Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 48

Sending-end voltage locus as
power and current increase

V S

j X I

d V R

f

R I

I

Figure 2.26 Voltage phasor diagram for a short transmission line

voltage decreases with load for the assumed f . However, a leading load current
could result in receiving-end voltage increasing with load.
We also introduce a line impedance angle j (not to be confused with the power
angle) such that

Z ¼ R þ j X ¼ Z ffj

The essential features of power transmission may be seen by obtaining an
equation for the power received by the load. From the complex VA product

j Q R ¼ V R I R
P R ¼< e V R I R
Let the receiving-end voltage be the reference:
V R ¼ V R ff 0 ¼ V R
Since I ¼ I R , we may use (2.21) to express I R in terms of the sending-and
receiving-end voltages:

P R þ

V S V R
Z

I R ¼

After some manipulation we obtain

V R

V R V S cos ð j d Þ
Z

cos j
Z

P R ¼ ð 2 : 22 Þ

2.5.3 Power transmission
For high-voltage lines, the series reactance is several times the series resistance.
Equation (2.22) can therefore be simplified by assuming R ¼ 0.
∴ j ¼ 90
∴ cos j ¼ 0
∴ cos ðj dÞ¼ cos j cos d þ sin j sin d ¼ sin d

ð 2 : 23 Þ

V S V R sin d
X

∴ P R ¼