Mathematical Model of Bridge-Linked Photovoltaic Arrays Operating Under Irregular Conditions

Abstract

This paper presents a mathematical procedure to model a photovoltaic array (N rows and M columns) in bridge-linked configuration operating under regular and irregular conditions. The proposed procedure uses the ideal single-diode model representation for each photovoltaic module and the Shockley equation to represent each bypass diode. To pose the system of NxM non-linear equations required to obtain the voltages of each module of the array, the proposed model apply the Kirchhoff current law to each internal node of the array and the Kirchhoff voltage law to: each loop created in the upper part of each connection of two consecutive strings and each string with respect to the output voltage of the array. Moreover, the model provide a procedure to obtain the Jacobian matrix to reduce the solution time of the equation system. The circuital model of two arrays (small: 3x3 and medium: 20x3) were implemented in Simulink to validate the proposed model. The accuracy and improved calculation speed of the proposed model allow its use to perform energetic evaluations of bridge-linked arrays or its comparison with other typical array configurations, which can be useful in the designing of photovoltaic plants.