Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 75 (2015) 1944 – 1949
The 7th International Conference on Applied Energy – ICAE2015
A data-driven based state of energy estimator of lithium-ion batteries used to supply electric vehicles YongZhi Zhang a, HongWen He a,*, Rui Xiong a
a
National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, South No.5 Zhongguancun Street, Beijing, 100081, China
Abstract The state of energy (SoE) of Li-ion batteries is a critical index for the remainder range forecasting, energy optimization and management. The paper attempts to make three contributions. (1) The definition of SoE is proposed and elaborated, which includes the output energy of battery, the internal resistance heating and the energy consumed on the electrochemical reactions. Based on this definition, the new mathematical model of estimating SoE is built, which can realize the real-time estimation of SoE. (2) Based on the combined general battery model, the recursive least square (RLS) method with an optimal forgetting fa ctor is used to identify the model parameters. The parameter identification results are obtained at relative SoE points, and the verification results indicate that the proposed battery model is accurate enough to simulate the battery characteristics. (3) Based on the SoE mathematical model and the combined general battery model, the extended Kalman filter (EKF) is built to estimate the SoE online. The simulation results show that the EKF-based SoE estimator performs well even under different incorrect initial SoE.
© Published by Elsevier Ltd. This © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of Applied Energy Innovation Institute
Keywords:electric vehicles, lithium-ion battery, data-driven, recursive least square, extended Kalman filter, state of energy
1.
Introduction
Since the state of charge (SoC) is not clear enough to predict the remainder range, optimize or manage the energy. Compared to the SoC, the SoE [1-7] is a mo re clear and scientific indicator of the battery energy. Because few researches have been done on how to estimate the So E accurately, at least three problems need to be solved here. Firstly, there is not a unified or clear definition of the So E. Although
* Corresponding author. Tel.: +86 10 6891 4842; fax: +86 10 6891 4842. E-mail address:
[email protected]
1876-6102 © 2015 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 Applied Energy Innovation Institute doi:10.1016/j.egypro.2015.07.228
1945
YongZhi Zhang et al. / Energy Procedia 75 (2015) 1944 – 1949
refs [3-5] propose the SoE definitions separately, they still have the shortcomings of not being clear enough or practical enough. The second problem is how to estimate the real-t ime So E accurately. Ref [3] proposes a black bo x model to estimate the So E online. In the input layer, the battery terminal voltage, the current and the temperature are taken as the input parameters, and the output layer is the estimated So E. However, the accuracy of a black box model based SoE estimator is always dependent on the training parameter set. While in practice, the battery conditions such as the aging and the applied environment such as the temperature change all the time, it is difficult fo r the training parameter set to contain all the informat ion needed, and the estimat ion accuracy is worse as time goes. Third ly, unlike the So C estimator, though different kinds of battery models are ready, there is no model based SoE estimator. We know that the model based estimator is easy to apply different filters like d ifferent kinds of EKFs to realize the closed-loop estimation with high accuracy. 2.
New definition of SoE This paper proposes to define SoE as SoEk
SoEk 1
KkU oc,k ik 't Ea
(1)
Where subscript k indexes the moment k ᇞt, ᇞt indexes the sampling interval, ¨ indexes the current efficiency, Uoc is the open circuit voltage (OCV), i is the current and Ea indexes the maximu m available energy of a full charged battery. 3.
Battery modeling and parameter identification
To model the dynamic voltage performance of the lithiu m-ion cell under different operating conditions, we should first construct a battery model. The dynamics of the battery can be described as a co mbined general battery model [6] and shown in Fig. 1. RD
Ri
iL
CD
UD
Ut
OCV
Fig. 1. Schematic diagram of combined general battery model
According to the Kirchhoff’s law, the mathematical equation of the proposed battery model is expressed as 1 1 UD iL °U D CD RD CD ® °U U U i R oc D L i ¯ t
(2)
1946
YongZhi Zhang et al. / Energy Procedia 75 (2015) 1944 – 1949
The relationship between SoE and OCV is described as U oc
D 0 D1 z D 2 z 2 D 3 z 3 D 4 z D 5 ln z D 6 ln 1 z
(3)
Where z represents the SoE, and α0,…ˈ6 is the fitting parameters which can be obtained by the OCVSoE test data. We use the recursive least square method with an optimal forgetting factor to identify model parameters and the parameter model is shown as U t ,k 1 a1 U oc ,k a1U t ,k 1 a2iL ,k a3iL ,k 1 (4) Where a1
4.
