SITUATION:

A three-phase, 60 Hz, 173 kV, 50 mile long transmission power line delivers complex power to known load. The line has been tested for it's characteristic parameters. These parameters (on a per-phase basis) are found to be:

• Resistance = 0.1 ohm/mile

• Inductance = 2.0 millihenry/mile

• Capacitance = 1.0 10 ^?2 ?F/mile

REQUIRED:

For a known load at the end of the line of 75+j30 (three-phase, total megavolt-amperes), determine the input (sending) current and the input power necessary to support the complex load.

Solution

(See Elgerd: "Basic Electric Power Engineering. Addison-Wesley, any edition.) The equivalent circuit may be represented as:

And a simpler approximation (on a per phase basis) is:

The complex power,S _pp, (which may also be expressed as the phasor voltage times the complex conjugate of the phasor current) on a per phase basis is:

The current at the receiving end, then, is:

The shunt and series currents are then found

And the voltage drop across the series branch may be found by first finding the series impedance:

Therefore the input voltage is

And the sending end shunt current is

Therefore the sending end current is

And then one may find the sending end complex power (again complex voltage times the complex conjugate of the current) as

Complex Power = (97.13 + j10.07) 10 ³(250.9 ? j118.55) = 25.56 + j1.38 mega volt-amps / phase

And, of course, the total complex power is three times this...