Performance Analysis

A 3-phase line is represented by nominal-$\pi$ model. The series impedance of the line is $12+j65\,\Omega/\text{phase}$ and shunt admittance is $j2.5\times10^{-4}\,\mathrm{S}/\text{phase}$. Compute the power delivered to a load at the receiving end and construct the phasor diagram for the line if the sending end voltage and current are:

$V_{S,L}=1385\angle 15.2^\circ\,\mathrm{kV}$ $IS,L=225\angle 18.3^\circ\,\mathrm{A}$

A three phase 220KV, 50Hz transmission line supplies a power of 200MW at a power factor of 0.8 lagging and line has ABCD parameters as follows:

$$\begin{bmatrix}A & B\\ C & D\end{bmatrix}=\begin{bmatrix}0.9\angle 0.001^\circ & B\,\Omega\\ 1.14\times10^{-3}\angle 90^\circ & 0.9\angle 0.001^\circ\end{bmatrix}$$

Determine the following:

i) Sending end voltage and current

ii) Real and reactive power at sending and at full load.

iii) Real and reactive power loss in line at full load.

iv) Voltage regulation and line efficiency at full load.

A 50Hz transmission line 300km long has a total series impedance of $40+j125\,\Omega$ and a total shunt admittance of $10^{-3}$ mho. The receiving-end load is 50MW at 220kV with 0.8 lagging power factor. Find the sending-end voltage, current, power and power factor using:

i) Short line approximation

ii) Nominal-$\pi$ method.