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.
Selected Examples of P90, P95 etc. Estimates from Wind Studies
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.
Study that includes components of one-year and 10-year P90
Study in which you can dissect the one-year and ten-year P90, P99 etc.
Dissecting Wind Variation in Analysis with MSE
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
Wind Case Study.xls
Hydro Case Study.xlsx
Solar Case Study.xls