For understanding the
relationship between the Reactive Power flow in a Transmission Line and Voltage
drop, we will consider Short Transmission Line for simplicity. A short
transmission line is one whose length is less than 80 km. For short
Transmission Line Resistance and Reactance of line is assumed lumped. The
important thing for short Transmission Line is that Shunt Capacitance is
neglected because as the line is short the effect of shunt capacitance will be
less while the reactance will predominate.

By using the above philosophy
we can represent a short Transmission Line as shown in figure below.

Vs = Sending End Voltage

Vr = Receiving End Voltage

R = Line Resistance

L = Line Inductance

Z = Impedance of Line

Is = Sending End Current

Ir = Receiving End Current

Now,

The sending end Voltage Vs
is related to the receiving end voltage Vr as below

Vr ≈ Vs – ZIr

where Z is the series impedance of the line
consisting of resistance R and inductive reactance X.

Z=R+jX

Therefore,

Vs – Vr ≈ ZIr ≈ RIrcosφ+
XIrsinφ ≈ (RP+XQ)/Vr

as VrIrcosφ =P and VrIrsinφ
=Q

Now as R is quite small in
comparison with X, it can be further simplified as:

Vs – Vr ≈ (XQ)/Vr

This expression indicates
that following important points:

*The voltage drop for a given Receiving End Voltage Vr depends on Reactive Power Flow,Q.*

*In a constant voltage line with Vs and Vr constant at all loads, then (XQ)/Vr is to be a constant which is achieved by varying Q as Vr tries to vary. Thus by controlling the Reactive Power flow through the Transmission Line voltage control is achieved.*

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## 3 comments:

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