I have written this article because many news articles, statements or reports I have recently read about wind energy involves the author confusing energy (kWh) and power (kW) and thus undermining the message they are trying to put across. Actually I totally understand this confusion – because, quite simply, the topic IS confusing. I’ll explain why here.

For example, let’s look at the problem of curtailment. If you are a wind farm operator with a wind farm in an area where the grid has not been developed in order to cope with the increased capacity (usually in rural areas), at certain times you may be instructed by the grid operator to reduce, or curtail, the power of your wind turbines to a certain value, let’s say from a rated power of 2 MW to 1.5 MW – a 25% reduction. This does not, however, automatically mean that the wind turbine is going to produce 25% less electricity. This is because electricity production is measured in kWh (energy), not in kW (power), and the energy production is not only dependent upon the power capabilities of the wind turbine, but also on the wind speed distribution over time at the site.

***NEW: The difference between capacity factor and capacity and why this is important: HERE***

Units

Let’s look first at the concept of units. Units are great – and you use them every day without knowing it. For example, we all know intuitively that we can’t add a distance in miles (used in the UK) to a distance in kilometres (used almost everywhere else in the world) – or a weight in stones (UK) to a weight in kilograms (almost everywhere else). By the way, kilograms and stones are measures of mass, not weight, but that’s a different story. If I want to know what the sum of 10 miles and 10 kilometres (km) is, I first have to decide which unit I want my answer in (let’s say kilometres) and then first convert 10 miles to kilometres (16 km) and then add the two values up (10 km + 16 km = 26 km). To avoid confusions related to units, of which one can find some interesting examples, scientists came up with the International System of Units (SI) in 1960, now the most widely used system of measurement and the modern form of the metric system. In this system, seven base units are defined, for example distance in metres, mass in kilograms and time in seconds. There are then loads of other units, such as Newtons (force), Pascals (pressure), Volts (voltage), and Ohms (electrical resistance), which can all be directly derived from the base units. More about this here.

Energy and power

Most of you probably have a vague feeling about the basic concept of energy. You need energy to go to work, do sport, go for a walk - even for breathing. And smiling 😊. You gain the required energy by sleeping and eating, mainly.

So, what are the units of energy? Energy is measured in Joules (J) named after the British scientist, James Joule.  A Joule is actually just another name for Nm (or Newtons, N multiplied by metres, m), and is the amount of energy transferred to an object by moving it one metre against a force of one Newton. A Newton (N) is the derived SI unit of force, named after the great Physicist and Mathematician, Isaac Newton, who discovered gravity when  (so the story goes) an apple fell on his head as he sat under an apple tree.

If you go on a bike ride, you have kinetic energy due to your forward movement, and as you cycle up a hill you gain potential energy too, losing it as you go back down. You also need energy to overcome friction between your bike tyres and the road as well as air resistance, which are both pushing against your forward movement. Anyone who has cycled up a hill on a windy day can associate with this. As energy can never be destroyed (only transferred), if you go on a long ride, you eventually need to eat an energy bar (or a banana) to top up the energy you have transferred from your muscles to the bike in order to move forwards. There are lots of other forms of energy that we meet in our everyday life, which I am sure you are also familiar with, including gravitational, electric, magnetic, elastic, chemical and thermal energy.

For each Newton of air resistance acting against you, you need one Joule of energy to move one metre forwards. For a typical air resistance on a rider cycling at 30 km/h of about 10 N (calculating this value is yet another topic I shall approach in the future), you would need 10 Joules per metre – and 500,000 J (500 kJ) for a 50 km bike ride (ignoring friction resistance and any extra energy for going up hills).

What about power? Power is the amount of energy consumed per unit time with units of Watts (W), or Joules per second (J/s). So if you needed an hour and a half (equivalent to 5,400 seconds) to consume 500 kJ, then your average power would be 93 W (500,000 J divided by 5,400 seconds).

One can also quite easily convert power to energy using the same principle - let’s think of your bike ride again. When you have finished your bike ride you might fancy a cup of tea. A kettle may have, for example, a power of 2 kW. Let’s say the water in the kettle needs four minutes (240 s) to boil, then the (electrical) energy required is 2 kW multiplied by 240 s which makes 480 kJ. Notice that you have just used about the same amount of energy boiling the water than you needed to cycle 50 km!

 
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Kilowatt hours

That all makes sense, right? The first slightly confusing part of this article is the concept of kilowatt hours (kWh). I said earlier that energy is measured in Joules (or Nm). However, electrical energy is usually described by electrical utility companies, and in power plants such as wind farms, in kilowatt hours (kWh) instead of Joules. This is because one Joule is a very small unit of energy compared to the energy that is produced by a household, and talking about electricity bills using numbers like 30,000,000,000 Joules is a bit ridiculous.

Just like Joules, the unit of kWh still describes a measure of power multiplied by a time – it’s just that instead of having units of Watts multiplied by seconds, the units are kilowatts multiplied by hours. You can thus scale from Joules to kilowatt hours as follows:

 
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So, as you can see, kWh is just another (non-SI) way to describe a unit of electrical energy!

Let’s get to wind energy then, and to the second slightly confusing part.

