Question

A three-phase, 50 Hz transmission line, 100 km long delivers 30 MW at 120kV and 0.7 p.f. lagging. The resistance and reactance of the lines per phase per km are 0.2 ohm and 0.5 ohm respectively while capacitance admittance is 2.2x10-6 mho/km/ph. Calculate the efficiency of transmission. Use the nominal π method

Answer 1

The efficiency of transmission is 73.83%.

Step-by-step explanation:

The efficiency of transmission can be calculated using the nominal π method. The formula for calculating transmission efficiency is given by:

Efficiency = (SI / SO) * 100%

Where SI is the power received at the load and SO is the power input to the transmission line.

In this case, the power received at the load is 30 MW at a power factor of 0.7 lagging. We can calculate the apparent power received using the formula:

SI = P / power factor

Substituting the given values, we get SI = 30 MW / 0.7 = 42.86 MVA.

The power input to the transmission line can be calculated using the formula:

SO = 3 * VL * IL

Where VL is the line voltage and IL is the line current. The line current can be calculated using the formula:

IL = SO / (√3 * VL)

Substituting the given values, we get IL = 30 MW / (√3 * 120 kV) = 135.93 A.

Substituting the calculated values into the formula for power input, we get SO = 3 * 120 kV * 135.93 A = 58.13 MVA.

Finally, substituting the calculated values into the formula for efficiency, we get Efficiency = (42.86 MVA / 58.13 MVA) * 100% = 73.83%.