Temperature Influences on State and Parameter Estimation Based on a Dual Kalman Filter Christian Campestrini * , Georg Walder † , Andreas Jossen * and Markus Lienkamp † * Institute for Electrical Energy Storage Technology, Technische Universit¨ at M¨ unchen, Email: c.campestrini@tum.de † Institute of Automotive Technology, Technische Universit¨ at M¨ unchen, Email: walder@ftm.mw.tum.de Abstract—The temperature dependency of a Dual Kalman Filter (DKF) is shown. For this purpose a validation process is developed to show the behaviour of the filter at various cell temperatures (5 ◦ C, 25 ◦ C, and 35 ◦ C). Additionally, the validation process reveals some unresolved problems such as the behaviour during constant voltage periods. The behaviour of the DKF is compared to experimental data. The state estimator predicts the state of charge (SOC) with an accuracy of 1.5 % within the investigated temperature range. Furthermore, the state estimator is able to reproduce the observed characteristics of the ohmic resistance (R dc1s ) of the equivalent circuit model (ECM). I. I NTRODUCTION Nowadays, electric mobility gains sufficiently importance. Due to the reduced range compared to a vehicle equipped with a conventional combustion engine battery electrical vehicles (BEV) and hybrid electrical vehicles (HEV) still play a minor role in today’s mobility. With a reliable state determination of the built in battery system, the usable amount of energy can be raised and, hence, the range can be increased. In literature, numerous algorithms for the state estimation can be found [1, 2, 3, 4, 5]. However, these algorithms are mostly tested within the laboratory scale at predefined conditions. The shortcomings of these algorithms are often not shown. Therefore, this paper presents a validation method to test state estimators for the mentioned shortcomings. Here, the Dual Kalman Filter is investigated. The focus lies on the temperature dependency of relevant state parameters of the battery and, consequently, on the high requirements of the filter. In chapter II the ECM used is presented and the identification process of the reference parameters is shown. In chapter III the DKF used here is explained [6]. The validation method is shown and some problems of the filter are revealed in chapter IV. The results are presented and discussed in chapter VI. II. BATTERY MODELLING To describe the behaviour of batteries an ECM can be applied. The most frequently used ECM is a simple model, which consists of a direct voltage source, a serial resistor and one or more RC-terms. With an increasing number of RC- terms, the accuracy of the model increases as well. However, this leads to a higher complexity and, consequently, to an increased demand on the computational effort (e.g. battery management system, BMS). Due to the limited computational power that can be implemented on a BMS, different ECMs were compared in [7] to find a compromise between accuracy and computational time. The resulting ECM is shown in figure 1. R 1 C 1 R dc1s U 0 (SOC) I T U 1 U T Fig. 1. The equivalent circuit model with one RC-term U 0 corresponds to the SOC dependent open circuit voltage (OCV). Due to the current sample rate of 1 s, R dc1s corre- sponds to the serial ohmic resistance and to the charge transfer effects. R 1 and C 1 corresponds to the elements of the RC-term. U 1 is the voltage drop by the RC-term and contains diffusion effects, U T and I T corresponds to the terminal voltage and current. Applying the mesh rule, the following set of equations can be found to describe the states in the time domain.  ˙ U 1 (t) ˙ SOC (t)  =  - 1 R1C1 0 0 0  U 1 (t) SOC (t)  +  1 C1 1 C N  I T (t) (1) U T (t)= U 0 (SOC (t)) + R dc1s · I T (t)+ ˙ U 1 (t) (2) C N is the capacity of the cell. The exact derivation of the equations can be found in [6]. After the discretisation of the ECM the DKF can be implemented. The parameters of the model can be identified by measuring the voltage response of a battery as a result of current pulses over the entire SOC range (5 % SOC steps). In figure 2 the voltage response as a result of a current pulse is shown. The voltage drop between P1 and P2 is used to calculate the resistor R dc1s . The following voltage drop between P2 and P3 is a result of the diffusion effects. After the end of the pulse, the cell relaxes. The pulses were performed at 5 ◦ C, 25 ◦ C and 35 ◦ C every 5% ΔSOC. Applying this method, the measured parameters can be compared to the estimation using the DKF as a function of SOC and temperature.