Comparison of the First Order and the Second Order Equivalent Circuit Model Applied in State of Charge Estimation for Battery Used in Electric Vehicles

Abstract

In this study, the first order model and the second order equivalent circuit models of NiMH battery for electric vehicle were used to determinate the battery state of charge. Different parameters for equivalent circuit models were explained. There are four phases in the battery change and discharge, which are charge phase, change idle phase, discharge phase, discharge idle phase. All of these phases are discussed and analyzed. For different phas-es of charge and discharge, mathematical relationships between parameters and state of charge were built. The calculation results fit well with the experimental results. A precision comparison between the first order model and the second order model was undertaken. Keywords electric vehicles, NiMH battery, equivalent circuit models, state of charge, model parameters 1. INTRODUCTION State of charge (SOC) represents the residual capac-ity of the battery and it is written as the percent of residual capacity by nominal capacity. The estima-tion of SOC of NiMH battery is a key point of energy management system in EV/HEV. With accurate SOC, the battery can extend its age and avoid being over charged or over discharged [Jung et al., 2002]. Moreo-ver it is benefit for controller to implement control strategy in HEV. Many methods are used to improve the precision of SOC. It is very popular to estimate the SOC with Ampere hours (Ah) algorithm, which apply in EV/HEV. The battery capacity is measured in Ah algorithm which is calculated by multiplying the current by time of discharge [Koehler et al., 2001, Stiegeler et al., 2005]. The residual capacity is calculated by initial capac-ity minus capacity discharged. Researcher found it is more precise when it considers the compensation, such as temperature, discharge rate, self discharge and age [Youn et al., 2005]. But Ah algorithm has three shortcomings. First, it is impossible to forecast the ini-tial SOC. Second its estimation precision is dependent on the precision of sensor .Third, the accumulated er-ror can not be ignored with the test time growing. For longer time periods and operation where incomplete charging is concerned, Ah-balancing results in high errors [Kremer et al., 1995, Terry and Wang, 2005, Ha et al., 1992].