EBF 483
Introduction to Electricity Markets

3.2.4. Long Run Average Cost of Capacity: The ARR

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The Annual Revenue Requirement (ARR) for a power plant shows the annual average cost of a unit of power generation capacity. It represents the amount of revenue (per unit of capacity) that a power plant must earn to break even. The units of ARR are $ per unit of capacity per year ($/kW-year or $/MW-year).

The ARR equation looks very similar to the LCOE equation, so we have already done a lot of the hard mathematical work. There are just a couple of tricks involved. First, we need to divide the Total Installed Cost term by the total capacity of the plant, which we'll call K, instead of by the amount of electric energy output. Second, we'll need to multiply the short run marginal cost term by the capacity factor and by the number of hours in a year to convert those operational costs into the annual variable cost to operate one unit of capacity, at a given capacity factor.

The ARR equation is:

ARR = ( TIC × r 1 -  ( 1 + r ) -T ) ÷ K + cf × MC × 8,760

(Eq. 3.4)
 

Example

Calculate the ARR for a 500 MW natural gas plant with a total installed cost of $500 million. The plant has a capacity factor of 25%, a heat rate of 7 mmBTU per MWh and faces a fuel price of $3 per mmBTU. Assume that r = 10% and T = 15 years.

Remembering that marginal cost equals fuel price times heat rate, we plug numbers into the equation:

ARR = ( $500 million × 0.1 1 -  ( 1 + r ) -15 ) ÷ 500 + 0.25 × ( × 3 ) × 8,760

The ARR is used to compare the average capacity cost of two different power plants that may be used with different frequencies. A typical 'screening curve' for the ARR would be developed by plotting the ARR of two or more different power plants as a function of capacity factor. The plant with the lowest ARR for a given capacity factor would be the cheapest to build.

The figure below shows a screening curve for two different power plants: A natural gas plant with a total installed cost of $350 per kW and a marginal cost of $35/MWh; and a coal plant with a total installed cost of $1,050 per kW and a marginal cost of $10/MWh. A discount rate of 10% per year is assumed in both cases, but T = 40 years for the coal plant and T = 20 years for the gas plant.

Image described in text above.
Figure 3.2: Screening curve for two power plants.
Source: Seth Blumsack

Suppose that you were an electric utility that needed a plant that would run only during the daytime in the summer - maybe 15% of the year. At a capacity factor of 15%, the ARR of the gas plant is below the ARR of the coal plant, and so for the purpose of meeting summer peak electricity demand, the gas plant is the best choice. Now suppose that you needed a plant that would run nearly all the time - a capacity factor of 90%. At this capacity factor, the coal plant has a lower ARR than the gas plant, and so the coal plant would be the cheaper choice.