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State of Charge Estimation of LiFePO4 Battery Based on a Gain-classifier Observer
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 105 (2017) 2071 – 2076
The 8th International Conference on Applied Energy – ICAE2016
State of charge estimation of LiFePO4 battery based on a gain-classifier observer Xiaopeng TANGa, Boyang LIUa, Furong GAOa,b * a
Department of Chemical and Biomolecular Engineering, The Hong Kong University of Science and Technology, Hong Kong b Guangzhou HKUST Fok Ying Tung Research Institute, Guangzhou 511458, China
Abstract A state of charge (SOC) estimation is required to work well over a wide range of conditions. In this study, a multigain observer based on classified conditions is proposed in order to estimate SOC efficiently. The feedback gain in the observer is switched by a proposed geometry classifier to categorize the voltage error into different groups so that the observing strategies can be designed for different error sources, and thereby robust and accurate SOC estimations. Different load conditions (including QC/T 897-2011 standard suggested condition) are tested to verify the proposed method. The results show that the proposed method is effective and accurate. It is possible to solve local model inaccuracies and data saturation problems in a computationally efficient way. ©©2017 Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2016The The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. Keywords: Electric vehicles; LiFePO4 battery; State-of-charge; Battery model; Multiple gain observer; Geometry classifier.
1. Introduction The estimation of the state of charge (SOC), describing the remaining percentage of battery capacity, is key in the power battery management system (BMS) [1]. Attaining online and accurate SOC remains a challenge due to strong nonlinear and complex electrochemical reactions in the battery. Also, battery characteristics change with the use of the battery. SOC estimation has drawn many researchers’ interest and many different methods have been proposed [2]. Existing SOC methods can be generally categorized into two groups: the open-loop based approach and model-based feedback approach. The open loop methods directly calculate the states of a system without using information feedback. Two common examples of such methods are Coulomb counting and the open-circuit approach. The Coulomb counting [3] SOC method integrates the current over time and obtains the SOC changes by dividing the battery
* Corresponding author. Tel.: +852-23587139; fax: +852-23580054. E-mail address: [email protected].
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.585
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Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
capacity, while the open circuit voltage SOC method [4] uses a look-up table to describe the relationship between the SOC and open circuit voltage. Although these example methods are simple, the former approach suffers from the sensor accumulated error and it requires a known initial SOC, while the latter is sensitive to voltage measurement noises. Model based approaches use a model to simulate the battery system, and adjust online the states of the system to make the model output converge to the measured terminal voltage. They are more competitive and they can avoid the problems of the open-loop based approaches. Over the years, many model-based SOC estimation methods have been proposed. Among them, Luenberger [5] observer, which uses a constant feedback gain to correct the system states, is a most simple observer based approach. Its convergence speed and noise filtering quality are heavily affected by the choices of the pole of the system. An extended Kalman filter (EKF) [6, 7] has been incorporated to adjust the feedback gain “optimally” in the minimal variance fashion in the state estimation problem. This results in a relatively complex algorithm. It is also not capable of dealing with the data saturation problem that often occurs in the BMS. To resolve the data saturation problem, a strong tracking (ST) approach [8] with sigma point Kalman filter (SPKF) has been further proposed. This would make the discrepancy orthogonal at each step. The resulted method is about eight times more complex than the original Luenberger approach [9]. Furthermore, many other model-based SOC estimation methods have been