This page addresses issues that are specific to electricity production from wind, wind resource analysis, wind power variability and wind financing. Wind resource analysis deals with some tricky wind resource subjects that I think are difficult including understanding the difference between measurements of production using a P90 ten year estimate and a P90 one year (you could substitute P90, P95, P75 etc.).
The webpage starts with a discussion of wind resources including where you can find the detailed hourly data. Once the wind data is reviewed, power curves that convert wind data to electric power on a gross basis is discussed. This is used to demonstrate the P90, P50 etc. without incorporating permanent and and modelling errors. The third section demonstrates some studies of 1-year and 10-year P50 and P90 and how to use the NORMINV function and the mean square error statistics.
Introduction to Wind Analysis and Power Point Slides
In the first section titled “Wind Resource Analysis” I have put together a case study from an old credit report that had one and ten year production estimates for different projects with different probabilities. I have also compiled an analysis of the variability in wind after projects are operating relative to before they are operating.
A key theme is that standard deviations underlying the ten year P90 are very subjective where standard deviation in things like wake effect, availability, turbulence, correlation to historic site, wind shear, losses and other factors. One of the main tools in analysis of wind production with different probabilities is use the NORMINV function in excel to understand data in wind studies. After the wind resource analysis, the effects of wind probabilities on debt sizing are evaluated in the second lesson set. The Final lesson set involves computing a wind project finance model that includes a partnership with a flip structure and a DRO.
Acquiring and Analysing Wind Data
To introduce issues associated with wind resource I often have people open the following website that has wind speeds around the world at any instant. The thing that pops out at you is the amount of resource off-shore. You can also look a places like Kenya, Ireland, south Argentina and the middle of North America. These places often have more on-shore wind than other areas.
The first lesson set addresses computing wind capacity factors from wind data and power curves as well
Case Study of Working with Wind Data
As I sometimes work for the Amsterdam Institute of Finance, I have made a case study with Dutch wind data. The good news is that a couple of years ago I found hour by hour wind data for many areas in the Netherlands (NL). (I cannot seem to find it now). With this hour by hour data you can do a lot of stuff. The hour by hour data and the website where I found the data is illustrated in the screenshot below. There is a whole lot of data in these wind files and the difference between different areas is dramatic.
Compute wind Shear Factor
To compute the wind shear when the wind speeds are measured at a different height than the hub height of the turbine, you use a power coefficient of 1/7 and then raise the ratio of the hub height to the measured height by that factor: The formula works as follows. First divide the hub height by the measured height (e.g. 80/10) to the power of the shear factor: (80/10)^(1/7). This gives you an number that is greater than 1.0. Then, multiply that result by the wind speed measured at 10 meters.
The files that contain the adjusted data with wind shear factors and analysis are available for download by pressing the buttons. These are large files and include various different graphs of the data. You can have a lot of fun playing around with the data. I do have other wind data in the resource library but I have not bothered yet uploading the data. If you send me an e-mail to firstname.lastname@example.org you can get the other wind speed data.
Another example of wind variation comes from a presentation made about a low wind year in Britain. Note the last number that was 90% of the index value in 2010. While this seems very low, the standard deviation relative to the average over the 15 year period was 4.67% which is about the level shown for the Dutch wind. You can use the NORMDIST value with an x-value of .9, a mean of 1.0 and a standard deviation of 4.65% and see that the probability is 1.58%. This is like the P values discussed later on.
Putting Together Wind Data with Power Curves to Derive Wind Production
A big deal is to find power curves.
Power Curves 2010 in Retscreen.xls
Putting Together Wind Data with Power Curves to Derive Wind Production
as causes of uncertainty that are not “mean revering”. The videos and files also cover a subject that I find one of the most difficult issues to explain — i.e. the difference between one year P90 and ten-year or twenty-year P90. I have tried to explain this with file named “Wind Study” listed below. This file uses a nice old financial analysis report that listed P50, P75, P90 and P95 for a series of different wind farms. It also reported the production statistics on an 1-year basis and on a 10-year basis. Using the P90 etc. production statistics you can back out the standard deviation that is related to wind variation only as well as the variation that is only related to permanent effects. I have also compiled an analysis of the variability in wind after projects are operating relative to before they are operating. My key theme is that standard deviations underlying the ten year P90 are subjective. I demonstrate how to use the NORMINV function in excel to understand data in wind studies.
