Mathematical Problems in Engineering

Volume 2018, Article ID 3793492, 13 pages

https://doi.org/10.1155/2018/3793492

## Development of Accurate Lithium-Ion Battery Model Based on Adaptive Random Disturbance PSO Algorithm

^{1}State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China^{2}School of Computer Science & Engineering, Hebei University of Technology, Tianjin 300130, China^{3}Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan

Correspondence should be addressed to Lin Hsiung-Cheng; wt.ude.tucn@nilch

Received 28 November 2017; Revised 8 May 2018; Accepted 5 June 2018; Published 3 July 2018

Academic Editor: Eric Monfroy

Copyright © 2018 Huang Kai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The performance behavior of the lithium-ion battery can be simulated by the battery model and thus applied to a variety of practical situations. Although the particle swarm optimization (PSO) algorithm has been used for the battery model development, it is usually unable to find an optimal solution during the iteration process. To resolve this problem, an adaptive random disturbance PSO algorithm is proposed. The optimal solution can be updated continuously by obtaining a new random location around the particle’s historical optimal location. There are two conditions considered to perform the model process. Initially, the test operating condition is used to validate the model effectiveness. Secondly, the verification operating condition is used to validate the model generality. The performance results show that the proposed model can achieve higher precision in the lithium-ion battery behavior, and it is feasible for wide applications in industry.

#### 1. Introduction

A battery management system (BMS) is an electronic system used to manage a rechargeable battery or battery pack, and it is widely applied to many applications that use a battery or batteries, such as portable electronic devices, electric vehicles, and power grids [1]. To ensure safe and efficient operation, it is essential for a BMS to be able to predict the static and dynamic behavior of the batteries.

Currently, there are three general types of battery models available in the literature: the electrochemical battery model, artificial neural network model, and equivalent circuit model (ECM) [2–9]. Among them, ECMs have been extensively researched in recent years owing to their excellent adaptability and simple realization [10, 11].

Parameter identification is an essential step in battery modeling, and its results directly affect the accuracy and reliability of the model. Identification methods are usually divided into two types [12, 13]: online and offline, corresponding to online and offline modeling, respectively.

Online identification methods adjust the parameters of the model in real time based on the condition and current state of the battery. Furthermore, the BMS makes use of such parameters and other information such as current, voltage, and temperature to evaluate the state of charge (SOC), state of health (SOH), and so on [14, 15], which are required for real time control [16, 17]. However, the processor should require higher calculation speed. Offline identifications can adopt mass experimental data that reflects the characteristics of the batteries. As a result, the identified parameters have higher precision and adaptability, and this makes such offline identifications more suitable for battery or battery pack modeling.

At present, there are two major types of offline identifications. The first type of methods is generally called traditional identification methods, like fitting method based on Least Squares [8], subspace identification [16], multiple linear regression method [18], and so on. This type of methods is simple and intuitive; however, the identified parameters have larger errors, and hence it is usually used in applications with lower accuracy demand [19, 20]. The second type of methods is generally called bionic intelligent optimization algorithms, like PSO [21], genetic algorithm (GA), [22] and so on. Compared with the first type of methods, the second one has obvious advantages in accuracy and reliability, and it has become a popular method for parameter identification. However, when GA is used in parameter identification [22–24], there are certain issues that cannot be avoided, such as the high computation time and easily falling into local optimum, i.e., local extremum. The particle swarm optimization (PSO) algorithm may have low precision and often fall into local optimum [24–29]. According to [25–27], the convergence speed and the inertia weight control can be improved. In [28], both GA and PSO were combined, and in [29], the double quantum PSO was adopted to identify the system parameters, which can increase the traverse ability of particles and simplify the evolution equation without using a velocity vector. However, the abovementioned method may not solve the problem in easily falling into the local optimum. In [30–32], the chaotic optimization algorithm (COA) and the improved PSO algorithm were combined to identify the parameters of the battery, load, and solar cell models. In abovementioned papers [30–32], upon accepting that the PSO algorithm has an issue of falling into local optimum, the COA is adopted to find the new searching swarm and continue the search, in order to increase global convergence and calculation precision. In [30], the difference between the covariance matrix of the particle location and the predetermined threshold has been used as the basis, while in [32] the difference between the variance of the population’s fitness and the predetermined threshold is used as the basis to judge whether the solution falls into local optimum. In addition, the predetermined threshold, which has certain influence on calculation precision, is set according to the experience.

For the development of the battery model using PSO algorithm, the particles may hover around local optimal solution during the iteration process without reaching the real optimal location. For this reason, an adaptive random disturbance PSO (ARDPSO) is proposed and its performances are validated by using a classical single model and a multiplex model as target optimization functions. Also, this algorithm can be used for identifying the parameters of the battery model thus achieving higher calculation precision.

The remaining contents of this paper are arranged as follows: Section 2 introduces the standard PSO algorithm. Section 3 describes ARDPSO algorithm and validates its performance. ECM parameters identification using ARDPSO is illustrated in Section 4. The experiment results and discussion are presented in Section 5. Section 6 concludes this paper.

#### 2. Standard PSO Algorithm

Particle swarm optimization (PSO) is an evolutionary computation technique, especially searching for optimization for continuous nonlinear, constrained and unconstrained, and nondifferentiable multimodal functions [21]. It can optimize a problem by iteratively moving particles around in the search space over the particle's position and velocity. Each particle's movement is updated as better positions in the search space [33]. Assume particles appear in a D-dimensional search space, and the sets can be expressed aswhere denoted by represents the group containing particles with -dimensional vector in the search space. The term represents the velocity of the particles. The term represents the local optimal solution, that is, the individual best solution of particle . The term* Gbest* represents the global optimal solution.

In each iteration, every particle updates its position and velocity in search space according to its individual best solution and the global optimal solution of the group* Gbest*, as follows:where is the current number of iterations; and are two positive constants called acceleration factors. and are random numbers in the range 0–1.

For a particle swarm optimization, a better global search is needed from a starting phase to help the algorithm converge to a target area quickly, and then a stronger local search is used to get a high precision value. Therefore, the modification of improved standard PSO introduces the inertia weight in formula (2), and its velocity is represented as follows:

For getting a high precision solution, *ω* needs to be kept as a variable value, generally a decreasing value. In the improvements of the standard PSO, the linear PSO (LPSO) [25] is very representative, which uses a linearly decreasing inertia weight, given by

in which is current inertia weight, is the minimum value (that is, the final value) of inertia weight, is the maximum value (that is, the initial value) of inertia weight, is the current iteration number, and is the maximum number of allowable iterations.

#### 3. ARDPSO Algorithm

##### 3.1. The Principle of ARDPSO

Although some related PSO algorithms in convergence speed and inertia weight control have been reported in the literature, the particles may still encounter problems such as hovering around the real optimal location but being unable to locate it. It means that the local optimal solution of the particle is not updated, then resulting in the global optimal solution not to be updated. Consequently, the distance between the searched solution and the real optimal solution will not become closer. For illustrating such a problem, a typical experiment uses the standard PSO and LPSO algorithms to find a solution that minimizes the single mode target function and obviously the real optimal solution is (0, 0). Without loss of generality, the number of particles is set as 50, and the maximum number of iterations is set as 100 in the tests. Note that the performances with different initial settings such as the number of the particles, iterative times, the initial range of the particles, and velocity may produce different results.

Figures 1(a) and 1(c) show the motion curves of the global optimal solution of the standard PSO and LPSO, respectively. On the other hand, Figures 1(b) and 1(d) show the corresponding fitness for standard PSO and LPSO, respectively.