Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 105 (2017) 4549 – 4554
The 8th International Conference on Applied Energy – ICAE2016
An online model-based battery parameter and state estimation method using multi-scale dual adaptive particle filters Min Yea, Hui Guoa, Rui Xiongb,*, Hao Mub a
National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an, 710064, China; b National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China.
Abstract Accurate estimations of battery parameter and state are very important for battery management in electric vehicles. To improve estimation accuracy and robustness of battery parameter and state, and to reduce computational cost, an online model-based estimation approach is proposed, Firstly , the lithium-ion battery is modeled using the Thevenin model, Then, A multi-scale dual particle filters has been proposed and applied to the battery parameter and state estimation. Finally, to elevate the accuracy and the ability of convergence to initial states’ offset, a multi-scale dual adaptive particle filter was proposed and applied to the battery parameter and state estimation. Experimental results on various degradation states of lithium-ion battery cells further verified the feasibility of the proposed approach. © Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ©2017 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: Battery management system; Lithium-ion battery; state estimation; dual PFs; dual APFs.
1. Introduction Nowadays, with the increasing car ownership, the amount of oil storage to the point of an emergency, so, EVs have gained great attention as one of the promising solution for energy shortage. Lithium-ion battery as a clean and efficient energy storage device has been widely used in EVs, As a critical index for a lithium-ion battery, parameter and stateof-charge (SoC) estimation it is difficult to measure directly due to the complicated electrochemical process when it working.
* Corresponding Author, Email:
[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.2017.03.976
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A large number of of SoC estimation methods have been put forward to improve battery SoC determination. For instance, Xiong et al.[1] proposed a multi-scale extended Kalman filter method to estimate parameter and SoC of lithium-ion battery which cannot only achieves more accurate and reliable system parameter estimates, but also largely reduces the computational cost of the control system. Lin at al.[2] introduced a Multi-model probabilities based state fusion estimation method to improve the accuracy and reliability of the SOC estimation. Wang at al.[3] presented a particle filter based method to joint estimate SoC and SoE. In this paper, to determine parameter and sate of a battery, an online model-based estimator using multi-scale dual adaptive particle filters is developed. The main contributions are expressed as follows: 1) the thevenin model is adopted to develop modelbased SoC estimation approach. 2) A multi-scale dual particle filters(D-PF) is proposed to estimate parameter and state of a lithium-ion battery cell. 3) To improve the accuracy and the speed of convergence for parameter and SoC estimation, a multi-scale dual adaptive particle filters(D-APF) is presented. 4) NMC batteries are tested to verify the effectiveness of these two algorithms. The results indicate that multi-scale dual particle filters method has the potential to accurately estimate battery parameter and SoC . The rest of this paper is organized as follows: Section 2 describes the thevenin model. Section 3 illustrates the algorithm of multi-scale dual PFs and multi-scale dual APFs. In section 4, NMC battery experiment data is adopt to verify the validity of the proposed methods and the relative analysis of results are given in the final section. 2.Battery model 2.1 Definitions of SOC The battery SoC is a relative quantity that describes the ratio of the remaining capacity to the maximum available capacity, expressed as the following equation:
zk
z0
1 Crated
t
³ K I dt 0
c k
(1)
Where zk is the SoC value at time k, z0 is the initial SoC value, Crated is the rated capacity of a battery, Kc stands for the coulombic efficiency (Kc|1), Ik represents the current through the battery. 2.2 Thevenin model An accurate battery model that can simulate the dynamic characteristic of a battery is essential to dynamic state estimation[4]. In this paper thevenin model is adopt to validate the algorithms. The thevenin model is shown in Eqs.(2) and (3).
