Mathematical model of total cross-tied photovoltaic arrays in mismatching conditions

This paper presents a mathematical procedure for modeling rectangular (N rows with M modules each) and non-rectangular photovoltaic (PV) arrays in Total Cross-Tied (TCT) configuration operating in uniform and mismatching conditions. The proposed model uses the simple single diode representation for each PV module; then each row of the TCT array is represented as an equivalent non-linear PV circuit with a bypass diode, which allows to represent the TCT array as one string of equivalent PV circuits. The inflection voltages (array voltages that turn off the bypass diodes) of the string are calculated in order to solve only the non-linear equation system related to the active equivalent PV circuits for calculating the array current for a given voltage. Such a strategy reduces the computational burden and improves calculation speed. A TCT array of 4×2 with deep mismatching conditions was implemented in PSIM software to validate the proposed model, obtaining a correlation between model predicted data and the circuital simulation. The accuracy and improved calculation speed of the proposed model allow its use altogether with reconfiguration techniques as well as to reduce the time of energetic evaluations of TCT arrays for PV planning.