Hello and welcome to the second video of this series and now we want to have a look how we can calculate the energy yield of a wind turbine with the help of the power curve.

First we have a look to a place at the North Sea coast at the German island of Süld and we start with the relative frequency diagram that we know from the Weibull distribution discussion in other videos.

The second curve we require is the power curve itself that we just have discussed in the previous video. And there we see now we need to have a look at each wind velocity class that we have marked here with those yellow bars and that starts with low probabilities of wind speed and zero power output, therefore also the output is zero and then we already see

it really makes little sense to further reduce the cut in velocity with a lot of engineering effort and costs because the power output is so small that the contribution to the overall energy yield is so small.

And then we go further step by step through all the wind velocity classes increasing the probability and somewhere we reach then the maximum probability of wind speeds and when we see the power output of the power curve is still quite low resulting then in

the product something in the medium range. And then we increase the wind speed classes and have then a high power output of the wind turbine but already a decreasing contribution from the probability of those higher wind

speeds. And that is even decreasing when we reach the nominal power and what is extreme is when we then come to the cut of wind speed then we see that the probability of those very high wind speeds is almost zero and there we again see it not really makes sense to even increase the cut of velocity because the contribution of those wind speeds is almost zero.

When we do then that multiplication of every relative frequency with the corresponding power for every wind velocity class and multiply that with 8760 hours then we get the third curve

and this is the relative energy yield in megawatt hours per meter per second wind velocity class per year. But what we are interested in is the cumulative energy the energy we can obtain in one year

and that we see here in this fourth graph and that means the yearly energy yield Ea that is the sum from zero meter per second to the infinite times always the relative frequency h of v times the power output of the turbine p of v times 8760 hours.

And in this example we get then a yearly energy yield of 10 700 megawatt hours per year and then we can write this formula a bit different when we replace the relative frequency h of v

by the term the cumulative frequency f of v plus one minus f of v we have the exact probability of a wind speed class for example between three and four meter per seconds. The difference is not very big but there is a slight difference.

Now we can come to a second example we just double the height from 50 to 100 meter and then we see we get a slightly different probability curve of the wind distribution and that also results in a slightly different relative energy yield and we see that the

energy output is also a bit higher it's now close to 12 000 megawatt hours a year then we can do a next step we even double again the height to 200 meters for sure we get then a third relative energy yield curve and have a final energy yield

of more than 13 000 megawatt hours per year it's clear the higher we build our towers the higher is the energy yield we will discuss later what it's really worth the expenditure to build high towers for that slightly small increase of energy yield.

But now we have a look to a second place a bad side a bad side we as somebody living and teaching in Cologne is Dusseldorf for sure but this time not because Dusseldorf is a bad city

but this place that is far away from the coastline is a bad wind side and there we have a different relative frequency of the wind velocity but we have the same power curve of the wind turbine and therefore we get again relative energy yield here for the place of

Dusseldorf and then a cumulative energy yield over the year and we already see the cumulative energy yield is significantly lower in Dusseldorf than it is at a coastline it is only a bit more than a 4000 megawatt hours per year and we already see from the yellow marked bars

when we have a high probability of the wind speed the power output is still close to be zero and when we get to a higher power output the probability of the wind velocity for that power output is not much higher than zero and that there we see is not really a good

adaptation of those two so what is when we double the height we go to a hundred meter and then we see this is now a completely different curve it suits we had been all those

curves close together but in a side far away from the coastline it is a difficult significant difference that we get here a significant higher cumulative energy yield so we go from a 4000 to more than a 6000 megawatt hours per year and the same we can see when we go to 200 meters

we have the dark green curve now significantly shifted to the right to higher wind speeds resulting in a significantly different shape of the relative energy yield and also a significantly

higher yearly energy yield that is now more than 9000 megawatt hours per year and when we now compare once more these values from dusseldorf to soot at the north sea coast then we see there is a big difference in behavior for sure in all heights it is always the coastline

side is the better one but when we increase the height from 50 over 100 to 200 meters we see the difference at the coastline at soot is only a little bit but at the mainland in dusseldorf it is more than doubling the energy yield that is also the reason why we

see in the mainland far away from coastlines that the towers we are building are getting higher and higher whereas when we are hiking at the coastline we see wind turbines that are

much much smaller in height because it just doesn't make sense at a coastline to build higher and higher towers but it's not really satisfying what we have seen here for dusseldorf so we go a second approach for sure we cannot change the wind speed at this place but we can use a different wind turbine and that we see here we have the same

nominal power so both turbines we see here have three megawatt of nominal power but the yellow one the new one i have displayed here now has a much better behavior in this phase where the

power curve is increasing quite steeply and what is the reason for that it's not a better efficiency but we use more or less the same turbine but we install a bigger or longer rotor blades rotor blade area is increasing and therefore already with smaller wind velocities we get

higher powers but for sure when we have constructed longer rotor blades for the turbine it's also increasing in costs but it now uses the wind velocity much better that we have here in dusseldorf for example and when we do that here this comparison between the two turbines

both at a height of 100 meters we see a significant difference and we also see that difference in the yearly energy yield that was the wind turbine more constructed for the coastline and that one is for this mainland construction with the bigger rotor area and that we see

just with the different rotor we have an increase from more than 6 000 to more than 8 000 megawatt hours per year in the same game we can do with 200 meters of height and again here we see a

significant difference that we come from more than 9 000 megawatt hours to more than 13 000 megawatt hours and that is why we use in the mainland wind turbines that have a different ratio between the rotor blade area divided by the genomial capacity of the generator so this

figure in the mainland is bigger than we have it in coastline locations and for the next video and last video in this series we will have a look whether that what the power curve is telling us really contains the whole truth or if we need to also discuss things there thank you very much