Capacity Factor

Capacity Factor(Full Lecture)

Good day and welcome to BigBadTech. I'm your instructor Jim Pytel and today's topic of discussion is, Capacity Factor. Our objective is to introduce a common performance measurement known as, Capacity Factor. We'll learn how to calculate capacity factor and discuss how capacity factor influences energy production. This lecture operates under the presumption the viewers have watched both the energy and power and efficiency lectures, both available at the BigBadTech channel.

If you haven't watched these lectures yet or didn't recall their contents, please take the time to do so now. Let's start this lecture on capacity factor with a brief discussion about how awesome I'm. When I say that I'm awesome, I mean I'm totally awesome. I do awesome things all the time and I do them smoothly, confidently with style i.e.

Awesomely. My dirty little secret though is, there have been periods in my past that have not gone so awesomely. Not only have I crushed and burned, I have crushed and burned upside down, backwards and sideways, both personally and professionally in manners unimaginably embarrassing. The point is, not everybody can be awesome all the time, even me. If you were to measure performances as a single snapshot on one particular day, you might get an artificial inflated or deflated sense of how things are truly going.

I'd like to think my history of awesomeness, outweighs my brief but intense periods of non-awesomeness though. When taken together, places me squarely on the awesome half of the dividing line. This holistic measurement of performance taken over time is known as Capacity Factor. Capacity factor measurements aren't single instantaneous snapshots but rather, they are indicated with performance over time. Capacity factor is a measure of how often power generation facilities like wind turbines, hydroelectric dams and coal fired power plants run at full capacity.

To calculate capacity factor, one determines the time the facility actually does run at full capacity and divide it by the time the facility could have been running at full capacity.

Theoretically, all facilities could operate 60 seconds of every minute, 60 minutes of every hour, 24 hours of everyday and 365 days of every i.e. All the time. Obviously, this is way to much to ask of the real world where things can and do go wrong and capacity factor is the measure of how close the generation facility reaches this ideal standard.

Capacity factor is typically expressed using a percentage although in practice I tend to ditch the percentage and think in terms of a ratio of Did over Could. If the answer needs to be expressed in percent format, you're smart enough to shift the decimal point as needed.

Point 8, 5 is 85%, 35% is point 3, 5 and so on. Express graphically, we can visualize this as a triangular relationship of capacity factor Did and Could with Did at the apex and capacity factor and Could side by side at the base. To solve for capacity factor, take the time the facility did run at full capacity and divide it by the time the facility could have been running at full capacity.

Solve for the time the facility did run at full capacity. Take capacity factor and multiply it by the time the facility could have been running at full capacity.

If the facility really does run at full capacity for 24 hours a day, it runs at full capacity or 100%. If however the facility typically runs at full capacity for only one hour a day, the capacity factor is one over 24. Which expressed as a percentage, is roughly 4.2%. Capacity factor is a critical performance measurement for generation facilities because capacity factor affects the amount of time the facility is available to generate power. If energy is power times time, capacity factor affects the time variable in this equation. A generation facility operating more often, will generate more energy than one that runs only occasionally. Let's try a couple of illustrated examples of simple capacity factor calculations.

Consider an industrial wind turbine. So you're no doubt aware, some days it's windy and some days it isn't. Let's say this is a two megawatt wind turbine that typically operates at full capacity for only six hours a day. The capacity factor of this wind turbine is Did over Could or six over 24 or 25%. If energy is power times time, on a typical day this turbine would be expected to produce two megawatts times six hours or 12 megawatt hours or 12,000 kilowatt hours of energy.

Considering however if this same turbine was installed in a slightly windier area with an increased capacity factor of 35%. An algebraic rearrangement of the capacity factor formula suggests this turbine is typically at full production for 35% of 24 hours or 8.4 hours. Again, if energy is power times time, this turbine with a higher capacity factor, typically produces two megawatts times 8.4 hours or 16.8 megawatt hours or 16,800 kilowatt hours of energy.

Compare and contrast the energy output of the two similarly related turbines operating and reads with different capacity factors. The higher capacity turbine can be expected to produce 4,800 more kilowatt hours everyday a little than the last windy area. If the owners were selling the output of this turbine at wholesale price of let's say four cents per kilowatt hour, the turbine with the increased capacity factor would generate 4,800 times four cents or 192 dollars more each day than the one with the smaller capacity factor. If this pattern repeats itself for 365 days or a whole year, this turbine with a higher capacity factor, would have generated 365 times 192 or 70,080 additional dollars.

