Page 101 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 89

sudden open-circuiting of the line at the receiving end, the sending-end voltage tends
to rise immediately to the open-circuit voltage of the sending-end generators, which
exceeds the terminal voltage by approximately the voltage drop due to the prior
current flowing in their short-circuit reactances.

3.3 Uncompensated lines under load

3.3.1 Radial line with fixed sending-end voltage

A load P ‡ jQ at the receiving end of a transmission line or cable (Figure 3.6) draws
the current

P jQ
I r ˆ (3:12)
V r

The sending- and receiving-end voltages are related by
P jQ
E s ˆ V r cos y ‡ jZ 0 sin y (3:13)
V r

If E s is fixed, this quadratic equation can be solved for V r . The solution shows how
V r varies with the load and its power factor, and with the line length. A typical result
is shown in Figure 3.7.
For each load power factor there is a maximum transmissible power, P max , the
steady-state stability limit. For any value of P < P max , there are two possible solu-
tions for V r , since equation (3.13) is quadratic. Normal operation is always at the
upper value, within narrow limits around 1.0 p.u. Note that when P ˆ P 0 and Q ˆ 0,
V r ˆ E s .
The load power factor has a strong influence on the receiving-end voltage. Loads
with lagging power factor tend to reduce V r , while loads with leading power factor
tend to increase it.

Fig. 3.6 Radial line or cable with load P ‡ jQ.