基于正则化方法的电池阻抗谱弛豫时间分布解析

Distribution of Relaxation Times Analysis From Battery Impedance Spectroscopy Using Regularization Method

对电池特性的深刻认识是电池应用研究的重要基础,而弛豫时间分布(distribution of relaxation times,DRT)法是解析电池阻抗谱(electrochemical impedance spectroscopy,EIS)、提取电极过程动力学信息和电池建模的有效手段。然而,DRT函数的求解是一个典型的不适定问题,经典的数值积分方法无法保证解的存在性或唯一性。首先采用分段线性插值近似连续的DRT函数;再通过正则化方法改善问题的不适定性,将DRT函数的求解归结为严格的凸二次规划(quadratic programming,QP)问题;进而运用有效集法(active set method,ASM)得到DRT函数的最优近似解。基于该方法解析液态金属电池的阻抗谱,并简要分析其内阻特性。研究结果表明:该方法为全局收敛,收敛速度快,计算精度高;得到的DRT函数近似解既精确、稳定,又具有明确的物理意义。在电池机理分析和建模中,该方法具有显著的潜在应用价值。

Battery applications rely on a deep understanding of cell characteristics,and the distribution of relaxation times(DRT)is an approach of particular validity to the interpretation of electrochemical impedance spectroscopy(EIS),the investigation of electrode kinetics,and battery modeling.However,a typical ill-posed problem must be solved to obtain DRT function,while the existence and uniqueness of solution could not be ensured in numerical integration algorithms.In this paper,the continuous DRT function was approximated by piecewise linear interpolation.Then,the aforementioned ill-posed problem was stabilized by regularization and further converted to a convex quadratic programming(QP)problem.Thus,the optimal approximate solution could be found by using the active set method(ASM).The EIS of liquid metal battery was interpreted by the proposed approach to clarify its effectiveness.Both fast convergence rate and high calculation accuracy can be achieved by this globally convergent algorithm.The obtained solution is accurate,stable,and has strong relations to the underlying electrode reaction process,which indicates that it can be further applied in mechanism analysis and modeling of different batteries.