A power system has two synchronous generators. The governor-turbine characteristics corresponding to generators are P1=50(50-f), P2=100(51-f). Where f denotes the system frequency in Hz and P1 and P2 are respectively, the power outputs (in MW) of turbines 1 and 2. Assume that the generators and transmission network are losses. Find out the system frequency (in Hz) for a total load of 400MW shared by both the generators.
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The correct answer to the given question is 48 Hz.
50(50-f)+100(51-f)= 400
Which gives f= 48Hz on solving the equation.
The frequency of synchronous generator is directly proportional to speed of synchronous generator. When multiple number of synchronous generator are connected in a grid, the frequency of each of the synchronous generator remains the same because they are in circuit. Synchronous generator which are connected to the grid run with same frequency but in different speed.
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