 F 1
E 1 R 33
−
R 22 X 33
R 33
( 5. 12 )
From (5.10) a new value ofR 33 can be found asR 33 N,
R 33 N=
G 0 R 230 −D 0 F 0
U^2 E 0 R 22
+
X 22 X 33
U^2 R 22
( 5. 11 )
Also from (5.10) a new value ofX 33 can be found asX 33 N,
X 33 N=
G 0 X 230 +C 0 F 0
UE 0 R 22
−
X 22 R 33
R 22
( 5. 12 )
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
G 1 =E 12 +F 12
and C 0 =U^2 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
G 0 =U^2 E 02 +F 02
The calculation process is simple and convergent provided some deceleration ‘k’ is applied.
An initial guess is required forR 22 ,X 22 ,R 33 andX 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