Two ac generators are to be operated in parallel at the same...

Two ac generators are to be operated in parallel at the same frequency. Alternator 1 has four poles and turns at a speed of $1800 \mathrm{r} / \mathrm{min}$. Alternator 2 has 10 poles. a. What is the frequency of alternator 1 ? b. What speed must alternator 2 have so that it can operate in parallel with alternator 1 ?

Two ac generators are to be operated in parallel at the same frequency. Alternator 1 has four poles and turns at a speed of $1800 \mathrm{r} / \mathrm{min}$. Alternator 2 has 10 poles.
a. What is the frequency of alternator 1 ?
b. What speed must alternator 2 have so that it can operate in parallel with alternator 1 ?

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Key Concepts

Frequency Calculation in AC Generators

The output frequency of an AC generator is directly determined by its rotational speed and the number of poles according to the relation f = (n × P) / 120. Knowing any two of these variables allows the calculation of the third, making it crucial for designing and operating synchronization systems for generators.

Parallel Operation Requirements

When multiple generators operate in parallel, they must have identical frequencies, phase sequences, and voltage characteristics. This ensures that they can share load evenly without causing circulating currents or damaging imbalances, which makes synchronization—matching frequency and speed according to the number of poles—vital.

Synchronous Speed

Synchronous speed is the speed at which the magnetic field rotates in an AC machine, determined by the formula n = (120 × f) / P, where n is the speed in rpm, f is the frequency in hertz, and P is the number of poles. This relationship is fundamental as it links the physical construction of the generator (number of poles) with its operating frequency and mechanical speed.

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