The maximum power matching of a nonlinear cell array

Abstract

The cell power can be expressed as the product of the independent variable and the voltage-current function (dependent variable). The maximum power points of different cells are shown as irregular scattered points in the voltage-current coordinates that have mismatch loss for connecting in array. Through setting up the power function of cell array, this paper points out the matching conditions of cell array is that the maximum power points of each cell locate in a same horizontal or vertical line. And the matching method of cell array is expanded to “line matching” by “same working point matching” under the maximum power. According to the mathematical description of mismatch loss of cell array, the independent variable and dependent variable matching criterion of the array without mismatch loss is given. The independent variable matching criterion proves that the method of “line matching” does exist and the dependent variable matching criterion reveals the shortcomings of the method of “same working point matching”. Using the series with finite terms to study different cells under the dependent variable matching criterion, that reveals the ratio of each coefficient in the expression of the series are constant and obtains the matching method of “same class function matching” that the ratio of the voltage-current function of each cell in a array is constant. Taking the medium of the Lambert W function establishes the corresponding relationship between the “same class function matching” method of uncertain number of series order and the cell voltage-current equation of determine the number of cell parameters, and deduces the method of “cell parameters matching” that only the photoelectric current and the diode reverse saturation current are the same in a series array and the parallel array is the same as the diode ideal factor, which can practically guide the “line matching” method of cell array. Finally, the feasibility and correctness of the matching methods are confirmed by the simulation experiment of solar cell.