Robustness Evaluation of Extended and Unscented Kalman ...eprints.whiterose.ac.uk/133918/1/08355786.pdf˝lter (EKF) and unscented Kalman ˝lter (UKF) for state of charge (SOC) estimation

SPECIAL SECTION ON BATTERY ENERGY STORAGE AND MANAGEMENT SYSTEMS

Received March 22, 2018, accepted April 27, 2018, date of publication May 7, 2018, date of current version June 5, 2018.

Digital Object Identifier 10.1109/ACCESS.2018.2833858

Robustness Evaluation of Extended andUnscented Kalman Filter for BatteryState of Charge EstimationCHAO HUANG1,2,3, (Member, IEEE), ZHENHUA WANG4, ZIHAN ZHAO5,LONG WANG 6, (Member, IEEE), CHUN SING LAI 1,7, AND DONG WANG 21School of Automation, Guangdong University of Technology, Guangzhou 510006, China2Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong3Guangdong Provincial Key Laboratory of New and Renewable Energy Research and Development, Guangzhou 510640, China4College of Water Resources and Architectural Engineering, Shihezi University, Shihezi 832003, China5School of Geosciences and Surveying Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China6School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China7School of Civil Engineering, University of Leeds, Leeds LS2 9JT, U.K.

Corresponding authors: Zhenhua Wang ([email protected]) and Long Wang ([email protected])

This work was supported in part by the Guangdong Provincial Key Laboratory of New and Renewable Research and Development underGrant Y807s61001, in part by the Grant from the Financial and Education Department of Guangdong Province 2016[202]: Key DisciplineConstruction Programme, in part by the Education Department of Guangdong Province: New and Integrated Energy System Theory andTechnology Research Group, in part by the Fundamental Research Funds for the Central Universities under Grant 06500078, and in part bythe National Key Research and Development Plan Research and Application of Water and Fertilizer Integration Technology Model forCash Crops under Grant 2017YFD0201506.

ABSTRACT In this paper, the robustness of model-based state observers including extended Kalmanfilter (EKF) and unscented Kalman filter (UKF) for state of charge (SOC) estimation of a lithium-ionbattery against unknown initial SOC, current noise, and temperature effects is investigated. To morecomprehensively evaluate the performance of EKF and UKF, two battery models including the first-orderresistor-capacitor equivalent circuit and combined model are considered. A novel method is proposed toidentify the parameters of the equivalent circuit model. The performance of SOC estimation is evaluatedby employing measurement data from a commercial lithium-ion battery cell. The experiment results showthat UKF generally outperforms EKF in terms of estimation accuracy and convergence rate for each batterymodel. However, the advantages of UKF over EKF with the combined model is not as significant as withthe equivalent circuit model. Both EKF and UKF demonstrate strong robustness against current noise. Theupdates of model parameters corresponding to operational temperatures generally improve the estimationaccuracy of EKF and UKF for both models.

INDEX TERMS Extended Kalman filter, lithium-ion battery, robustness, state of charge, unscented Kalmanfilter.

I. INTRODUCTIONIn the auto industry, electric vehicles (EVs) have attractedincreasing attention and achieved ever better developmentas an important technology to reduce the greenhouse gasemission and the consumption of natural resources [1].Battery system, as one of the key parts in EVs, plays signifi-cant role in determining the efficiency, reliability, and safetyof EVs systems. Due to the demanding driving operations,a battery management system (BMS) is required to guaranteethe good performance of the battery. An accurate estimationof state of charge (SOC) is one of the main functions for

a BMS [2], [3]. The SOC quantifies the remaining chargeof the battery, which indicates the remaining available rangefor EVs. Correct SOC estimation can decrease the risk ofover-charging/discharging [4], improve the efficiency of thewhole EVs energy management, and extend the battery cyclelife [5]. Nevertheless, the battery is a strong nonlinear andtime-variable system due to its complicated internal electro-chemical process, whichmakes it difficult to directly measurethe SOC. Moreover, various factors such as ambient tem-perature, battery aging, and charging/discharging current rateaffect the accuracy of SOC estimation [6], [7]. Thus, a robust

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C. Huang et al.: Robustness Evaluation of Extended and UKF for Battery State of Charge Estimation

and time-saving technique is required to estimate the SOCon-board.

