The lower heating value combined heat and power (CHP) efficiency of the plant can be calculated using the following formula:
Efficiency = (Useful Energy Output / Energy Input) * 100
Where:
Useful Energy Output = Electrical Energy Output + Heat Energy Output
Electrical Energy Output = Rated Power * Capacity Factor * 1 hour
Heat Energy Output = Heat Energy Output at Rated Power * Capacity Factor * 1 hour
Energy Input = Fuel Energy Input * Capacity Factor * 1 hour
Given the information:
Rated Power = 200 kW
Capacity Factor = 60% (0.6)
Heat Energy Output at Rated Power = 300,000 Btu/h
Fuel Energy Input = Rated Power / Heat Rate
First, let's calculate the fuel energy input using the heat rate:
Fuel Energy Input = Rated Power / Heat Rate
Fuel Energy Input = 200 kW / 9000 Btu/kWhe = 0.0222 MMBtu (Million Btu)
Now, let's calculate the useful energy output:
Electrical Energy Output = Rated Power * Capacity Factor * 1 hour
Electrical Energy Output = 200 kW * 0.6 * 1 h = 120 kWhe
Heat Energy Output = Heat Energy Output at Rated Power * Capacity Factor * 1 hour
Heat Energy Output = 300,000 Btu/h * 0.6 * 1 h = 180,000 Btu
Useful Energy Output = Electrical Energy Output + Heat Energy Output
Useful Energy Output = 120 kWhe + 180,000 Btu = 120 kWhe + 0.18 MMBtu
Now, we can calculate the efficiency:
Efficiency = (Useful Energy Output / Energy Input) * 100
Efficiency = (120 kWhe + 0.18 MMBtu) / (0.0222 MMBtu) * 100
Calculating this value will give you the lower heating value combined heat and power efficiency of the plant as a percentage.