Fundamentals of electrochemical impedance spectroscopy in energy storage devices: principles and innovative curve fitting approaches

Electrochemical impedance spectroscopy (EIS) is a widely utilized diagnostic tool for probing charge-transfer mechanisms, mass transport behavior, and interfacial phenomena in modern energy storage systems, yet its practical interpretation often requires both a solid grasp of its theoretical foundations and access to advanced fitting software. This study enhances the accessibility and rigor of EIS analysis by clarifying essential EIS principles and introducing a straightforward curve-fitting methodology based on the Generalized Reduced Gradient (GRG) nonlinear optimization algorithm. Applying the method to representative supercapacitor-type and metal-ion battery-type electrodes, the work elucidates how electrode architecture influences key model parameters, as demonstrated through detailed Nyquist plots, Bode analyses, and complex dielectric constant evaluations. The GRG-based fitting procedure, implemented entirely within Microsoft Excel, provides high-fidelity modeling of impedance spectra, achieving accuracy comparable to ZView with a low mean absolute error and validated through multiple error metrics such as MAE and RMSE. By combining theoretical clarity, computational robustness, and broad accessibility, this methodology strengthens the practical utility of EIS and enables more efficient, reliable interpretation of impedance behavior across diverse energy storage technologies.