Electrical Power Systems

Denominator of eqns. (i) and (ii)
Z 1Z 2 + Z 0(Z 2 + Z 1)
Z1Z2 = (1 + j2) (1 + j1.9) = 2. 236 63. 43°´ 2147 . 62. 24°
= 4. 8 125. 67°
= (– 2.8 + j3.9)
Z 1 + Z 2 = 1 + j2 + 1 + j1.9 = (2 + j3.9)
\ Z1 + Z2 = 4. 383 62. 85°
Z0 = 2 + j6.45 = 6. 753 72. 77°
\ Z0 (Z1 + Z2 ) = 29. 6 135. 62°
= – 21.15 + j20.7
\
Z 1Z 2 + Z 0 (Z 1 + Z 2) = – 2.8 + j3.9 – 21.15 + j 20.7
Numerator of eqn. (i)
\ = 13.4 – 32. 40°
\ E a =
\ I b =
Numerator of eqn. (ii)
Z 2 (b – 1) + (b – b 2 ) Z 0
= (– 23.95 + j24.6) = 34.33 134 23 0
.
Z 2 (b 2 – 1) + (b 2 – b) Z 0
Unbalanced ault Analysis 265
= (1 + j1.9) (– 0.5 – j0.866 – 1) + (2 + j6.45) (– 0.5 – j0.866
= – 2.147 62. 24°
× 1.732 30° – j × 1.732 (2 + j6.45)
= – 3.718 92. 24°
– j3.464 + 11.17 = 11.31 – j7.18
13. 8
3
0° KV = 7.96 0° KV.
134 . –32. 4°´ 7.96 0°
34.33 134. 23°
= 3.107 – 166. 63° KA
= 2.147 62. 24°
(– 0.5 + j0.866 – 1) + (– 0.5 + j0.866
+ 0.5 – j 0.886)
+ 0.5 + j0.866) ( 6.753 72. 77°
)
= – 2.147 62. 24°
× (1.5 – j0.866) + 1.732 × 6.753 162. 77°
= 3.718 212. 24°
+ 11.696 162. 77°
= – 3.144 – j1.983 – 11.17 + j3.464
= – 14.314 + j1.481 = 14.39 174. 09°