Page 426 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 405
p p
(iii) We have E s ˆ 345/ 3 ˆ 199:2e j0 kV line-neutral and y ˆ ba ˆ (0:56
6 p 6

50 10 ) 19:8 ˆ 0:105 radians ˆ 6:003 ,and Z 0 ˆ (0:56/50 10 ) ˆ
105:83
,so
p 
3
j0
345 10 / 3 e sin 6:003
I s ˆ I r ˆ j ˆ j98:7A
105:83 1 ‡ cos 6:003
j0
At the mid-point, V m ˆ 199:2e /cos (6:003/2 ) ˆ 199:46 kV line-neutral,

hardly changed from the sending-end and receiving-end values, since this is
quite a short line. Also I m ˆ 0.
Supplementary problems (no solutions)
29. (i) What are the functions of reactive compensation applied to electrical trans-
mission systems? Distinguish between active and passive compensation.
(ii) By means of a sketch showing V r /E s vs. P/P 0 , illustrate how the receiving-
end voltage of a transmission cable can be maintained within a narrow
range near 1.0 p.u. by means of switched shunt compensating devices. E s
is the sending-end voltage, P is the power transmission, and P 0 is the
natural load.
(iii) Write an equation for the phasor voltage E s at the sending end of a loss-
less 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. Use this equation to
derive an expression for the reactance X required to make the no-load voltage
at the receiving end of a radial transmission cable equal to the sending-end
voltage.
(iv) (a) Determine the value of a reactor placed at the mid-point of a 500 kV, 80-
km symmetrical line such that the mid-point voltage is 1.0 p.u. The
synchronous machines at the two ends maintain the voltage equal to
1.0 p.u. at both ends. The line series inductive reactance is 0:60
/km
and shunt capacitive susceptance is 50:0 mS/km.
(b) What is the maximum voltage in the compensated line at no-load, and
where does it occur?
(c) What is the reactive power of the mid-point reactor?
30. (i) Define the term surge impedance as used with electrical power transmission
lines and cables. Briefly describe the properties of the voltage and current
along a line that is operating at the so-called surge-impedance load.
(ii) Write down an equation for the sending-end voltage of a transmission line in
terms of the receiving-end voltage V r , the receiving-end current I r , the surge
impedance Z 0 , and the electrical length of the line y.
(iii) A transmission cable has a receiving end voltage V r ˆ 345 kV line±line. The
load is wye-connected and is 264 ‡ j142:5 MVA/phase. 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 50 Hz. The cable length is
a ˆ 14:8 km. Calculate

(a) the receiving-end current, expressed as a phasor with V r as reference;
(b) the surge impedance Z 0 ;