# Parameter Identification of Lithium Battery Model Based on Chaotic Quantum Sparrow Search Algorithm
###### Abstract  
An accurate battery model is of great importance for battery state estimation. This study considers the parameter identification of a fractional-order model (FOM) of the battery, which can more realistically describe the reaction process of the cell and provide more precise predictions. Firstly, an improved sparrow search algorithm combined with the Tent chaotic mapping, quantum behavior strategy and Gaussian variation is proposed to regulate the early population quality, enhance its global search ability and avoid trapping into local optima. The effectiveness and superiority are verified by comparing the proposed chaotic quantum sparrow search algorithm (CQSSA) with the particle swarm optimization (PSO), genetic algorithm (GA), grey wolf optimization algorithm (GWO), Dingo optimization algorithm (DOA) and sparrow search algorithm (SSA) on benchmark functions. Secondly, the parameters of the FOM battery model are identified using six algorithms under the hybrid pulse power characterization (HPPC) test. Compared with SSA, CQSSA has 4.3%, 5.9% and 11.5% improvement in mean absolute error (MAE), root mean square error (RMSE) and maximum absolute error (MaAE), respectively. Furthermore, these parameters are used in the pulsed discharge test (PULSE) and urban dynamometer driving schedule (UDDS) test to verify the adaptability of the proposed algorithm. Simulation results show that the model parameters identified by the CQSSA algorithm perform well in terms of the MAE, RMSE and MAE of the terminal voltages under all three different tests, demonstrating the high accuracy and good adaptability of the proposed algorithm. s 2022 20221  
model and equivalent circuit model (ECM). Firstly, the black-box model usually employs artificial neural networks [5] or support vector machines [6] to learn the nonlinear relationship between the battery input and output. [PERSON] et al. [7] introduced a method employing a recurrent neural network with long short-term memory (LSTM-RNN) to perform correct \(SOC\) estimation for the lithium-ion battery. [PERSON] et al. [8] combined the advantages of LSTM and the Gaussian process and achieved accurate estimates. With a large amount of data, this method is able to estimate \(SOC\) without using any physical models or filters. However, since the model parameters have no explicit physical meaning, they require a large amount of data under different experimental conditions to train the model, which puts a heavy demand on the quality of the sample data as well as the computation capability [9; 10]. The electrochemical model needs to develop a detailed and complex model [11; 12] to describe the internal chemical reaction. It involves a variety of chemical parameters, which requires a great amount of tedious and expensive chemical experiments. As a result, this model cannot realize real-time online detection. Compared with the electrochemical model, the ECMs have been widely applied, which can mimic the electric behavior of the battery through simple circuit elements, including a serial resistor, one or more resistor-capacitor (RC) circuits and an ideal voltage source. Therefore, only a few parameters are required in ECMs. By appropriately adjusting the model structure, it is easy to reach a balance between accuracy and complexity. [PERSON] et al. [13] compared 12 commonly used ECMs in terms of accuracy, robustness and complexity and concluded that the first-order RC model is the most suitable one. Furthermore, as the RC order increases, the model accuracy improves, whereas the computational efficiency decreases. Related research [14; 15] shows that the diffusion effect in lithium-ion batteries is more appropriate to be described based on fractional order. This fact facilitated the rapid development of the fractional-order model (FOM) of the battery. One improvement of the ECMs was to replace the ideal capacitor with a constant phase element (CPE) in the first-order RC model to more accurately simulate the behaviors of double layers on the electrode [16].