Modelling and Simulation in Engineering

Volume 2016, Article ID 2353521, 12 pages

http://dx.doi.org/10.1155/2016/2353521

## Thermoelectric Modeling and Online SOC Estimation of Li-Ion Battery for Plug-In Hybrid Electric Vehicles

Electrical and Electronics Engineering Department, B.I.T.S. Pilani, Jhunjhunu, Rajasthan 333031, India

Received 21 September 2015; Revised 26 November 2015; Accepted 14 December 2015

Academic Editor: Joseph Virgone

Copyright © 2016 Aishwarya Panday 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 increasing oil price, energy demand, and environmental concern are leading to a global switch towards Plug-In Hybrid Electric Vehicles (PHEVs). In a PHEV, Li-ion battery is considered as the primary propelling source. Therefore, an accurate battery model is required to predict the characteristic and dynamic behavior of a battery. This paper presents a highly effective thermoelectric model of Li-ion battery developed in Simulink. An algorithm is proposed for estimation of state of charge (SOC) and open circuit voltage (OCV) adaptively to notify the exact SOC level for better utilization of battery power and optimal vehicle performance. Thermal behavior of Li-ion battery is investigated for wide temperature range and its effect on resistance, capacity, and OCV is recorded. The minimum SOC level to which battery can get depleted is calculated using gradient method. The proposed simulation results are analyzed with those of earlier models and found to be better.

#### 1. Introduction

Internal Combustion Engine (ICE) based automobiles have been causing toxic emissions, global warming, and environmental and ecological danger. Petroleum as a finite fuel and increasing prices of crude oil were motivation to find alternative approaches to propel vehicles. The world is now moving towards hybrid vehicles, which contain an alternative power source along with ICE to reduce the liquid fuel consumption without affecting vehicle performance.

Hybrid Electric Vehicles (HEVs) and PHEVs are now available in the market with reduced petroleum consumption. In PHEV, the battery is used as primary power source and ICE as secondary power source. It provides a longer driving range and easy refueling (recharging) with reduced liquid fuel consumption and toxic emissions. Thus, PHEV is a means to reduce the energy demand and replacing the liquid fuel consumption by storing electrical energy in large on-board rechargeable batteries with high fuel economy and better energy efficiency [1].

Depending upon the application and specification different types of batteries are available in market like lead-acid, Nickel, and Li-ion based batteries. Among these, Li-ion batteries are preferred in portable electronics today because they provide higher specific energy, higher specific density, extra durability, and lower self-discharge rate with better safety issues [2, 3].

Since batteries play a vital role in PHEVs, it is essential to study their behavior. A holistic understanding of the same would result in better performance of the vehicle. The battery can be modeled using electrochemical, mathematical, analytical and stochastic, impedance based, and electrical circuit based models. The electrical circuit based model depicts the battery behavior easily [4]. Electric models are of varying degrees of complexity to capture battery performance with respect to a set of parameters which are explained in detail in the next section. In this paper, a second-order electrical battery model considering diffusion and double layer effects and self-discharge current is proposed. It reflects the effect of temperature on various parameters. And a modified SOC estimation is considered here which incorporates both open circuit voltage method and ampere hour counting. To inquire about instantaneous SOC and OCV during battery usage, an adaptive estimation algorithm is developed. To use the battery, effectively without deteriorating battery health, the threshold SOC value of the battery is also computed.

This paper is organized with different sections; unfolding existing battery models in literature is in Section 2. Section 3 contains the proposed SOC estimation method with the detailed description of weighting factor and correction factor. Section 4 describes the development of the proposed 2RC thermoelectric model. Section 5 discusses the simulation results. Section 6 determines the threshold SOC and Section 7 finally concludes the paper.

#### 2. Overview of Existing Models

Sean proposes a PSPICE macromodel showing the voltage dependency on SOC, discharge current, resistance, and capacity variation with respect to temperature [5]. This is further used by [6] to propose a discrete-time model which is capable of battery lifetime estimation. In 1994, The National Renewable Energy Laboratory (NREL) modeled Li-ion battery with a voltage source and internal resistance as a function of SOC, temperature, and current flow direction in ADVISOR. Saft America developed the high-power Li-ion cells and implemented 2-capacitance battery model in PSPICE. It shows a slightly better performance in comparison to NREL’s model [7]. Chen et al. proposed a model to be used with an equilibrium potential and two internal resistances and where is a function of discharge current, temperature, and life cycle and is a function of state of discharge and temperature but did not count for transient response of the battery [8].

