Wind Financial Modelling and Resource Analysis

This page addresses issues that are specific to electricity production from wind, wind resource analysis, wind power variability and wind financing. Sources of wind data are reviewed followed by introducing a database of power curves and estimates of power production. In this analysis statistics that measure the variability of both wind and power production are introduced.  The subsequent page extends the analysis to deal with some tricky wind resource subjects and discussion of the difference between measurements of production using a P90 ten year estimate and a P90 one year (you could substitute P90, P95, P75 etc.).

Introduction to Wind Analysis and Power Point Slides

The ideas of measuring wind speeds, wind power, power curves and variation in wind are explained in the slides that you can download below. The slides also use the Netherlands feed-in tariff as a case study and use the perspective of credit analysis from the perspective of a bank.  You can get the slides by clicking on the button and downloading the file. As with the discussion below, the slides begin with speed analysis (no electric power or turbine).  Then the turbines are added using a power curve to convert the wind into electricity and the power curve database is introduced.  Finally actual wind production variation from year to year is evaluated.

 

Power Point Slides Used for Analysis of Wind Power Including Resource Analysis and Financing and Merchant Prices

 

Acquiring and Analysing Wind Data

The first subject addressed here is what does the wind speed data look like and what kind of variation is there from year to year in wind speeds. (Finance people care most about annual data because debt repayment is not made on a day by day basis and cash flow variation over years drives risk). This section includes a discussion of where you can find the detailed hourly data and how you can analyse the wind data. Once the wind data is reviewed, power curves that convert wind data to electric power is discussed in the next section.

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. You can convert the wind speed into meters per second data and click on any place in the world to see how fast the wind is blowing. The thing that pops out at you is the amount of resource off-shore relative to on-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.  Screenshots below the link illustrate a couple examples of the wind speeds during a particular instant. Note that the place I selected in NL has a wind speed of 4.4 meters/second. Note that the wind speed is measured at a height of

 

https://earth.nullschool.net/#current/wind/surface/level/orthographic=-181.12,26.58,243/loc=-2.562,53.213

 

 

You can also find wind data in other places.  If you go the the website for feed-in tariffs in the Netherlands, you will see a wind map.  Notice how the wind speed is higher near the coast.  The problem with wind is that speeds cannot come from a simple map like this as shown in the next section.  Notice in the insert how the feed-in tariff is structured around the wind speeds.

 

 

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.  The files that you can download below have the hour by hour wind speed data for many years.

 

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.

 

Annual Variation in Wind Speeds

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 edwardbodmer@gmail.com you can get the other wind speed data.  This is what you want if you are a banker or an investor.

 

 

 

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.

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Some files with hourly wind speeds are shown below.

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Excel File with Formatted Hour by Hour Wind Speeds in the Netherlands and Analysis of Variation for Arcen

Excel File that Goes to NCOAA Data and Retrieves Hourly Wind Speeds for up to 30 Historic Years

Excel File with Examination of German Wind Speeds and Question of Whether Wind Speed is Declining

File with Documentation of Methods for Collecting Wind Data and Website Source for NCOAA

 

In addition to finding annual average wind speeds, you can evaluate the distribution of wind speeds.

Putting Together Wind Data with Power Curves to Derive Wind Production

In this section I convert the wind speed data to wind production data. The manner in which this is really done is shown in the table below where the analysis includes various losses as well as the power that comes from the wind. The manner in which wind production can be converted to electricity production is illustrated in the screenshot below.

Power curves translate wind speed into power. They are perhaps the most crucial element in understanding wind power.  You can sometimes guarantee the power curve.

A big deal is to find power curves.

 

 

Power Curve Database

 

 

 

 

 

Excel File with Data Base of Power Curves from Various Sources and Normalised Power Curves for Comparios

 

Power Curves 2010 in Retscreen.xls

Power Cuves.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

 

Files associated with Lesson Set 1: Wind Resource Analysis

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.

 

 

 

File with Analysis of P50 and P90 with Monte Carlo Simulation and Mean Square Error Evaluation

 

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.

 

S&P Credit Analysis of Multiple Wind Farm Describing Risks including Wind Resource Risk with P95

 

Wind Resource Analysis.xls

Shipol.zip

 

Case Study Plymouth Wind Farm.pdf

German Wind Speeds.XLS

Wind Shear.xlsx

EIA Updating Instructions for Generation Databases that Evaluate the Variation in Production

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:
https://drive.google.com/open?id=0B5r4OP_dQLe8Y1JfaUlXZldveGM

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

Long-term Data Example with Analysis.xlsx

Shipol Wind Analysis.xlsm

Wind Resource Analysis.xls