proposed. For example, a particle filter [10] uses the statistic approach to estimate the SOC. The performance is directly associated with the number of the particles, and the algorithm complexity increases sharply with the increase of the particle number. An artificial neural network [11] is applied for SOC estimation by using a large number of inter-connected nodes to approximate the true battery performance. The performance depends on the network topology and training methods, and typically requires sets of large training data. Fuzzy logic [7] is used also to estimate the SOC. In this case, a clear battery characteristic rule is needed. Machine learning methods such as SVM [12] has also been used for the SOC estimation where proper training data is available. The above methods all use mathematical or data-based approaches to attenuate noises and estimate the SOC with a mono-static model structure, but they cannot provide reasons (or causes) for the resulting error between the model and the measured results. Understanding different error sizes and error characteristics may be attributed to different causes, we propose a multi-gain observer to estimate the SOC efficiently. These gains of the observer are determined by a classifier which categorizes the causes of the voltage errors into different groups. Correspondingly, different observing strategies are designed for different error sources and for better SOC estimation robustness and accuracy. The proposed method has the following advantages: a classifier-based-gain-selecting strategy to improve the convergence speed; avoidance of building a single structure model to cover a wide range of conditions; and ability to solve the data saturation problem in a computational-efficient way. The remainder of this paper is organized as follows: in Section 2, the proposed methods are introduced, and part of the preliminary experimental results are also presented. The superiority of the proposed method are illustrated in Section 3, by comparing it with the conventional Luenberger observer and extended Kalman filter. The conclusions are given in Section 4. 2. Algorithm Design 2.1. Battery Model and System Identification Generally, the SOC can be defined as: SOC (t )
t
SOC 0 K ³ i (W )d W / C n
(1)
0
Where SOC0 is the initial state of charge, Ș is the Coulomb efficiency, i is the current and Cn is the battery capacity. The relationship between the SOC and battery terminal voltage can be described by the combined
Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
model [13]: (2) where Vt is the terminal voltage, which is also the output of the model. Iinput is the input current of the model, and r is the battery impedance E0 and ki (i= 0, 1, 2, 3) are the model parameters. This model is simpler than the electronic circuit based model because the polarization effect is not taken into account. At each sampling time k, based on (2), the terminal voltage can be calculated by: (3) Vt,k Y( k ) H ( k , :) P >1 I input 1 / SOC k SOC k ln( SOC k ) ln(1 SOC k )@ [ E 0 r k 0 k1 k 2 k 3 ]T Then, the least-square solution of the model parameters can be obtained through: (4) Pˆ ( H T H ) 1 H T Y With the battery and devices listed in Table 1, Load Condition 1 (shown in Fig.1-(a)) is applied to identify the model parameters. The results are provided in Table 2 and Fig.1-(b): Vt
E0 I input r k 0 / SOC k1 SOC k 2 ln( SOC ) k 3 ln(1 SOC )
Table 1 Battery and Device Model Battery Manufacturer and Type
Capacity
Device Model
OPTIMUM 32650
5.00Ah (Manufacturer Data) 5.13Ah (Experimental Data)
(Dis)charging Device: Sunway CT3002W Thermal Chamber: Bole GDS150
Table 2 Model Parameters Parameters
E0
r
k0
k1
k2
k3
Values
3.317V
0.023ȍ
0.047V
0.016V
0.040V
-0.012V
2.2. Review of Conventional Luenberger Observer The conventional feedback strategy of a Luenberger observer can be given as: SOC k 1 SOC k I input, k /( 3600 C n ) L (errk ) (5) where errk is the error between the measured battery terminal voltage and the model terminal voltage in (2) at time k, and L is a constant feedback gain. Different L can lead to different observing results, as is shown in Fig.1-(c). When L=0, the Luenberger observer becomes a Coulomb Counting method.
Fig.1. (a): Load Conditions; (b): Parameter Identification Result; (c): Luenberger Observer with Different Feedback Gains; (d): EKF Estimation Result; (e): Structure of the Estimator; (f): Illustration of the Classifier.
