The Adaptive Fading Extended Kalman Filter SOC Estimation Method for Lithium-ion Batteries

The Adaptive Fading Extended Kalman Filter SOC Estimation Method for Lithium-ion Batteries

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Energy (2018) 000–000 357–362 EnergyProcedia Procedia145 00 (2017) www.elsevier.com/locate/procedia

Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, Applied Energy Symposium and Forum, Energy Integration REM 2017, 18–20 Renewable October 2017, Tianjin, China with Mini/Microgrids, REM 2017, 18–20 October 2017, Tianjin, China

The Adaptive Fading Extended Kalman Filter SOC Estimation The 15thFading International Symposium on DistrictFilter HeatingSOC and Cooling The Adaptive Extended Kalman Estimation Method for Lithium-ion Batteries Method for Lithium-ion Batteries Assessing the feasibility of, Xiao using the heat demand-outdoor Yunfei Zhaoa,b,c , Jun Xua,b,c,* Wanga,b,c , Xuesong Meia,b,c a,b,c a,b,c,* a,b,c Yunfei Zhao , for Jun Xu , Xiao Wang , Xuesong Meia,b,c forecast temperature function a long-term district heat demand State Key Laboratory for Manufacturing System Engineering, Xi’an, Shaanxi 710049, China a

b Shaanxi Key Laboratory of Intelligent Robots, Xi’an, Shaanxi 710049,710049, China China State Key Laboratory for Manufacturing System Engineering, Xi’an, Shaanxi c Shaanxi Key Laboratory of Intelligent Robots, Xi’an, Shaanxi 710049, China c School of Mechanical Engineering, Xi'an Jiaotong University, Xi’an, Shaanxi 710049, China a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract a

a,b,c a a b c School bof Mechanical Engineering, Xi'an Jiaotong University, Xi’an, Shaanxi 710049, China

I. Andrić c

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

The adaptive fading extended Kalman filter (AFEKF) is proposed for the accuracy and convergent speed problem of state of The adaptive extended filter (AFEKF) proposed the accuracy and convergent speed problem of state of charge (SOC) fading estimation. This Kalman filter algorithm combinesisthe adaptivefor extended Kalman filter and fading extended Kalman filter, charge (SOC)the estimation. filter algorithm combines extended Kalman and fading circuit extended Kalman filter, which solves problem This of uncertainty of system noisethe andadaptive over-reliance on old data.filter The equivalent model is utilized Abstract which theforgetting problem of uncertainty system noise and over-reliance data. the Themodel equivalent circuit Experimental model is utilized and thesolves variable factor recursiveofleast square(VFFRLS) is adoptedon to old identify parameters. test and the variable forgetting factor recursive leastResults square(VFFRLS) is adopted to able identify the model improve parameters. test platform is established to validate the method. show that the method is to effectively the Experimental convergent speed District networks are commonly addressed in the literature as oneisofable thetomost effective solutions for decreasing the platform isheating established to validate thethe method. Results show that the method effectively improve the convergent speed and accuracy of SOC estimation, and SOC error is less than 2%. greenhouse emissions from and the building systems and accuracy gas of SOC estimation, the SOC sector. error isThese less than 2%. require high investments which are returned through the heat sales. Due to theElsevier changed climate conditions and building renovation policies, heat demand in the future could decrease, Copyright © 2018 Ltd. All rights reserved. Copyright © 2018 The Authors. Published by Elsevier Ltd. prolonging the investment return period. Copyright and © 2018 Elsevier Ltd. Allresponsibility rights reserved. Selection peer-review under of the scientific committee of the Applied Energy Symposium and Forum, Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, The main scope of this paper is to assess the feasibility of using thecommittee heat demand – outdoor temperature function forand heatForum, demand Selection and peer-review under responsibility of the scientific of the Applied Energy Symposium Renewable Energy Integration with Mini/Microgrids, REM 2017. Renewable Energy Integration with Mini/Microgrids, REM 2017 forecast. The district of Alvalade, located in Lisbon (Portugal), Renewable Energy Integration with Mini/Microgrids, REM 2017. was used as a case study. The district is consisted of 665 buildingslithium-ion that vary battery; in bothstate construction period andKalman typology. weather scenarios medium, Keywords: of charge; the adaptive filter;Three the adaptive fading extended(low, Kalman filter high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained Keywords: lithium-ion battery; state of charge; the adaptive Kalman filter; the adaptive fading extended Kalman filter heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1.The Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The battery management system is one of key components of an electric vehicle. Precision of state of charge The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the The battery management is oneforofthe keyduring components of an electric vehicle. Precision of state of charge (SOC) estimation, laying thesystem foundation battery management system control can directly decide decrease in the number of heating hours of 22-139h the heating season (depending on strategy, the combination of weather and (SOC) estimation, laying the foundation for the battery management system control strategy, can directly decide power performance, safety and economy of ahand, vehicle [1]. However, many factors can influence SOC, including renovation scenarios considered). On the other function intercept increased for 7.8-12.7% per decade (depending onthe the power performance, safety andsuggested economy of a be vehicle [1].modify However, many factors can for influence SOC, considered, including the working current, internal resistance of batteries, temperature of the the function surrounding environment, self-discharge, aging, coupled scenarios). The values could used to parameters the scenarios and working internal resistance of batteries, temperature of the surrounding environment, self-discharge, aging, improve current, the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Jun Xu. Tel.: +86-029-82663870; fax: +86-029-82663870. Cooling. E-mail address: [email protected]. * Jun Xu. Tel.: +86-029-82663870; fax: +86-029-82663870.

