The I-U characteristics of the photovoltaic (PV) module are highly nonlinear and depend, among other factors, on solar insolation level and on the module surface temperature. At a fixed value of insolation level to which the module is subjected, the terminal voltage decreases nonlinearly as the load current increases. Most of previous research in this area depends on a nonlinear mathematical equations relating the module voltage with its current. Therefore, numerical methods of analysis are required to determine the performance of a system in which a photovoltaic module, or array, is an element.
It is known that most of operating points in such systems lie in the range between the no-load voltage and the maximum power point voltage of the PV module.
In this paper, an approach is presented to obtain approximate closed-form analytical expressions for the I-U characteristics of any PV array in the range from no-load condition up to the maximum power point condition. The technique presented allows direct method to predict the operating conditions of PV arrays when feeding loads, such as DC motors, without using tedious and time consuming iterative numerical techniques, and the approximated I-U characteristics obtained analytically are compared with corresponding exact characteristics with very close agreement obtained. To validate the proposed closed-form analytical expressions of the I-U characteristics of the PV array when feeding DC motors, the torque speed characteristics of different types of DC motors are obtained analytically and compared with the corresponding exact characteristics. The difference between the approximate and exact characteristics are very small.