2.3. Error Cause Analysis and Countermeasures To select a suitable feedback gain in order to estimate the state, we need to analysis the causes of the voltage error arisen between the model and the real measurement. In this study, the errors are categorized into five groups and are noted below, together with the suggested countermeasures: 1) Sensing noise: sensing noise is inevitable in practical cases for both current and voltage sensors. The low pass filter (LPF) technique can be applied to deal with the sensor noises. It is worth noting that the Luenberger observer performs like a first-order LPF. 2) Modeling error: although the least square solution of the parameter fitting provides an accurate model parameter set, the inaccuracy of a model still exists. For instance, the combined model
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cannot reflect the impedance increase during the end of the discharge process. A short period open-loop strategy (L=0 in Fig.1-(c)) can deal with the local inaccuracies of the model [14]. 3) Normal error: close loop methods use the error to correct the states. So, the existence of the error is normal. A moderate gain (L=0.005 in Fig.1-(c)) can provide a smooth output with less noise. 4) Large state error: if the state is inaccurate, the model output can be far away from the real cases. An uncertain initial SOC is an example of this. As is shown in Fig.1-(c), an aggressive feedback gain (L=0.2) makes the convergence much faster. 5) Unclear error: in this case, we cannot clearly point out the cause of the error. It may have been caused by some unknown reasons or the combination of errors noted above. A normal feedback gain (L=0.02 in Fig.1-(c)) is suggested for a reasonable performance globally in this case. 2.4. Design and Training of the Classifier To classify the causes of the error in real time, the following two criteria are selected: 1) The absolute value of the filtered error (E1); 2) The absolute value of the accumulated filtered error with forgetting factor (E2); where the filtered error is generated through a simple first order LPF. In this way, we only need to deal with errors 2) to 5) above. To train the classifier, standard samples are needed to represent the errors caused by different reasons. Then, a classifier can be described as follows: If a1, a2, …, an are n pattern classes represented by their standard samples, C1, C2, …, Cn respectively, an unknown sample X belongs to ai if: C i X 2 Min { C j X }, j 1, 2, ..., n (6) 2 j where ||·||2 stands for the 2-norm of the vector, and the data needs to be unified first. Since EKF relies highly on the battery model, we can use the result of the conventional EKF with Load Condition 2 (in Fig.1-(a)) to obtain the standard samples for normal error and modelling error. When the SOC error increases after 4500s (shown in Fig.1-(d)), the mean of E1 and E2 in this period can be used as the standard sample (C2 in Fig.1-(f)) to represent the modelling error, while the accurate results can be used to represent the normal error (C1 in Fig.1-(f)). But it is difficult to model the unknown cases and cases with a large state error because they may appear in any possible way. So, ȝ±6ı criterion is introduced to deal with this problem: if E1 and E2 both exceed the ȝ±6ı limit, then a large state error is assumed to be the error source; when only one index exceeds the ȝ±6ı limit, it is difficult to tell the error source, where ȝ and ı stand for the mean and standard deviation of E1 or E2 of the entire EKF process, respectively. In this way, the entire procedure of the algorithm can be illustrated through Fig.1-(e), and the corresponding classifier is shown in Fig.1-(f). It is worth noting that instead of using mechanism modelling, data driven approaches usually require large training datasets and a complex training process. However, in this paper, the designing of the classifier has a clear guideline, through which we can reduce the size of the training dataset. 3. Experiment results and analysis With the equipment listed in Table 1, Load Condition 3, 4 and 5 in Fig.1-(a) are carried out to verify the algorithm performance, and a laptop with Core i5-5220U CPU and an 8G RAM is used to record the operating time. In the first test, the initial SOC is known for the Luenberger observer, EKF, and the proposed method, while in the second test, some unexpected errors are added to the process, including the uncertain initial SOC error and sudden SOC error. In both tests, experiment are carried out at 25ϨC, the battery capacity in the algorithm is 5Ah (assuming we cannot obtain the accurate battery capacity) and the sensing noise of the voltage and current are ±20mV and ±20mA, respectively. The results of both tests are
Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
shown in Fig.2. The detailed results of the first test are shown in Table 3. Although the Luenberger observer has the shortest operating time (OT), it has the largest maximum absolute error (MAE) and root mean square error (RMSE). EKF has much smaller RMSE and MAE, but the operating time increases sharply. The proposed method can distinguish the model’s inaccuracy and tries to avoid it by using open loop current integral. This way, it can be more accurate than EKF, which relies very much on model accuracy. As shown in Fig.2-(a) and (c), between 1000 and 2000s, the proposed method uses the Coulomb counting (L=0) rather than state feedback to avoid the inaccuracy of the model, leading to better local accuracy. In the second test, the proposed method shows the best ability to deal with the data saturation problem by timely finding out the cause of the errors and taking corresponding countermeasures, as shown in Fig.2–(d) and (e) for Load Condition 3. Fig.2-(f) further provides the distribution of this feedback gain, in which three large disturbances can be observed. Fig.2-(g) and (h) further verifies the accuracy and robustness of the proposed method using Load Condition 4 and 5.
