Isomorphism-Based Fast Simulation of Mismatched Photovoltaic Arrays

Mismatched operating conditions occur very frequently in photovoltaic arrays, especially in urban installations or those that are commonly referred to as agrivoltaic. Mismatches are not only due to partial shading, but also to modules’ construction tolerances and installation mistakes, to maintenance operations, to a different effect of aging on modules, to an uneven distribution of dust, pollution, and snow on the module surfaces. The simulation of photovoltaic arrays operating in mismatched conditions is required in many applications, from plant design to model-based control, from monitoring and diagnosis up to the implementation of a digital twin. Some applications require not only an extreme granularity level (even at the single cell or fractions of it) but also a very fast computation compatible with real-time applications, running on embedded processors. This article introduces a new approach to the simulation of mismatched photovoltaic arrays based on isomorphism. The approach exploits similarities among subsections of the array to minimize the number of nonlinear equations modeling it. The lower the simulation accuracy required, the smaller the rank of the system of equations to solve. The application examples proposed in the article, concerning a PV array affected by a partial shading by nearby objects that changes during the day and a faulty PV field made up of half-cut modules, allow one to quantify the reduction in model complexity and the consequent computation time granted by the proposed technique as a function of the desired accuracy of the simulation results.