## 1 Introduction  
As fossil fuel reserves continue to decrease, new means of transportation that are independent of traditional fuels have to be found to meet the requirements of our daily life. Consequently, electrical vehicles (EV) have been regarded as a potential solution. In order to increase the acceptance of EV in the market, the performance of the energy storage system has attracted much attention from both industry and academia. As the only power supply in pure EV, the capability of the battery pack is of great importance. Lithium-ion (Li-ion) batteries have higher energy density, longer cycle life, and no memory effect compared with other battery types [1; 2]. Additionally, the price of the li-ion battery continues to decline, which makes it a popular choice for EV applications [3]. In order to ensure the safety and reliable operation of the battery pack, SOC has to be estimated [4; 5].  
Although numerous SOC estimation methods have been exhibited and classified in [6; 7; 8; 9; 10], accurate, efficient, and reliable SOC estimation solutions are still needed in real-time applications. As discussed in our previous work [10], SOC estimation methods are mainly divided into five categories: the Coulomb counting method; the Open Circuit Voltage (OCV) method; the impedance spectroscopy-based method; the model-based method, and the artificial neural network-based method. The Coulomb counting method calculates SOC through the integration of current, and has high computational efficiency. The accuracy of Coulomb counting method is sensitive to initial SOC and the accumulation of the current measurement error. OCV method depends on the relationship between SOC and OCV. The long battery relaxation time for measuring the OCV makes it impractical for most online SOC estimations. Impedance spectroscopy is hard to measure accurately, while artificial neural networks are closely related to the training samples. Generally, model-based SOC estimators are supposed to have a superior performance. However, their performance relies on an accurate battery model. In the model-based estimation structure, much attention has been paid to different estimation algorithms, while a complete review of the battery modeling methods is seldom seen in the literature. Therefore, this paper reviews important battery modeling methods from the SOC estimation point of view.  
The modeling technologies for Li-ion batteries are discussed in [11], where data-driven battery models are not discussed. Battery modeling methods for EV are discussed in [12], but the paper does not give the detailed features of each method or the connections between each method. Different from previous works [11; 12], this paper divides the battery modeling method into four categories: empirical model, Equivalent Circuit Model (ECM), electrochemical model, and data-driven model. According to the structure of the model-based estimation, the advantages and disadvantages of each modeling method are presented. In addition, the future trends for next-generation modeling technology are also presented. Moreover, four typical modeling methods in SOC estimation area including the combined model [13], two Resistance-Capacitance (RC) ECM [10], Single Particle Model (SPM) [14] and Support Vector Machine (SVM) battery model [15] are compared through an experiment on a LiFePO4 battery in terms of accuracy and computational efforts.  
The rest of this paper is organized as follows. After introducing the principle of model-based SOC estimation, the features of the four modeling methods are detailed in Section 2. Section 3 gives the advantages and disadvantages of each modeling method and previews future trends in battery modeling methods. Four typical modeling methods are compared in terms of modeling accuracy and execution time in Section 4. Conclusions are drawn in Section 5.