Fig.2. (a): SOC Estimation Results of the First Test Using Load Condition 3; (b): SOC Error of (a); (c): Feedback Gain of the Proposed Algorithm in the First Test Using Load Condition 3; (d): SOC Estimation Results of the Second Test Using Load Condition 3; (e): Feedback Gain of the Proposed Algorithm in the Second Test Using Load Condition 3; (f): Feedback Gain Distribution in the Second Test Using Load Condition 3; (g): SOC Estimation Results of the Second Test Using Load Condition 4; (h) SOC Estimation Results of the Second Test Using Load Condition 5. Table 3 Comparison of Different Algorithms
RMSE (%) MAE (%) OT (ms)
Load Condition 3 Proposed EKF L=0.02 0.42 0.79 1.84 1.29 2.15 5.44 11.682 173.549 9.795
Load Condition 4 Proposed EKF L=0.02 0.51 0.65 1.58 1.76 1.82 3.75 8.119 64.191 7.258
Load Condition 5 Proposed EKF L=0.02 0.86 1.52 1.77 3.09 4.98 5.75 8.208 50.318 6.013
4. Conclusions In this study, an observer with multiple feedback gains is proposed to estimate the SOC efficiently. The causes of the terminal voltage error are categorized and different observing strategies are correspondingly employed. A geometry classifier is proposed to categorize the errors. Different load conditions are tested with the proposed method. The results show that the proposed method has better accuracy and robustness compared to the EKF method and Luenberger observer. Through this approach, the problems of data saturation and model dependence can be solved in a computationally efficient way. 5. Copyright Authors keep full copyright over papers published in Energy Procedia.
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Acknowledgements The authors would like to thank Zhou Lv and Kaori Lkegaya for supporting this work. This work is supported in part by the Natural Science Foundation of China (NSFC) project (61227005) and Guangzhou Science and Technology Bureau Project (2016201604030019). References [1] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, A review on the key issues for lithium-ion battery management in electric vehicles, Journal of power sources, 226 (2013) 272-288. [2] X. Liu, Z. Chen, C. Zhang, J. Wu, A novel temperature-compensated model for power Li-ion batteries with dual-particle-filter state of charge estimation, Applied Energy, 123 (2014) 263-272. [3] K.S. Ng, C.-S. Moo, Y.-P. Chen, Y.-C. Hsieh, Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries, Applied energy, 86 (2009) 1506-1511. [4] S. Lee, J. Kim, J. Lee, B. Cho, State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge, Journal of power sources, 185 (2008) 1367-1373. [5] D.G. Luenberger, Observers for multivariable systems, Automatic Control, IEEE Transactions on, 11 (1966) 190-197. [6] X. Tang, B. Liu, F. Gao, Z. Lv, State-of-Charge Estimation for Li-Ion Power Batteries Based on a Tuning Free Observer, Energies, 9 (2016) 675. [7] S. Sepasi, L.R. Roose, M.M. Matsuura, Extended kalman filter with a fuzzy method for accurate battery pack state of charge estimation, Energies, 8 (2015) 5217-5233. [8] D. Li, J. Ouyang, H. Li, J. Wan, State of charge estimation for LiMn 2 O 4 power battery based on strong tracking sigma point Kalman filter, Journal of Power Sources, 279 (2015) 439-449. [9] J.K. Barillas, J. Li, C. Günther, M.A. Danzer, A comparative study and validation of state estimation algorithms for Li-ion batteries in battery management systems, Applied Energy, 155 (2015) 455-462. [10] Y. Wang, C. Zhang, Z. Chen, A method for state-of-charge estimation of LiFePO 4 batteries at dynamic currents and temperatures using particle filter, Journal of Power Sources, 279 (2015) 306-311. [11] Y. Wang, D. Yang, X. Zhang, Z. Chen, Probability based remaining capacity estimation using datadriven and neural network model, Journal of Power Sources, 315 (2016) 199-208. [12] H. Sheng, J. Xiao, Electric vehicle state of charge estimation: Nonlinear correlation and fuzzy support vector machine, Journal of Power Sources, 281 (2015) 131-137. [13] G.L. Plett, Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification, Journal of power sources, 134 (2004) 262-276. [14] X. Tang, Y. Wang, Z. Chen, A method for state-of-charge estimation of LiFePO 4 batteries based on a dual-circuit state observer, Journal of Power Sources, 296 (2015) 23-29.
Biography Prof. GAO Furong is the chair professor of Dept of Chemical & Biomolecular Engineering of HKUST, and he is also the director of CPPS, Fok Ying Tung Graduate School. His research interest includes process modeling, control and monitoring, polymer processing, and battery management system.
