P50? P90? Exceedance Probabilities Demystified

Travis Lowder's picture

One of the big risks for wind (not to mention solar) developers is the variability of their fuel source. While day ahead and hour ahead forecasting is getting better by the day, no developer can guarantee that a site with a history of strong and sustained gusts won’t go flukey for a season or two and underproduce. Thus, to protect themselves against such shortfalls and possible loan defaults, lenders and investors have implemented production requirements on potential projects. These requirements involve the calculation of exceedance probabilities for wind-driven energy production, which are expressed as P values (the “P” stands for probability). P90 denotes the level of annual wind-driven electricity generation that is forecasted to be exceeded 90% of the year. P50 is average level of generation: half of the year’s output is expected to surpass this level, and the other half is predicted to fall below it.

The math behind the calculation of exceedance probabilities isn’t difficult, but it bears a quick explanation for a more thorough understanding the P value’s importance in the development and financing of wind projects.

Exceedance Probability: The Elevator Pitch

Exceedance probability refers to the chances that a particular measure will be surpassed in value by another, randomly selected measure. For example: you may want to know what the chances are of meeting an American man who is taller than 5’10”, (which we’ll call average height for this example). One way to determine this would be to graph out a cumulative distribution function, or CDF, for a sample of American men.

Line graph illustrating exceedance probability using hypothetical data about the height of American males.

Figure 1. Exceedance Probability Explained with an Example 

Note: the above graph is not based on real data.

Note that P90 does not mean that there is a 90% chance of occurrence; P50 is actually more likely to occur because it is the mean. P90 is, however, is a high-confidence measure, because it implies a high probability for exceedance.The advantage of using a CDF is that it displays the range of exceedance probabilities for a sample, and does not limit calculations to a single value. I’ll avoid the mathematics involved in plotting a CDF (although this source has a pretty good, basic explanation), and just skip the gist of the function, which is this: as x values increase, the probability that a randomly selected value has of exceeding them lessens. Turning back to our example on height, if we’re assuming that 5’10” is the average or mean height, the point where it would hit on the graph would be at P50. That is, there is a 50% chance that a randomly selected man in the sample will be taller than someone who is 5’10”. Let’s say that 6’5” is at the P10 level—this indicates that there is a 10% chance of a randomly selected American male being taller than this. And at 5’0”, or the P90 level, there is a 90% chance of a random man being taller.

What this Means for Wind

To appropriately size the amount of debt a wind project should receive, financiers will peg certain P values to debt service coverage ratios, or DSCRs. A DSCR is a proportion of project income to the costs of servicing loans (see blog posts by Karlynn Cory and Michael Mendelsohn for more on this). A DSCR of 1.4-1.5—which has become common for the P50 level—indicates $1.40-$1.50 of revenue for every $1 paid out to debt. At P99, i.e. the level of output that will supposedly be exceeded 99% of the time (which is the closest thing to a guarantee that a wind farm can offer), the DSCR will be lower—typically somewhere closer to 1. Notice the P value and DSCR are inversely related: as one goes up, the other goes down. Lenders may assign DSCRs to the P99, P90, and P50 levels, and, after considering the spread, determine the amount of debt a particular project can comfortably support for the various levels of predicted production.

The takeaway here is that the DSCR is chosen by the financier, not the developer. However, developers stand to benefit from a basic understanding of P values and DSCRs so that they can get a handle on the terms of their debt. Variability means risk, risks are costly, and costs can be better managed with the proper information. It will be interesting to see, going forward, how variability risk can be further mitigated through the increasing sophistication of forecasting models and innovations in storage technology. Time will tell.

 

References

Cooper Energy. "Cumulative Probability – P90, P50, P10. Cooper Energy Investor Series." http://www.cooperenergy.com.au/media/files/Cumulative%20Probability%20P90%20P50%20P10.pdf