A Fuzzy StateofCharge Estimation Algorithm Combining AmpereHour and an Extended Kalman Filter for LiIon Batteries Based on MultiModel Global Identification
Abstract
:Featured Application
Abstract
1. Introduction
1.1. Literature Review
1.2. Main Contributions
 (1)
 By comparing and analyzing nine models and five commonly used parameter identification algorithms, the most suitable ECM and parameter identification algorithm are decided.
 (2)
 The whole SOC area is divided into the high SOC area and low SOC area. Different ECMs and parameter identification algorithms are adopted considering SOC distribution. Based on this, a multimodel and multialgorithm method is developed to fit the battery model. Experimental results show that the proposed composite model has higher model accuracy compared with a single model.
 (3)
 According to the error characteristics of EKF and AH, a fuzzy fusion SOC estimation algorithm, combining AH and EKF in the whole SOC area, is proposed, and the accuracy and robustness of the proposed algorithm are verified by six cases.
1.3. Organization of the Paper
2. Experiments
3. Model and Parameter Identification
3.1. Equivalent Circuit Models
3.2. Optimization Variables and the Objective Function for ECMs
3.3. MothFlame Optimization Algorithm
3.4. Comparative Study of Optimization Methods
3.5. MultiModel and MultiAlgorithm Combination
4. SOC Estimation Method
4.1. EKF Method
Algorithm 1. Summary of the extended Kalman filter (EKF) method for SOC estimation. 
The nonlinear statespace model: $\{\begin{array}{l}{x}_{k+1}=f\left({x}_{k},{u}_{k}\right)+{w}_{k}\\ {y}_{k}=f\left({x}_{k},{u}_{k}\right)+{v}_{k}\end{array}$ where the first equation is the state equation, the second one is the output equation. $f\left({x}_{k},{u}_{k}\right)$ is a state transition function and $g\left({x}_{k},{u}_{k}\right)$ is a measurement function; ${w}_{k}$ and ${v}_{k}$ are independent zeromean white Gaussian stochastic processes with covariance matrices $\sum}_{w$ and $\sum}_{v}\text{\hspace{0.17em}$ respectively. 
Step 1. Initialization. For $k=0$, set ${\widehat{x}}_{0}^{+}=E\left[{\widehat{x}}_{0}\right],\text{}{\displaystyle {\sum}_{x,0}^{+}=E}\left[\left({x}_{0}{\widehat{x}}_{0}^{+}\right){\left({x}_{0}{\widehat{x}}_{0}^{+}\right)}^{T}\right]$. 
Step 2. Computation. For $k=1,2,\cdots ,$ compute:

4.2. AmpereHour Counting Method
4.3. Fuzzy Fusion Algorithm
 When $\Delta {K}_{SOC}\left(k\right)$ is relatively small and $\Delta {{K}_{SOC}}^{\prime}\left(k\right)$ is negative, very large ${k}_{FLC}$ should be chosen to ensure that $\Delta {\mathrm{SOC}}_{EKF}(k)$ is more credible in the fuzzy fusion algorithm.
 When $\Delta {K}_{SOC}\left(k\right)$ is relatively large and $\Delta {{K}_{SOC}}^{\prime}\left(k\right)$ is positive, very small ${k}_{FLC}$ should be chosen to ensure that $\Delta {\mathrm{SOC}}_{AH}(k)$ is more credible in the fuzzy fusion algorithm.
 When $\Delta {K}_{SOC}\left(k\right)$ is relatively large and $\Delta {{K}_{SOC}}^{\prime}\left(k\right)$ is negative, small ${k}_{FLC}$ should be chosen.
 When $\Delta {K}_{SOC}\left(k\right)$ is relatively small and $\Delta {{K}_{SOC}}^{\prime}\left(k\right)$ is positive, medium ${k}_{FLC}$ should be chosen to improve the stability of the control system.
5. Results and Discussion
5.1. Estimation Results Based on EKF
5.2. Case Studies for the Fuzzy Fusion Algorithm
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
 Hannan, M.A.; Lipu, M.S.H.; Hussain, A.; Mohamed, A. A review of lithiumion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations. Renew. Sustain. Energy Rev. 2017, 78, 834–854. [Google Scholar] [CrossRef]
 Ouyang, M.G.; Liu, G.M.; Lu, L.G.; Li, J.Q.; Han, X.B. Enhancing the estimation accuracy in low stateofcharge area: A novel onboard battery model through surface state of charge determination. J. Power Sources 2014, 270, 221–237. [Google Scholar] [CrossRef]
 Patil, M.S.; Panchal, S.; Kim, N.; Lee, M.Y. Cooling performance characteristics of 20 ah lithiumion pouch cell with cold plates along both surfaces. Energies 2018, 11, 2550. [Google Scholar] [CrossRef]
 Panchal, S.; Mcgrory, J.; Kong, J.; Fraser, R.; Fowler, M.; Dincer, I.; AgelinChaab, M. Cycling degradation testing and analysis of a lifepo4 battery at actual conditions. Int. J. Energy Res. 2017, 41, 2565–2575. [Google Scholar] [CrossRef]
 Zou, C.F.; Hu, X.S.; Wei, Z.B.; Wik, T.; Egardt, B. Electrochemical estimation and control for lithiumion battery healthaware fast charging. IEEE Trans. Ind. Electron. 2018, 65, 6635–6645. [Google Scholar] [CrossRef]
 Lai, X.; Zheng, Y.J.; Zhou, L.; Gao, W.K. Electrical behavior of overdischargeinduced internal short circuit in lithiumion cells. Electrochim. Acta 2018, 278, 245–254. [Google Scholar] [CrossRef]
 Tang, X.P.; Wang, Y.J.; Chen, Z.H. A method for stateofcharge estimation of lifepo4 batteries based on a dualcircuit state observer. J. Power Sources 2015, 296, 23–29. [Google Scholar] [CrossRef]
 Xiong, R.; Cao, J.Y.; Yu, Q.Q.; He, H.W.; Sun, F.C. Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access 2018, 6, 1832–1843. [Google Scholar] [CrossRef]
 Li, Z.; Huang, J.; Liaw, B.Y.; Zhang, J.B. On stateofcharge determination for lithiumion batteries. J. Power Sources 2017, 348, 281–301. [Google Scholar] [CrossRef]
 Zheng, Y.J.; Ouyang, M.G.; Han, X.B.; Lu, L.G.; Li, J.Q. Investigating the error sources of the online state of charge estimation methods for lithiumion batteries in electric vehicles. J. Power Sources 2018, 377, 161–188. [Google Scholar] [CrossRef]
 Xiong, R.; Zhang, Y.Z.; He, H.W.; Zhou, X.; Pecht, M.G. A doublescale, particlefiltering, energy state prediction algorithm for lithiumion batteries. IEEE Trans. Ind. Electron. 2018, 65, 1526–1538. [Google Scholar] [CrossRef]
 Wang, Y.J.; Zhang, C.B.; Chen, Z.H.; Xie, J.; Zhang, X. A novel active equalization method for lithiumion batteries in electric vehicles. Appl. Energy 2015, 145, 36–42. [Google Scholar] [CrossRef]
 Lu, L.G.; Han, X.B.; Li, J.Q.; Hua, J.F.; Ouyang, M.G. A review on the key issues for lithiumion battery management in electric vehicles. J. Power Sources 2013, 226, 272–288. [Google Scholar] [CrossRef]
 Barillas, J.K.; Li, J.H.; Gunther, C.; Danzer, M.A. A comparative study and validation of state estimation algorithms for Liion batteries in battery management systems. Appl. Energy 2015, 155, 455–462. [Google Scholar] [CrossRef]
 Li, Y.W.; Wang, C.; Gong, J.F. A wavelet transformadaptive unscented kalman filter approach for state of charge estimation of LiFePo_{4} battery. Int. J. Energy Res. 2018, 42, 587–600. [Google Scholar] [CrossRef]
 Yang, F.F.; Xing, Y.J.; Wang, D.; Tsui, K.L. A comparative study of three modelbased algorithms for estimating stateofcharge of lithiumion batteries under a new combined dynamic loading profile. Appl. Energy 2016, 164, 387–399. [Google Scholar] [CrossRef]
 Hu, X.S.; Li, S.B.; Peng, H. A comparative study of equivalent circuit models for Liion batteries. J. Power Sources 2012, 198, 359–367. [Google Scholar] [CrossRef]
 Liu, X.T.; He, Y.; Zheng, X.X.; Zhang, J.F.; Zeng, G.J. A new stateofcharge estimation method for electric vehicle lithiumion batteries based on multiple input parameter fitting model. Int. J. Energy Res. 2017, 41, 1265–1276. [Google Scholar] [CrossRef] [Green Version]
 Wang, Q.Q.; Wang, J.; Zhao, P.J.; Kang, J.Q.; Yan, F.; Du, C.Q. Correlation between the model accuracy and modelbased SOC estimation. Electrochim. Acta 2017, 228, 146–159. [Google Scholar] [CrossRef]
 Lai, X.; Zheng, Y.J.; Sun, T. A comparative study of different equivalent circuit models for estimating stateofcharge of lithiumion batteries. Electrochim. Acta 2018, 259, 566–577. [Google Scholar] [CrossRef]
 Mesbahi, T.; Khenfri, F.; Rizoug, N.; Chaaban, K.; Bartholomeus, P.; Le Moigne, P. Dynamical modeling of Liion batteries for electric vehicle applications based on hybrid Particle SwarmNelderMead (PSONM) optimization algorithm. Electr. Power Syst. Res. 2016, 131, 195–204. [Google Scholar] [CrossRef]
 Dai, H.F.; Xu, T.J.; Zhu, L.T.; Wei, X.Z.; Sun, Z.C. Adaptive model parameter identification for large capacity Liion batteries on separated time scales. Appl. Energy 2016, 184, 119–131. [Google Scholar] [CrossRef]
 Mirjalili, S. Mothflame optimization algorithm: A novel natureinspired heuristic paradigm. Knowl. Based Syst. 2015, 89, 228–249. [Google Scholar] [CrossRef]
 Holland, J.H. Building blocks, cohort genetic algorithms, and hyperplanedefined functions. Evol. Comput. 2000, 8, 373–391. [Google Scholar] [CrossRef] [PubMed]
 Ferreira, K.M.; de Queiroz, T.A. Two effective simulated annealing algorithms for the locationrouting problem. Appl. Soft Comput. 2018, 70, 389–422. [Google Scholar] [CrossRef]
 Bratton, D.; Kennedy, J. Defining a standard for particle swarm optimization. In Proceedings of the 2007 IEEE Swarm Intelligence Symposium, Honolulu, HI, USA, 1–5 April 2007; p. 120. [Google Scholar]
 Wei, J.; Dong, G.; Chen, Z.; Kang, Y. System state estimation and optimal energy control framework for multicell lithiumion battery system. Appl. Energy 2017, 187, 37–49. [Google Scholar] [CrossRef]
 Li, Y.W.; Wang, C.; Gong, J.F. A combination kalman filter approach for State of Charge estimation of lithiumion battery considering model uncertainty. Energy 2016, 109, 933–946. [Google Scholar] [CrossRef]
 Shen, P.; Ouyang, M.G.; Lu, L.G.; Li, J.Q.; Feng, X.N. The coestimation of state of charge, state of health, and state of function for lithiumion batteries in electric vehicles. IEEE Trans. Veh. Technol. 2018, 67, 92–103. [Google Scholar] [CrossRef]
 Wang, Y.J.; Zhang, C.B.; Chen, Z.H. Online battery stateofcharge estimation based on an integrated estimator. Appl. Energy 2017, 185, 2026–2032. [Google Scholar] [CrossRef]
 Fotouhi, A.; Auger, D.J.; Propp, K.; Longo, S. Lithiumsulfur battery stateofcharge observability analysis and estimation. IEEE Trans. Power Electron. 2018, 33, 5847–5859. [Google Scholar] [CrossRef]
Nominal Capacity (Ah)  Nominal Voltage (V)  Lower CutOff Voltage (V)  Upper CutOff Voltage (V)  Maximum Charge Current (A) 