ScienceDirect Energy Procedia 105 (2017) 2071 – 2076
The 8th International Conference on Applied Energy – ICAE2016
State of charge estimation of LiFePO4 battery based on a gain-classifier observer Xiaopeng TANGa, Boyang LIUa, Furong GAOa,b * a
Department of Chemical and Biomolecular Engineering, The Hong Kong University of Science and Technology, Hong Kong b Guangzhou HKUST Fok Ying Tung Research Institute, Guangzhou 511458, China
Abstract A state of charge (SOC) estimation is required to work well over a wide range of conditions. In this study, a multigain observer based on classified conditions is proposed in order to estimate SOC efficiently. The feedback gain in the observer is switched by a proposed geometry classifier to categorize the voltage error into different groups so that the observing strategies can be designed for different error sources, and thereby robust and accurate SOC estimations. Different load conditions (including QC/T 897-2011 standard suggested condition) are tested to verify the proposed method. The results show that the proposed method is effective and accurate. It is possible to solve local model inaccuracies and data saturation problems in a computationally efficient way. ©©2017 Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2016The The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. Keywords: Electric vehicles; LiFePO4 battery; State-of-charge; Battery model; Multiple gain observer; Geometry classifier.
1. Introduction The estimation of the state of charge (SOC), describing the remaining percentage of battery capacity, is key in the power battery management system (BMS) [1]. Attaining online and accurate SOC remains a challenge due to strong nonlinear and complex electrochemical reactions in the battery. Also, battery characteristics change with the use of the battery. SOC estimation has drawn many researchers’ interest and many different methods have been proposed [2]. Existing SOC methods can be generally categorized into two groups: the open-loop based approach and model-based feedback approach. The open loop methods directly calculate the states of a system without using information feedback. Two common examples of such methods are Coulomb counting and the open-circuit approach. The Coulomb counting [3] SOC method integrates the current over time and obtains the SOC changes by dividing the battery
* Corresponding author. Tel.: +852-23587139; fax: +852-23580054. E-mail address: [email protected].
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.585
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Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
capacity, while the open circuit voltage SOC method [4] uses a look-up table to describe the relationship between the SOC and open circuit voltage. Although these example methods are simple, the former approach suffers from the sensor accumulated error and it requires a known initial SOC, while the latter is sensitive to voltage measurement noises. Model based approaches use a model to simulate the battery system, and adjust online the states of the system to make the model output converge to the measured terminal voltage. They are more competitive and they can avoid the problems of the open-loop based approaches. Over the years, many model-based SOC estimation methods have been proposed. Among them, Luenberger [5] observer, which uses a constant feedback gain to correct the system states, is a most simple observer based approach. Its convergence speed and noise filtering quality are heavily affected by the choices of the pole of the system. An extended Kalman filter (EKF) [6, 7] has been incorporated to adjust the feedback gain “optimally” in the minimal variance fashion in the state estimation problem. This results in a relatively complex algorithm. It is also not capable of dealing with the data saturation problem that often occurs in the BMS. To resolve the data saturation problem, a strong tracking (ST) approach [8] with sigma point Kalman filter (SPKF) has been further proposed. This would make the discrepancy orthogonal at each step. The resulted method is about eight times more complex than the original Luenberger approach [9]. Furthermore, many other model-based SOC estimation methods have been proposed. For example, a particle filter [10] uses the statistic approach to estimate