A novel dual H infinity filters based battery parameter and state estimation approach for electric vehicles application

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1 Available online at ScienceDirect Energy Procedia 3 (26 ) Applied Energy Symposium and Forum, REM26: Renewable Energy Integration with Mini/Microgrid, 9-2 April 26, Maldives A novel dual H infinity filters based battery parameter and state estimation approach for electric vehicles application Cheng Chen a,b, Fengchun Sun a,b, Rui Xiong*,a,b, Hongwen He a,b a National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 8, China. b Beijing Co-innovation Center for Electric Vehicles, Beijing Institute of Technology, Beijing 8, China Abstract An accurate battery parameter and state estimation method is one of the most significant and difficult techniques to promote the commercialization of electric vehicles. This paper tries to mae three aspects of effort. First, to avoid the battery state-of-charge (SoC) estimation inaccuracy brought by the variation of the model parameter under different aging level and operation condition, a novel dual H infinity filters was proposed and employed to execute the online measured data based battery parameter and SoC estimation. Second, to overcome the drawbac of the H infinity filters are sensitive to their initial noise information. An adaptive H infinity filter employing the covariance matching approach was proposed and applied to realize a robust SoC estimation. Last, the accurate estimate of battery parameter and SoC were obtained real-timely through model-based dual H infinity filters. A systematic evaluation on the different algorithms based SoC estimation was carried out. Experimental results on various degradation states of lithium-ion polymer battery cells further verified the feasibility of the proposed approach. 26 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( 26 The Authors. Published Elsevier Ltd. Peer-review Selection and/or under responsibility peer-review of under the scientific responsibility committee of of REM26 the Applied Energy Symposium and Forum, REM26: Renewable Energy Integration with Mini/Microgrid. Keywords: Battery management system; H infinity filter; the dual H infinity filters; Adaptive update. Introduction With the superiority of high specific energy and power, the lithium-ion battery promotes the development of electric vehicles and stationary energy storage systems. For the safe and efficient operation during the entire life-cycle of battery, an intelligent battery management system (BMS) is indispensable to online estimate the battery states and monitor its condition. As one of the core functions in BMS, SoC estimation is the basis of fault diagnosis, health management, thermal management. * Corresponding author. Rui Xiong, Tel.: ; fax: address: rxiong@bit.edu.cn The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, REM26: Renewable Energy Integration with Mini/Microgrid. doi:.6/j.egypro