A variety of approaches have been proposed to estimatethe SOC including coulomb-counting methods [8], machinelearning methods [9], and state observer methods [10].Coulomb-counting is widely used in many commercial bat-tery management systems as it is simple and can be eas-ily implemented online. This approach constantly measurescurrent, and simply integrates the charge and discharge cur-rent with respect to time, which makes this method highlydepend on the precision of current sensor and the accuracyof initial SOC [11]. In [12], an enhanced coulomb-countingmethod is proposed to improve the SOC estimation effi-ciency by considering the charging and operating efficiencies.Moreover, coulomb-counting is an open-loop estimator thataccumulated error and uncertainties can lower the accuracyof SOC estimation. To reduce initial SOC error and accu-mulated error, the open-circuit voltage (OCV) method [13],which estimates SOC according to the mapping betweenOCV and SOC, is employed to recalibrate SOC. Unfortu-nately, the OCV method requires long-time relaxation toreach steady state, which makes it not suitable for onboardSOC estimation.

For machine learning methods, nonlinear relationshipbetween SOC and relative factors is described by powerfulintelligent computational algorithms such as artificial neuralnetworks (ANNs) [14], fuzzy logic [15], and their hybridapproaches [16], [17]. Given an appropriate training data set,machine learning methods can provide good estimation ofSOC. In [18], the measured parameters including current,voltage, and temperature are used as inputs of a Gaussianprocess regression model to predict SOC, and the proposedmethod outperformed state-of-the-art techniques for SOCestimation. However, it’s time consuming to train the model,and the performance of these methods relies on the amountand the reliability of the training data set. Once the operatingconditions exceed the training data set, the robustness can bepoor, and the uncertainty of the testing data set can exacerbatethe prediction error.

Recently, model-based state estimating methods arewidely applied into SOC estimation. The accuracy of suchmethods highly depends on the battery model and theobserver. The frequently utilized battery models includephysics-based models. References [19], [20], equivalentcircuit models [21], [22], machine learning models [23], [24],and empirical models [7]. The design of observers to estimatethe state can be in different ways, such as Kalman filterfamily [25], [26], sliding observer [10], [24], H-infinityobserver [27], [28], and Luenberger observer [29], [30].Among all the kinds of observers, Kalman filter family takesup the largest percentage. Extended Kalman filter (EKF)was introduced to estimate SOC of a lithium-ion polymerbattery by Plett [31] in 2004. Later, sigma-point Kalmanfilter was proposed to improve estimation accuracy [32].Simultaneously, the methodologies to enhance the Kalmanfilter family’s performance on SOC estimation emerged, such

FIGURE 1. Schematic of Lithium-ion battery equivalent circuit.

as adaptive extended Kalman filter (AEKF) [33], adaptiveunscented Kalman filter (AUKF) [34], square root sphericalunscented Kalman filter [35]. In [36], the EKF was appliedinto SOC estimation and the performance was improved byupdating the parameters related to aging. Zou et al. [37]developed a deterministic version of EKF for the estimationof SOC and state of health (SOH) in a lithium-ion bat-tery. Meanwhile, studies have been conducted to comparethe performance of different state estimating approaches.In [7], the performance of EKF, UKF, and particle filter (PF)were compared in terms of accuracy and computational costfor SOC estimation under various loading profiles, and theexperimental results show that the UKF was most robust tounknown initial SOCs.