32.5  3.75  2.5  4.15  65 
Models  Equations 

nRC  $\{\begin{array}{l}{U}_{L}\left(k\right)={U}_{OCV}\left(k\right)+I\left(k\right){R}_{0}+{\displaystyle \sum _{i=1}^{n}{U}_{i}\left(k\right)}\\ {U}_{i}\left(k+1\right)={U}_{i}\left(k\right){e}^{\frac{{T}_{s}}{{\tau}_{i}}}+I\left(k\right){R}_{i}\left(1{e}^{\frac{{T}_{s}}{{\tau}_{i}}}\right)\end{array}$ 
nRCH  $\{\begin{array}{l}{U}_{L}\left(k\right)={U}_{OCV}\left(k\right)+I\left(k\right){R}_{0}+{\displaystyle \sum _{i=1}^{n}{U}_{i}\left(k\right)+{u}_{h,k}}\\ {U}_{i}\left(k+1\right)={U}_{i}\left(k\right){e}^{\frac{{T}_{s}}{{\tau}_{i}}}+I\left(k\right){R}_{i}\left(1{e}^{\frac{{T}_{s}}{{\tau}_{i}}}\right)\\ {u}_{h,k}=H\left(1{e}^{\left{k}_{p}I\left(k\right)t\right}\right),H=\{\begin{array}{ll}M& I\left(k\right)\le 0\\ M& I\left(k\right)>0\end{array}\end{array}$ 
PNGV  $\{\begin{array}{l}{U}_{L}\left(k\right)={U}_{OCV}\left(k\right)+I\left(k\right){R}_{0}+{U}_{1}\left(k\right)+{U}_{\mathrm{cb}}\left(k\right)\\ {U}_{1}\left(k+1\right)={U}_{1}\left(k\right){e}^{\frac{{T}_{s}}{{\tau}_{1}}}+I\left(k\right){R}_{1}\left(1{e}^{\frac{{T}_{s}}{{\tau}_{1}}}\right)\\ {U}_{cb}\left(k+1\right)={U}_{cb}\left(k\right)+\frac{1}{{C}_{b}}I\left(k\right)\left(1{e}^{\frac{{T}_{s}}{{\tau}_{1}}}\right)\end{array}$ 
Method Type  Algorithm Name  Inspiration  Year of Proposal 

