Page 402 - Power Electronic Control in Electrical Systems

//SYS21/F:/PEC/REVISES_10-11-01/075065126-CH009.3D ± 381 ± [373±406/34] 17.11.2001 10:33AM

Power electronic control in electrical systems 381

(iii) the sending end voltage when the load is 900 MVA with a lagging power
factor of 0.88;
(iv) the transmission angle d in degrees;
(v) the sending-end current;
(vi) the power and reactive power at the sending end; and
(vii) draw the phasor diagram showing the phase voltage and current at both
ends.
o` ˆ 0:60
/km and oc ˆ 50 10 6 S/km
p p p
6
(i) Z o ˆ (`/c) ˆ (o`/oc) ˆ (0:60/(50 10 )) ˆ 109:545
p p
6
(ii) b ˆ (o` oc) ˆ (0:60 50 10 ) ˆ 0:005477 radians/km
ˆ 0:31382 /km

y ˆ ba ˆ 0:005477 14:8 ˆ 0:08106 radians ˆ 4:64456
(iii) E s ˆ V r cos y ‡ jZ o I r sin y
From Question 6, I r ˆ 1:50613e j28:3576 kA
p
\E s ˆ (345/ 3)cos 4:64456 ‡ j109:545 sin 4:64456 1:50613e j28:3576 kV

ˆ 198:532 ‡ 13:35984 e j(90 28:3576)
ˆ 198:532 ‡ 6:34556 ‡ j11:757 ˆ 204:878 ‡ j11:757
ˆ 205:214e j3:2843 kV l n, i:e: 355:442 kV line line
p
Thus if V r ˆ 1:0p:u, E s ˆ 205:215/(345/ 3) ˆ 1:0303 p:u:
(iv) Transmission angle d ˆ 3:2843 .

Check the power transmission: Z o sin y ˆ 109:545 sin 4:64456 ˆ 8:87031

p
P ˆ (205:215 345 3/8:87031) sin 3:2843 ˆ 264:0 MW/phase.

(v) I s ˆ j(V r /Z o ) sin y ‡ I r cos y
p
ˆ j(345/ 3)/109:545 sin 4:64456 ‡ 1:50613e j28:3576 cos 4:64456

ˆ 1:32104 j0:56579 kA ˆ 1:43710e j23:1850 kA
(vi) P s ‡ jQ s ˆ E s I ˆ 3 205:214e j3:2843 1:43710e j23:1850

s
ˆ 792:0 ‡ j394:3 MVA.
(vii)

Fig. 9.5