Video Transcript
The installed capacity of a wind turbine is the maximum power output that it can produce. What is the installed capacity of a wind farm containing 180 turbines if the installed capacity of one wind turbine is 3.6 megawatts?
There is a second part to this question, which we’ll look at in a bit. But for now, we’ll just focus on this. So this question is actually quite nice because it starts off just with a general fact, which is really useful to know. The installed capacity of any wind turbine is the maximum power output that it can produce.
Let’s start by recalling that a wind turbine is a device which takes kinetic energy from the air. This causes its blades to spin, which turn a turbine, which produces electrical energy. When we talk about power, we’re talking about the rate at which energy is transformed from one form into another. We can represent this with the equation 𝑃 equals 𝐸 over 𝑡, where 𝑃 represents power. 𝐸 represents the amount of energy which is converted from one form into another. So, for example, this might be the amount of electrical energy which goes into a refrigerator. Or it might be the kinetic energy produced by the engine in a car. And 𝑡 represents the time period over which that energy was transformed.
So when we’re talking about the power output of a wind turbine, 𝐸 represents the energy that we get out of the turbine, which we know is electrical energy. And 𝑡 represents the amount of time over which this energy was produced. In other words, the power output of a wind turbine is the rate at which it produces electrical energy.
In this question, we’re told that the installed capacity of one wind turbine is 3.6 megawatts. This means that each individual wind turbine is capable of producing 3.6 megawatts of electrical power. As long as the wind is blowing hard enough to turn the blades at their optimum speed. To find the installed capacity of the wind farm, all we need to do is add together the individual installed capacities of each wind turbine in the wind farm. In other words, the installed capacity of the farm, which we can call 𝑃 farm, is equal to 180 times the installed capacity of each turbine, which we can call 𝑃 turbine.
Because we’re told that the installed capacity of one turbine is 3.6 megawatts, what we need to do is multiply 3.6 megawatts by 180. But before we do that, let’s take a quick look at the units that are being used. Let’s recall that the base unit for power is the watt, which we represent with a capital W. But this question deals with megawatts, which is represented by putting a capital M in front of the W. Putting a capital M or the mega- prefix in front of any unit increases its size by a million times. So 3.6 megawatts is the same as 3.6 million watts, which we could write as 3600000 watts or 3.6 times 10 to the power of six watts.
Now in this case, we’re actually free to substitute in a value for 𝑃 turbine in watts or megawatts. If we use a value in watts for 𝑃 turbine, then we will get a value for 𝑃 farm which is also in watts. Equally, if we use a value in megawatts for 𝑃 turbine, then we’ll get an answer which is in megawatts as well. In this case, we can see that the value is much more simple if we express it in megawatts. So we can substitute this in to give us 180 times 3.6 megawatts. And if we type that into our calculator, we get an answer of 648 megawatts.
So that’s our answer. If the installed capacity of one wind turbine is 3.6 megawatts, then the installed capacity of a wind farm containing 180 of those turbines will be 648 megawatts.
Okay, so now let’s move on and look at the second part of the question.
Which of the following is the main reason why a wind farm does not achieve its installed capacity most of the time? A) A lot of energy is lost to heat in the transmission of the electrical current from the wind farm to where it connects to the electricity grid. B) A lot of energy is lost to heat in the generators in the wind turbines. Thus, the actual power output of a wind farm is always lower than the installed capacity. C) Wind turbines become less efficient over time. Thus, the maximum power output that they can produce decreases over time. D) The wind speed is not constant. Thus, wind turbines are not always producing their maximum power output. Or E) Wind turbines are unreliable and often break. Thus, most of the time, not all of the wind turbines on the wind farm are operating.
Okay, so there are five options here. Let’s look at each of them in turn. And think about whether or not they’re the main reason a wind farm does not achieve its installed capacity most of the time.
Option A suggests that this might be because transmitting electrical current from the wind farm to where it connects to the electricity grid causes a lot of energy to be lost as heat. Now it is generally true that whenever electrical current flows through wires, some of the electrical energy will be converted into heat energy. We say that that energy is lost to heat.