Nonlinear programming  Find minimum of constrained nonlinear (FMIN)  N/A  1951 
Evolutionbased  Genetic Algorithm (GA) [20,24]  Biological evolution  1992 
Physicsbased  Simulated annealing algorithm (SA) [25]  Solid annealing  1983 
Swarmbased  Particle Swarm optimization (PSO) [26]  Bird flock  1995 
Natureinspired  Mothflame optimization (MFO) [23]  Moth  2015 
${\mathit{k}}_{\mathit{F}\mathit{L}\mathit{C}}\text{}$  $\mathbf{\Delta}{\mathit{K}}_{\mathit{S}\mathit{O}\mathit{C}}\left(\mathit{k}\right)\text{}$  

VS  S  M  L  VL  
$\Delta {{K}_{SOC}}^{\prime}\left(k\right)$  N  VL  L  M  S  VS 
Z  L  M  S  VS  VS  
P  M  S  S  VS  VS 
Case Name  Describe  Parameters Setting 

Case A  The influence of initial SOC error (${e}_{SOC0}$) on fuzzy algorithm  $SOH=90\%$, ${I}_{drift}=0.1\mathrm{A}$, ${U}_{drift}=5\text{}\mathrm{mV}$, ${\mathrm{ECM}}_{drift}=3\text{}\mathrm{mV}$, ${e}_{OCV}=5\text{}\mathrm{mV}$ 
Case B  The influence of model error (${\mathrm{ECM}}_{drift}$) on fuzzy algorithm  ${e}_{SOC0}=0.3\%$, $\mathrm{SOH}=95\%$, ${I}_{drift}=0.08\mathrm{A}$, ${U}_{drift}=5\text{}\mathrm{mV}$, ${e}_{OCV}=5\text{}\mathrm{mV}$; 
Case C  The influence of voltage measurement error (${U}_{drift}$) on fuzzy algorithm  ${e}_{SOC0}=0.3\%$, $\mathrm{SOH}=90\%$, ${I}_{drift}=0.1\mathrm{A}$, ${\mathrm{ECM}}_{drift}=3\text{}\mathrm{mV}$, ${e}_{OCV}=5\text{}\mathrm{mV}$ 
Case D  The influence of current measurement error (${I}_{drift}$) on fuzzy algorithm  ${e}_{SOC0}=0.5\%$, $\mathrm{SOH}=95\%$, ${U}_{drift}=5\text{}\mathrm{mV}$, ${\mathrm{ECM}}_{drift}=5\text{}\mathrm{mV}$, ${e}_{OCV}=5\text{}\mathrm{mV}$ 
Case E  The influence of the SOH on fuzzy algorithm.  ${e}_{SOC0}=0.3\%$, ${I}_{drift}=0.1\mathrm{A}$, ${U}_{drift}=5\text{}\mathrm{mV}$, ${\mathrm{ECM}}_{drift}=5\text{}\mathrm{mV}$, ${e}_{OCV}=5\text{}\mathrm{mV}$ 
Case F  The influence of SOC–OCV curve error (${e}_{OCV}$) on fuzzy algorithm.  ${e}_{SOC0}=0.3\%$, $\mathrm{SOH}=95\%$, ${I}_{drift}=0.1\mathrm{A}$, ${\mathrm{ECM}}_{drift}=5\text{}\mathrm{mV}$${U}_{drift}=5\text{}\mathrm{mV}$ 
SOC Estimation Algorithm  Time (s) 

AH  0.0479 
EKF  65.8570 
Fuzzy fusion  65.8793 
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lai, X.; Qiao, D.; Zheng, Y.; Zhou, L. A Fuzzy StateofCharge Estimation Algorithm Combining AmpereHour and an Extended Kalman Filter for LiIon Batteries Based on MultiModel Global Identification. Appl. Sci. 2018, 8, 2028. https://doi.org/10.3390/app8112028
Lai X, Qiao D, Zheng Y, Zhou L. A Fuzzy StateofCharge Estimation Algorithm Combining AmpereHour and an Extended Kalman Filter for LiIon Batteries Based on MultiModel Global Identification. Applied Sciences. 2018; 8(11):2028. https://doi.org/10.3390/app8112028
Chicago/Turabian StyleLai, Xin, Dongdong Qiao, Yuejiu Zheng, and Long Zhou. 2018. "A Fuzzy StateofCharge Estimation Algorithm Combining AmpereHour and an Extended Kalman Filter for LiIon Batteries Based on MultiModel Global Identification" Applied Sciences 8, no. 11: 2028. https://doi.org/10.3390/app8112028