2 376 Cheng Chen et al. / Energy Procedia 3 ( 26 ) To better practical application, there are a wide variety of SoC estimation methods proposed continuously, which can be divided into four categories: loo-up table methods, ampere-hour methods, model-based methods and data-driven methods in []. Loo-up table methods are simple, but these methods require regular recalibration for offline parameter, which isn t suitable for the actual application [2, 3]. The ampere-hour methods can achieve the online estimation of SoC with low computational cost expediently and quicly [4, 5]. However, as the open-loop methods, it is easy to be greatly affected by a small disruption, such as the change of woring temperature. Different from the above-mentioned two methods, the model-based methods are the close-loop methods, which provides the robust performance for the SOC estimation by sustained revision of error, and are widely used, such as KF, EKF, SPKF, AEKF, etc. [6 8]. Data-driven methods include the neural networ method, the method of fuzzy controller, support vector regression (SVR) and so on. Recent results from [9 ] showed that these methods have their respective advantages and their estimation precision is very high for training data, which isn t affected by nonlinear model, but relatively low when the data are new. However, the uncertainty of model parameters influences the estimation performance significantly. For the almost model, SoC is obtained with offline parameters and these parameter value will change greatly with different degrees of aging, which will lead to inaccurate estimation value and even some more serious results, such as over charge/discharge, thermal abuse, etc.. In order to overcome these drawbacs, online parameter identification methods were proposed. Suns [2] researched the joint estimation of state and parameters with recursive least square (RLS) and adaptive extended Kalman filter (AEKF). But RLS and AEKF are independent modules in this method, which is hard to ensure its convergence performance. So this paper proposes the dual estimation algorithm to obtain the state and parameters in steps. Compared with the separate calculation of state and parameters in above joint estimation method, this dual estimation method can realize cooperative convergence by the same correction equation. Meanwhile, [3] proposed that H infinity filter can obtain the accurate results when model exists error and input is uncertain, which exhibits a better robustness than series of KF. So the dual H infinity filters algorithm was further put forward, and got successful application aiming at the uncertain SoC initial value and parameters. The purpose of this paper is to establish general battery parameter and state dual estimation method using dual H infinity filters. The description of algorithms is presented in Section 2. Section 3 describes their implementation flowchart in the battery system. To evaluate these approaches, the verification experiments shown in Section 4 were done. The experiment, simulation results and evaluation of the proposed methods are reported in Section 5 and the conclusions are drawn in Section Dual H infinity filters The KF provides an efficient approach for estimation of the state of a discrete-time dynamical system. It is assumed that the system model is accurate and the statistical characteristics of external input is nown, but in fact it is impossible to meet it. In order to achieve the accurate estimation of state when the model exists error and the noise is uncertain, H infinity filter that has better robustness is put forward [4]. For better practice application, this paper has improved the above algorithm, which is shown in Table. Furthermore, considering that H infinity filter can be used to identify parameters as well, this paper proposes a novel dual H infinity filters to achieve dual estimation of battery parameter and state estimation on line, and it is summarized in Table 2. Finally, based on the above analysis, the adaptive update of noises in [8], which could change statistical characteristics of the noises by the historical data, also can be used in these algorithms. M ee T T T T i i, R M C C, Q Kee K i i i i () N N in in+

3 Cheng Chen et al. / Energy Procedia 3 ( 26 ) Table. Algorithm of the H infinity filter Nonlinear system x f x, u w y g x, uv d f( x, u ) d g( x, u ) Definition : A, C (2) d x dx x xˆ xxˆ T Initialization : xˆ E x, P E x xˆ x xˆ, 2,,,calculation: For Step : Time-update equations xˆ f xˆ, u, P A P A Q (4) T Step 2: Measurement-update equations T T K P I SP C R CP C R + xˆ ˆ ˆ x K y g x, u (5) T P P I SP C R CP Table 2. Algorithm of the dual H infinity filters (3) Nonlinear system x f x,, u w y gx,, uv ˆ ˆ,, d ˆ,, d f x,, u dg x u g x u x Definition: A, C, C dx dx d xxˆ xxˆ x T Initializato i n : xˆ T E x, P ˆ ˆ ˆ ˆ ˆ E x x x x, E, P E For, 2,,,calculation: Step : Time-update equations for parameters ˆ ˆ,,, P P Q (8) Step 2: Time-update equations for state ˆ ˆ, ˆ x x x x f x, u, P A P A Q (9),, T Step 3: Measurement-update equations for state x x, x x, x x x x, x x K P I xsp C R CP C R + x ˆ ˆ ˆ, ˆ x x K y g x, u T x, x, x x, x x x x, P P I xsp C R CP Step 4: Measurement-update equations for parameters,,, K P I SP C R CP C R ˆ ˆ ˆ, ˆ K y g x, u T,,,, P P I SP C R CP T T T T ˆ (6) (7) () ()

