Mismatched Series-Parallel Photovoltaic Generator Modeling: An Implicit Current-Voltage Approach

Models of series-parallel (SP) photovoltaic (PV) generators under nonhomogeneous conditions commonly represent each submodule with the single-diode model. However, most of those models require high calculation burdens because they need to evaluate the LambertW function for each submodule in the generator to calculate the submodule current as a function of its voltage. This paper proposes a model for SP generators, operating under nonhomogeneous conditions, which uses the implicit current-voltage relation of each submodule to propose a system of nonlinear equations that describes the electrical behavior of an SP generator. The generator can be divided into strings, which are analyzed independently since they are parallel connected. Each string is composed of N submodules and one blocking diode connected in series; hence, the model has N+2 unknown: N+1 voltages of the submodules and the blocking diode, and the string current. The system of N+2 nonlinear equations is formed by the N implicit current-voltage relationships of the submodules, the blocking diode model, and the Kirchhoff's voltage law applied to the string. The system of nonlinear equations can be solved with the same numerical methods used by traditional models. The main advantage of the proposed model is the avoidance of evaluating the LambertW function, which reduces the computational burden and the calculation time. Moreover, simulation and experimental results show the feasibility of using implicit submodules' current-voltage relationships for models of PV generators, since it significantly reduces the calculation time with the same errors provided by traditional models.