Abstract
Photovoltaic (PV) array installations have been burgeoning in sunny weather regions. In this paper, using the numerical PV array power model [3], and for PV arrays with Np parallel strings, and Ns serially-connected PV cells per string, we derive, by trial and error, the various series-parallel PV array configurations leading to a certain optimum power (10KW). For these various (Np, Ns) configurations generating this output power, we also obtain the equations linking Np to Ns, and formulate the total array cost. The maximum PV array power is mathematically formulated agreeing within a small error with the numerical PV array model results, thereby validating it. The presented mathematical maximum power formulations can be manually used instead of the software implementing the numerical PV array model, when unavailable, to obtain the maximum power and derive the corresponding Np and Ns values leading to it. We also present a method for PV array sizing based on the average power per PV cell. After obtaining the average power per PV cell from the numerical PV array model, the various combinations of number of parallel strings and number of PV modules per string leading to a desired array power can then be obtained and evaluated without further needing the numerical PV array model. It was verified that the proposed array sizing method results agree, within a 0.55% error, with the array configurations obtained laboriously by trial and error from the numerical PV array model. Thus, the mathematical formula and sizing method presented in this paper agree with the results of the numerical PV array model, thereby cross-validating each other.