't 2 RD CD , a2 't 2 RD CD
Ri 't RD 't 2 Ri RD CD , a3 't 2 RD CD
Ri 't RD 't 2 Ri RDCD 't 2 RD CD
(5)
Extended Kalman filter-based SoE estimator One discretization form of equation (2) is as follows [7]: °U D,k exp 't / W uU D ,k 1 ¬ª1 exp 't / W ¼º u iL,k RD ® ° ¯U t ,k U oc zk U D,k iL,k Ri
(6)
Combined with equation (1), the state-space model can be built as ° X k f X k 1 , uk wk 1 Ak 1 X k 1 Bk 1uk wk 1 ® ° ¯Yk h X k , uk vk =Ck X k Dk vk
Xk
T
ª¬U D ,k zk º¼ , Yk
U t ,k , Ak 1
Where Dk
h X k , u k Ck X k
ª 1 exp 't W RD ,k 1 º « » , Ck «¬ K iL ,k 1 U oc ,k 1't Ea »¼
ªexp 't W 0 º « » , Bk 1 1¼ ¬0
U oc ,k U D ,k Ri ,k uk Ck X k , uk
(7) dU oc z º ª « 1 », dz ¼ ¬
iL ,k .
Both wk and vk are assumed unrelated white Gaussian random processes, with zero mean and covariance matrices with known value: Qk , n k ; ® ¯0, n z k .
E ª¬ wn wkT º¼
Rk , n k ; ® ¯0, n z k .
E ª¬vn vnT º¼
From equation (3), it can be deduced: dU oc z dz
D1 2D 2 z 3D3 z 2
D4 z2
D5 z
D6 1 z
(8)
The extended Kalman filter can filter rando m noise and co mpensate for model error, which is therefore widely used in application and has achieved great success. It can obtain an optimal state set by adjusting initial values of state vector and its error covariance matrix, as well as covariance matrices of the two Gaussian random processes. Based on equation (7), the calculat ion process of the EKF algorith m for So E estimation is described in Fig. 2.
1947
YongZhi Zhang et al. / Energy Procedia 75 (2015) 1944 – 1949
Initialization
Error covariance mesurement update
Pk
X 0 , P0 , Q0 , R0
I K k Ck Pk
The collection of current, voltage
k 1ok
U t ,k 1
State estimation time update
Xˆ k
f Xˆ k1, uk
Static Energy Test State estimation mesurement update
Xˆ k
Xˆ k K k Yk Yˆk
Error covariance time update k
P
T k 1
Ak 1 Pk 1 A
Yˆk
Output update
h Xˆ k , uk
Repeat 3 Times
The combined model
Hybrid Pulse Test
Qk 1
Characteristic Test (25ć ) Estimator gain matrix
Kk
PkCkT Ck PkCkT Rk 1
1
The parameter identification with the genetic algorithm
OCV-SoE Test
Fˆ EKF estimator
Parameter identification
Loading Profiles Test
Data collection module
Fig. 2. T he general diagram of the data-driven based SoE estimator
5.
Fig. 3. T he battery test schedule
Data set of LiMn2 O4 cell for verification
As an application case, the LiMn 2 O4 cell is used to verify the proposed approach. The test schedule for our research is shown in Fig. 3 and is designed to collect the cell test data. It is important to note that in this research, we only consider the operation temperature at 25 ć and other temperatures will be discussed in our future research. 6.
Verification and discussion
Considering practical applicat ions, only the portion of the test data within 10% -90% So E in these datasets is used in SoE estimation. The So E estimation is executed by the BJDC test. Fig. 4 is the So E estimation results of the voltage and SoE, where the initial So E value is set at the exact 90%. Fig. 4(a) is the true terminal voltage and the estimated terminal voltage. Fig. 4(b) is the voltage estimation error. Fig. 4(c) is the reference So E and the estimated So E. Fig. 4(d) is the SoE estimat ion error. The statistical results of the SoE estimat ion are listed in table 1. Fro m Fig. 4(a) and Fig. 4(b) we can find that the estimated voltage is almost the same with the true voltage, and table 1 shows that the maximu m voltage error is only 0.78 mV and the mean error and the standard deviation are respectively only 8.9e -4 mV and 0.02 mV. It should be noted that the reference SoE is obtained by integration of the output energy of battery, which is integration of product of the terminal voltage and the charge/discharge current. However, the true So E should be obtained by integration of the whole output energy of battery, wh ich is integration of product of the OCV and the charge/discharge current. In fact, we can on ly get the reference So E in the experiment, which has neglected the internal resistance heating and the energy consumed on the electrochemical react ions, so the true SoE should be larger than the reference So E. It can be seen fro m Fig. 4(c) and Fig. 4(d) that the estimated So E is always larger than the reference So E, which is consistent with the above analysis. Table 1 shows that the maximu m So E estimation error is 5.5%, and the mean error and the standard deviation are respectively -3.3% and 1.2%, while the statistical results of the true SoE estimation error must be better. T able 1. Statistical results of the SoE estimation error Maximum error
Mean error
Standard deviation
Voltage(mV)
0.78
8.9e-4
0.02
SoE(%)
5.5
-3.3
1.2
Estimate
YongZhi Zhang et al. / Energy Procedia 75 (2015) 1944 – 1949
3.6 1
2
Estimation
5
0
1
2
3 4 Time(h)
5
6
(b) 1
Estimation
3.6
1
2
(d)20
50
True
4
3.8
0
-0.5
6
Reference
0.5
Error(%)
SoE(%)
(c)100
3 4 Time(h)
(a) 4.2
3 4 Time(h)
5
2
(c)
3 4 Time(h)
100
0
-20
1
6
1
2
3 4 Time(h)
5
Estimation
5
0
1
2
Fig. 4. SoE estimation results.
