# What is the transcendental probability statistics of solar resources?

Exceeding Probability Statistics is a statistical measure that describes the probability that a particular value is equal to or exceeds. For example, a 90% exceedance probability (usually denoted by “90”) value is equal to the value of the probability density function of a population, with probability densities below and above that value being 10% and 90%, respectively. In a symmetric distribution, the P50 value is equal to the mean. Figure 1 shows the P50 and P90 values ​​in a normally distributed population with a mean of 50 and a standard deviation of 10. The P50 value is 50 (equal to the mean) and the P90 value is about 37 (standard deviation from the mean is 1.3). Figure 1. Probability of surpassing P50 (a) and P90 (b) in a normally distributed population with a mean of 50 and a standard deviation of 10.

Exceeding probability is often used to express the risk associated with power generation and is fundamentally related to the revenue of a solar power generation project. The variability of solar resources is a major factor that causes changes in projected project performance. While project revenue ultimately determines the financial performance of a solar project, the most common scenario is that the probability of exceedance is limited to electricity production, and that revenue is calculated uniformly using a financial model on the basis of annual electricity generation. While this limits the integration of complex payment structures in statistical analysis of project performance, it integrates most of the key factors and simplifies the analysis. In some instances, the lender (or a third party to perform it) may further analyze the payment structure, however this is limited to the specific requirements of individual transactions.

When considering transcendental probabilities, it is important to be clear about the factors that vary in statistics and the proportions of these sources in the statistical distribution. The most common variables in solar resource assessments are: interannual variability, uncertainties associated with solar resource base data, uncertainties associated with modelling of electricity production, or solar plant revenues.

While it is not necessary to integrate all elements into a statistical analysis, they all have real impacts and must therefore be addressed in the overall project analysis. For example, assessing the probability of exceedance only on the basis of inter-annual variation and looking at uncertainty as an understanding of the sensitivity of the project’s financial model to variation. Similarly, in the modeling of uncertainty and the project financing process for basic yield estimates, it is most common to reflect the uncertainty allowed by the contractor providing performance guarantees. For example, if a contractor sets a “cap” for testing uncertainty (e.g., setting performance within 3% of expected levels given instrumental uncertainty), the same “cap” will often reduce the fundamental The formal assumptions of the situation. Similarly, contractors often set performance values ​​lower than expected to allow for some contingencies to occur; however, non-recourse lenders often make base case formal assumptions based on contractors’ guarantees , while the contractor only fulfills certain obligations (or pays liquidated damages to reduce debt) on the condition of guaranteed performance levels. These assurance levels remove ambiguity and uncertainty when choosing modeling assumptions.

There is no unified industry standard in this type of analysis, and there are many viewpoints and methods in the market. From the perspective of project financing risk assessment, the most important point is to consider the variables and uncertainties that affect the project’s power output (and ultimately revenue) in the overall financial analysis of the project.