Implicit Mathematical Model of Photovoltaic Arrays with Improved Calculation Speed Based on Inflection Points of the Current–Voltage Curves

Abstract

Dynamic reconfiguration, the monitoring of power production, and the fault diagnosis of photovoltaic arrays, among other applications, require fast and accurate models of photovoltaic arrays. In the literature, some models use the Lambert-W function to represent each module of the array, which increases the calculation time. Other models that use implicit equations to avoid the Lambert-W function do not use the inflection voltages to simplify the system of nonlinear equations that represent the array, increasing the computational burden. Therefore, this paper proposes mathematical models for series-parallel (SP) and total-cross-tied (TCT) photovoltaic arrays based on the implicit equations of the single-diode model and the inflection points of the current–voltage curves. These models decrease the calculation time by reducing the complexity of the nonlinear equation systems that represent each string of SP arrays and the whole TCT. Consequently, the calculation process that solves the model speeds up in comparison with processes that solve traditional explicit models based on the Lambert-W function. The results of several simulation scenarios using the proposed SP model with different array sizes show a reduction in the computation time by (Formula presented.) in contrast with the traditional solution. Additionally, when the proposed TCT model for arrays larger than (Formula presented.) is used, the reduction in the computation time is between (Formula presented.) and (Formula presented.). In dynamic reconfiguration, the results demonstrate that the proposed SP model provides the same optimal configuration but 7 times faster than traditional solutions, and the TCT model is solved at least 4 times faster than classical solutions.