In this paper, the robustness of EKF and UKF in SOC esti-mation of lithium-ion battery against unknown initial SOC,current noise, and temperature will be investigated. In SOCestimation, incorrect initialization of SOC is inevitable whichis considered as one of the biggest problems of coulomb-counting for SOC estimation. Moreover, the current sensoris much more precise in the laboratory than in the indus-trial applications which requires robust state observers withstrong robustness against current noise. Temperature cansignificantly affect the performance of lithium-ion bat-tery in discharging capacity, OCV-SOC relationship, andmodel parameters which can deteriorate the model accuracy.Thereby, the investigation on the robustness of EKF andUKF against those factors is of great value for accurate SOCestimation.

The battery model is essential for SOC estimationusing EKF and UKF, therefore two models namely first-order RC (resistor-capacitor) equivalent circuit model andcombined model are considered. With first-order RC equiv-alent circuit model, the recursive least square (RLS) algo-rithm [36] is frequently applied to identify the model param-eters. In this paper, multi-swarm particle swarm optimization(MPSO) [38] will be applied to derive model parameters andcompared with RLS algorithm in terms of modeling accuracy.

The remainder of the paper is organized as follows:Section II introduces the battery models, the experiments,and the methods to identify model parameters. In section III,the EKF and UKF algorithms are briefly introduced, andthis is followed by experiment results and analysis in SOCestimation. Finally, conclusions of the paper are given insection IV.

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FIGURE 2. Schematic of Lithium-ion battery test bench.

FIGURE 3. OCV-SOC curves: (a) OCV curve at room temperature; (b) OCV curve at 0 ◦C, 20 ◦C, and 40 ◦C.

II. BATTERY MODELINGA. DEFINITION OF SOCSOC is defined as the ratio of the remaining charge to themaximal capacity of an operating battery [39], and it is com-puted by

SOCt = SOC0 −1

Cmax

∫ t

0i (τ )dτ (1)

where SOCt is the SOC at time t , SOC0 is the initial valueof SOC, i(τ ) is the instant loading current assuming positivefor discharging and negative for charging, and Cmax is themaximal capacity of the battery which can be different fromthe nominal capacity due to temperature effect and agingeffect.

B. MODEL STRUCTUREIn this paper, two models are used to characterize the batterydynamic behavior for EVs’ application.

1) EQUIVALENT CIRCUIT MODELThe first-order RC model shown in Fig. 1 [40] is consideredand the electrical characteristic of the model can be discretelyexpressed as follows:

SOCk+1 = SOCk −1tkCmax

Ik + ω1,k (2)

Up,k+1 = exp(−1tkRpCp

)Up,k

+Rp

(1− exp

(−1tkRpCp

))Ik + ω1,k (3)

TABLE 1. Specification about the Test Battery.

Uterm,k = Voc,k (SOC)− Up,k − R0Ik + νk (4)

where Uterm is the battery terminal voltage, I is the loadingcurrent, Voc is the battery OCV which is a time varying dcvoltage source related to SOC, and R0 is the internal ohmicresistance. Battery dynamic characteristics caused by the dif-fusion effect and a double layer charging/discharging effectsare illustrated by the RC network. Rp is the polarizationresistance, Cp is the polarization capacitor, and Up is thevoltage cross Cp. ω1, ω2 and ν represent the uncertaintiescaused by the model and external noise or disturbance, whichare uncorrelated zero-mean Gaussian white noise. 1t is thesampling interval and the subscript k represents the time step.With the equivalent circuit model, SOC andUp are consideredas states to be estimated by observers. To simply the model,it is assumed that the model parameters are independentof SOC. However, the dependence of model parameters ontemperatures is well studied.

• Parameter identification with RLS

The RLS is applied to identify the model parametersincluding R0, Rp, and Cp, and the linear identifiable form (5)

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FIGURE 4. DST test profile: (a) current; (b) voltage.

is obtained by iteratively substituting (3) into (4):

1Uk+1 = a ·1Uk + b · Ik + c · Ik+1 (5)

where 1Uk = Voc,k (SOC) − Uterm,k , a = exp(−

1tkRpCp

),

b = Rp−Rp · exp(−

1tkRpCp

)−R0 · exp

(−

1tkRpCp

), and c = R0.

