Imposing Limits
Many of the input parameters to SunSolve-P90 are constrained by limits. These limits can modify the PDF. For example, soiling loss is restricted to the range 0% to 100%. Thus, if soiling is set to be 2% with a Gaussian distribution of x0 = 1 and σ = 0.6, the possible distribution would extend beyond the allowable range. This example is plotted in Figure 4.3(a).
SunSolve therefore clips the PDF such that soiling loss cannot extend beyond its allowable range. As shown in Figure 4.3(b), this is achieved by setting PDF(x) = 0 for x < 0 and x > 50 (although the latter limit is irrelevant here).
Figure 4.3: Example showing (a) the soiling distribution centred on v0 = 2% with a Gaussian distribution with a relative standard deviation of 0.7. This distribution should not permit negative soiling and so the PDF in (b) is clipped such that PDF(x) = 0 when x < 0.
Gaussian Distribution Clipping
Section titled “Gaussian Distribution Clipping”In fact, SunSolve-P90 also clips Gaussian distributions, irrespective of any input limits, such that PDF(x) = 0 when x lies outside the range of x0 – 4σ to x0 + 4σ. This clipping makes the calculations faster without a significant loss of accuracy; a range of ±4σ includes 99.9937% of the distribution.
Skewed Gaussian Distribution Clipping
Section titled “Skewed Gaussian Distribution Clipping”SunSolve-P90 also clips skewed Gaussian distributions such that PDF(x) = 0 when x lies outside the range of ξ – 4ω to ξ + 4ω.