U d , k 1
exp 't W U d ,k Rp 1 exp 't W I k Ut , k
U ocv zk - I k R0 - U d , k
(2) (3)
where 't is the sampling time and Ik is current, Ud and τ=RpC are the voltage and time constant of the RC network respectively. Ut is the battery terminal voltage, R0 is the
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internal ohmic resistance which depends on the current direction.so, the battery parameters θ include Rp, τ, and R0DŽ Through the discretization of Eqs. (1)–(3), the discrete-time state space equations can be depicted as follows:
xk f ( x1, k -1 , uk -1 ,Tl -1 ) w1, k -1 ° ®Tl Tl -1 w2,l -1 ° g ( x2, k -1 , uk -1 ,Tl -1 ) vk -1 ¯ yk
(4)
where x is the state variables which include SoC and Ud, θ represent parameter variables of battery model, y represent the observed variables, u represents the model input, w and v are the Gaussian system noise with covariance Qw and Gaussian observation noise with covariance Qv. 3.Algorithm implementation The PF methods have become a popular class of algorithms for solving the optimal estimation problems of non-linear and non-Gaussian state space models[3]. Based on dual PFs, the battery parameter can be estimated on line, regarding that battery parameter vary slowly than battery SoC, thus the battery parameter can be estimated with macro scale to reduce the computation cost of the BMS, and the battery state can be estimate with micro scale due to the fast-varying characteristic[1]. In order to improve the accuracy and the ability of convergence to initial states’ offset, a multi-scale dual adaptive particle filters is proposed in this paper. Thealgorithms of multi-scale dual particle filters and multi-scale dual adaptive particle filters are described in Table 1 and the flowchart of multi-scale dual adaptive particle filters is shown in Fig.1. Parameter estimation
State estimation Initialization x0i (i 1, 2,...N )
Initialization
T0 j ( j 1, 2,...M )
k=k+1
k%L==0?
Yes
l=l+1
No Importance sampling
Calculate and normalize importance weight
resampling
noise variance update
Importance sampling
Calculate and normalize importance weight
State estimation
xˆ
k
¦
N i 1
Yes
w1, k i xk i
More observations?
Parameter estimation
Tˆl
¦
M j 1
w2, l j Tl j
No Output
Stop
Output
Fig. 1. Flowchart of the proposed multi-scale dual adaptive particle filters estimator Table 1. Summary of multi-scale D-PFs and multi-scale D-APFs.
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1. Initialization: k, j = 0, l=0. Randomly generateNinitial particles x0i (i 1, 2,...N ) for state and M initial particles T0 j ( j 1, 2,...M ) for parameter, and initial weight for every particle. Set maximum and minimum noise variance of each state. 2. State estimation. For k = 1, 2, ... (a) Importance sampling: The particle weight is calculated according to the equation as below: 1 1 ½ w1,k i exp ®( yk yk i )2 ¾ 2 R1 ¿ 2S R1 ¯
w1,k i / ¦i 1 w1, k i N
(b) Normalize the importance weights as below: w1,k i (c) state estimation: xˆ
k
¦
N i 1
w1,k i xk i
(d) Evaluate the effective sample size: Neff1 1/ ¦i 1 ( w1,k i )2 to judge the necessity of resampling N
3. parameter estimation(if k %L For l
0)
l 1 : (a) Importance sampling: The particle weight is calculated according to the equation as below: 1 1 ½ j w2,l j exp ®( yk yl )2 ¾ 2 R2 ¿ 2S R2 ¯ j (b) Normalize the importance weights as below: w2,l
(c) parameter estimation: Tˆl
¦
M j 1
w2,l j / ¦ j 1 w2, l j M
w2, l j Tl j
j 2 (d) Evaluate the effective sample size: Neff 2 1/ ¦ j 1 ( w2,l ) to judge the necessity of resampling M
4. noise variance update for dual adaptive particle filter (this step is absent in D-PFs algorithm) (a) Compute the demand value of noise variance: ex,k | xˆk f xˆi1, ui1,Tk 1 | ; eT , l | Tˆl Tˆl -1| (b) noise variance update: V a, k
V b, l
° min(ea, k , V a,max ) ® ° ¯max( EV a , k 1 , V a,min )
min(eb , l , V b,max ) ° ® °max( EV b , l 1 , V b,min ) ¯
if ea,k ! V a, k 1 if ea,k d V a, k 1 if eb ,l ! V b , l 1 if eb ,l d V b , l 1
(where β is attenuation factor, σ represent standard deviation of noise variance, a, b {x, T }
4. Verification and discussion The nominal voltage of the NMC cell is 3.6 V and its nominal capacity is 2.5Ah, 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 conducted at the same temperatures of 10ć, in this paper the parameter and state estimation of NMC battery is based on UDD test data. Here select the SoC in the range of 80% to 20%. Figs. 2 and 3 present the comparison of the estimated performance of the mutil-scale DPFs and mutil-scale D-APFs under UDD test, where the initial SoC is initialized to 60% and with 20% offset.
