Question

Consider a distribution feeder, with \( R/X \) ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is: \[ \text{(round off to three decimal places).} \]

Hint:

In distribution systems, maximum voltage drop occurs when the load power factor angle matches the impedance angle of the line: \( \tan^{-1}(R/X) \). Use this relationship to find the corresponding power factor.

Answer 1

In distribution systems, the maximum voltage drop occurs at a specific power factor due to the angle between current and voltage. The angle \( \theta \) (of power factor) that maximizes the voltage drop in a feeder with \( R/X \) ratio is given by: \[ \tan \theta = \frac{R}{X} \Rightarrow \theta = \tan^{-1}(5) \Rightarrow \theta \approx 78.69^\circ \] Then, \[ {Power Factor} = \cos \theta = \cos(78.69^\circ) \approx 0.980 \] Thus, the power factor at which maximum voltage drop occurs is approximately: \[ \boxed{0.980} \]