Gao et al. demonstrated a dynamic model of Li-ion battery which depicts a capacity variation on the basis of C-rate and temperature change, equilibrium potential, and transient response of the battery [9]. It consists of equilibrium potential, internal resistance (with two components), and a capacitor (transient response of charge double layer) but may result in a better performance by involving self-discharge current and diffusion effect between electrodes. Tremblay et al. presented a battery model, for dynamic simulation software, and added the same in the SimPowerSystems library MATLAB/Simulink. It consists of an internal resistance and a voltage source which is a nonlinear function of battery SOC. It does not account for Peukert, self-discharge, memory effect, and temperature variation [10].

Lee et al. used Li-ion battery model with internal resistance, one RC combination, and a voltage source (OCV as a function of SOC). They estimated SOC using ampere-hour counting and capacity estimation, neglecting coulomb based counting which is also required for accurate SOC estimation [11]. Using lumped model, the SOC estimation algorithm is developed at varying temperatures [12, 13]. It consists of one resistance with two components (series and charge transfer), one RC ladder (diffusion resistance and diffusion capacitance), and voltage source (OCV) but does not account for self-discharge current and transient behavior of a battery. Bhide and Shim developed a circuit based Li-ion battery model using AMESim and also represented the temperature rise in core and the crust. But the model considers only particular discharge rate and different temperature and discharge rate factor functions for different rates [14]. Reference [15] combined the electric model developed in [10] and thermal model developed in [14] to derive a thermoelectric analytical model. This model can inspect the behavioral change of battery due to temperature variation, but contains others lacking in [10].

For online SOC estimation, [16] proposes the model with internal resistance, OCV, and two RC circuit combinations. For SOC estimation they considered only coulomb counting and neglected voltage based counting which is required for better accuracy. The model developed in [17] is a blend of previous models and overcomes few of their limitations. It predicts runtime, steady state, and transient response accurately by capturing all the dynamic electrical characteristics of batteries. The RC network is modeled to account the effect of self-discharge losses due to long time storage and also includes transient response but it does not include thermal effects. Reference [18] used a model developed in [17] and incorporated temperature and capacity fading effect, to propose a dynamic model of Li-ion battery using MATLAB/Simulink. To determine online SOC of Li-ion battery, [19] estimated electrical parameters with temperature variation. Determination of battery SOC using a second-order model is introduced in [16, 20].

Kroeze and Krein proposed two models for predicting SOC, terminal voltage, and power losses. These are the following: (1) SOC can be predicted when temperature and cycle number are given and (2) transient behavior of terminal voltage can be figured out where each parameter is a function of SOC [21]. Zhang and Chow constructed an equivalent circuit of battery cell which is based on Thevenin’s theorem. It describes the SOC variation with current and considers the battery relaxation effect too but lacks online-parameter variation which is important in HEV/PHEV applications [22]. This also neglects self-discharge current which results in an approximate error of 3% between experimental and estimated SOC. Randles’ model [23] developed for lead-acid batteries is remapped by Gould et al. [24]. They implemented an equivalent circuit model to determine state of function of Li-ion battery but did not consider the temperature effect. Based on experimental results, 2RC battery model is proposed and mathematical modeling is performed in [25], but self-discharge current is not discussed. References [26–28] also proposed 2RC battery model, but no discussion of self-discharge current is performed. Reference [29] has also used 2RC battery model and temperature effect is also incorporated, but again self-discharge current is not discussed.