3 4 Time(h)
5
1
2
3 4 Time(h)
5
6
1
2
3 4 Time(h)
5
6
(d)40
50
6
0
-0.5
6
Reference
0.5
Error(%)
3.8
(b) 1
Voltage(V)
Estimation
SoE(%)
True
4
Error(mV)
Voltage(V)
(a) 4.2
Error(mV)
1948
6
20 0
-20
Fig. 5. SoE estimation results
Fig. 5 is the estimation results of the terminal voltage and So E with an erroneous initial So E, where the initial So E is incorrectly set to 60%. Fig. 5(a) is the true terminal voltage and the estimated terminal voltage. Fig. 5(b) is the voltage estimation error. Fig. 5(c) is the reference So E and the estimated So E. Fig. 5(d) is the So E estimation error. Fro m Fig. 5, we find that the estimated voltage and So E converge to the reference t rajectory quickly after a few seconds for correcting the erroneous initial state of the EKF estimator; the maximu m estimation error of voltage is around 1 mV. On the other hand, the maximu m estimation error of SoE is about 5.5% after a few seconds. (b)90 SoE(%)
SoE(%)
(a)100 50 0 0
1
2 3 Time(h)
4
0 1
2 3 4 Time(h) Reference
10
20
(d)40
20
-20 0
70 60
5
Error(%)
Error(%)
(c) 40
80
5 90%
30 40 Time(s)
50
60
20 0
-20 0 80%
20 70%
40
60
Time(s) 60%
Fig. 6. Estimation results of the SoE
Fig. 6 is the estimation results of the SoE with different erroneous initial So E, where the initial So E is respectively incorrectly set to 60%, 70%, 80%. Fig. 6(a) describes the reference So E and the estimated SoE. Fig. 6(b ) describes the reference So E and the estimated So E within the prior 60 seconds. Fig. 6(c) describes the estimated So E error and Fig. 6(d) describes the estimated So E error within the prio r 60 seconds. Fro m Fig. 6 we find that the estimated So E with different erroneous initial So E converges to the reference trajectory quickly after about 60 seconds, and the converged SoE is almost the same, with the maximu m error of about 5.5%. 7.
Conclusions z
z
Different definitions of SoE are summarized and analyzed, and to get the correct and stable realtime So E estimate, this paper proposes a new mathematical model to define the So E. Except the output energy of battery, the new definit ion of So E also includes the internal resistance heating and the energy consumed on the electrochemical reactions, which are difficult to detect in practice. The comb ined general battery model is proposed to simulate the characteristics of battery. The RLS method with an optimal fo rgetting factor is used to identify the model parameters. By hand-
YongZhi Zhang et al. / Energy Procedia 75 (2015) 1944 – 1949
z
8.
tuning the optimal forgetting factor, the identified model parameters close to the stable value quickly and the verification results prove that the proposed battery model is accurate enough to simulate the characteristics of battery. The EKF is built to estimate the So E and the estimat ion results are presented in the form of figures and tables. Because the true SoE is hard to obtain in practice, the reference So E is proposed to evaluate the SoE estimator accuracy. The estimat ion results show that although the errors exist, the SoE estimator still has good estimation ability, even under different erroneous initial SoE. Copyright Authors keep full copyright over papers published in Energy Procedia.
References [1] Clemente Capasso, Ottorino Veneri. Experimental analysis on the performance of lithium based batteries for road full electric and hybrid vehicles. Appl Energ 2014; 136: 921-930. [2] Bruno Scrosati, Jürgen Garche. Lithium batteries: Status, prospects and future. J Power Sources 2010; 195: 2419-2430. [3] Liu XT , Wu J, Zhang CB, et al. A method for state of energy estimation of lithium-ion batteries at dynamic currents and temperatures. J Power Sources 2014;270:151-7. [4] Mamadou K, Delaille A, Lemaire-Potteau E, et al. The State-of-Energy: A New Criterion for the Energetic Performances Evaluation of Electrochemical Storage Devices, in: Proceedings of the 216th Meeting of the Electrochemical-Society (ECS) 2009;105–112. [5] Mamadou K, Lemaire E, Delaille A. Definition of a State-of-Energy Indicator (SoE) for ElectrochemicalStorage Devices: Application for Energetic Availability Forecasting. J ELECTROCHEM SOC 2012;159:A1298-A1307. [6] Xiong R, Sun F, Chen Z, et al. A data-driven multi-scale extended Kalman filtering based parameter and state estimation approach of lithium-ion polymer battery in electric vehicles. Appl Energ 2014;113: 463-476. [7] Dan Simon. Optimal state estimation: Kalman, H∞, and nonlinear approaches. Wiley 2006, p. 123-326.
Biography Hongwen He received the M.E. degree fro m the Jilin Un iversity of Technology, Changchun, China, in 2000 and the Ph.D. degree fro m the Beijing In stitute of Technology, Beijing, Ch ina, in 2003, both in vehicle engineering. He is currently a Professor with the Nat ional Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology.
1949