Assume 1tk = 1t for k = 1, 2, . . . ,N , then a, b, and c areconstants and linear least square (LLS) is applicable for theidentification of coefficients in (5) thereby the values of R0,Rp, and Cp.

• Parameter identification with MPSO

The determination of the parameters R0, Rp, and Cp canbe formulated as an optimization problem (6) to minimizethe mean squared error (MSE) between observed1Uk+1 andvalues of 1Ûk+1 calculated by (4) - (5):

minMSE =1

N − 1

N−1∑i=1

(1Uk+1 −1Uk+1

)2(6)

In this paper, the solution of (6) is obtained by using theMPSO algorithm [38]. This method required Up,1, and ifits value is unknown it can be considered as an unknowparameter to be determined together with R0, Rp, and Cp.The advantages of the proposed method over RLS will beillustrated with experimental data.

2) COMBINED MODELThe combined model in (7) is also used to describe thedynamic characteristics of the battery. This model linearlydepends on parameters k0, k1, k2, k3, k4, and R0, hence the

FIGURE 5. FUDS test profile: (a) current; (b) voltage.

TABLE 2. Identified parameters by two algorithms under DST test profileat room temperature.

TABLE 3. Modeling errors by two different algorithms.

LLS is applied to derive these parameters.

Uterm,k = k0 −k1

SOCk− k2SOCk

+ k3 ln (SOCk)+ k4 (1− SOCk)− R0Ik (7)

C. EXPERIMENTSThe battery test bench consists of a Votsch thermal cham-ber, an Arbin battery test system BT2000, and a host com-puter with Arbin’s Mits Pro Software shown in Fig. 2.This test bench was also used in [6] and [7]. The cylin-drical B18650CD battery (LiNMC) manufactured by BAK(Shenzhen, P. R. China) is used in the test, and the keyspecifications are shown in Table 1.

1) OCV-SOC TESTTo obtain the relationship between SOC and OCV at varioustemperatures, the OCV-SOC test is conducted at temperatures

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TABLE 4. Fitted parameters and modeling errors at different temperatures.

FIGURE 6. Modeling performance by the two algorithms: (a) modelingvoltage; (b) modeling error.

from 0 ◦C to 50 ◦C at an interval of 10 ◦C as well as atroom temperature 25 ◦C. The test procedures are describedin detail in [6]. The OCV-SOC curves are depicted in Fig. 3.It is observable in Fig. 3(a) that the charging and dischargingcurves show hysteresis phenomenon. To mitigate the effectsof hysteresis and internal ohmic resistance, the averaged cellvoltage is used to compute the OCV. The OCV-SOC curvesat three different temperatures in Fig. 3(b) show that theOCV difference caused by temperature is not very significantfor LiNMC lithium-ion battery especially when the SOC isgreater than 10%. Two approaches are adopted to describe theOCV-SOC relationship, OCV-SOC table and seventh poly-nomial function. The former is used by the UKF algorithmwhile the latter is employed by the EKF algorithm for SOCestimation in this study.

2) MODEL IDENTIFICATION AND VALIDATION TESTSFamous test profiles including the dynamic stress test (DST)and the federal urban driving schedule (FUDS) are executedon the battery cells at temperatures from 0 ◦C to 50 ◦C at an

TABLE 5. Fitted parameters of combined model at different temperatures.

interval of 10 ◦C and room temperature. The current profilesand the corresponding terminal voltage at room temperatureare depicted in Fig. 4 and Fig. 5, respectively. The DST testsare utilized to identify the batterymodel parameters, while theFUDS tests are used to evaluate the accuracy of the model aswell as the correctness of SOC estimation.

D. MODEL CALIBRATION1) EQUIVALENT CIRCUIT MODELThe performance in parameter identification by the two algo-rithms, RLS andMPSO, are compared. The identified param-eters based on the DST test profile at room temperature aresummarized in Table 2 while the measured and modelingvoltages as well as the modeling errors by the two algorithmsare depicted in Fig. 6.

