### Reading Assignment

- A. Dobos, P. Gilman, M. Kasberg (2012). "P50/P90 Analysis for Solar Energy Systems Using the System Advisor Model." Presented at the 2012 World Renewable Energy Forum Denver, Colorado May 13-17, 2012.
- Rhino Energy web page: "Exceedance Probabilities." Accessed Oct. 20, 2013.

### Using Exceedance Probabilities

Because the solar resource is intermittent (variable), so too is the power production from a technology such as PV. The expected values and the spread for natural data like the weather is not necessarily "normally distributed" or even unimodal (one peak). This is why we often plot histograms of the data to observe the manner in which the data is spread out.

We would like to describe our level of confidence that a certain level of power production (or capacity) will be met, in order to minimize the risk in managing a system. In our "Try This" example, we saw how a data set can be summarized using quartiles (minimum, 25%, 50% or mean, 75%, and maximum). So, in this case, we would like to break the spread of data into bins that are both useful and tied to probabilities.

A value of "P50" or "P90" (or any value from 0-100) describes an annual value of power production from the intermittent resource with a probability of 50% or 90%, respectively. In fact, that quartile summary can be viewed as P25, P50, and P75. For P50, there is a 50% chance that the mean power production will not be reached at any given time. For P90, there is a 10% chance that the P90 level will not be reached.

Banks and investment firms working on wind farm projects often require P50 and P90 values of the wind resource at a location to determine the risk associated with a project’s ability to service its debt obligations and other operating costs.

-Dobos, Gilmanjavascript:submit_mid('sp_ig_all'), Kasberg (2012)

Inside of the SAM software, there is an advanced feature to evaluate P50/P90. There is an accessible database (*.cbwfdb file format, a proprietary format developed for SAM's P50/P90 capability) from the National Climatic Data Center (NCDC). The database is quite large (1.1 GB) but allows us to explore a number of cases for this course.

The long term NCDC/NSRDB dataset includes the impact of large volcanic activity and other phenomena that occur on timescales larger than one year. In particular relevance to solar plants, the eruption of Mt. Pinatubo introduced large quantities of aerosols into the atmosphere that reduced incident irradiance levels between 1991 and 1993. Other variations include the cyclic El Niño and La Niña phenomena, as well as the 11 and 22 year sun spot cycles.

-Dobos, Gilman, Kasberg (2012)