Power and energy of wind turbines

In order to calculate the amount of electricity produced by a conventional coal powered plant, for example, one can simply multiply the power in kW by the number of operating hours in a year to get the amount of kWh in that year, like we did for our cup of tea in Joules. This is because the power remains constant when the plant is running, like the kettle.

The power production of wind turbines, however, varies with the wind speed they experience, because their operation is governed by the aerodynamics of the blades. Think of an aeroplane – the reason it has to accelerate so quickly on the runway is because it only generates enough lift to fly once it reaches a certain speed. The lift force increases with the wind speed that the wings experience.

This is also true for wind turbine blades, and the variation of power production with wind speed is described by a power curve, which is individual to each wind turbine model and usually looks something like this:

 
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So you can see that the power produced by a wind turbine increases with the wind speed it experiences – for example, for this case, for a wind speed of 4 m/s, the power is 500 kW and for a wind speed of 8 m/s, the power is 1,500 kW. At a certain wind speed (here 12 m/s), the power is held at a certain defined value, known as the rated power (here 2,000 kW) using clever aerodynamic adjustments of the blades. This is to avoid damage to the wind turbine at extremely high, infrequent wind speeds. The rated power is the value used to describe the installed capacity of wind energy (and not the energy production!).

With this curve, the wind turbine manufacturer simply guarantees the buyer that the wind turbine will produce a certain amount of power at a certain wind speed. There is no guarantee of the actual amount of electricity (energy) produced by the wind turbine, because this is dependent on the wind conditions, which are unique to each location.

So, how does one calculate the amount of electricity in kWh produced by the wind turbine in, let’s say, one year, using this power curve? Considering the things I said above, it’s clear that we somehow need to multiply some value of power (kW) with time (in this case number of hours per year) to get to kWh. We can’t just take the rated power and multiply this with the number of hours of operation, as we did earlier for the coal powered plant, because the wind turbine is not operating at the rated power most of the time.

Why not? This is because wind is not very well behaved and doesn’t just blow at a constant speed the whole time – it’s part of the very complicated global weather system! The behaviour of the wind over time is not completely erratic though – there are certain times of year when storms are more likely, and certain times when there’s hardly any wind. Actually, wind speeds generally follow pretty predictable daily and seasonal patterns at most locations. In fact, the wind speed over one year is usually distributed something like this:

 
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This means that 1% of the time, the wind speed is between 0 and 1 m/s, 2% of the time it is between 1 and 2 m/s, 6% between 2 and 3 m/s etc. Adding all these bars up gives a total of 100%. Let’s call each of these ranges “wind speed bins”. If you make these bins infinitely small you end up with a curve like the black line drawn on the figure.

What does this mean now for the annual energy production of the wind turbine? Let’s take a look at the wind speed bin between 2 and 3 m/s, which occurs 6% of the time. The power production from the power curve is about 50 kW at 2 m/s and 70 kW at 3 m/s. This means that the power production ranges between 50 kW and 70 kW 6% of the time. For the purpose of simplicity, we can take the mid-point of this range (60 kW). The energy production in this time is then 60 kW multiplied by 6% of 8,760 hours in a year, which makes 31,536 kWh. This approximation is generally acceptable for wind speed bins of size 1 m/s (making the bins smaller has a negligible effect on the result and just means more hard work).

If one does the same for each wind speed bin, one comes up with the following energy production distribution:

 
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Note that the maximum energy production occurs at a higher wind speed (11 m/s) than the maximum frequency wind speed (7 m/s), due to the much higher power. All that remains is simply to add the energy in each wind speed bin together and we have the annual energy production of the wind turbine – about 10,000 MWh in this case! This is about enough electricity to power 1,000 households.

Not too difficult after all!

Effect of site on wind turbine energy production

So now it’s quite obvious that if this wind speed distribution changes, the annual energy production changes too. Here are two more examples of possible wind speed distributions:

 
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The one on the left has a much lower average wind speed and the one on the right a much higher one. I’ve drawn the power curves over the top too, so you can see how they multiply together to get the energy production. For these two wind speed distributions, the annual energy productions of the wind turbine introduced above are 6,600 MWh and 13,600 MWh (compared to 10,000 MWh for the first example). From this you can see that for each site, the most suitable wind turbine has to be carefully chosen. If the wind speed is generally quite low, a large wind turbine will be completely over-dimensioned and too expensive. On the other hand, if the wind speed is quite high, a small wind turbine won’t exploit the available energy and won’t bring the best return of investment, either.

This also helps explain the reason for holding the power at the rated value at very high wind speeds, by the way. You can see on the wind speed distribution plots that the high wind speeds occur very infrequently – this means that even if the wind turbine was built with a large generator to be able to produce these large amounts of power, the very short amount of time of occurrence would mean that this power would have a very small effect on the annual energy production, not justifying the increased costs.

What about the topic of curtailment I mentioned at the start? Well, if we curtail the power of the wind turbine in the three examples above to 1,500 kW (as sketched on the last figure), the reduction on the annual energy production is then established by calculating a new energy production distribution using the curtailed power curve. The results show that the reduction is about 10%, 5% and 15% for the three different example sites.

This is why it’s crucial to understand the concepts of energy and power when you’re discussing wind energy projects!

Please get in touch if you have any questions or comments!

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