The Flaws Inherent in Capacity Factor

Capacity Factor is a performance indicator for generation assets, and must always be calculated retrospectively. It is a measure of how a generator has performed. Strictly speaking it is the annual generation divided by nameplate capacity times 8760 (hours in a year). So it is a percentage indicator, of how much electricity the generator produced, compared to its theoretical maximum.

It is often used, badly, in internet arguments about the relative merits of the available generating technologies. But, like any of these gross indicators if you don’t fully understand what is bundled up in the calculation, you don’t really understand the metric.

The big coal-burners aim for very high capacity factors. As noted in the first baseload post, their business is based on burning as much coal as possible, ideally running flat out all the time. Anything over 90% would be a pretty solid result, with numbers around 70% far more common, and I’ve even seen some in the 50s. As you can be pretty sure these plants want to run all the time, the capacity factor is a very gross indicator of how much maintenance the plant needs, and their operating profile within the market. Coal is a pretty cheap fuel, and their maintenance costs are relatively fixed, so they run as often as possible to smear that maintenance cost across more generation.

Consider too all of this in the context of “baseload”. A plant that only runs half the time is considered baseload? This is our benchmark for reliable electricity production?

For the gas burners, their fuel cost is the main driver, so they run less frequently, waiting for the moments when the price for electricity is high enough to make some money. I will do a series on generation-technology, but for the moment it is sufficient to say that gas lends itself more readily to this sort of on/off operation. For these generators, the capacity factor, taken in isolation, is an indicator of volatility in the market, a proxy for how often electricity was valuable enough to cover the costs of burning gas. Not surprisingly, there is a huge range in gas-plant capacity factors, with 50% being very high, and low single figures for some of the acute peaking plants. I have even heard a story of a small gas engine that was commissioned the day before the market went to their maximum price (it is capped at $12,500/MWh), ran for a few hours, paid off the capital and made some money, and then mothballed it the next day to wait for the next maximum.

Using capacity factor as the sole comparison with renewables is farcical.

For wind power, the problem comes from the inclusion of “nameplate capacity” in the calculation. Unlike steam turbines, wind turbines don’t really have a hard upper limit. In a standard coal plant, the 4 x 250MW turbines will all produce 250MW when running hard; they will never go above this. Their nameplate capacity is the limit of their performance.

For a wind turbine there is an element of arbitrariness in the declaration of capacity. Sure, they have a safe upper limit, at which the turbine does a few things to protect itself, but that’s not the nameplate capacity. That capacity is usually chosen to represent the output at a given wind-speed; say 5m/s. So they might call it a 2MW turbine, but that is not the maximum output, nor even the average output. And that difference is important, because the relationship between wind-speed and output is non-linear; ie the difference between output at 3m/s and 4m/s is LESS than the difference between 4m/s and 5m/s. The output gets bigger, faster as wind-speed increases. So averaging that output over a year, and dividing it by the flawed theoretical maximum gives some idea of how much they were used, but not a very detailed picture. It is little better than a guess at how likely a wind-farm is to meet production, within a one year window, which is a proxy for how windy it was last year. It is essentially a weather report.

Knowing all of that, capacity factors for wind-farms range from about 20% to 40%.

While this is linked to a long-term problem I have with qualitative analysis in this field, there are better ways to talk about renewables output. They will be complex, but renewable energy interactions with our demand profile is a pretty dynamic problem and so we need a more complicated dialogue to make sense of it.

There are two major flaws with using capacity factor to describe the output of renewables; the first is that there is no comment on the “shape” of the profile. A 40% capacity factor suggests that the farm ran flat out exactly 40% of the time. But is that how wind works? The wind blows at exactly 5m/s four out of ten days? Seems unlikely. Perhaps it ran at half capacity for 80% of the time? Or better yet, maybe it ran at exactly 40% capacity all the time? That would be terrific! My main point here is that the detail is lost, and no consideration of how this output meets our needs fits into such a coarse indicator. So, and we’re nearing the limits of my maths here, there might be a fancy Fourier transform one could do with a wind-farm’s output data-set, to describe the profile more accurately. My understanding is that the Fourier-transform of a continuous function paints a picture of the data; how often it achieves maximum, how long it is at zero, the range of values, that sort of thing. It is a frequency histogram of the values in the data set. Complicated? Yes, no doubt. Useful? Absolutely. An even simpler method might be just to describe the mean and standard deviation; the average production and how often production is near that average. Again though, this will be thrown out severely by days of zero production, where the Fourier-transform would capture this.

The second is related to the first, and is particularly pertinent when considering solar electricity. Solar is regularly reported as having a capacity factor of around 25%, and given that it requires sunlight this isn’t really surprising. There is even a decent argument that 20% should really be 40%; the “theoretical maximum” for solar surely doesn’t include night time does it? Leaving that aside, this suggests that solar panels achieve maximum output for about 6 hours a day. Intuitively we know this is probably three hours before and after midday. The internet argument goes that 25% capacity factor isn’t enough, and that means we need to install four times as much generation. But this idea is mired badly in the baseload mindset and utterly ignores the fact that demand changes during the day, and by quite a lot. Again a better descriptor is possible, considering the relationship with what is essentially free energy, and network demand. What if solar output matched air conditioner demand? That seems pretty likely too; hot days are sunny days. I’ve linked to this article before, but it’s still useful. Look at how solar power is contributing to our grid at the moment. Perhaps with a bit of clever engineering and some insulated houses we could directly match solar output to air conditioners, and come home to a house that has been cooled automatically, with power generated on-site?

