Question

A balanced three phase source is supplying a balanced three phase load through a transmission line with impedance of 10+j30 ohm per phase. Load is consuming 300 MW at power factor of 0.8 lagging. Load voltage (line-line) is held constant at kV. Frequency is 60 Hz. 1. Find the real power lost in the line. 2. By adding capacitors power factor is improved to one (unity power factor) find the real power lost in the line.

Answer 1

Answer:

1. the real power lost is 7.5 MW

2. the real power lost by adding capacitors is 4.8 MW

Explanation:

1.

$|I|=\frac{300x10^{6} }{\sqrt{3}*250*\sqrt{3}*0.8*10^{3} } =500A$

the real power lost is

$P=3|I|^{2} R=3*500^{2} *10=7500000W=7.5MW$

2.

$|I|=\frac{P}{\sqrt{3}V } =\frac{300x10^{6} }{\sqrt{3}*\sqrt{3}*250*10^{3} } =400A$

the real power lost is

$P=3*400^{2} *10=4800000W=4.8MW$