the SOC. The performance is directly associated with the number of the particles, and the algorithm complexity increases sharply with the increase of the particle number. An artificial neural network [11] is applied for SOC estimation by using a large number of inter-connected nodes to approximate the true battery performance. The performance depends on the network topology and training methods, and typically requires sets of large training data. Fuzzy logic [7] is used also to estimate the SOC. In this case, a clear battery characteristic rule is needed. Machine learning methods such as SVM [12] has also been used for the SOC estimation where proper training data is available. The above methods all use mathematical or data-based approaches to attenuate noises and estimate the SOC with a mono-static model structure, but they cannot provide reasons (or causes) for the resulting error between the model and the measured results. Understanding different error sizes and error characteristics may be attributed to different causes, we propose a multi-gain observer to estimate the SOC efficiently. These gains of the observer are determined by a classifier which categorizes the causes of the voltage errors into different groups. Correspondingly, different observing strategies are designed for different error sources and for better SOC estimation robustness and accuracy. The proposed method has the following advantages: a classifier-based-gain-selecting strategy to improve the convergence speed; avoidance of building a single structure model to cover a wide range of conditions; and ability to solve the data saturation problem in a computational-efficient way. The remainder of this paper is organized as follows: in Section 2, the proposed methods are introduced, and part of the preliminary experimental results are also presented. The superiority of the proposed method are illustrated in Section 3, by comparing it with the conventional Luenberger observer and extended Kalman filter. The conclusions are given in Section 4. 2. Algorithm Design 2.1. Battery Model and System Identification Generally, the SOC can be defined as: SOC (t )
t
SOC 0 K ³ i (W )d W / C n
(1)
0
Where SOC0 is the initial state of charge, Ș is the Coulomb efficiency, i is the current and Cn is the battery capacity. The relationship between the SOC and battery terminal voltage can be described by the combined
Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
model [13]: (2) where Vt is the terminal voltage, which is also the output of the model. Iinput is the input current of the model, and r is the battery impedance E0 and ki (i= 0, 1, 2, 3) are the model parameters. This model is simpler than the electronic circuit based model because the polarization effect is not taken into account. At each sampling time k, based on (2), the terminal voltage can be calculated by: (3) Vt,k Y( k ) H ( k , :) P >1 I input 1 / SOC k SOC k ln( SOC k ) ln(1 SOC k )@ [ E 0 r k 0 k1 k 2 k 3 ]T Then, the least-square solution of the model parameters can be obtained through: (4) Pˆ ( H T H ) 1 H T Y With the battery and devices listed in Table 1, Load Condition 1 (shown in Fig.1-(a)) is applied to identify the model parameters. The results are provided in Table 2 and Fig.1-(b): Vt
E0 I input r k 0 / SOC k1 SOC k 2 ln( SOC ) k 3 ln(1 SOC )
Table 1 Battery and Device Model Battery Manufacturer and Type
Capacity
Device Model
OPTIMUM 32650
5.00Ah (Manufacturer Data) 5.13Ah (Experimental Data)
(Dis)charging Device: Sunway CT3002W Thermal Chamber: Bole GDS150
Table 2 Model Parameters Parameters
E0
r
k0
k1
k2
k3
Values
3.317V
0.023ȍ
0.047V
0.016V
0.040V
-0.012V
2.2. Review of Conventional Luenberger Observer The conventional feedback strategy of a Luenberger observer can be given as: SOC k 1 SOC k I input, k /( 3600 C n ) L (errk ) (5) where errk is the error between the measured battery terminal voltage and the model terminal voltage in (2) at time k, and L is a constant feedback gain. Different L can lead to different observing results, as is shown in Fig.1-(c). When L=0, the Luenberger observer becomes a Coulomb Counting method.
Fig.1. (a): Load Conditions; (b): Parameter Identification Result; (c): Luenberger Observer with Different Feedback Gains; (d): EKF Estimation Result; (e): Structure of the Estimator; (f): Illustration of the Classifier.
