A close-form solution for the maximum-power operating point of a solar cell array

A solar cell array is inherently a nonlinear device consisting of several solar cell modules connected in series-parallel combinations to provide the desired DC voltage and current. At a fixed insolation level, the terminal voltage decreases nonlinearly as the load current increases. Due to this nonlinearity, it is difficult to determine analytically the operating point at which the output power is maximum; a condition required for maximum utilization efficiency of the array. Iterative techniques are normally used to determine this operating condition. These techniques are lengthy, time-consuming, and have to be repeated for any change in the array's parameters, temperature, and insolation level. In this paper, an accurate closed-form solution is derived in terms of the array's parameters and solar insolation level. This solution is useful to the system designer or researcher as a fast and accurate tool for system design and performance analysis.