Page 100 - Power Electronic Control in Electrical Systems

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88 Transmission system compensation

Fig. 3.4 Phasor diagram of uncompensated line on open-circuit.

Fig. 3.5 Voltage and current profiles for a 300-km line at no load (open-circuit).

The general forms of these profiles are shown in Figure 3.5. For a line 300 km in
5
length at 50 Hz, b ˆ 360 f /3 10 ˆ 6 per 100 km, so y ˆ 6 3 ˆ 18 . Then

V r ˆ E s / cos y ˆ 1:05E s and I s ˆ (E s /Z 0 ) tan y ˆ 0:329 p:u: based on the SIL. The
voltage rise on open-circuit is called the Ferranti effect.
Although the voltage rise of 5% seems small, the `charging' current is appreciable
and in such a line it must all be supplied by the generator, which is forced to run at
1
leading power factor, for which it must be underexcited. Note that a line for which
y ˆ ba ˆ p/2 has a length of l/4 (one quarter-wavelength, i.e. 1500 km at 50 Hz),
producing an infinite voltage rise. Operation of any line approaching this length is
completely impractical without some means of compensation.
In practice the open-circuit voltage rise will be greater than is indicated by
equation (3.10), which assumes that the sending-end voltage is fixed. Following a

1
The extent to which generators can absorb reactive power is limited by stability and core-end heating.
Operation of generators in the absorbing mode, with a leading power factor, is called `under-excited'
because the field current and open-circuit emf are reduced below their normal rated-load values.