The values of internal resistance R0 obtained by twoalgorithms are very close, and the main difference lies inthe values of the first-order RC network which describesthe dynamic behavior of the battery. The time constant(τ = RpCp) of the RC network derived by the MPSO algo-rithm is much longer than that by the RLS algorithm. It usu-ally takes several hours to get the battery totally relaxed, thusthe MPSO algorithm better describes the battery behaviorwhich can be demonstrated by the voltage errors in Fig. 6(b).

The mean absolute error (MAE) and the root meansquared error (RMSE) are employed together to evaluate thegoodness-of-fit of the model. In Table 3, the modeling errorsby the two algorithms are compared where the DST andFUDS are used as the training and test data set, respectively.The MPSO algorithm greatly improves the model accuracyin terms of MAE and RMSE on the DST profiles. The MPSOalso performs better on the FUDS profiles as expected. Thus,the MPSO algorithm is chosen as the algorithm to identifythe parameters at different temperature, and the identifiedparameters and modeling errors are summarized in Table 4.

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TABLE 6. Comparison of modeling errors of different battery models.

FIGURE 7. SOC estimation with an initial SOC of 90%: (a) SOC estimation; (b) SOC estimation error.


TABLE 7. Nomination of methods used for SOC estimation.

2) COMBINED MODELThe parameters at different temperatures are listedin Table 5 while the comparison of the errors by this modelagainst equivalent circuit model is shown in Table 6. FromTable 6, it is observable that no model dominates the otherfor all the temperatures in terms of MAE and RMSE.

III. SOC ESTIMATION AND ANALYSISTo estimate the state of a dynamic linear system, Kalmanfilter (KF) is an optimal recursive solution, which has beenwidely used in various fields such as navigation, targettracking, and global positioning. Since KF is only available

for linear system, two extensions of KF including EKF andUKF are applied into lithium-ion battery SOC estimation.The basic idea of KF is to compare the measured terminalvoltage with the modeling terminal voltage, and the differ-ence is fed back to correct the predicted SOC by a gainmatrix.EKF and UKF are developed to deal with the nonlinearproblems. A linearization is realized at each step to approx-imate the nonlinear system by the EKF algorithm. The UKFalgorithm addresses the approximation problems of EKF byintroducing the concept of weighted sigma points, which aredeterministically selected from the Gaussian approximation.These points propagate through the true nonlinearity, and themean and covariance of the Gaussian approximation are thenre-estimated. The details on the EKF andUKF algorithms andtheir applications in SOC estimation are well described in [6]and [7].

The FUDS tests are employed to evaluate the performanceof SOC estimation. The SOC ranging from 90% to 10% is

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TABLE 8. Comparison of SOC estimation with different initial SOCs.


TABLE 9. Robustness evaluation of soc estimation against current noise.

considered as the parameters vary slightly within the rangeand the battery SOC is seldom permitted to exceed this rangein battery management systems for EVs. The performance ofSOC estimation methods handling various practical problemsincluding unknown initial SOC, current noise, and tempera-ture effects is studied. To clearly distinct the observers andmodels used in each SOC estimation method, the nominationof different methods is given in Table 7.

A. SOC ESTIMATION WITH UNKNOWN INITIAL VALUEAT ROOM TEMPERATURETo illustrate the robustness of EKF andUKF against unknowninitial SOC, the behavior including estimation accuracy andconvergence rate of EKF and UKF in SOC estimation withunknown initial SOCs is discussed. The accuracy is illus-trated by RMSE, and the convergence rate is defined as thetime that the estimated SOC converges to the ±3% errorbands.

FIGURE 10. Comparison between the measured current and noisy current.