A large number of researchers attempted to calculate exact SOC of the battery. Pang et al. [30] used OCV method to calculate the SOC (voltage based SOC, i.e., ) of the battery. The OCV based SOC estimation technique is advantageous in various aspects as follows: (i) OCV versus SOC characteristic is independent of the age of the Li-ion battery [31] and (ii) this is very accurate but requires some rest time [32]. Ampere-hour counting method (current based SOC, i.e., ) is a suitable method to estimate SOC of the battery as it is easy, direct, and easily implementable. If the current measurement is accurate, then the method is also reliable. But it may have some initial value or accumulated error problems [33]. To overcome the shortcomings of both and to utilize the added advantages, these two methods can be combined together. References [19, 34] identified the contribution of both and together to estimate accurate SOC of the battery but do not include the effects of temperature.

#### 3. Proposed Model

The proposed model considers the effects of temperature as an independent variable and incorporates self-discharge current as well in calculations. The objective is to model a Li-ion battery to represent its actual characteristics to achieve high accuracy and robustness in run-time SOC estimation. The model is aimed to simulate the dynamic behavior of a Li-ion battery as a second-order equivalent circuit in SIMULINK. All the parameters in the proposed model are multivariable functions of the SOC, current, and temperature.

##### 3.1. SOC Estimation

It is appreciable to characterize the Li-ion battery to dynamically compute the SOC even in case of temperature variation. Li-ion battery has a very eminent effect of temperature on its performance and various parameters. Under optimal temperature range batteries behave as prescribed, but outside battery cell experiences severe loss of capacity. To characterize the battery performance under the influence of temperature, thermal effect during modeling is deemed. Temperature dependent modeling provides the pertinent information about the parameters under temperature variation.

The vehicle performance is characterized by SOC of battery defined as the ratio of remaining capacity to fully charged capacity: is the initial SOC level of battery.

###### 3.1.1. Calculation

Cell voltage under reversible conditions, that is, all the reactions are balanced, is called equilibrium voltage which is occasionally referred to as OCV or rest voltage. With this OCV, voltages based SOC () can be estimated usingwhere is battery terminal voltage when SOC = 0% and is battery terminal voltage when SOC = 100%. But, due to change in temperature, equilibrium voltage of battery at any temperature gets changed as is temperature coefficient and is constant for the considered temperature range. So the consideration of this OCV with temperature effect will lead to modifying and will contribute in the final SOC calculation.

###### 3.1.2. Calculation

The coulomb counting method involves the current integration flowing through the battery to get : is battery capacity in Ah. Due to change in temperature, the cell reaction rate gets changed which has been depicted here using (5), (6), and (7). From the Arrhenius equation, the reaction rate is given as is reaction constant, is gas constant, is activation energy, and is operating temperature. During the electron transfer reaction, electrons require the additional amount of energy to surmount the energy barrier called the activation energy ( = J·mol^{−1}) which depends on temperature. As for every 10°C temperature increase, current gets doubled so for temperature change, reaction rate ratio is articulated as is the reaction rate (mole/s) and can be expressed as current. Suppose is the reaction rate at a temperature (), that is, , and at temperature , that is, . To represent the effect of temperature on , (5) and (6) are equated as (7) and hence is presented as (8):

Li-ion batteries exhibit self-discharge phenomenon even at moderate oxidation levels. It is primarily due to loses occurring at the negative electrode, which results from several side reactions, each with their own activation energy and rate constant. From Arrhenius equation self-discharge current can also be modeled as (5). The battery capacity also affects it; hence self-discharge current is sculpted as (9) considering the effect of temperature on activation energy from (8):

###### 3.1.3. Modified SOC Calculation

Temperature dependent SOC can be deduced as (10) by combining and with a weighting factor . Charging and discharging efficiency influence battery dynamics to a great extent; weighting factor allied with should govern the combined SOC. Correction factor (CF) is integrated here, which is a function of SOC as (11) which helps in getting exact SOC during discharging:

##### 3.2. Weighting Factor Calculation

To calculate the weighting factor, the value of OCV and time required to get steady OCV should be considered because under steady condition has higher accuracy. The entire OCV range is divided into 100 sections; each section weighting value is calculated asAccording to experimental data, average time taken by OCV to get steady condition is s and time between two samples is s. As , weighting factor is deduced as (13). Table 1 lists the values of weighting factors and correction factor at various SOC levels: