# Posts tagged math

## T_cell_typ_avg

- 2021-06-17

This is a short note that derives the “typical average cell temperature” used in the “Weather-Corrected Performance Ratio”. The Weather-Corrected Performance Ratio 1 is defined as:

The denominator is essentially the PVWatts DC model, except the reference cell temperature is not \(T_{\mathrm{STC}}\) but rather a “typical/average” cell temperature. The report has this to say about that decision:

## Summing Uniform Distributions

- 2020-09-25

The distribution of the sum of N uniformly distributed variables came up in a recent RdTools PR. The approach taken there was to just sample each distribution and sum the samples, but I wondered how it could be done analytically. This notebook is inspired by this StackExchange post and extends the derivation from just summing two uniform distributions on \([0,1]\) to two distributions with arbitrary bounds.

Given two independent random variables \(A\) and \(B\) with probability densities \(f_a(x)\) and \(f_b(x)\), the probability density \(f_c(x)\) of their sum \(A + B = C\) is given by the convolution \(f_a * f_b\):

## PVWatts and PVUSA

- 2020-02-01

I read a paper recently that turned on a lightbulb about why the PVUSA/ASTM E2848-13 equation is defined the way it is. To quote the paper 1:

The concept of modeling power by modeling current and voltage separately (other than IV-curve modeling, of course) is obvious in hindsight but had never occurred to me before… so let’s have some fun and try it out!