Variable costs, recall, refer to the costs of power generation that change as the amount of electricity is generated. The simplest model for variable cost of power generation is:
Marginal cost of generation ($/MWh) = Marginal cost of Fuel + Variable operations and maintenance costs.
The marginal cost of generation for power plants that run on fossil fuels plants (coal, oil, gas) is dominated by fuel costs. Labor and maintenance are additional costs, but these are smaller (less than 10% of total variable cost), and often times we will simply assume that these costs are negligible, or zero.
Marginal costs for renewable power generation and nuclear power are dominated by operations and maintenance (O&M) costs. This is because fuel from the sun, wind and water is (at the margin) basically free, and because the market price of nuclear fuel has historically been extremely low.
You will recall from your economics courses that there are two forms of "marginal cost." The short-run marginal cost measures the cost to produce a unit of electric energy (not power), given an existing power plant. So the short run marginal cost captures fuel and variable O&M costs. The "long run marginal cost" measures the cost to produce a unit of electric energy where we don't assume that the capacity of the plant is fixed. For example, if a plant was operating at maximum capacity and we wanted to figure out the cost of going beyond that maximum capacity, that would be long-run marginal cost because we would need to incorporate the costs of additional boilers or other equipment.
When we talk about marginal cost in this lesson and most of the time in this course, we will be referring to the short run marginal cost. Remember that the short run marginal cost takes units of dollars per energy unit ($ per MWh). Don't confuse this with the cost of capacity ($/MW or $/kW)!
The marginal fuel cost of a plant that uses coal, oil or natural gas is determined by the plant's efficiency or "heat rate," which is the the ratio of input energy to output energy [BTU/kWh], or how much fuel it takes to produce a unit of electrical energy. To make our lives easier, we will use the heat rate in units of [million BTU/MWh]. We will also use the abbreviation "mmBTU" for "million BTU."
The heat rate determines the efficiency with which a power plant converts fuel to electricity. One MWh of electricity has the same amount of energy as 3.412 mmBTU. Thus, a plant with a heat rate of 3.412 would be perfectly efficient.
We can convert easily between the efficiency of a power plant and its heat rate. If E is the efficiency of a power plant (in percentage terms) and HR is the heat rate, we can convert between the two as follows:
We will now illustrate this with two examples:
A power plant with a heat rate of 8 mmBTU/MWh would have an efficiency of:
A power plant that converts fuel to electric energy with a 30% efficiency (E = 0.3) would have a heat rate of:
We can now use the heat rate plus a market price of fuel (in units of $/mmBTU) to calculate the fuel cost portion of the short run marginal cost. For a plant with a heat rate HR and fuel cost $F/mmBTU the short run marginal cost of generation (ignoring labor and O&M), in $/MWh, would be the product of the fuel price and the heat rate:
An example will illustrate how the short run marginal cost is calculated.
Natural gas costs $5 per million BTU. The heat rate of your natural gas plant is 8,000 BTU/kWh. The plant's marginal cost, in $/MWh, would be given by:
Coal costs $2.50 per million BTU. Your coal plant is 35% efficient. To calculate the plant's marginal cost, we would first convert the efficiency to a heat rate:
Next, we would multiply the heat rate by the fuel price to get the plant's marginal cost: