Online measurements of the battery impedance provide valuable information on the battery state-of-charge and stateof-health, which can be utilized for improving the safety and the performance of the associated system. The electrochemicalimpedance spectroscopy (EIS) is widely used for battery impedance measurements, but it is not the most applicable solution for online measurements due to its slowness and complexity. These drawbacks can be improved using broadband signals, such as pseudorandom sequences (PRS), which are fast and easily implementable. However, the nonlinear behavior of batteries have a significant effect on the impedance measurements and the selection of the PRS signal. Majority of the PRS signals are applicable for measurements of linear systems, but also signals for nonlinear system identification do exist. Moreover, the reduced accuracy and signal-to-noise ratio of the PRS signals compared to the EIS make the filtering of the results as well as the amplitude design important aspects. This paper demonstrates the use of two PRS signals, the pseudorandom binary sequence (PRBS), and a ternary sequence with better toleration to battery nonlinear effects, with comprehensive amplitude and filtering design for battery impedance measurements. It is shown that the ternary sequence provides accurate measurements and the effects of nonlinear dynamics of the battery impedance are reduced with respect to the PRBS measurements. The results are referenced and validated to practical EIS measurements in various operating conditions for lithium-iron-phosphate (LiFePO 4 ) cell.
The impedance of Li-ion batteries contains information about the dynamics and state parameters of the battery. This information can be utilized to improve the performance and safety of the battery application. The battery impedance is typically modeled by an equivalentcircuit-model (ECM) which provides the dynamic information of the battery. In addition, the variations in the model parameters can be used for the battery state-estimation. A fitting algorithm is required to parametrize the ECM due to the non-linearity of both the battery impedance and ECM. However, conventional fitting algorithms, such as the complex-nonlinear-least-squares (CNLS) algorithm, often have a high computational burden and require selection of initial conditions which can be difficult to obtain adaptively. This paper proposes a novel fitting algorithm for the parametrization of battery ECM based on the geometric shape of the battery impedance in the complex-plane. The algorithm is applied to practical and fast broadband pseudo random sequence impedance measurements carried out at various state-of-charges (SOC) and temperatures for lithium-iron-phosphate cell. The performance of the method is compared to conventional CNLS algorithm with different initial conditions. The results show that the proposed method provides fast and accurate fit with low computational effort. Moreover, specific ECM parameters are found to be dependent on the battery SOC at various temperature. NOMENCLATURE CNLS Complex non-linear least squares ECM Equivalent circuit model. EIS Electrochemical impedance spectroscopy. EoD End of the diffusion. LiFePO4 Lithium iron phosphate. PRS Pseudo random sequence. NRMSE Normalized root mean square error. SEI Solid electrolyte interface SOC State of charge. SOH State of health. TSC Top of the semicircle. f gen Generation frequency of PRS. f res Frequency resolution of PRS measurements. C CT Capacitance of the charge-transfer region.
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