Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 47

2.5.2 Line models
A 1-m length of transmission line may be represented by a p section, as shown in
Figure 2.24.
For a known length and frequency, the parameters become

R series resistance, r length
X series reactance, w l length
B shunt susceptance, w c length

2.5.2.1 The short line model
The shunt capacitive effect is negligible up to around 100 km for overhead lines
(but not for cables!), so a short line model can ignore B . The resulting line model is
shown in Figure 2.25.
The behaviour of the line under various loading conditions may be described
by expressing the sending-end voltage in terms of the receiving-end voltage and the
voltage drop in the line series impedance:

V S ¼ V R þð R þ j X Þ I ð 2 : 21 Þ

This equation leads to the phasor diagram shown in Figure 2.26. Assume the
load current to lag the receiving-end voltage by f . It may be seen that the angle, d ,
by which the sending-end voltage leads the receiving-end voltage increases with
load. This angle is known as the load or power angle. Also, the sending-end voltage
phasor terminates on a straight line locus whose orientation depends on f .In
practice, the sending-end voltage may be fixed, implying that the receiving-end

r , l

c /2 c /2

r resistance per m

l inductance per m

c line-to-neutral capacitance per m

Figure 2.24 Transmission line parameters

R + j X

I

V S V R

Source
Sending end (S)

Load
Receiving end (R)

Figure 2.25 Short line model