E-mail address: [email protected]. Keywords: Heat demand; Forecast; Climate change 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the Applied Energy Symposium and Forum, Renewable Energy Integrationand with Mini/Microgrids, REM 2017. of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Selection peer-review under responsibility Integration with Mini/Microgrids, REM 2017. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 Copyright © 2018 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2017 10.1016/j.egypro.2018.04.064

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Yunfei Zhao et al. / Energy Procedia 145 (2018) 357–362 Yunfei Zhao, Jun Xu, Xiao Wang, Xuesong Mei / Energy Procedia 00 (2018) 000–000

etc. Moreover, lithium-ion batteries have a complex structure. All this increases difficulty of accurate SOC estimation. Many research attempts have been made to optimize SOC estimation methods. Among them, the ampere-hour integral method [2] is simple and easy, but it cannot automatically confirm the initial value and cumulative error of SOC. The open circuit voltage method [3] is known for its precision of SOC estimation, but it calls for a long standing before obtaining a stable open circuit voltage, which cannot meet requirements of online measurement. The model-based method builds a battery model based on the battery information. Different from the amperehour integral method, the model-based method makes use of the measured current and voltage signals. The measured voltage signals serve as the feedback to form a closed-cycle estimation so as to achieve a more accurate estimation of SOC. In general, the commonly-used model-based estimation methods include the Luenberger observer [4], the adaptive extended Kalman filter (AEKF) [5], and the proportional integral observer [6]. When the extended Kalman filter (EKF) algorithm is adopted to estimate SOC, divergence might be easily caused due to uncertainty of system noises. Thus, in order to obtain better convergence results and robustness, the AEKF algorithm can be employed [7-9]. However, excessive reliance of estimation on historical data usually impairs precision of estimation. This gives rise to the fading Kalman filter (FKF) [10-11]. Concerning uncertainty of system noises and excessive reliance on historical data, this paper proposes an adaptive fading extended Kalman filter (AFEKF). Experimental results suggest that the method can effectively improve the convergence speed and estimation precision of SOC. 2. Battery equivalent circuit model and its parameter identification 2.1. Battery model In terms of the model-based SOC estimation method, the more complex the battery model is, the higher the estimation precision is. To realize real-time application, this paper adopts the RC model, which is widely used in industrial sectors because of its simple use, as shown in Figure 1. V

R E

V

2

R

2

C

2

1

1

0

V

0

I

Figure 1 The first-order RC battery model.

In Figure 1, the relationship between V2 and the current I , can be obtained through the paralleled R2 and C2 , namely:  V I  2  V2  (1) R2C2 C2 Meanwhile, according to the Kirchhoff Voltage Law : (2) V0 =E0  IR1  V2 Where, z stands for SOC . According to the definition of SOC:  I z (3) Cn A nonlinear relationship between the voltage, E0 , and z can be observed: E0 (z)=an z  bn , and the model is:

x Ax  Bu   y Cx  Du 

(4)



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2.2. Battery model identification methods To build an accurate battery model, it is necessary to identify unknown parameters in the model. Currently, the impulsive discharge method and the least square method are two commonly-used methods for parameter identification. The impulsive discharge method is simple and convenient, but it is confined to offline parameter identification. The least square method, however, is characterized by a high identification precision, which can realize online identification. Many estimation algorithms for system identification can be interpreted as the least square method. The basic idea of the recursive least squares algorithm is that the new estimation value is equal to the sum of the old estimation value and the correction value, and the forgetting factor can be used to improve the convergence speed and the tracking performance of the recursive algorithm. Therefore, the recursive least square method with adaptive forgetting factor is used to identify the battery model parameters in this paper. Detailed computation processes of the VFFRLS algorithm are as follows: (5) y(k )  φT (k )θ T e(k)  y(k )  φ (k )θˆ(k  1) (6) 1 ( I  K (k )φT (k )) P (k  1) P (k ) 

(7)

P (k  1)φ(k )  (k )  φT (k ) P (k  1)φ(k )

(8)



K (k ) 





 (k )  min  (1   min )2L ( k )

(9)

L(k )  round (e ) θˆ(k ) θˆ(k  1)  K (k )e(k )

(10)

2

(11)

Where K (k) is the gain factor; P (k) is the covariance;  (k ) is the forgetting variable; min is the minimum value of the forgetting variable; round is the round-off integral function.

