Page 408 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 387

In this solution, the line capacitance and inductance do not appear explicitly since
they are incorporated in the constants Z 0 and y.
The two ends of the line and the compensator in the middle are all absorbing
reactive power, indicating that the line is working below its surge impedance loading.
2
To check this, note that P 0 ˆ 500 /109:545 ˆ 2282 MW, which is indeed greater than
the power transmission of 1540 MW.
14. (i) What is meant by the system load line in relation to the voltage at a busbar in
a power transmission system?
(ii) A power transmission system with a high X:R ratio has a short-circuit level of
14 500 MVA. What is slope of the system load line in p.u./MVAr?
(i) The system load line shows the relation between V/E and Q/S, where V is the
actual bus voltage, E is the no-load voltage, Q is the reactive power drawn
from the bus, and S is the short-circuit level. The equation of the load line is
approximately V/E ˆ 1 Q/S.
(ii) Slope of load-line ˆ d(V/E)/d(Q/S) ˆ 1.
15. An unbalanced three-phase load is delta-connected to a balanced power supply
at 415 V line±line. The impedances are Z ab ˆ 0:9584
at unity power-factor;
Z bc ˆ 0:9584
at 0.9 power-factor leading; and Z ca ˆ 0:9584
at 0.7 power-
factor lagging. Determine the impedances of three reactive compensating cap-
acitors or reactors connected in parallel with the three load impedances, such
that the resulting load is balanced and has unity power factor. What is the line
current of the compensated load?
Y ab ˆ G ab ‡ jB ab ˆ 1/0:9584 ˆ 1:04341 S

Y bc ˆ G bc ‡ jB bc ˆ 1/[0:9584e j Arc cos (0:9) ] ˆ 0:93907 ‡ j0:45481 S
Y ca ˆ G ca ‡ jB ca ˆ 1/[0:9584e j Arc cos (0:7) ] ˆ 0:73038 j0:74514 S
p p
B gab ˆ B ab ‡ (G ca G bc )/ 3 ˆ (0:73038 0:93907)/ 3
ˆ 0:12049 (inductive)
p p
B gbc ˆ B bc ‡ (G ba G ca )/ 3 ˆ 0:45481 ‡ (1:04341 0:73038)/ 3
ˆ 0:27408 (inductive)
p p
B gca ˆ B ca ‡ (G bc G ab )/ 3 ˆ 0:74514 ‡ (0:93907 1:04341)/ 3
ˆ 0:68490 (capacitive)
Z gab ˆ 1/( j0:12049) ˆ j8:30
(inductive)
Z gbc ˆ 1/( j0:27408) ˆ j3:65
(inductive)
Z gca ˆ 1/( j0:68490) ˆ j1:46
(capacitive)
p
Line current I L ˆ (V LL /3)/G
where G ˆ G ab ‡ G bc ‡ G ca ˆ 1:04341 ‡ 0:93907 ‡ 0:73038 ˆ 2:71286.
p
Thus I L ˆ (415/ 3)/2:71286 ˆ 88:3A.
16. (i) Explain the difference between a wye connection and a delta connection, and
mention one advantage of each connection.