This is the example that's intended to illustrate capacity factor has a profound impact on the economics of energy production. It is for this reason that the wind resources of a proposed wind farm must be thoroughly investigated before development. Windier regions result to wind farms with higher capacity factor and more profitable results. Let's try a slightly more sophisticated example of capacity factor calculation. So you're no doubt aware, wind speeds can vary from gentle breezes to full-force scales.

The nominal or nameplate power of our a wind turbine is experienced only at a particular related speed typically around 12 meters per second. In the previous example, we assume the two megawatt wind turbine in a higher capacity factor area, experience exactly 12 meters per second for exactly 8.4 hours. In reality, it might be startlingly different. Wind turbines operate using something called a power curve typically defined by three points.

The cut-in speed, the rated speed and the cut-out speed.

The cut-in speed typically at four meters per second, is when the turbine actually starts producing power. Between the cut-in speed and the rated speed, power output increases. At the rated speed typically around 12 meters per second, the turbine generates it's nominal or nameplate value, in this example, two megawatts. Between the rated speed and the cut-out speed, power flat lines at the nominal value and finally at the cut-out speed typically around 25 meters per second, the turbine shuts down and prevents damage.

Let's say 10 meters per second, this turbine is up and it's only 1.2 megawatts.

Let's now take a look at wind's speed as a function of time for a particular day. To keep this problem manageable, let's say this turbine typically experiences wind speeds of 10 meters per second for two hours. Then six hours of 12 meters per second at greater land and then the wind throttles back to 10 meters per second for another two hours.

If we're asked to calculate the capacity factor of this particular turbine, we quickly run into a complication because although the turbine is operating for 10 hours of everyday, so it's has been running at full capacity for six of these 10 hours.

How can we calculate capacity factor or for a resource with variable output?

Simple, think not in terms of time but rather energy. How much energy could this turbine have produced verses how much it did actually produce.

Theoretically, two megawatt turbine running at full capacity for 24 hours a day will produce two megawatts times 24 hours or 48 megawatt hours of energy.

In actuality, this turbine produces less. For the first two hour period of 10 meters per second wind, the turbine produces 1.2 megawatts times two hours or 2.4 megawatt hours of energy. For the middle six hour period of 12 meters per second of greater wind, the turbine produces two megawatts times six hours or 12 megawatt hours of energy.

Finally for the last two hour period of 10 meters per second wind, the turbine produces 1.2 megawatts times two hours or 2.4 megawatt hours of energy. In summation, the turbine produces 2.4 megawatt hours plus 12 megawatt hours plus 2.

 

4 megawatt hours or 16.8 megawatt hours on energy in total. What's the capacity factor of this turbine if it could produce 48 megawatt hours of energy a day but in reality it only produces 16.8 megawatt hours of energy? 16.8 megawatt hours over 48 megawatt hours is the capacity factor of 35% as previously.

This is to imply that although the turbine experiences periods of variable output for a variable length of time, in this case two hours at 1.2 megawatts, six hours at two megawatts followed by another two hours at 1.2 megawatts ultimately appears as if it was operating at full capacity for 35% of 24 hours or 8.4 hours at two megawatts.

Either scenario, the real variable output or the simplified version results in the production of 16.8 megawatt hours of energy which is 35% of what the turbine could theoretically produce. What's nice about capacity factor is that, it's a super convenient way of estimating energy output for a particular facility without getting bogged down in excessive details like the availability and variability of a generation resource, maintenance schedules, unplanned outages or regulatory curtailment. Consider a massive hydroelectric dam consisting of 16, 50 megawatt turbine operating in a 50% capacity factor. This most assuredly does not mean that for 12 hours of everyday, the river is quite as a pod and the next 12 hours turn into a raging maelstrom of white water and so all the 16 turbines open up to full capacity.

It doesn't even mean that eight of the 16 available turbines run at full capacity all day. It does however imply that the dam over the course of its history typically produces enough energy as if it was running at half capacity all the time.

In reality, we might expect the dam output to fluctuate daily and seasonally throughout the year. For example, water might be intentionally spilled to aid in fish passage, navigation or flood control. Certain turbines might be periodically inoperable as they undergo maintenance repair or upgrade and certain turbines may run at reduced capacity for longer periods.

