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.
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
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.
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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