# Capacity factor illustrated: Calculator & self-test Quiz

### Illustrating Capacity Factor (& its Business Importance)

The capacity factor of a power project is a key metric in its business success (or failure). That’s not surprising, since capacity factor is providing a measure of the degree to which your expensive asset is approaching its theoretical maximum energy (and hence revenue) production.

The best way to appreciate how much different capacity factors can change the economics of a project is to play around with some very simple numbers.

Again a simple online calculator is provided to allow you to do this – click below to open it (in a new window):

CALCULATOR: Capacity Factor

Below is a self-test quiz to help you get a feel for how the different variables and outputs in the calculator are connected.

Q1.

Onshore wind in a market costs \$1.5 per Watt to build and operates at a capacity factor of 30%. Offshore wind can operate at a capacity factor of 50%. For both to offer the same simple investment/revenue ratio at an energy price of \$70 per MWh, what would the installed cost of offshore need to be?

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\$2.5 per Watt

In fact the energy price here is irrelevant. So long as both sell at the same energy price, the investment/revenue ratio will be the same as an investment/energy production ratio (since revenue = energy x price). Energy production is a function of capacity factor (= CF x capacity x time period). So for a given capacity and the same time period, energy production offshore is 50%/30% or 1.66 times that onshore. To keep the investment/energy ratio in balance between the two, the same needs to be true of investment cost: i.e. offshore cost = 1.66 x 1.5 = \$2.5 per Watt.

Q2.

Two wind farms are bidding in a competitive auction. Both can be built for \$1.5 per W. Based on wind measurements, one expects a capacity factor of 35% and intends to bid a price of \$50/MWh. The second one expects a capacity factor of only 30%. To generate the same annual revenue for investors, what price would it have to bid?

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\$58-59 per MWh

This illustrates the rather obvious point that if you have access to a better resource and all other things are equal, you will generate more energy to sell for the same investment in capacity. You could make more money or, in a competitive situation, you could charge less for your energy and still give your investors the same returns. Again, because everything else is equal, the maths here are actually rather simple. The ratio in capacity factors is 35/30 = 1.166 and so the ratio in prices is the same, just reversed (i.e. lower capacity factor = higher price). So. \$50 x 1.166 = \$58.3 (but our calculator only allows whole number prices to be input).

Interesting follow-up questions would be:

• If the less windy project needs to make a competitive bid on price, how much cheaper do its installed costs need to be to offer a similar rate of investment payback (using the investment/revenue ratio as a simple proxy for this)?
• If the less windy project needs to compete on price and can’t cut its costs, how much later is that simple payback?

No surprise that again – at least in these very simple calculations – both answers scale with the difference in capacity factors. Try it and see!

Q3.

100MW of coal generation, operating at 70% capacity factor, is due to be shut down. If replaced by solar PV, operating at 25% capacity factor, what capacity of PV would need to be built in order to generate equivalent annual energy?

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280 MW

This an illustration of the classic capacity vs. energy issue that you’ll encounter when people talk about market shares and energy mixes. Many charts and articles focus on installed capacity and capacity growth, but it’s important to realise that large installed capacity doesn’t necessarily mean lots of generated energy! The latter depends on the capacity factor of the capacity you install.

It should be evident here that the ratio of coal/solar in energy terms, measured by the respective capacity factors, is 70/25 (= 2.8). So to equal the energy generation up, you’ll need 2.8 times as much capacity of solar than you do coal.

Q4.

If Solar PV costs \$2 per W to install, what is the difference in investment cost between two plants, both of which must produce 219,000 MWh each year but one of which will operate at a capacity factor of 25% and the other at 20%.

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\$50m

If you have an energy target to reach but operate further from the maximum potential of your power plant (perhaps because it’s in a less sunny location), you’ll have to build more capacity to get there. To produce 219,000 MWh at a capacity factor of 25%, you’ll need 100 MW of capacity (capacity = energy / (capacity factor x 8760 hours). Do the same calculation with a capacity factor of 20% and you need 125 MW. At \$2 for every Watt of capacity, that’s an extra 25 million Watts at \$2 each = \$50m

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