Question

A power system has two synchronous generators whose governor turbine characteristics are given by P1 = 50(50 - f) MW and P2 = 100(52 - f) MW, where f is the system frequency. When the total load supplied is 1000 MW, what is the system frequency if the operation is lossless.
1. 58 Hz
2. 44.66 Hz
3. 52.4 Hz
4. 48 Hz

Answer 1

Correct Answer - Option 2 : 44.66 Hz

Concept:

• Droop speed control is a control mode used for AC electrical power generators, whereby the power output of a generator reduces as the line frequency increases.
• It is commonly used as the speed control mode of the governor of a prime mover driving a synchronous generator connected to an electrical grid.
• With droop speed control, systems will remove energy from the grid at higher than average frequencies and supply it at lower frequencies.

Calculation:

A power system has two generators having powers P1 and P2

P1 = 50 (50 - f) MW

P2 = 100 (52 - f) MW

Given total load, PT = 1000 MW

PT = P1 + P2

PT = 50(50 - f) + 100(52 - f)

⇒ 1000 = 50(50 - f) + 100(52 - f)

⇒ 1000 = 2500 - 50f + 5200 - 100f

⇒ 150f = 6700

⇒ f = 44.66 Hz