Question

A power system has two synchronous generators having governor turbine characteristics as

P₁ = 50 (50 - f)

P₂ = 100 (51 - f)

where f represents the system frequency. Assuming a lossless operation of the complete power system, what is the system frequency for a total load of 800 MW?
1. 55.33 Hz
2. 50 Hz
3. 45.33 Hz
4. 40 Hz

Answer 1

Correct Answer - Option 3 : 45.33 Hz

A power system has two generators having powers P₁ and P₂

P₁ = 50 (50 - f)

P₂ = 100 (51 - f)

Given total load, P_T = 800 MW

P_T = P₁ + P₂

P_T = 50(50 - f) + 100(51 - f)

⇒ 800 = 50(50 - f) + 100(51 - f)

⇒ 800 = 2500 - 50f + 5100 - 100f

⇒ 150f = 6800

⇒ f = 45.33 Hz