### Battery Model

The electrochemical reaction process of power batteries is complex, with many influencing factors and uncertainties. Its mathematical modeling is a multi-domain and multi-disciplinary problem, and it has always been the focus and difficulty of academic and industrial research. The external representation of the power battery is limited. Currently, the parameters that can be directly obtained through the battery management system are usually only voltage, current, and temperature. From the experiment, it can be found that the terminal voltage of the power battery is affected by factors such as working conditions, climate, positive and negative electrode materials, and aging conditions, and exhibits strong time-varying and nonlinear characteristics. The terminal voltage of the power battery can be divided into two parts: dynamic and static. The static part mainly refers to the open circuit voltage (equilibrium potential), and the dynamic part mainly contains fast-changing voltage components (ohmic polarization) and slowly-changing voltage components (concentration and electrochemical polarization, etc.), where the lagging voltage component is closely related to the current state of the system and the historical excitation trajectory.

In order to more accurately describe the external characteristics of the power battery, design a reliable power battery state estimation algorithm, and develop the optimal new energy vehicle energy management system, accurate modeling is essential. Common power battery models are mainly divided into electrochemical mechanism models, equivalent circuit models and fractional frequency domain models. This part will systematically introduce the construction, parameter identification and verification of Electrochemical Model, Equivalent Circuit Model and Fractional-order Model. The diagrams of the common structures of the three types of models are as follows.

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Schematic diagram of P2D model principle

The electrochemical model starts from the internal reaction principle of the power battery, and has high accuracy, but the amount of calculation is large, and dimensionality reduction is usually required in the practical application. The advantage of the electrochemical model lies in its clear physical meaning, which can accurately reflect the mapping relationship between the electrochemical parameters of the power battery and the external excitation, and has good prospect in the fields such as the analysis of battery performance degradation mechanism, aging modeling, SOH estimation and fault diagnosis.

N-order RC equivalent circuit model

The equivalent circuit model describes the voltage response of the power battery with ideal electrical components, the static voltage characteristics of the power battery with a voltage source, and the dynamic voltage characteristics such as the polarization of the power battery with the RC network. The parameter identification is simple and the model calculation amount is small and the real-time performance is good, so it is widely used SOC, SOH estimation and SOP prediction, and energy management algorithms in various BMS. However, because the model has no explicit boundary of constraints on each parameter, the identified parameters may deviate significantly from the reasonable interval. Therefore, the model is difficult to reflect the internal characteristics of the power battery, and it is difficult to applied in the thermal-electric coupling modeling and mechanism analysis of the power battery.

A commonly used fractional model

Compared with the equivalent circuit model, the fractional order model is based on the measurement results of electrochemical impedance spectroscopy, combined with the fractional order theory to calculate in the time domain. The accuracy of voltage prediction and SOC estimation of the fractional order model is higher than that of the equivalent circuit model, but the amount of calculation is often large. This model can be regarded as a generalization of the traditional equivalent circuit model, and because the fractional order model can be used to fit the EIS, which can obtain a lot of information on the reaction mechanism of power battery, it also has great application value in SOH estimation.

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