Calculate Receiving End Current of a Power Line
What is the receiving end current of a 200-km, 60-Hz three-phase line at full load, delivering 250MW at 0.99 power factor lagging and at 220kV?
Calculating Receiving End Current:
I = P / (√3 * V * p.f.)
where:
I is the receiving end current,
P is the power transmitted (in watts),
V is the voltage (in volts),
p.f. is the power factor.
In this case, the power transmitted is 250 MW (250,000,000 watts), the voltage is 220 kV (220,000 volts), and the power factor is 0.99 lagging. Substituting these values into the formula:
I = 250,000,000 / (√3 * 220,000 * 0.99)
Simplifying the expression:
I = 663.237 A
The receiving end current is approximately 663.237 A. Now let's convert this into polar form. The angle of the lagging power factor can be calculated using the formula:
θ = cos^(-1)(p.f.)
Substituting the power factor (0.99) into the formula:
θ = cos^(-1)(0.99) ≈ 8.11°
Therefore, the receiving end current in polar form is:
IR = 663∠8.11° A
So, the correct answer is option b: IR = 663∠8.11° A.