Performance of solar systems with non-linear behavior calculated by the utilizability method: application to PV solar pumps

Abstract

Based on the utilizability method we derived, in the first part of the paper, an analytic expression to calculate the time average of physical quantities non-linearly dependent on collected solar radiation. Results are applied to photovoltaic pumping systems (PVPS). Water flow propelled by various types of pumps, centrifugal or progressive cavity displacement, for example, can be conveniently written as a second degree polynomial of the collected solar radiation. In that case, the long-term time average of relevant physical parameters, like water flow or hydraulic power, can be calculated with a very simple expression. The procedure is validated comparing long-term averages of maximum water volume pumped by a PV system, obtained with the utilizability method, with those found by running a 10-year time series. Comparison is made for several climatic regions in Brazil. Results show very good agreement for every month of the year and all locations, with a maximum deviation of 1.7%. The method applied to calculate long-term averages, maximum water volume for example, can be useful for evaluation and design procedures of photovoltaic pumping equipment.