超级电容器恒流充电的时域分数阶电路模型

随着超级电容器作为新的储能装置得到广泛的应用,建立超级电容器的精确等效模型具有重要意义。根据分数阶微积分定义,结合分抗元的恒流充电曲线和超级电容器实际物理结构,直接在时域建立超级电容器恒流充电的分数阶RF串联电路模型和分数阶RFR混联电路模型,并给出模型参数辨识与拟合误差分析方法。在结合超级电容器恒流充电数据完成分数阶RF串联电路模型和分数阶RFR混联电路模型的参数辨识与误差分析的过程中,发现分数阶RF串联电路模型和分数阶RFR混联电路模型的拟合精度均远优于一阶RC电路模型和经典等效电路模型,且这两种分数阶模型的精度相当。分析更简洁的分数阶RF串联电路模型的参数敏感性,得到模型中分抗元运算阶、分抗元特征值和电阻值对超级电容器恒流充电的影响规律。该文同时还说明经典等效电路模型是分数阶RFR混联电路模型的特殊情况,一阶RC电路模型是分数阶RF串联电路模型的特殊情况,分数阶RF串联电路模型是分数阶RFR混联电路模型的特殊情况。

With the extensive application of supercapacitor as a new energy storage device,it is of great significance to establish accurately equivalent model for the supercapacitor.According to the definition of fractional calculus and based on the combination of the constant current charging curve of the fractor as well as the actual physical structure of the supercapacitor,a fractional RF series circuit model and a fractional RFR hybrid circuit model for constant current charging of supercapacitor were directly established in the time domain.In addition,the model parameter identification and the fitting error analysis method were also provided in the current work.In the process of the parameter identification and the error analysis of both the fractional RF series circuit model and the fractional RFR hybrid circuit model combined with the constant current charging data of the supercapacitor,the fitting precision of both the fractional RF series circuit model and the fractional RFR hybrid circuit model are proved to be much advanced than the first-order RC circuit model and the classical equivalent circuit model,having quite similar accuracy.Through analyzing the parameter sensitivity of the more succinct fractional RF series circuit model,the influence rules of the operation order,the eigenvalue and the resistance value of the resistor element on the constant current charging of the supercapacitor can be obtained.In the meanwhile,the proposed study also demonstrates that the classical equivalent circuit model belongs to a special case of the fractional RFR hybrid circuit model,the first-order RC circuit model is a special case of the fractional RF series circuit model,and the fractional RF series circuit model refers to a special case of the fractional RFR hybrid circuit.