Page 420 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 399

(e) the reactive power at the sending end, in MVAr; and
(f) the reactive power at the sending end, expressed as a fraction of the surge-
impedance loading.
2 p p
(i) The surge impedance load P 0 is equal to V /Z 0 where Z 0 ˆ (l/c) ˆ (x L x C ),
0
l being the inductance per unit length, c the capacitance per unit length, x L
the series inductive reactance per unit length, and x C the shunt capacitive
reactance per unit length along the line; and V 0 is the rated voltage. If V 0 is
the line±line voltage, P 0 is the total power over all three phases. If V 0 is the
line-neutral voltage, it is the power per phase. When the transmitted power
P is equal to the surge impedance load, the voltage profile is flat and the
reactive power requirements at the ends are zero.
(a) When P < P 0 the voltage rises towards the mid-point and reactive
power must be absorbed at both ends to maintain the voltage equal
to V 0 .
(b) When P > P 0 the voltage falls towards the mid-point and reactive
power must be generated at both ends to maintain the voltage equal to
V 0 .
p p p
6
(ii) (a) Z 0 ˆ (x L x C ) ˆ (x L /y C ) ˆ (0:60/50 10 ) ˆ 109:55
p p
(b) b ˆ (x L /x C ) ˆ (x L y C ) ˆ
p
6
(0:60 50 10 ) ˆ 5:477 10 3 radians/km ˆ 0:3138 /km

so y ˆ ba ˆ 0:3138 74:8 ˆ 23:47
E s 1:0
(c) V r ˆ ˆ ˆ 1:0902 p:u: ˆ 267 kV
cos y cos 23:47
p 
E s 245/ 3

(d) I s ˆ j tan y ˆ tan 23:47 kA ˆ j561 A
Z 0 109:55
p
(e) Q s ˆ 3 245 0:561 ˆ 238 MVAr
2
(f) P 0 ˆ 245 /109:55 ˆ 548 MVA, so Q s /P 0 ˆ 238/548 ˆ 0:434 p:u:
26. (i) Explain why the TCR is preferred over the TSC when it is desired to have a
reactive compensator with continuous control of the current.
(ii) Draw the complete power circuit diagram for a three-phase TCR, including
shunt capacitors/filters, and a step-down transformer.
(iii) Draw the phase current waveform in relation to the phase voltage waveform,
for a typical conduction angle of, say, s ˆ 120 .

(iv) A delta-connected TCR is connected to a 400-kV transmission line through a
7:1 step-down transformer. Its maximum reactive power at rated voltage is
100 MVAr. For a conduction angle of 115 , calculate

(a) the rms fundamental component of the line current at the high-voltage
terminals of the transformer; and
(b) the peak current in each thyristor.
(i) The TCR permits continuous control of the fundamental component of line
current by phase control, whereas the TSC can only adjust the current by
switching between discrete values.