2.3. Error Cause Analysis and Countermeasures To select a suitable feedback gain in order to estimate the state, we need to analysis the causes of the voltage error arisen between the model and the real measurement. In this study, the errors are categorized into five groups and are noted below, together with the suggested countermeasures: 1) Sensing noise: sensing noise is inevitable in practical cases for both current and voltage sensors. The low pass filter (LPF) technique can be applied to deal with the sensor noises. It is worth noting that the Luenberger observer performs like a first-order LPF. 2) Modeling error: although the least square solution of the parameter fitting provides an accurate model parameter set, the inaccuracy of a model still exists. For instance, the combined model
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cannot reflect the impedance increase during the end of the discharge process. A short period open-loop strategy (L=0 in Fig.1-(c)) can deal with the local inaccuracies of the model [14]. 3) Normal error: close loop methods use the error to correct the states. So, the existence of the error is normal. A moderate gain (L=0.005 in Fig.1-(c)) can provide a smooth output with less noise. 4) Large state error: if the state is inaccurate, the model output can be far away from the real cases. An uncertain initial SOC is an example of this. As is shown in Fig.1-(c), an aggressive feedback gain (L=0.2) makes the convergence much faster. 5) Unclear error: in this case, we cannot clearly point out the cause of the error. It may have been caused by some unknown reasons or the combination of errors noted above. A normal feedback gain (L=0.02 in Fig.1-(c)) is suggested for a reasonable performance globally in this case. 2.4. Design and Training of the Classifier To classify the causes of the error in real time, the following two criteria are selected: 1) The absolute value of the filtered error (E1); 2) The absolute value of the accumulated filtered error with forgetting factor (E2); where the filtered error is generated through a simple first order LPF. In this way, we only need to deal with errors 2) to 5) above. To train the classifier, standard samples are needed to represent the errors caused by different reasons. Then, a classifier can be described as follows: If a1, a2, …, an are n pattern classes represented by their standard samples, C1, C2, …, Cn respectively, an unknown sample X belongs to ai if: C i X 2 Min { C j X }, j 1, 2, ..., n (6) 2 j where ||·||2 stands for the 2-norm of the vector, and the data needs to be unified first. Since EKF relies highly on the battery model, we can use the result of the conventional EKF with Load Condition 2 (in Fig.1-(a)) to obtain the standard samples for normal error and modelling error. When the SOC error increases after 4500s (shown in Fig.1-(d)), the mean of E1 and E2 in this period can be used as the standard sample (C2 in Fig.1-(f)) to represent the modelling error, while the accurate results can be used to represent the normal error (C1 in Fig.1-(f)). But it is difficult to model the unknown cases and cases with a large state error because they may appear in any possible way. So, ȝ±6ı criterion is introduced to deal with this problem: if E1 and E2 both exceed the ȝ±6ı limit, then a large state error is assumed to be the error source; when only one index exceeds the ȝ±6ı limit, it is difficult to tell the error source, where ȝ and ı stand for the mean and standard deviation of E1 or E2 of the entire EKF process, respectively. In this way, the entire procedure of the algorithm can be illustrated through Fig.1-(e), and the corresponding classifier is shown in Fig.1-(f). It is worth noting that instead of using mechanism modelling, data driven approaches usually require large training datasets and a complex training process. However, in this paper, the designing of the classifier has a clear guideline, through which we can reduce the size of the training dataset. 3. Experiment results and analysis With the equipment listed in Table 1, Load Condition 3, 4 and 5 in Fig.1-(a) are carried out to verify the algorithm performance, and a laptop with Core i5-5220U CPU and an 8G RAM is used to record the operating time. In the first test, the initial SOC is known for the Luenberger observer, EKF, and the proposed method, while in the second test, some unexpected errors are added to the process, including the uncertain initial SOC error and sudden SOC error. In both tests, experiment are carried out at 25ϨC, the battery capacity in the algorithm is 5Ah (assuming we cannot obtain the accurate battery capacity) and the sensing noise of the voltage and current are ±20mV and ±20mA, respectively. The results of both tests are
Xiaopeng Tang et al. / Energy Procedia 105 (2017) 2071 – 2076
shown in Fig.2. The detailed results of the first test are shown in Table 3. Although the Luenberger observer has the shortest operating time (OT), it has the largest maximum absolute error (MAE) and root mean square error (RMSE). EKF has much smaller RMSE and MAE, but the operating time increases sharply. The proposed method can distinguish the model’s inaccuracy and tries to avoid it by using open loop current integral. This way, it can be more accurate than EKF, which relies very much on model accuracy. As shown in Fig.2-(a) and (c), between 1000 and 2000s, the proposed method uses the Coulomb counting (L=0) rather than state feedback to avoid the inaccuracy of the model, leading to better local accuracy. In the second test, the proposed method shows the best ability to deal with the data saturation problem by timely finding out the cause of the errors and taking corresponding countermeasures, as shown in Fig.2–(d) and (e) for Load Condition 3. Fig.2-(f) further provides the distribution of this feedback gain, in which three large disturbances can be observed. Fig.2-(g) and (h) further verifies the accuracy and robustness of the proposed method using Load Condition 4 and 5.
