Time Dilated Bundt Cake Analysis of PV Output

Manuscript, May 2024.

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We present a method for modeling the power generated by a photovoltaic (PV) system that takes into account seasonal variation. The method is interpretable and auditable, and works directly from observed PV output data, which can include missing data. It relies on multiperiodic basis functions and convex optimization, and so is reliable and efficient. The first step is to model the variation in PV sunrise and sunset times across the year. We then time dilate the original PV signals, given in uniform time segments, into uniform ‘PV days’, which start at PV sunrise and end at PV sunset, which vary over the year. A 3D plot of this time dilated data shows the variations of cloud and obstruction effects across a year, and resembles a Bundt cake, which gives the method its name. We can then use a multiperiodic basis to fit marginal quantiles of PV output, taking into account variation over the year and within one PV day. These quantiles can be used for several applications, such as anomaly detection or automatic clear sky modeling.