An alternator is supplying a load of 300 kW at a power factor of 0.6 lagging. If the power factor is

Question

An alternator is supplying a load of 300 kW at a power factor of 0.6 lagging. If the power factor is raised to 0.9 lagging, how much more kW can alternator supply ?

Examoogle · Accepted Answer

150 kW

Explanation: An alternator is rated by its apparent power (kVA), which remains constant regardless of the power factor. When the power factor is improved from 0.6 to 0.9, the reactive power component decreases, allowing a greater portion of the kVA capacity to be utilized as active power (kW).

Working Principle: The apparent power $S$ of an alternator is defined as $S = \frac{P}{\cos\Phi}$. Since $S$ is constant, $P_1 = S \cdot \cos\Phi_1$ and $P_2 = S \cdot \cos\Phi_2$. By maintaining the same total kVA loading, the improvement in power factor increases the real power output limit.

Key Formulas: $S = \frac{P}{\cos\Phi}$ — Apparent power relationship; $\Delta P = S(\cos\Phi_2 - \cos\Phi_1)$ — Additional power capacity formula

Key Points: Alternators are designed based on kVA ratings due to current limitations in windings.; Higher power factor means less reactive current flows for the same real power output.; Improving power factor reduces transmission line losses and increases effective load capacity.

Advantages: Increased effective load capacity of existing machinery; Improved voltage regulation of the alternator

Disadvantages: Requires installation of capacitor banks or synchronous condensers; Potential risk of over-correction leading to leading power factor issues

Applications: Industrial power plant capacity optimization; Distribution system efficiency enhancement

Additional Info: The initial kVA is $300/0.6 = 500$ kVA.. The new power at 0.9 pf is $500 	imes 0.9 = 450$ kW.. The additional power is $450 - 300 = 150$ kW.. Option B (450 kW) is the total power capacity, not the 'more' power supplied.

Answer: D is correct — The alternator can supply an additional 150 kW because the total kVA capacity is fixed at 500 kVA.

Exam Tip: Always verify if the question asks for total capacity or additional capacity to avoid common pitfalls like selecting 450 kW instead of 150 kW.

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