Analytical optimization of photovoltaic output with Lagrange Multiplier Method

This paper proposes a non-iterative and direct optimization method for the optimization of the output characteristics of single and double diode of cell model, including series and shunt resistances. The proposed method is based on the Lagrange Multiplier Method (LMM). Typically, the proposed method is used under necessary conditions of the optimization, and it is adopted to optimize power outputs as objective functions of different solar cell technologies and Photovoltaic (PV) modules. The objective functions are formulated to determine the greatest rectangle inside I(V) characteristics and the efficiency frontier. Furthermore, by an analytical mathematical resolution we obtain the optimal current and the formula of efficiency frontier. The efficiency frontier for single diode model is a polynomial equation of second order, and fourth order in the case of double diodes model. A realistic numerical example for different technologies via computer simulations are presented to verify the performance of the proposed optimization method.