Question

onsider a 200 kW fuel cell combined heat and power (CHP) plant that is fueled with natural gas that has a lower heating value of 48.3 MJ/kg. Based on the lower heating value of the fuel, the power plant has a heat rate of 9000 Btu/kWhe. The heat rate accounts only the production of electricity from the fuel cell and not the delivery of heat. The capacity factor of the plant is 60%. The fuel cell is a combined heat and power (CHP) plant which produces 300,000 Btu/h of heat energy at the rated power of 200 kW. What is the lower heating value combined heat and power efficiency of the plant (%)? 5. What is the lower heating value combined heat and power efficiency of the plant (%)?

Answer 1

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.