Abstract
The probabilistic modeling technique is used in this paper to ascertain the performance of energy conversion of a photovoltaic (PV) array under the influence of partial shading. Three cases of increasing complexity are studied in this paper. The first case is to find the probability density function (pdf) of the maximum power output (MPO) of a single PV module exposed to a random level of solar irradiance. Given that the probability distribution of solar irradiance is knowna priori, the pdf of the MPO of the PV module is derived analytically. A Monte Carlo simulation is then conducted to validate the analysis. This is followed in the second case by studying the MPO of an array composed of two series PV modules, each exposed to a random and independent level of irradiance. The third case further involves the effects of bypass diodes which are commonly installed to reduce partial shading losses.
Highlights
Partial shading is a commonly encountered problem in applications of photovoltaic (PV) energy generation
This paper is intended to ascertain how the maximum power output (MPO) of a PV array is distributed when its modules are subject to randomly varying levels of solar irradiance
Partial shading is modeled in this study by a randomly varying level of solar irradiance
Summary
Partial shading is a commonly encountered problem in applications of photovoltaic (PV) energy generation. As partial shading exhibits some degree of uncertainty, efforts have been made to extend traditional analysis into cases where the pattern, number, and shading percentage of shaded PV modules may vary at random. A randomly generated shading pattern was tested in Wang and Hsu’s study [7]. This paper is intended to ascertain how the maximum power output (MPO) of a PV array is distributed when its modules are subject to randomly varying levels of solar irradiance. The first case, which is a univariate analysis, is to find the pdf of the MPO of a PV module exposed to randomly varying irradiance. Once the univariate problem can be solved, it is extended to a more complicated bivariate case where a PV array composed of two series modules, each exposed to independent and randomly varying irradiance, is analyzed. The modules are assumed to be equipped with bypass diodes, which are commonly used to reduce partial shading losses
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