*Article* **Polarization Voltage Characterization of Lithium-Ion Batteries Based on a Lumped Diffusion Model and Joint Parameter Estimation Algorithm**

**Bizhong Xia, Bo Ye \* and Jianwen Cao**

Division of Advanced Manufacturing, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China; xiabz@sz.tsinghua.edu.cn (B.X.); jw-cao18@mails.tsinghua.edu.cn (J.C.) **\*** Correspondence: yb18@mails.tsinghua.edu.cn; Tel.: +86-186-1385-9890

**Abstract:** Polarization is a universal phenomenon that occurs inside lithium-ion batteries especially during operation, and whether it can be accurately characterized affects the accuracy of the battery management system. Model-based approaches are commonly adopted in studies of the characterization of polarization. Towards the application of the battery management system, a lumped diffusion model with three parameters was adopted. In addition, a joint algorithm composed of the Particle Swarm Optimization algorithm and the Levenberg-Marquardt method is proposed to identify model parameters. Verification experiments showed that this proposed algorithm can significantly improve the accuracy of model output voltages compared to the Particle Swarm Optimization algorithm alone and the Levenberg-Marquardt method alone. Furthermore, to verify the real-time performance of the proposed method, a hardware implementation platform was built, and this system's performance was tested under actual operating conditions. Results show that the hardware platform is capable of realizing the basic function of quantitative polarization voltage characterization, and the updating frequency of relevant parameters can reach 1 Hz, showing good real-time performance.

**Keywords:** battery polarization; lumped diffusion model; parameter identification; particle swarm optimization; Levenberg-Marquardt method
