Class 2 (2nd Engineer) MET 📅 Oct 2019

Exam Question

With reference to A.C Distributions systems:

(a) Define power factor and explain the effects of low power factor. (6)

(b) A 72 kVA transformer supplies a heating and lighting load of 12 kW at unity power factor and a motor load of 70 kVA at 0.766 (lagging) power factor. Calculate the minimum rating of the power-factor improvement capacitors which must be connected in the circuit to ensure that the transformer does not become overloaded. (10)

Reference Answer

(a) Definition of Power Factor:
Power factor is a measure of the efficiency of an electrical system, indicating how effectively electrical power is converted into useful work output. It is defined as the ratio of True Power (real power in kilowatts, kW) to Apparent Power (total power in kilovolt-amperes, kVA). Mathematically, it is expressed as:
$$Power\:factor\:\left(PF\right)=\frac{True\:power\:\left(kW\right)}{Apparent\:power\:\left(kVA\right)}$$
The power factor is a dimensionless quantity, represented as a value between 0 and 1 or as a percentage. A power factor of 1 (or 100%) signifies that all the apparent power is being effectively used as true power. For most shipboard systems, the power factor is typically 0.8 lagging , indicating that the current lags the voltage by an angle θ due to inductive loads.

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