4 378 Cheng Chen et al. / Energy Procedia 3 ( 26 ) Initial guess value at t states estimation xˆ, + x, P Initial guess value at t parameters estimation, ˆ+, P Current(A) Time(min) i (2)Time-update equations xˆ, P + x, xˆ f xˆ, ˆ, u P A P A Q,, T x x x ˆ ˆ, P +, ()Time-update equations ˆ ˆ, P P Q,, i, U t, xˆ, P x, i, U t, ˆ, P, i, U t, 3 Measurement update equations Eq. e, K, x, P x x x, ˆ+ + xˆ 4 Measurement update equations +, ˆ Eq. e, K,, P 3. Application to battery system Fig.. Implementation flowchart of the dual H infinity filters In order to examine and compare performance of different filter algorithms, here, we choose the Thevenin model with one-state hysteresis, which is a nonlinear model. Its terminal voltage is affected by four parts: open circuit voltage, hysteresis voltage, polarization voltage and partial voltage on the ohm internal resistance. Among them, the open circuit voltage can be described as a fitting equation from [6]. / ln ln Uoc z z 2 z 3 z 4 z (2) On the other hand, the SoC can be expressed as an integral formula: ilildt z = z (3) C a where z is SoC, i L is the load current, is coulomb efficiency, C a is cell maximum available capacity. According to the dual H infinity filters shown in Table 2, we build the dual H infinity filters methods to estimate the above state and parameter matrix and the implementation flowchart is shown in Fig.. 4. Battery experiment The experiment data used for this study are acquired through the battery test bench set up in [5], and it includes a series of characterization tests (which consist of a static capacity test using current rate ½C, a hybrid pulse test, loading profiles test) conducted at the same temperatures of 25 C. We can get the cell maximum available capacity by means of the capacity test approximately. Then with the data of the hybrid pulse test, we get the offline values parameters, which would be used to estimate the cell state with the offline EKF and H infinity filter. The loading profiles test is used to simulate the typical urban driving cycle of vehicle, which can reflect the change of SoC in the actual process Here select the SoC in the range of % to 2%. 5. Verification and discussion Based on these experiment data, there are four methods proposed in order to estimate SoC: the H infinity filter, the EKF, the dual H infinity filters and the adaptive dual H infinity filters. And these methods will be evaluated from four sides: the estimation precision of SoC and terminal voltage, error bound of SoC and the convergence rate. Their voltage and SoC estimation results with the erroneous initial SoC (8%) are plotted in Fig. 2 and Fig. 3. The H infinity filter was proposed to improve the robustness of estimation algorithms for an inaccurate

Cheng Chen et al. / Energy Procedia 3 ( 26 ) 375 38 379 system. The results show that the absolute value of voltage estimation error is slightly less than.

As a contrast, the EKF has the extremely similar estimation precision, but for the convergence rate, it need 4s to converge to the real values, which is far longer than 7s of the H infinity filter.

5 Cheng Chen et al. / Energy Procedia 3 ( 26 ) system. The results show that the absolute value of voltage estimation error is slightly less than. V and the absolute value of SoC estimation error is less than % after the system is stable. As a contrast, the EKF has the extremely similar estimation precision, but for the convergence rate, it need 4s to converge to the real values, which is far longer than 7s of the H infinity filter. This means the H infinity filter can speed up the convergence rate of the erroneous initial SoC and have a better robustness to outside interference. From the above discussion, we found that the fitting errors of voltage are slightly high, which is caused by inaccurate model. The dual H infinity filters proposed can provide more accurate parameters and reduce the fitting errors of voltage, which is beneficial to estimate SoC. Form Fig. 2 and Fig. 3, it shows that the absolute value of voltage estimation error is slightly less than.5 V and the absolute value of SoC estimation error is less than.5% with the dual H infinity filters. Compared with the H infinity filter, for the four evaluation indexes above, the dual H infinity filters is far superior to the offline H infinity filter, which means that it can improve the previous algorithms in the great degree. For better practical application, we add the adaptive update of noises to the state estimation process of the dual H infinity filters. Through the comparison, it shows results of the adaptive dual H infinity filters aren t superior to the dual H infinity filters, and even for some results, the former is inferior to the latter. But as mentioned above, the adaptive update of noises is for better practical application and the data used to estimation in this paper are simplex and one-case. So this phenomenon is reasonable and the adaptive update of noises will be discussed with different data further in the next research. Fig. 2. Results of estimated voltage error with four different methods Fig. 3. Results of estimated SoC error and bound with four different methods Finally, these numeric results are recorded in Table 3 for easy comparison. Table 3. Comparison of the above four methods in the profiles test results estimating SoC (with the erroneous initial SoC_8%) RMS error of voltage (mv) RMS error of SoC (%) Bounds error of SoC (%) convergence time of SoC (s) EKF H infinity filter Dual H infinity filters Adaptive dual H infinity filters Conclusions By the comparison with the dual H infinity filters and other methods, the results show that (i) all the pea errors of stable voltage and SoC are less than ±%; (ii) the convergence rate of H infinity filter with the erroneous initial SoC has been improved by 5% compared with KF; (iii) the prediction precision of voltage with the dual H infinity filters has been improved by 54% compared with the offline H infinity filter, the prediction precision of SoC has been improved by 64% and its results of error bound and

