Voltage Compensation for AC Transmission Lines

Shunt capacitors are used to compensate for voltage drops in AC transmission lines. The article explains the phasor diagrams and equations involved in voltage compensation. It also discusses the effects of load loss in a compensated AC transmission line.

VOLTAGE COMPENSATION
Many electrical devices work efficiently under steady state voltage conditions close to their rated
voltage. Shunt capacitors are used to increase receiving end voltages while resistive loads and line
inductances reduce receiving end voltages. Therefore, receiver voltage can be compensated by properly
switching capacitive shunt reactance. Shunt capacitance in case of excessive receiver voltage are
removed into the transmission line to reduce the line current. Phasor diagrams representing ac
uncompensated transmission line, shunt capacitor compensated transmission line and increased line
current when the transmission line is compensated more is as shown below.
As in the first figure, the load is purely resistive and as a result, the line current lags the sender voltage
ES by a certain angle θ that is determined by line inductance and load resistance. Also, the receiver end
voltage ER lags the sending end voltage Esby the same angle θ . Similarly, the transmission line voltage
drop ELleads line current by 900 . The scalar computation of these voltages is as shown below
ER=ES− EL

For compensation, the receiver end voltage should be equivalent to the sending end voltage which can
be achieved by adding a shunt capacitor that modifies phasor voltages. The shunt capacitance shifts
phasor angle of the transmission line current and transmission line voltage drop making sure the scalar
magnitude of ES=ER. To find the appropriate capacity of shunt capacitance, following equation is
used. XC =
| R
XL
( −R− √ R2− XL
2 )|
From the equation, the value of load resistance should not be less than the line inductance lest the
receiver end voltage can’t be totally compensated. The second diagram in the table above shows a
phasor of compensated transmission line using shunt capacitance. The compensator splits line current
phasor into two between the receiver and the sender. As a result, the receiver voltage is maintained to
equal magnitude as the sender voltage. For the third figure in the table above, increasing the line
current increases the angle between the receiver and the sender voltage since high current leads to
higher line voltage drop EL=X L I L.
Ac transmission line with uncompensated receiver voltage.
In uncompensated system, voltage and current can be obtained using the vectorial calculation below;
ZT =R+ XL , I L= ES
ZT
, and EL=X L I L , and ER=ES− EL
These formulas illustrate that the magnitude of receiver end voltage is always less than the sending end
voltage.
AC transmission line with compensated receiver voltage.
The shunt capacitance values require for the compensation of reactive power can be found using the
equation described about. The voltages and currents can then be calculated using the formulas below.
ZRC= RXC
R− XC
,and ZT =ZRC +X L ,and I L= ES
ZT
,and EL=X L I L ,and ER=ES− EL
Thus the receiver end voltage is approximately equal to the sender end voltage.
AC transmission line with compensated receiver voltage when the line current increases.
The transmission line current is increased by reducing the load resistance. The compensation is again
done by modifying the shunt capacitive reactance. The exact value of the shunt capacitance can be
obtained from the equation discussed before while different values of the ac transmission system can be
found the equations below.
ZT =R+ XL , I L= ES
ZT
, and EL=X L I L , and ER=ES− EL
Load loss in a compensated ac transmission line
For the shunt capacitance compensation system, variation of the receiving end voltages subjects the
system under severe over-voltages across the transmission line. For instances where receiver load

resistance is significantly reduced, the transmission line sees the capacitive load causing receiver end
voltage to increase significantly. Also, with regard to the magnitude of capacitive and inductive
reactance, ac line current also increases significantly leading to damage of the transmission line.