However, there are two reasons that A is not the correct answer here. Firstly, it’s not exactly fair to say that a lot of energy is lost to heat in this process. At least not compared to the total amount of energy produced by the wind farm. Transmission of electrical current through wires is actually a very efficient process.
Secondly, even if this process did result in a lot of energy being lost to heat, this wouldn’t necessarily mean that the wind farm wasn’t achieving its installed capacity. Remember that the installed capacity of a wind farm is the maximum amount of energy that can be produced by the wind farm. It doesn’t actually matter how much of that energy is transferred to the grid. That won’t affect the installed capacity. That means that A is not the correct answer.
Option B suggests that a wind farm might not achieve its installed capacity most of the time because a lot of energy is lost to heat in the generators in the turbines themselves. Now, again, it is generally true that some energy is lost to heat in this process. However, like with option, A, it’s not really fair to say that a lot of energy is lost in this process because generators are generally very efficient as well.
However, the most important thing to consider with this option is that the installed capacity of a wind turbine refers to the maximum power that can be produced by a wind turbine. So any energy losses in the generator or anywhere else inside the turbine have already been factored in when the installed capacity is determined. So, for example, if we built a wind turbine that had a really inefficient generator that lost loads of energy as heat. Then we would find that the installed capacity of this wind turbine was really low. However, this wouldn’t actually mean that the wind turbine never achieved its installed capacity. So option B is not the correct explanation either.
Option C suggests that the reason a wind farm might not achieve its installed capacity most of the time is that wind turbines become less efficient over time. Which causes the maximum power output that they can produce to decrease. Now it is actually true that wind turbines become less efficient over time. This can happen for many different reasons, from a loss of lubrication in moving parts to buildup of dirt on the blades that can make them less effective. And any loss of efficiency over time would mean that the maximum power output does indeed decrease over time. Which could prevent the wind turbine from ever achieving its installed capacity, which was decided when it was built.
However, the question does ask us to find the main reason that a wind farm doesn’t achieve its installed capacity. It’s not yet clear whether option C is the main reason. So for now, let’s just put a question mark next to it, and we’ll come back to it in a minute.
Option D suggests that the main reason why a wind farm does not achieve its installed capacity most of the time is that the wind speed is not constant. Which means that wind turbines are not always producing their maximum power output. Now this option is also a correct reason why a wind farm does not achieve its installed capacity all the time. The power output of a wind turbine depends on how quickly its blades are rotating. And that depends on the speed and direction of the wind. If the wind speed is too slow, then the blades will turn at less than their optimum speed, which means the turbine will produce less than its installed capacity. This can actually also happen if the wind is blowing too quickly. So this is definitely one good reason why a wind farm might not achieve its installed capacity most of the time. So we’ll put a question mark next to option D as well.
Finally, option E suggests that the main reason a wind farm does not achieve its installed capacity most of the time is that wind turbines are unreliable and often break. Which means that, most of the time, not all the wind turbines on a wind farm are operating. Once again, this option is actually based on the truth. Wind turbines can and do break. And when they do, that will prevent the wind farm from ever reaching its installed capacity. So that means option E is potentially the correct answer as well.
Okay, so we’ve ruled out options A and B. But now we need to decide which of these three options is the main reason why a wind farm does not achieve its installed capacity most of the time. Well, it turns out that if we compare the amounts of power that are lost due to each of these factors, the main contributor to power loss is wind speed. So while wind turbines do become less efficient over time, we usually find that this efficiency loss is only around one or two percent per year. And while wind turbines can break, it’s not really fair to say that they’re unreliable, as wind turbine breakdown is actually quite rare.
However, wind speed, as we know, is highly variable. It’s easy for the wind to be either blowing slightly too hard or not quite hard enough to prevent a wind turbine from achieving its installed capacity. In fact, this makes it pretty unlikely that any single wind turbine would be achieving its installed capacity at any given moment. Which makes it really unlikely that the entire wind farm achieves its installed capacity.
So the correct answer to this question is D. The main reason why a wind farm does not achieve its installed capacity most of the time is that the wind speed is not constant. Thus, wind turbines are not always producing their maximum power output.
