Wind P99, P90, P50 for 1-year and 10-year and Debt Sizing

This page explains how to evaluate the probability of achieving different levels of wind production that I refer to as P90, P99 etc. Probability of achieving electricity from wind are a central part financing a wind project and are prepared before the financial close of a project.  The tricky part of the P90, P99 etc. is to understand the sources of variation in wind production estimates that are mean reverting and that are related to modelling errors that do not self-correct. This webpage also describes how to size debt with alternative parameters. 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.

The discussion on this page builds from the prior page that dealt with variation in electricity production arising from variation in year to year wind speeds. Additional sources of variation come from factors such as modelling error, turbulence, wake measurement error, correlation with reference data, availability, environmental issues and other factors. This page explains how to put sources of variation together and evaluate wind reports.  Power point slides that explain these concepts are in the file available for download below (these slides are the same as the slides for the previous page).

 

 

 

 

Selected Examples of P90, P95 etc. Estimates from Wind Studies

In this section I have included selected examples of wind studies where results of the sources of wind uncertainty are presented. I begin by showing some results where the P90, P95 etc. are presented.  The presentations of probability analysis and P90, P95 etc. generally are shown at the end of the wind study. I will explain the data in three different wind studies in the discussion below.  You can download a couple of the wind studies by pressing the buttons below.

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 variability in production estimates for different projects with measured variability. 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.

 

Study with multiple wind farms and presentation of one-year and ten-year P90.

In this study the 10-year and the one-year wind production estimates were presented in a table that is replicated below. Note that P50 case is the same in all of the tables as the mean does not change.  The driver of the variation is…
Include the sources.

Study that includes components of one-year and 10-year P90

You can download the second wind study by clicking on the button below.  Note that the mean squared error is described in the table. In addition there is separate components for the different items. To present data from this PDF file is a little tricky.  It is a locked file and you can read it into google drive. Once it is in google drive you can use the read pdf file.  The excel files associated with the tables are included.

Study in which you can dissect the one-year and ten-year P90, P99 etc.

The third case includes a few extracts from a study of a larger wind farm where multiple factors were addressed. In this case I have just replicated selected tables and put them into an excel file using the read pdf tool.

Dissecting Wind Variation in Analysis with MSE

If the components of the wind variation are independent from one another, you cannot add up the variation. But you can use the mean square error concept.  Here, you can square all the components of the standard deviation and then sum all of the squares.  Then, you can take the square root of the sum of the squares.
The concept of mean squared error is demonstrated in the excel file below. I have assumed multiple sources of variation and no mean reversion and an correlation.

Replicating P90, P95 etc. with NORMSINV and Goal Seek

In the case with 1-year and 10-year P90, P95 etc. you car given selected results.  But you cannot evaluate how much of the production of electricity from wind comes from the wind variation by itself. In this section I will demonstrate how this can be done. Part of the reason for this is because you can have a better understanding of what causes variability and what causes the variation.  After the variation is understood you can compare the wind only variation to the analysis discussed in the prior page.

Debt Sizing with P50 and P99 etc.

It has become standard in the industry to apply different debt service coverage ratios to different wind production cases. A typical scenario is that a 1.35x coverage ratio is applied to the P50 case while either a 1.2x coverage is applied to a P90 ten-year case or a 1.0x coverage is applied to the P99 one year case. The modelling issues can be a little difficult as the debt may be sized on one scenario but the equity IRR is computed from a different scenario. The exercise below applies these concepts.

 

 

P90, P99 and DSCR Debt Sizing.xlsm

P90, P99 and DSCR Constraint.xlsm

 

Computing P50 from Historic Wind Data and Power Curves

 

 

Wind Case Study.xls

Hydro Case Study.xlsx

Solar Case Study.xls