Fig.2. (a): SOC Estimation Results of the First Test Using Load Condition 3; (b): SOC Error of (a); (c): Feedback Gain of the Proposed Algorithm in the First Test Using Load Condition 3; (d): SOC Estimation Results of the Second Test Using Load Condition 3; (e): Feedback Gain of the Proposed Algorithm in the Second Test Using Load Condition 3; (f): Feedback Gain Distribution in the Second Test Using Load Condition 3; (g): SOC Estimation Results of the Second Test Using Load Condition 4; (h) SOC Estimation Results of the Second Test Using Load Condition 5. Table 3 Comparison of Different Algorithms
RMSE (%) MAE (%) OT (ms)
Load Condition 3 Proposed EKF L=0.02 0.42 0.79 1.84 1.29 2.15 5.44 11.682 173.549 9.795
Load Condition 4 Proposed EKF L=0.02 0.51 0.65 1.58 1.76 1.82 3.75 8.119 64.191 7.258
Load Condition 5 Proposed EKF L=0.02 0.86 1.52 1.77 3.09 4.98 5.75 8.208 50.318 6.013
4. Conclusions In this study, an observer with multiple feedback gains is proposed to estimate the SOC efficiently. The causes of the terminal voltage error are categorized and different observing strategies are correspondingly employed. A geometry classifier is proposed to categorize the errors. Different load conditions are tested with the proposed method. The results show that the proposed method has better accuracy and robustness compared to the EKF method and Luenberger observer. Through this approach, the problems of data saturation and model dependence can be solved in a computationally efficient way. 5. Copyright Authors keep full copyright over papers published in Energy Procedia.
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Acknowledgements The authors would like to thank Zhou Lv and Kaori Lkegaya for supporting this work. This work is supported in part by the Natural Science Foundation of China (NSFC) project (61227005) and Guangzhou Science and Technology Bureau Project (2016201604030019). References [1] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, A review on the key issues for lithium-ion battery management in electric vehicles, Journal of power sources, 226 (2013) 272-288. [2] X. Liu, Z. Chen, C. Zhang, J. Wu, A novel temperature-compensated model for power Li-ion batteries with dual-particle-filter state of charge estimation, Applied Energy, 123 (2014) 263-272. [3] K.S. Ng, C.-S. Moo, Y.-P. Chen, Y.-C. Hsieh, Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries, Applied energy, 86 (2009) 1506-1511. [4] S. Lee, J. Kim, J. Lee, B. Cho, State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge, Journal of power sources, 185 (2008) 1367-1373. [5] D.G. Luenberger, Observers for multivariable systems, Automatic Control, IEEE Transactions on, 11 (1966) 190-197. [6] X. Tang, B. Liu, F. Gao, Z. Lv, State-of-Charge Estimation for Li-Ion Power Batteries Based on a Tuning Free Observer, Energies, 9 (2016) 675. [7] S. Sepasi, L.R. Roose, M.M. Matsuura, Extended kalman filter with a fuzzy method for accurate battery pack state of charge estimation, Energies, 8 (2015) 5217-5233. [8] D. Li, J. Ouyang, H. Li, J. Wan, State of charge estimation for LiMn 2 O 4 power battery based on strong tracking sigma point Kalman filter, Journal of Power Sources, 279 (2015) 439-449. [9] J.K. Barillas, J. Li, C. Günther, M.A. Danzer, A comparative study and validation of state estimation algorithms for Li-ion batteries in battery management systems, Applied Energy, 155 (2015) 455-462. [10] Y. Wang, C. Zhang, Z. Chen, A method for state-of-charge estimation of LiFePO 4 batteries at dynamic currents and temperatures using particle filter, Journal of Power Sources, 279 (2015) 306-311. [11] Y. Wang, D. Yang, X. Zhang, Z. Chen, Probability based remaining capacity estimation using datadriven and neural network model, Journal of Power Sources, 315 (2016) 199-208. [12] H. Sheng, J. Xiao, Electric vehicle state of charge estimation: Nonlinear correlation and fuzzy support vector machine, Journal of Power Sources, 281 (2015) 131-137. [13] G.L. Plett, Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification, Journal of power sources, 134 (2004) 262-276. [14] X. Tang, Y. Wang, Z. Chen, A method for state-of-charge estimation of LiFePO 4 batteries based on a dual-circuit state observer, Journal of Power Sources, 296 (2015) 23-29.
Biography Prof. GAO Furong is the chair professor of Dept of Chemical & Biomolecular Engineering of HKUST, and he is also the director of CPPS, Fok Ying Tung Graduate School. His research interest includes process modeling, control and monitoring, polymer processing, and battery management system.