3. Model-based SOC estimation The discrete battery model can be obtained through discretization of Eq. (2): xk 1 ( A  E)x k  Buk  ωk  yk  Cxk  Duk  vk 

(12)

The basic idea of Kalman Filter is to achieve optimal estimation of the dynamic system status in terms of minimum variance. The recursion formulas could be referred to the former literature [5]. Concerning uncertainty of noises and excessive reliance on historical data, this paper proposes Adaptive Fading Extended Kalman Filter, and the recursion process are as follows: (1) Time Update:  xˆ k / k 1 (A+E)xˆ k 1  Buk 1 (13) (2)

Pk / k 1 (A  E) Pk 1 (A  E)T  Qk

(14)

Measurement data update:  K k Pk / k 1CT [(CPk / k 1CT  Rk )]1  xˆ k / k xˆ k / k 1  K k ek

(15)

T

(3) (4)

Pk  [E  K k C]Pk / k 1[E  K k C]  K k R k K k Noise covariance Judgment ek T ek  rTr (E(ek T ek )) Noise Covariance Update

(16) T

(17) (18)

YunfeiWang, Zhao Xuesong et al. / Energy ProcediaProcedia 145 (2018) 357–362 Yunfei Zhao, Jun Xu, Xiao Mei / Energy 00 (2018) 000–000

4360

Qk  Qk 1  1 LQ (Q*  Qk 1 ) T

*

(19)

T

T

 Q K k ek ek K k  Pk  (A  E)Pk 1 (A  E)

(20)

*

Rk  Rk 1  1 LR ( R  Rk 1 ) *

T

R  ee  Ck Pk 1Ck Where,

e yk  yˆk ;  k

denotes the fading factor ; LQ and

noise, respectively; K k denotes the Kalman gain;

Pk

(21)

T

(22)

LR

are adjustment of the process and measurement

denotes the error covariance.

4. Experimental validation The battery test platform is established as Figure 2[12]. There are three main components, including the battery detection system, the Neware battery testing system and constant temperature and humidity testing machine. The battery detection system sends the current information to the battery testing equipment. The battery testing device charges and discharges the battery according to the current information of the battery detection system. The current, voltage and temperature are collected by the sensor and transmitted to the battery detection system. The NCR18650 lithium-ion battery was used in this paper, the rated voltage is 3.7V, and the actual measurement capacity is 1573 mAh. The battery is fully charged before the experiment. The battery was discharged with the UDDS cycle to the cut-off voltage and the total time is 5000s.

constant temperature humidity machine battery detection system

battery

neware testing s ystem

Figure 2 Battery test platform

4.1. Model validation The battery model parameters is identified by VFFRLS and the results is shown in Figure 3, where the real value R1、R2、C2 were obtained by the battery hybrid pulse power characteristics (HPPC) test and off-line parameter identification. From Figure 3, we know that parameters quickly converge to the real value and fluctuate very little after arrival. It indicated that VFFRLS is suitable for online identification with the battery. 0.3

R1 esimation value R1 actual value

0.2 0.1

0.1 0

0 -0.1 0

R2 esimation value R2 actual value

0.2

R2/Ω

R1/Ω

0.3

1000

2000

3000

Time/s

4000

5000

-0.1 0

1000

2000

3000

Time/s

4000

5000



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3000 C2 esimation value C2 actual value

C2

2000 1000 0

1000

1500

2000

2500

3000

3500

4000

Time/s

Figure 3 Parameter comparison: (a) Ohm resistance, (b) Polarization resistance, (c) Polarization capacitance.

4.2. Algorithm validation The SOC of the battery is estimated by using the ampere-hour integral method, the extended Kalman filter, the fading Kalman filter, the adaptive Kalman filter and the adaptive fading Kalman filter. The SOC is obtained by using the ampere-hour integral method as the reference value. The experimental results as follows: 0.3

1

SOC Error

SOC

FKF-based SOC EKF-based SOC Ah-based SOC

0.5

0

0

1000

2000

3000

Time/s

4000

0.1 0 -0.1 0

5000

FKF-baesd SOC error EKF-baesd SOC error ±2% error upper/lower bound

0.2

1000

2000

3000

Time/s

4000

5000

Figure 4 FKF/EKF-based SOC estimation: (a) SOC estimation, (b) SOC estimation error.

