Difference between sectoral and cumulative gross AEP?

[vob]

Dear all,

while experimenting with a power curve that is shut down (power = 0) for a certain wind speed range I have come across a puzzling issue: The gross AEP as calculated by IRveaProductionRose.SectorForIndex(SectorIndex).GrossContribution for a given sector is greater than the sectorial AEP calculated from IRveaProductionDistribution.ProductionForSpeed (of course after accounting for the sector frequency).


In my example I used a power curve that cuts in at 19m/s. For sector 2, the calculated .ProductionForSpeed values are:
19 m/s: 15705 kWh/y
20 m/s: 2099 kWh/y
21 m/s: 237 kWh/y
22 m/s: 23 kWh/y
23 m/s: 2 kWh/y
and zero above 23m/s. The sector frequency is 7.497%.
This results in a gross AEP of (15705+2099+237+23+2)*0.07497 = 1354.4 kWh/y, but the .GrossContribution is reported as 3215 kWh/y, almost 40% higher.

For other sectors with higher wind speeds, the difference is only in the order of some 20%, but .GrossContribution is always greater than the sum of the non-zero .ProductionForSpeed bins.

When I use a non-curtailed power curve (cut-in at 3 m/s) the difference is less than 0.2%, for high-yield sectors even down to 0.01%.


I always thought the AEP is simply the sum (or integral) of the production values determined in each wind speed bin (based on the power curve and the bin frequency), but apparently this is not the case. Could someone please explain in detail how AEP is calculated?


Thanks in advance!

[Duncan]

Hi Vob,

Sorry that no-one has responded to your question yet. I'll try to explain whatever you're seeing.

To simplify things, could you maybe send me a WAsP workspace which shows the confusing data? Then I can make sure that I am answering the right question. I don't need your automation code: just tell me which property of which object you're accessing and I'll work through an explanation of the numbers.

Send to duncan.heathfield@wasptechnical.dk.

Best wishes, Duncan.

[Duncan]

Hello again Vob,


Sorry again for the delay. I finally had time to look into this properly.


IRveaProductionRose.SectorForIndex(SectorIndex).GrossContribution is calculated by folding the power curve with the Weibull distribution for that sector, using a gamma function integration. The result is multiplied with the number of hours in a year, and then multiplied by the sector frequency.


IRveaProductionRose.SectorForIndex(SectorIndex).ProductionDistribution.ProductionForSpeed(Speed) is the probability of that speed (from the Weibull distribution), multiplied by the power for that speed (read off from the power curve), multiplied by the number of hours in a year.


If I understood your message correctly, you wanted to emulate the GrossContribution but summing ProductionForSpeed for a range of speeds and multiplying by sector frequency. In principle, that will give a similar value, but in practice the emulation result will be sensitive to the integration step if you’re looking at an extreme part of the Weibull distribution and have a funny power curve.


I tried to show this by doing something similar to what you reported. I made a power curve where there was uniform power delivered only between 15 and 19 metres per second. Then I applied this (with no air density correction) to a site from the Canela sample workspace. I have uploaded the workspace here
http://wasptechnical.dk/Services/Redirect.aspx?token=cfcb6b96-d10d-4e49-b43b-be46f31af590
and I have put a screen shot of the site power prediction here
http://wasptechnical.dk/Services/Redirect.aspx?token=d80504d7-88c8-4430-87b6-9006325c5496.


I guess this is a slightly less extreme case than yours, because more of the Weibull distribution will intersect with the range 15-19 m/s compared with >19 m/s. It’s also clearer because the power curve is perfectly rectangular (if you remember to turn off air density corrections): either there is no power, or there is exactly 1MW.


Let’s look at sector 4, where the Weibull A, k and f are 9.982139, 2.529297 and 0.097123 respectively. For sector 4 the gross contribution is 46483550 Wh. This is confirmed in the WAsP user interface. This is the ‘official’ answer.


We can ask the production rose about the production for speeds from the sector. If we iterate from 14 to 20 metres per section we get the following yields:
Speed: 14 0000000000
Speed: 15 0251475900
Speed: 16 0168905800
Speed: 17 0107288600
Speed: 18 0064389630
Speed: 19 0036474820
Speed: 20 0000000000


One can try to emulate the sector gross contribution by summing these values and multiplying by the sector frequency. In this test case, the result is 61045199 Wh. This is indeed quite different.


There’s nothing wrong with the method, but the numbers don’t match because the integration step in our emulation here is far too wide at 1 m/s. This step cannot hope to capture the actual shape of the Weibull distribution as it overlaps with the power curve in this speed range.


When I reduced the arithmetic integration step, the summation result started to converge with the GrossContribution result. At a step of 1/10000, the production summed to 46483685 Wh. This is very close to the ‘real’ gamma function version.


Does this explain what you have observed? I think that if you have a more normal power curve - and are concentrating on a wider part of the Weibull distribution - the correspondence is closer. But when you are looking at a strange part of the distribution, and applying a funny power curve, then you can see this divergence.


I hope this answers your question about how the values are calculated and that this explains why the numbers differ. If you’ve got some data that can’t be explained by this, then send them to me and I’ll run the same analysis on your numbers to check I’ve got things right.


Best wishes, Duncan.