38 Cheng Chen et al. / Energy Procedia 3 ( 26 ) 375 38 convergence rate are far superior to the offline method.

6 38 Cheng Chen et al. / Energy Procedia 3 ( 26 ) convergence rate are far superior to the offline method. Acnowledgement This wor was supported by the National Natural Science Foundation of China (Grant No. 5572). The systemic experiments of the lithium-ion batteries were performed by the Advanced Energy Storage and Application (AESA) Group of the National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology. Any opinions expressed in this paper are solely those of the authors and do not represent those of the sponsor. References [] Lin C, Mu H, Xiong R, Shen. A novel multi-model probability battery state of charge estimation approach for electric vehicles using H-infinity algorithm. Applied Energy 26;66: [2] Einhorn M, Conte F, Kral C, Fleig J. A method for online capacity estimation of lithium ion battery cells using the state of charge and the transferred charge. IEEE Trans Ind. Appl. 22;48:7344. [3] Waag W, Sauer D. Adaptive estimation of the electromotive force of the lithium-ion battery after current interruption for an accurate state-of-charge and capacity determination. Appl. Energy 23;:4627. [4] TH L, Chen DF, Fang CC. Design and implementation of a battery charger with a state-of-charge estimator. International Journal of Electronics 2;87:2 6. [5] Cadicri Y. Microcontroller-based on-line state-of-charge estimator for sealed lead-acid batteries. J. Power Sources 24;29: [6] Plett GL. Extended Kalman filtering for battery management systems of LiPB-based HEV battery pacs. Part 2: Modelling and identification. J. Power Sources 24;34: [7] Plett GL. Sigma-point Kalman filtering for battery management systems of LiPB-based HEV battery pacs. Part : Introduction and state estimation. J. Power Sources 26;6: [8] Sun F, Xiong R. A novel dual-scale cell state-of-charge estimation approach for series-connected battery pac used in electric vehicles. J Power Sources 25;74: [9] Weigert T, Tian Q, Lian K. State-of-charge prediction of batteries and battery-super capacitor hybrids using artificial neural networs. J. Power Sources 2;96(8): [] Dai H, Guo P, Wei X, Sun Z, Wang J. ANFIS (adaptive neuro-fuzzy inference system) based online SoC (State of Charge) correction considering cell divergence for the EV (electric vehicle) traction batteries. Energy 25;8:35 6. [] Sheng H, Xiao J. Electric vehicle state of charge estimation: Nonlinear correlation and fuzzy support vector machine. J. Power Sources 25;28:337. [2] Sun F, Xiong R, He H. A systematic state-of-charge estimation framewor for multi-cell battery pac in electric vehicles using bias correction technique. Appl. Energy 26;62: [3] Zhang F, Liu G, Fang L, Wang H. Estimation of battery state of charge with H observer: applied to a robot for inspecting power transmission lines. IEEE Trans. Ind. Electron. 22;59(2):8695. [4] Chen X. Discrete H filter design with application to speech enhancement. Department of Electrical and Computer Engineering 995. [5] Xiong R, Sun F, Gong X, He H. Adaptive state of charge estimator for lithium-ion cells series battery pac in electric vehicles. J. Power Sources 23;242: Biography Rui Xiong received the Ph.D. degree in mechanical Engineering from Beijing Institute of Technology, China, in 24. Since 24, he has been appointed an Associate Professor at the Department of Vehicle Engineering, Beijing Institute of Technology, China. His research focuses mainly on electrical/hybrid vehicles, energy storage system and battery management.

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