Low-frequency impedance spectroscopy generated by two equal square waves as a fast and simple tool for states estimation without battery relaxation

Electrochemical impedance spectroscopy (EIS) is an experimental technique that reveals battery impedances, notably with its low-frequency components exhibiting significant correlations with battery states. However, traditional EIS (T-EIS) necessitates expensive instrumentation and extended battery relaxation periods, rendering it impractical for rapid state estimation applications. To overcome these two shortcomings, square wave EIS (Sq-EIS) in the low-frequency range, generated using a simple two-cycle square wave, emerges as a more cost-effective and time-efficient alternative, capable of achieving results comparable to low-frequency T-EIS. Even when the battery is in unrelaxed states, the total root mean square error (RMSE) between Sq-EIS and T-EIS can be <0.5 mΩ. We conduct thorough investigations into the number, amplitude, and sampling rate of 50-s period square waves, showing that a two-cycle square wave with an amplitude of 1 A and a sampling rate above 50 Hz can achieve optimal similarity between Sq-EIS and T-EIS across different scenarios, including constant current charging/discharging and dynamic discharging. Square waves of different periods, such as 30 s and 10 s, also effectively achieve this similarity. Based on these findings, by applying two 10-s square waves (for a total of 20 s) immediately after battery charging or dynamic discharging, the Sq-EIS data enables machine learning models to concurrently estimate the battery's state of charge and state of health with an RMSE of <2 % in each case. • Using two equal square waves of total 20 s to estimate battery states without relaxation • The first wave drives the battery voltage towards its open circuit voltage. • The impedance spectrum from the second wave resembles the typical low-frequency spectrum. • Various wave parameters such as number, magnitude, period, and polarization are analyzed.