Ultimately, capacity factor takes into account all this occasions which the dam does not run at full capacity such that it automatically produces half the energy it theoretically could produce. Given this capacity factor and name-plate power rating, it's a very simple matter of determining the typical daily energy output of this dam. If all 16, 50 megawatt turbines were operating at full capacity, this dam would produce 16 times 50 or 800 megawatts of power.

If it did this for 24 hours a day, it would produce 800 megawatts times 24 hours or 19,200 megawatt hours of energy or more appropriately, 19.2 gigawatt hours of energy each day.

It doesn't. The capacity factor figure of 50% tells us the dam typically only produces half of that per day. Half of 19.2 is 9.6 gigawatt hours of energy.

All of this without having to worry about reservoir levels, seasonal fluctuations of flow rate, maintenance schedules or bagged traffic.

Capacity factor is a quick means of estimating how much energy a facility can regularly produce. Again, energy is power times time. Massive power plants with large capacity factors produce massive amounts of energy. A nuclear power plant might fit this description.

Smaller power plants with low capacity factors produce small amounts of energy. The small residential photovoltaic array, might fit this description. Speaking of photovoltaic arrays, consider a small three kilowatt residential scale PV system installed in a house in a relatively sunny area of the country known to produce 5,037 kilowatt hours of energy annually.

What's the capacity factor of this PV array? Obviously a solar resource will have a capacity factor of less than 50%.

This is sun only shines for roughly half the day and during those times it is above the horizon, it will shine with varying intensity and experience varying cloud cover. Theoretically, this plant could operate 24 hours a day. Three kilowatts times 24 hours yields 72 kilowatt hours of energy each day. If it did this for 365 days or a whole year, it could theoretically produce 26,280 kilowatt hours of energy each year. Capacity factor is Did over Could.

5,037 kilowatt hours for 26,280 kilowatt hours, it's a capacity factor of roughly 19.2%. This implies that the solar array produces enough energy as if it did run at full capacity for 19.2% of a day, or roughly 4.6 hours.

This most assuredly does not mean that the sun immediately rises and shines at full intensity for roughly 4.6 hours and then immediately sets but rather the sun shines with varying intensity for varying periods with varying cloud cover such that it ultimately produces an equivalent amount of energy as if it did shine at full intensity for only 4.6 hours a day.

For solar resource measurement, this span of time is what is commonly referred to as peak-sun hours but if you think about it, it's just another method of expressing capacity factor. 4.6 hours is 19.2% of 24 hours expressed using the time format, peak-sun hours just makes it easy to quickly estimate the average output of the solar array of a given size.

Those of you with a calculus background will realize the energy output of the array, each day is the area under the power curve. Three kilowatts times 4.6 hours yields the daily block of energy with an area 13.8 kilowatt hours. If you squint your eyes just right, both scenarios, the real varying output in brown and the mathematical equivalent in light orange, yield the same energy output I.e. Area under the power curve. I'll be at calculations employing the peak-sun hours simplification is much much easier.

All things being equal, this three kilowatt array ultimately produces 13.8 kilowatt hours of energy each day or 5,037 kilowatt hours per year whether the sun shines with varying intensity for varying periods of time or if immediately pops over the horizon and shines at it's full intensity for 4.6 hours and pops below the hills, plain in to the world into total darkness.

We'll examine PV systems in peak-sun hours in greater detail in later lectures. For now, you should simply appreciate that peak-sun hours and capacity factor both influence the amount of time a facility is able to generate.

There is simply different methods of expressing the same quantity. Before we bring this lecture to a close, let me remind you as I hope this examples I've illustrated, facilities with high capacity factors generate a lot of energy and as a result, they are more economically successful. If you're in the energy business, even a small increase in capacity factor reaps tremendous financial rewards. It is for this reason the intelligence scheduling of routine maintenance and timely repair of critical systems during periods of high resources availability are so important.

Alright, that's about it for today.

In conclusion, this lecture present a capacity factor calculations. Well, capacity factor is a performance measurement of how much energy was generated verses how much could have been generated. Remember to review these concepts as often as you need to really drive it home. Imagine how well lab will go if you know what you're doing. Thank you very much for your attention and interest.

Let's see you again during the next lecture of our series. Remember to tell your lazy lab partner about this resource and be sure to check out the BigBadTech channel for additional resources and updates.

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