Capacity Factor II

Capacity factor is a so-called figure of merit for power stations (and for various other capital assets). For a power station, it is the ratio of the total amount of energy generated over a period to the amount that would have been generated if the output had been maximum for the whole period.

So if the output was actually maximum for the whole period, the capacity factor would be 1, normally written as 100%. If the output was 50% of maximum for the whole period, the capacity factor would be 50%; if output was 80% for half the time and zero for the other half, the capacity factor would 40%. Typically the output varies up and down between 0% and 100%, and you have to average the percentage output.

The reason why output is less than 100% of maximum could be either because the demand for power is not there, or because the power station is for some reason unable to deliver 100% of its maximum power some of the time.

The higher the capacity factor, the better are the economics of your power station. You’re getting a better return on the capital cost. It’s a nuclear enthusiast’s favourite figure of merit, because in general nuclear power stations have high capacity factors.

Nuclear, fossil fuel, waste combustion, and some hydroelectric power stations can achieve high capacity factors, generally limited only by downtime for maintenance. Whether they actually achieve high capacity factors is largely determined by demand. Nuclear power stations, with high capital costs to pay interest on whether they’re delivering power or not, like to keep their capacity factors high. Other power stations also like to keep their capacity factors high, but it’s not quite as important to others, with lower capital charges. They still have to pay their capital charges regardless, but their fuel bills go down when their output is reduced.

The capacity factor of hydroelectric power stations with large turbines and generators in proportion to the water supply in their catchment areas is lower. They run out of water if they run at maximum output continuously. This is still worthwhile because they can supply large amounts of power at times of peak demand.

These preferences, and the relative strengths of the preferences, can be reflected in different price structures if the price of energy is continually adjusted according to supply and demand: when demand is low, the price should be low, and for fossil fuel stations it ceases to be worthwhile running, because the income from the power output drops below their fuel costs. Nuclear stations would keep running, because their fuel costs are lower and they want to keep paying at least some of their high capital charges. Peak-demand hydroelectric stations have higher capital costs than others with similar water supplies, but can afford this because they sell all their power at premium rates at times of peak demand.

The capacity factor of wind or solar power is limited by the strength of the wind, or daylight hours and cloud cover – as well as demand. In the case of wind power, this is compensated for by low capital costs and zero fuel costs. Solar power needs to bring down its capital costs before the same can be said about it, but it’s getting close and can be expected to get there before long – sooner and at much lower costs in research than nuclear, whether a new generation of fission reactors or pie-in-the-sky fusion reactors.

Just as you can design hydroelectric power stations to have high capacity factors (small turbines and generators that run most of the time) or to be able to deliver high peak power when demand is high (large turbines and generators that use too much water to run all the time), so you can design wind farms to have high capacity factors (small generators, in relation to the turbine driving them, that run flat out even in light winds), or high peak output when strong wind is available (large generators, in relation to the turbine driving them, that produce less than maximum output in average winds). The significant difference is that the wind farm’s peak available output does not necessarily occur at times of high demand, and at such times will have to be sold cheaply enough to undercut fuel costs at fossil fuel power stations. But that’s the whole point of having them: to reduce fossil fuel consumption – and more importantly, correspondingly reduce carbon dioxide emissions.

So what’s a more appropriate figure of merit?

We want to take into account not only the percentage of the maximum power output that a power station is supplying at any given moment, but also the value of the power it’s producing. There’s no point generating power when it’s worth nothing because nobody wants it, and if you’re going to store it for later use, you’ve got to take the cost of storage into account. One way to do that (not necessarily the only one, but a perfectly good one) would be for the storage facility (say a pumped storage system) to buy the excess power (from a nuclear station at times of low demand, or a windfarm at times of high winds) at a relatively low price, and sell it back to the grid at times of high demand.

The difference between the price the storage system receives for peak power, and what it pays for off-peak or excess power, has to be enough to pay for the system’s costs – which either holds the price of off-peak/excess power down, or pushes the price of peak power up, or a bit of both. It’s worth building more storage capacity if the price difference, and the demand for the service, is high enough to pay for it. (All that, not forgetting that no storage system returns as much energy as you put into it. The pumped storage system at Dinorwig returns about 75%, which is pretty good as these things go.)

We also want to take into account the capital cost of the installation. If a power station costs twice as much (per peak megawatt) to build, it needs to have double the capacity factor to be equally economic – ignoring fuel costs.

And of course we want to take fuel costs into account, too.

So the proper figure of merit is this:

(Value of energy generated – variable costs) / (fixed costs)

(where the value of the energy generated varies over time according to available supply and demand, and fixed costs may be mostly capital financing costs, but may include a non-variable part of maintenance and staffing costs)

which doesn’t really look much like capacity factor at all.

The corresponding figure of merit for a pumped storage system is:

(Value of energy returned at peak times – value of energy received off-peak) / (fixed costs)

– and of course that would be negative if you didn’t take into account the different values of peak and off-peak energy, since a storage system never returns as much energy as it receives!

Further reading

Something we’ve still not taken account of is the fact that the value of energy generated, and fuel costs, are not known at the time of construction of a power station. Add to that, if (as is generally the case) you borrow the money to build the power station, then the amount of interest you have to pay on the capital cost will vary in the future, too. And of course what you actually have to pay for the construction is not usually the same as the estimate given to you by the contractor building the power station. For more information about this, see Economics again – Discounting.

If you want to know why I describe fusion reactors as pie in the sky, see Nuclear Fusion? No thanks.

All this assumes that all these facilities, and consumers, are connected by a power grid. This assumption need not hold in all places at all times. See Not Melting the Grid.