I’ll leave it there for the moment, but I wanted to seed some ideas. There are some huge opportunities to link renewable energy supply with electricity use, and even some very interesting options for direct energy use, in say a thermal cycle air-conditioner, rather than a compressor driven unit.

I’ll summarise the whole lot with “I don’t really like capacity factor as a stand alone descriptor” and to encourage you to be skeptical of anyone who does like it. You’re not getting the whole picture.

 

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About evcricket

Extreme gardener, engineer and bird nerd. View all posts by evcricket

7 responses to “The Flaws Inherent in Capacity Factor

  • Robert Merkel

    I agree it’s simplistic, but it’s partly a response to the even more simplistic arguments sometimes made by proponents of renewable energy.

    You often read posts about a megawatt of wind capacity being as cheap as coal/gas/nuclear etc, without any acknowledgement that a megawatt of wind capacity will actually produce a lot less saleable energy than a megawatt of capacity from traditional sources, won’t produce any energy at all for extended periods, and its production may or may not be correlated to demand (with the acknowledgement that current pricing models don’t expose the real cost of energy to consumers and that demand profiles may look very different when that happens).

    The question of how we’re going to build a clean energy system that meets demand affordably is still very much an open one in my view. Will simple thermal energy storage at the consumer end, simple demand management and the easily switchable energy sink that electric car charging represents be enough, or are we going to need a lot of supplementary energy storage and if so of what form?

    • evcricket

      I think you need to be careful with the benefits of electric cars Robert; a few commentators have counted those chickens incorrectly in my opinion. To use electric vehicles as grid storage they must be plugged in, fully charged and with a known amount of time available before they are to be used. Otherwise people will get into cars with empty batteries, but a couple of dollars in their pockets.

      • Ender

        Hi evcricket,

        Just stumbled across your blog today – looks good.

        Just as an aside to this studies have found that even at peak hour up to 80% of all the cars in a city are parked and not moving. This battery resource is a changing thing however over the day we can count on a large amount of cars parked and (hopefully) plugged in. An idea I had was a free city carpark for EVs. Instead of charging for parking the lot operator would buy the rights to sell the parked EVs power while they are parked there. This way the lot operator would appear on the grid as a battery and be able to sell peaking power. The car owner would get free city parking in return.

        The cars themselves would report to the grid how much energy they have and how much they can give. All these parameters could be set from your iPhone or Samsung from wherever you are. You will be able to remotely set the minimum charge required to get home and the time that you are travelling from anywhere. There is no chance that the chargers and inverters in these cars will be dumb. They will be smart nodes on the grid and in full communication with the grid and their owners at all times.

      • evcricket

        Interesting idea Ender… the problem might be when the cars are idle; there is loads of cheap power available over night, but less so during the day. Maybe if the battery capacity far exceeds that needed to drive to work they could supply peaking bursts during the day?

      • Ender

        evcricket – “the problem might be when the cars are idle; there is loads of cheap power available over night, but less so during the day. ”

        Even during the day, except for taxis and delivery trucks most of the cars are in parking stations idle or at home also idle. Think of how you use your own car. I am sure you use it on average for less than two hours per day leaving the other 22 hours available to use your battery.

        The depth of discharge can also be controlled. Lithium batteries have cycle lives of 1000 to 2000 cycles to 80% DOD however if the DOD is controlled to 50% or 30% then the cycle life is double or triple this. If there are enough EVs with 40 kWhr batteries or larger 30% of this capacity is a staggering amount.

        There are about 7 million cars in Australia if 10 % of them were EVs or Plug in Hybrids (PHEV) the there would be 700 000 * .8 batteries available most times of the day = 560 000. The full capacity of these batteries is 40 kWhr * 560 000 = 22 400 000 kWhrs. Using 30% still leaves 6 720 000 kWhr that is available for use at any one time. As you can see the batteries if there was sufficient feeder line capacity could supply 6 GW for an hour which would be sufficient to be a spinning reserve for any large power station.

        Also something that has not been thought of is the each of the car inverters are precisely controllable in phase, frequency and amplitude in millisecond intervals. If large ripples were present on the power grid that threatened the supply then the cars could be programmed in milliseconds to deliver the anti-wave of the interference like Bose noise cancelling headphones. In this way EVs could be a immense stabilising influence on the grid.

  • dos74

    Hi evcricket. Just discovered your blog today and have very much enjoyed your posts. Just a couple of points about this one though. These days, the rated capacity of a wind turbine is essentially the same as the maximum output of the turbine, give or take a couple of %, unless something has gone very wrong. The turbines typically reach their rated capacity at speeds of about 12m/s, while their generation at 5m/s is only a tiny fraction of the rated capacity. Have a look at page 18 of the Vestas V112 3MW turbine specs for a typical power curve.
    http://v112.vestas.com/Vestas_V_112_web.pdf
    In terms of how the output of a wind turbine looks, try downloading the output data from wind farms at this site:
    http://windfarmperformance.info/
    For example, the Cullerin Range 30MW wind farm had an average CF of 40% for 2011. Within that 40% figure, you can discover that about 27% of the time is was generating at less than 10% rated capacity, about 14% of the time it was generating more than 90% of rated capacity, and obviously the remaining 59% of the time it was somewhere between 10% & 90%. This is not quite the same as the output of an individual turbine, but it’s not far from it.

    • evcricket

      Thanks David, great comment.

      I don’t know much beyond the theory of wind farms, I must be one of the few power engineers in Australia who hasn’t worked on one. I wonder what wind developments as a % of new developments have been over the last ten years? Apparently wind output has grown every month over that period.

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