The estimation accuracy and convergence rate by EKF andUKF with different settings of initial SOCs from 90% to10% at the step interval of 10% is summarized in Table 8.It is observable that the RMSE and convergence rate gener-ally increases with increasing initial SOC errors. The UKF

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FIGURE 11. Illustration of SOC estimation with and without current noise: (a) SOC estimation with circuit equivalent; (b) SOCestimation error with circuit equivalent model; (c) SOC estimation with combined model; (d) SOC estimation error with combinedmodel.

algorithm based on combined model (M4) generally providesmost accurate estimation, while the EKF algorithm basedon equivalent circuit model (M1) performs worst. The UKFconverges much faster than EKF regardless of the lithium-ion battery model used. The advantage of UKF over EKFwith combined model is not as significant as with equivalentcircuit model. This can be partially explained that with equiv-alent circuit model the UKF employs OCV-SOC table whichis more accurate than the polynomial OCV-SOC relationshipused by EKF.

The estimation of SOC by different methods with ini-tial SOC settings of 90%, 50%, and 20% are illustrated inFigs. 7-9. In Fig. 7, the initial setting of SOC is set to the truevalue, however, the EKF and UKF based on the equivalentcircuit model take some time to converge to the true SOC.This is partially due to that the EKF and UKF based on theequivalent circuit model should also accurately estimate Up.From these figures, it’s clear that the convergence of theestimation of SOC based on combined model is much fasterthan that based on the equivalent circuit model. This leadsto the higher accuracy of combined model based estimationof SOC. However, the combined model based estimation ofSOC is less reliable at low true SOCs due to large errors.

B. SOC ESTIMATION WITH CURRENT NOISEAT ROOM TEMPERATURETo illustrate the robustness of EKF and UKF against currentnoise due to sensor drift in SOC estimation, a zero-mean

TABLE 10. Battery discharge capacity (Ah) under different loads atvarious temperatures.

Gaussian noise whose variance equals 0.25 A2 is added intothe measured current. The comparison between the measuredcurrent and the noisy current is depicted in Fig. 10. Theamplitude of the noise can be as high as 0.5 A which takesup 12% of the maximal current value under FUDS test.

The performance of SOC estimation by different meth-ods is given in Table 9. As the noise is randomly addedinto the current, the impacts of current noise on SOCestimation is also random that the performance can beimproved or degraded in terms of estimation accuracy andconvergence rate. From Fig. 11, however, it is observablethat both the EKF and UKF can handle current noise forSOC estimation regardless of the lithium-ion battery modelused.

C. SOC ESTIMATION AT VARIOUS TEMPERATURESThe OCV-SOC relationship and model parameters dependon temperature. Moreover, the battery discharging capacityunder different loading profiles are related with temperatures

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TABLE 11. RMSE (%) of SOC estimation by different methods.

FIGURE 12. SOC estimation with and without updates of parameters at 10 ◦C: (a) SOC estimation with circuit equivalent; (b) SOCestimation error with circuit equivalent model; (c) SOC estimation with combined model; (d) SOC estimation error with combinedmodel.

as shown in Table 10. At infinitesimal discharging rate (C/25),the discharging capacity varies less than 4% of the nominalcapacity for various temperatures. However, the situation isvery different for DST and FUDS test profiles in which thevariation can reach 30% of the nominal capacity. At lowtemperature (0 ◦C) the discharge capacity under DST andFUDS is much smaller than that at high temperature (50 ◦C).This is explained by the battery performance degradation dueto the reducing internal chemical reaction at low temperature,and that’s why reheating is required for a battery to crank atlow temperature. In this paper, the robustness of EKF and

UKF based on different lithium-ion battery model againsttemperature for SOC estimation is also investigated.

The accuracy of SOC estimation at different tempera-tures with and without updates of parameters are summa-rized in Table 11. No update means that the parameters atroom temperature are employed to estimate SOC at othertemperatures. It’s observable that the updates of parameterscan greatly improve EKF and UKF based SOC estimationaccuracy with equivalent circuit model at any temperatureregardless of the settings of initial SOC. However, at 0 ◦Cthe estimation based on equivalent circuit model is much

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less accurate than at other temperatures. With the combinedmodel, the updates of parameters improve the estimationaccuracy at all the temperatures except at 50 ◦C due to theinaccurate model. The UKF generally outperformed EKFwith a given model, but no method dominates the others atall the temperatures considering the battery model utilized.Fig. 12 depicts the SOC estimation with and without updatesof parameters at 10 ◦C. It is observable that the updates ofparameters greatly reduce the estimation errors for both UKFand EKF.

