Page 97 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 85

Table 3.2 Advantages and disadvantages of different types of compensating equipment for transmission
systems
Compensating equipment Advantages Disadvantages

Switched shunt reactor Simple Fixed value
Switched shunt capacitor Simple Fixed value
Switching transients
Series capacitor Simple Requires over-voltage protection and
subharmonic filters
Limited overload capability
Synchronous condenser Has useful overload capability High maintenance requirement
Fully controllable Slow response
Low harmonics Heavy
Polyphase-saturated Rugged construction Fixed value
reactor (TCR) Large overload capability Noisy
Low harmonics
Thyristor-controlled reactor Fast response Requires shunt capacitors/filters
(TCR) Fully controllable Generates harmonics
No effect on fault level
Thyristor-switched capacitor No harmonics No inherent absorbing capability
(TSC) to limit over-voltages
Complex buswork
Low frequency resonances
with system

Fig. 3.1 Transmission line with distributed series inductance and shunt capacitance.

If a is the length of the line, y ˆ ba is the electrical length; for example, if a ˆ 100 km,
y ˆ 6:0 .

The solution to equation (3.1) for a lossless line is
V x†ˆ V r cos b(a x) ‡ jZ 0 I r sin b(a x)
(3:2)
V r
I(x) ˆ j sin b(a x) ‡ I r cos b(a x)
Z 0
p
where Z 0 ˆ (l/c) is the surge impedance [ohm]. A typical value of Z 0 for a high-
voltage line is 250
, but cables have lower values because of their higher capacitance.
Note that if x L ˆ ol is the series inductive reactance [ohm/m] and x C ˆ 1/oc is the
p
shunt capacitive reactance [also ohm/m] then we can write Z 0 ˆ (x L x C )and
p
b ˆ (x L /x C ).