Page 419 - Power Electronic Control in Electrical Systems

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398 Examples, problems and exercises

(ii)

Fig. 9.20
(iii) In the open-circuit test with no current at the HV terminals, the impedance
2
looking in to the LV terminals is [(R e ‡ jX e ) ‡ (R c k jX m )] (66/230) , i.e.

Z LV ˆ [2 ‡ j20 ‡ 13 000 j6500/(13 000 ‡ j6500)] (66/230) 2
ˆ 214:259 ‡ j429:836
ˆ 480:277e j63:505
/phase(equivalent star)

p
3
The line current is I ˆ 0:25 66 10 /3/480:277e j63:505 ˆ 19:835e j63:505 A.
p
3
\ P ‡ jQ ˆ 0:25 3 66 10 19:835e j63:505 ˆ 252:886 ‡ j507:326 kVA:
In the short-circuit test the impedance looking in at the HV terminals is
(R e ‡ jX e ) k (R c k jX m ) ˆ (2 ‡ j20) k (13 000 k j6500) ˆ 20:035e j84:219
p
The current is I ˆ 0:02 230/ 3/20:035e j84:219 ˆ 132:559e j84:219 A.
p j84:219
\ P ‡ jQ ˆ 0:02 3 230 132:559e ˆ 106:38 ‡ j1050:8 kVA:

25. (i) Define the surge impedance of a transmission line or cable.
Describe the operation of a power transmission cable under the following
conditions:
(a) when the load is less than the surge impedance load; and
(b) when the load exceeds the surge impedance load.
Assume that the voltage is maintained constant at rated value at both ends,
and make particular reference to the voltage profile and the reactive power
requirements at the ends.
(ii) A transmission cable has a sending-end voltage E s ˆ 245 kV line±line.
Losses may be neglected. The cable has an inductive reactance per unit length
of 0:60
/km and a capacitive admittance of 50:0 mS/km at 60 Hz, and its
length is a ˆ 74:8 km. Assuming that the receiving end is open-circuited,
calculate
(a) the surge impedance Z 0 ;
(b) the electrical length y in degrees;
(c) the receiving-end voltage expressed in per-unit with E s as reference;
(d) the sending-end current;