Mathematical Modeling of Li-Ion Battery Using Genetic Algorithm Approach for V2G
2.1 Introduction
With the increased penetration of electric vehicles in the market, batteries are considered as one of the important components in the automobile industry [117, 118]. Among various available batteries, Lithium-ion batteries are more suitable for EV due to its long cycle life, less self discharge rate, high energy density, high efficiency, low maintenance and safe use [119].
EVs’ batteries are charged from the distribution node and can be support the DN during parking hours or having excess amount of energy [120]. This concept is referred as grid-to-vehicle (G2V) and vehicle-to-grid (V2G) technology [121]. If EVs’ batteries are intended to perform G2V and V2G operations, it would get subjected to varying node voltage conditions [120]. Also, during acceleration and regenerative breaking conditions, the EVs’ batteries would get discharged and charged frequently.
Such frequent charging/discharging operating conditions affect the internal circuit parameters due to change in state-of-charge (SOC) or depth-of-discharge (DOD), charge rate (Cr) or discharge rate (Dr) of the battery. Moreover, the capacity of EVs’ batteries would decrease due to frequent charg- ing/discharging process at different Cr/Dr [122, 123]. Therefore, a precise model of EV battery is very much required, to predict the performance of EVs in real-time V2G interaction. Capacity fade study is mainly required to predict batteries life time, which has been neglected in most battery mod- els [124–126]. The capacity fade is proportional to charge or discharge rate and temperature of the battery [122, 123, 127].
An accurate battery model (BM) and capacity fade model (CFM) have three advantages as follows:
(i) It provides precise battery data for the simulation of EVs to predict the performance of the system.
(ii) To analyze the changes in circuit parameters according to SOC variations, for providing stable control in the system.
(iii) It is possible to analyze the capacity loss and hence to predict the lifetime of the battery.
In literature, there are four types of battery models such as experimental, electrochemical, mathe- matical and electric circuit models [121, 128–141] which is given in Fig. 2.1.
Mathematical Models Battery Models
Electrochemical Models
Electric circuit Models Experimental
Models
Figure 2.1: Types of battery Models.
The electrochemical models are the most accurate models, but they require complex nonlinear differential equations and detailed knowledge of the chemical reactions of the batteries [128, 142].
Experimental models require experimentation to determine the internal parameters of the battery [121, 129–131]. However, experimental and electrochemical models are not well suited to represent the cell dynamics for the purpose of SOC estimation of battery packs [132, 133]. The mathematical models are based on stochastic approaches to predict the efficiency and runtime of the batteries [134–136].
Due to high complexity and intensive computations, the above mentioned models are difficult to use in real-time power management and circuit simulations to predict the performance of the systems [137].
Electric circuit based battery model can be used to represent the electrical characteristics of the EVs’
batteries [132, 137–141]. The simple common electric circuit model has a voltage source in series with an internal resistance [138]. However, this model does not take the account of battery SOC, Cr and Dr. There is another model based on an open circuit voltage in series with resistance and parallel RC circuit called as Warburg impedance [141]. The parameters of this model are identified using complicated impedance spectroscopy method [139,140,143]. From the literature, it is identified that the accurate estimation of internal battery parameters is a challenging task due to their nonlinear behavior.
Many soft computing and optimization techniques have been developed for battery parameter estimation [144–147]. Genetic algorithm (GA) is one of the best and robust kind of probability search algorithm, which has been used in this work [148]. In this Chapter, the GA is used to extract the battery parameters and gives optimum value. The Cr and Dr characteristics are calculated using the parameters of the BM which are obtained from the GA and it compared with the different types of battery manufacturers’ data. The results from BM and data given by the different types of battery
manufacturers’ are in good agreement. Hence, it can be concluded that the GAs are able to extract the parameters of the BM effectively.
There are several other experimental works found in the literature, which have focused on capacity fade analysis of a particular manufacturers’ battery [122, 123, 149–151]. However, performing exper- iments to determine the capacity fade of a battery for different Crand Dr is a tedious as well as time consuming process [127]. Moreover, these studies are confined only for a particular type of battery.
The results would differ for other battery types with different Cr and Dr, which cannot be performed experimentally every time. Therefore, there is a requirement of BM and CFM which can be used for any type of battery by reducing testing time and optimizing battery parameters for different Cr and Dr. Based on these aspects, the main motivations of this work are:
(i) To develop a simple circuit based BM and CFM, which can be used for any type of battery.
(ii) To extract the parameters of the model using GA approach.
(iii) To validate the developed model with different types of battery manufacturers’ catalogue.
(iv) The model is computationally inexpensive and does not need experimentation.
This Chapter describes an electric circuit based BM and CFM which represents different type of battery manufacturers’ Cr and Dr characteristics. The parameters of the BM is represented by a polynomial equation, which is optimized using GA approach. A control algorithm has been developed inside the battery, which calculates the processed energy, Cr/Dr, current SOC (S OCcr) and DOD (DODcr) constraints of the battery. Simulations are performed with the developed BM and CFM. The validation of the models have been carried out by comparing the simulated results with the real-time battery data obtained from four manufacturers’ data sheets such as EIG [1], Sony US18650 [127,152], Panasonic [153] and Sanyo [154]. Due to the unavailability of battery manufacturers’ data, this work consider the low nominal voltage and Ampere-Hour ratings.
The Chapter is organized as follows. Section 2.2 describes the proposed battery model. The details of battery parameter extraction using GA approach is discussed in Section 2.3. Section 2.4 describes the capacity fade model. The model validation have been done in Section 2.5 by comparing
the proposed model result with manufactures’ data and summary of the present work is given in Section 2.6.