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0 SOC estimation error(%)
Voltage estimation error (V)
0.01
D-PF D-APF
0.02
0.01
0
-0.01
-0.01 -0.02
0.01 0
-0.04
-0.01 -0.02
-0.06 -0.08
-0.02
50
100
150
200
D-PF D-APF
-0.1
5
50
Time (min)
10
15
100
20
25
150
30
35
40
200
Time(min)
Fig.2. Results of estimated voltage error with D-PF and D-APF
Fig.3. Results of estimated SoC error with D-PF and D-APF
The statistical analysis list of estimation result with two methods are listed in Table 2. As shown in Table 2, for dual PFs, the absolute value of stable voltage estimation error is less than 0.0194 V, which is the 0.54% of its nominal voltage, and the absolute value of stable SoC estimation error is less than 1%. The absolute value of stable voltage estimation error for dual APFs is less than 0.018 V, which is the 0.5% of its nominal voltage, and its absolute value of stable SoC estimation error is less than 0.6 %, for the convergence rate, it need 298s to converge to the real values, which is far shorter than 950s of the dual PFs. Based on the above analysis, we can conclude that multi-scale dual PFs can achieve accurate and reliable parameter and state estimates against inaccurate initial parameter and state, more importantly, the peak estimation error of stable voltage, and SoC with multiscale is less than ±1.25%. For better practical application, we add the adaptive update of noises variance to the parameter and state estimation process of the multi-scale dual PFs. Through the comparison, it shows that the dual APFs can provide more accurate and robust estimation, this is mainly because adaptive PF can generate appropriate noise variance to the algorithm in the estimation process. Table 2. The statistical analysis list of voltage and SoC estimation error (after 16 min). Method
MVE c (V)
SDVE (mV)
MSE (%)
SDSE (%)
convergence time of SoC (s)
D-PF
0.0194
3.9
1.25
0.38
950
D-APF
0.018
3.5
0.66
0.18
298
c
MVE=Maximum voltage error, SDVE=Standard deviation of voltage error, MSE= Maximum SoC error, SDSE= Standard deviation of voltage error.
6. Conclusions In considering that the system parameter change more slowly than state in the estimation process, the multi-scale dual PFs is developed to reduces the computational cost of the control system, and in order to improve accuracy and robustness for SoC estimation, the multi-scale dual APFs is presented. To verify the two proposed estimation approach, the test of the algorithms have been executed and the results show that (i) for multi-scale dual PFs, the peak errors of stable voltage and SoC are less than ±0.54% and
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±1.25% respectively, the convergence time with the erroneous initial SoC is sbout 16 minutes. (ii) For multi-scale dual APFs, the peak errors of stable voltage and SoC are less than ±0.5% and ±0.66% respectively, the convergence time with the erroneous initial SoC is about 5 minutes. (iii) The multi-scale dual APFs method can provide more accurate and robust estimation than the multi-scale dual PFs method. Acknowledgement This work was supported by the National Science Foundation of China (Grant No. 51507012). The experiments were performed at 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.
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Biography Rui Xiong received the Ph.D. degree in mechanical Engineering from Beijing Institute of Technology, China, in 2014. Since 2014, 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.
