For unity power factor, the voltage regulation of a short transmission line is:

Voltage regulation

Voltage regulation of a transmission line is defined as the ratio of the difference between receiving end voltage at no load and receiving end voltage at full load to the rated voltage.

The receiving end voltage at full load is considered as rated voltage.

\(VR={V_{R(no \space load)}-V_{R(full \space load)}\over V_R}\)

The sending end voltage is given by:

\(V_S=AV_R+BI_R\)

At no-load condition, I_R = 0

\(V_{R(no \space laod)}={V_S\over A}\)

For a short transmission line, the parameter A = 1

\(V_{R(no \space laod)}={V_S\over 1}=V_S\)

So, the expression for voltage regulation for a short transmission line is:

\(VR={V_S-V_R\over V_R}\)

Circuit diagram of short transmission line:

For the unity power factor, the load will be purely resistive.

Hence, the current (I) and voltage (V_R) across the load will be in the same phase.

From the above phasor:

\(V_S=V_R+IX_L\)

\(V_S-V_R=IX_L\)

\(VR={V_S-V_R\over V_R}\)

\(VR={IX_L\over V_R}\)

\(VR={IX_L\over IR}\)

\(VR={X_L\over R}\)