非线性电池阵列的最大功率匹配

The maximum power matching of a nonlinear cell array

电池功率可表述为自变量与伏安函数(因变量)的乘积.通过建立电池阵列功率函数,把阵列在最大功率下的"同工作点匹配"拓展为"线匹配".根据电池阵列失配损失的数学描述,给出了阵列的自变量和因变量匹配准则,证明了"线匹配"确实存在.在因变量匹配准则下用级数来研究不同电池,可得到级数表述中的各系数之比值恒为常数,给出类函数匹配方法.再以Lambert W函数为媒介,在类函数匹配方法和实际的电池电流方程之间建立起对应关系,给出电池参数匹配方法,可实践指导电池阵列的"线匹配".最后给出了光伏阵列的匹配案例.

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.