Page 403 - Power Electronic Control in Electrical Systems

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382 Examples, problems and exercises

8. If the load in Problem 7 is disconnected, and no change is made to the sending-
end voltage, what will be the value of the receiving-end voltage? Also calculate
the charging current and the charging MVAr at the sending end.
WithI r ˆ 0,E s ˆ V r cosysoV r ˆ 355:442/cos4:64456 ˆ 356:613kV ˆ1:03366p:u:

Charging current is I s ˆ j(E s /Z o )tany ˆ j(205:214/109:545) tan4:64456 ˆ

p
j0:15219kA: Charging MVAr ˆ 3 355:442 0:15219 ˆ 93:695MVAr.
9. A 29.6-km lossless transmission cable has synchronous machines at both ends, which
maintain the terminal voltages at 345kV line±line. If the inductive reactance per unit
length is 0:60
/km and the capacitive admittance is 50:0 mS/km at 50Hz, calculate
(i) the Surge Impedance Load P 0 ;
(ii) the maximum transmissible power P max ;
(iii) the reactive power requirements at both ends, when the load power is
0:23P 0 and the mid-point voltage is held at 1.0 p.u. by adjusting the send-
ing- and receiving-end voltages; and
(iv) the values of the sending- and receiving-end voltages required to maintain
1.0-p.u. voltage at the mid-point.
The surge impedance Z 0 is the same as the cable in Question 7, i.e.
Z 0 ˆ 109:545
.
2
2
(i) P 0 ˆ V /Z 0 ˆ 345 /109:545 ˆ 1086:54 MW
0
(ii) Electrical length y ˆ 2 4:64456 ˆ 9:28912 P max ˆ P 0 / sin y ˆ 1086:54/

sin 9:28912 ˆ 6731:28 MW

P V o V m siny 2 sin9:28912
2 2 2
(iii) Q s ˆP 0 ˆ1086:54 [0:23 1] ˆ 83:054MVA
2
2
P V m V o 2 2 2
o
Q s < 0, i.e. absorbing reactive power. At the receiving end Q r ˆ Q s , also
absorbing. 
s
P 2 y 2
2 q 
2

(iv) E s ˆ E r ˆ 1 1 2 sin ˆ 1 [1 0:23 ]sin 4:64456 ˆ 0:99689p:u:
P 2
0
10. (i) Define the terms surge impedance loading, transmission angle and electrical
length in relation to an electrical transmission line or cable.
(ii) Write an equation for the phasor voltage E s at the sending end of a lossless
cable, in terms of the voltage V r , power P r and reactive power Q r at the
receiving-end, if the electrical length is y radians. Include the transmission
angle d in the expression for E s , and use it to derive an equation for the
reactive power requirements Q s and Q r in terms of the transmission angle d,
the electrical length y, and the voltages E s and E r .
(iii) A cable having an electrical length of 8:7 has a rated voltage of 500 kV line±

line, and a surge impedance Z 0 ˆ 50:4
. (i) Determine the maximum trans-
missible power P max when it is operated as a symmetrical line with E s ˆ E r ˆ
500 kV; and (ii) Determine the transmission angle d and the reactive power
requirements at both ends of the cable when the power transmission is 47%
of the surge impedance load.
(i) Surge impedance load ˆ that load which produces a flat voltage profile, i.e.
2
V /Z 0 .
0
Transmission angle d ˆ angle between E s and E r .