Wind Resource Analysis
|Subject||Excel File||Video Link|
|Working with P50 and P90 One Year and Ten Year||Wind Analysis.xlsm||https://www.youtube.com/watch?v=WXP6x74QmHE|
|Isolating Permanent Effects and Wind Movements||Wind Analysis.xlsm||https://www.youtube.com/watch?v=hXwlTeSpjuw|
|Different Production Constraints and||P90, P99 DSCR Constraint||https://www.youtube.com/watch?v=UAMed97wCRk|
|Debt Sizing with P99, P90 and P50||P90, P99 Debt Sizing||https://www.youtube.com/watch?v=47XBFymVzCQ|
|Acquiring EIA Data on Wind Forecasts||EIA Database||https://www.youtube.com/watch?v=NUdYzd1rEOQ|
|Wind Data Analysis with EIA Data – Part 1||Wind Generation Database||https://www.youtube.com/watch?v=PoAvXzsrZqQ|
|Wind Data Analysis with EIA Data – Part 2||Wind Generation Database||https://www.youtube.com/watch?v=Hhx3trJMZck|
In this section I describe how to compute the P90, P99 etc. from power curves and historic wind data. This involves compiling hourly wind data and matching the wind data against power curves. In addition, actual wind variation is evaluated for a number of wind farms using the Generation Database below. Computing the P90 or P99 etc. can be derived from hourly wind data and power curves. You can use the LOOKUP function to evaluate the amount of power at different wind speeds and the NORINV function to evaluate probability distributions. The hourly distribution of wind can also be computed from a Wiebull function as illustrated in one of the files below.
The file below demonstrates the credit analysis of a wind farm from a long time ago. It demonstrates how the P90 and P95 can be used in assessing the credit analysis of a wind farm with downside analysis. As this write-up has multiple wind farms, it can be used to compare capacity factors and other factors for different wind farms.
Wind Resource Analysis.xls
Case Study Plymouth Wind Farm.pdf
German Wind Speeds.XLS
For solar, wind and hydro I have included files that include historic monthly and more importantly annual production for U.S. plants. This is included so you can see the variation in year to year production. You can compare for example the P99 to the annual production to see how much of a DSCR buffer is necessary relative to the average production. This can then be compared to the P90, P75 etc. that is estimated by consultants. The analysis comes from a database named EIA 923 that records month by month production for electricity plants in the U.S. since 1970.
1. Find the file named EIA 923 database. This is an enormous file with data on the generation from each plant in the U.S. from 1970 to the current year. It contains month by month generation by unit. A lot of work was done on this file to get consistent fuel category names and plant names and codes accross years. I have copied the file into a google drive with the following link:
2. Go to the EIA 923 database page in the EIA website and find the latest dataset (you can google EIA 923). Open the file and copy it into the EIA 923 database file. If the file is for a new year, then copy the prior year and create a new sheet (e.g. 2018) with ALT,E,M. Make sure the merged cells are removed from the EIA file when you copy a new file. Make sure that the formulas in columns A-C of the file are copied to the bottom of the sheet.
3. Go to the Summary Page of the EIA 923 database and update formulas. This involves copying formulas to the right. As the EIA 923 file is so big, you should do this with the calculation set to manual. After you have copied the formulas, press the macro titled “FULL CALCULATE”
4. Create an intermediate summary page that is not as giagantic as the the EIA 923 database. Copy and paste special the yellow area in the summary page of the EIA 923 file to a new file. Find the databases for solar, wind and hydro. In the google drive, these files are in Chapter 5, under the Renewable section and then in the Resource Studies Folder. Copy and paste special as values the Summary page to each of the files.
5. Find the databases for solar, wind and hydro. In the google drive, these files are in Chapter 5, under the Renewable section and then in the Resource Studies Folder. Copy and paste special as values the Summary page to each of the files after using the filter tool to select the appropriate prime-mover. After tyou have created the file you can sort the file by the number of months for which data is available.
Generation Database – Wind.xlsm
Computing P50 from Historic Wind Data and Power Curves
Wind Case Study.xls
Hydro Case Study.xlsx
Solar Case Study.xls
Long-term Data Example with Analysis.xlsx
Shipol Wind Analysis.xlsm
Wind Resource Analysis.xls