From Figure 4, we know that when the SOC initialization error is 20%. The SOC estimated error by FKF algorithm Within 2% is less than error estimated by EKF algorithm, but convergent speed is slower. The error of EKF is more than 2%. 0.3

1

SOC Error

SOC

AEKF-baesd SOC EKF-baesd SOC Ah-based SOC

0.5

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5000

AEKF-baesd SOC error EKF-baesd SOC error ±2% error upper/lower bound

0.2

1000

2000

Time/s

3000

4000

5000

Time/s

Figure 5 AEKF/EKF-based SOC estimation: (a) SOC estimation, (b) SOC estimation error.

From Figure 5, we know that when the SOC initialization error is 20%. The convergent speed of AEKF algorithm is faster than that of EKF. But between 800s and 2200s, the SOC estimated error exceeds EKF, and the error estimated by AEKF algorithm is more than 2%. 0.3

1

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SOC

AFEKF-based SOC AEKF-based SOC Ah-based SOC

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AFEKF-baesd SOC error AEKF-baesd SOC error ±2% error upper/lower bound

0.2 0.1 0 -0.1 0

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4000

Time/s

Figure 6 AFEKF/AEKF-based SOC estimation: (a) SOC estimation, (b) SOC estimation error.

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From Figure 6, we know that the SOC estimated error by AFEKF algorithm is less than error estimated by AEKF algorithm and converges faster. At the same time AFEKF algorithm solves the overshoot problem of AEKF. The overall error remains at 2%. AFEKF algorithm combines the advantages of FKF and AEKF. 5. Conclusion The AFEKF algorithm is proposed for Kalman filter algorithm with large estimation error and slow convergent speed in the SOC estimation of lithium ion battery. The ECM is used to model the lithium ion battery and the model parameters were identified by the VFFRLS. The experimental results show that the AFEKF algorithm has two advantages: (1) It is helpful to improve the SOC estimation accuracy of the battery which is less than 2% and with great robustness. (2) It can improve the convergent speed which means it can access to accurate SOC estimates faster. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51405374), the Postdoctoral Science Foundation of China (Grant No. 2014M560763), the Postdoctoral Science Special Foundation of China (Grant No. 2016T90904), the Fundamental Research Funds for the Central Universities, and the Postdoctoral Science Foundation of Shaanxi. References [1] Xu, J., et al., An online state of charge estimation method with reduced prior battery testing information. International Journal of Electrical Power & Energy Systems[J], 2014. 63: p. 178-184,2013,233:277-284. [2] Ng, K.S., et al., Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries. Applied Energy[J], 2009. 86(9): p. 1506-1511. [3] Lee, S., et al., State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge. Journal of Power Sources[J], 2008. 185(2): p. 1367-1373. [4] Hu, X., F. Sun, and Y. Zou, Estimation of State of Charge of a Lithium-Ion Battery Pack for Electric Vehicles Using an Adaptive Luenberger Observer. Energies[J], 2010. 3(9): p. 1586. [5] Xu, J., et al. A Comparison Study of the Model Based SOC Estimation Methods for Lithium-Ion Batteries[c]. in 2013 IEEE Vehicle Power and Propulsion Conference (VPPC). 2013. [6] Xu, J., et al., The state of charge estimation of lithium-ion batteries based on a proportional-integral observer. IEEE Transactions on Vehicular Technology[J], 2014. 63(4): p. 1614-1621. [7] He, H., et al., State-of-Charge Estimation of the Lithium-Ion Battery Using an Adaptive Extended Kalman Filter Based on an Improved Thevenin Model. IEEE Transactions on Vehicular Technology[J], 2011. 60(4): p. 1461-1469. [8] Xiong, R., et al., Evaluation on State of Charge Estimation of Batteries With Adaptive Extended Kalman Filter by Experiment Approach. IEEE Transactions on Vehicular Technology[J], 2013. 62(1): p. 108-117. [9] Yao, L.W., et al. Online battery modeling for state-of-charge estimation using extended Kalman filter with Busse's adaptive rule[c]. in IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society. 2015. [10] Lim, K.C., et al. Online SoC estimation of lithium ion battery for EV/BEV using Kalman filter with fading memory[c]. in 2014 IEEE 3rd Global Conference on Consumer Electronics (GCCE). 2014. [11] Lim, K., et al., Fading Kalman filter-based real-time state of charge estimation in LiFePO4 battery-powered electric vehicles. Applied Energy[J], 2016. 169: p. 40-48. [12] Xu, J., et al., A Method to Simultaneously Detect the Current Sensor Fault and Estimate the State of Energy for Batteries in Electric Vehicles. Sensors[J], 2017.16: p. 1328.