# A power system has three synchronous generators.The turbine-governor characteristics corresponding to the generators are P1 =50(50 − f), P2 = 100(51 − f), P3 = 150(52 − f) Where, f denotes the system frequency in Hz, and P1, P2, P3 are the power outputs of the turbines in MW. Assuming generators and transmission network to be lossless, the system frequency for a load of 700 MW is

A power system has three synchronous generators. The turbine-governor characteristics corresponding to the generators are P1 =50(50 − f), P2 = 100(51 − f), P3 = 150(52 − f) Where, f denotes the system frequency in Hz, and P1, P2, P3 are the power outputs of the turbines in MW. Assuming generators and transmission network to be lossless, the system frequency for a load of 700 MW is

### Right Answer is: 49 Hz

#### SOLUTION

The turbine-governor characteristics of three synchronous generators are

P1 = 50(50 – f), P2 = 100(51 – f), P3 = 150(52 – f)

Total load supplied by three synchronous generators is 700 MW

or,

P1 + P2 + P3 = 700

Putting the value of P1, P2, Pin the above equation,

50(50 – f) + 100(51 – f) + 150(52 – f) = 700

⇒ 2500 – 50f + 5100 – 100f + 7800 – 150f = 700

⇒ 300f = 14700

f = 49 Hz

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