IV. CONCLUSIONIn this paper, the robustness of EKF and UKF for lithium-ion battery SOC estimation against core problems such asunknown initial SOC, current noise, and temperature effectsis studied. As EKF and UKF are sensitive to the batterymodel, twomodels including first-order RC equivalent circuitmodel and combined model are utilized to characterize thedynamic behavior of the lithium-ion battery. The methodsfor model parameter identification is also discussed. Withequivalent circuit model, the MPSO outperformed RLS formodel parameter identification in terms of modeling accu-racy. However, for the considered battery models no oneoutperformed the other at all the test temperatures.

The experiment data on a commercial lithium-ion batterycell (LiNMC) is utilized to evaluate the performance of dif-ferent methods in SOC estimation. Computational resultsillustrate that UKF algorithm generally outperforms EKFalgorithm in terms of SOC estimation accuracy and conver-gence rate with unknow initial SOC. However, the advantagesof UKF over EKF are more significant with the equivalentcircuit model than with the combined mode. Both UKF algo-rithm and EKF algorithm show strong robustness againstcurrent noise regardless of the battery model. More impor-tantly, it’s of great importance to update the parameters atdifferent temperatures for both EKF and UKF to improve theestimation accuracy. It also should be noted that the accuracyof combined model is greatly reduced at high temperatureleading to inaccurate SOC estimation with updates of modelparameters.

REFERENCES[1] Q. Wang, B. Jiang, B. Li, and Y. Y. Yan, ‘‘A critical review of thermal

management models and solutions of lithium-ion batteries for the devel-opment of pure electric vehicles,’’ Renew. Sustain. Energy Rev., vol. 64,pp. 106–128, Oct. 2016.

[2] M. A. Hannan, M. S. H. Lipu, A. Hussain, and A. Mohamed, ‘‘A review oflithium-ion battery state of charge estimation and management system inelectric vehicle applications: Challenges and recommendations,’’ Renew.Sustain. Energy Rev., vol. 78, pp. 834–854, Oct. 2017.

[3] F. C. Sun, R. Xiong, and H. W. He, ‘‘A systematic state-of-charge estima-tion framework for multi-cell battery pack in electric vehicles using biascorrection technique,’’ Appl. Energy, vol. 162, pp. 1399–1409, Jan. 2016.

[4] C. Zou, X. Hu, Z.Wei, T.Wik, and B. Egardt, ‘‘Electrochemical estimationand control for lithium-ion battery health-aware fast charging,’’ IEEETrans. Ind. Electron., vol. 65, no. 8, pp. 6635–6645, Aug. 2018.

[5] G. Dong, J. Wei, C. Zhang, and Z. Chen, ‘‘Online state of charge esti-mation and open circuit voltage hysteresis modeling of LiFePO4 batteryusing invariant imbedding method,’’ Appl. Energy, vol. 162, pp. 163–171,Jan. 2016.

[6] Y. Xing, W. He, M. Pecht, and K. L. Tsui, ‘‘State of charge estimationof lithium-ion batteries using the open-circuit voltage at various ambienttemperatures,’’ Appl. Energy, vol. 113, pp. 106–115, Jan. 2014.

[7] F. Yang, Y. Xing, D. Wang, and K.-L. Tsui, ‘‘A comparative study ofthree model-based algorithms for estimating state-of-charge of lithium-ionbatteries under a new combined dynamic loading profile,’’ Appl. Energy,vol. 164, pp. 387–399, Feb. 2016.

[8] J. H. Aylor, A. Thieme, and B. W. Johnso, ‘‘A battery state-of-chargeindicator for electric wheelchairs,’’ IEEE Trans. Ind. Electron., vol. 39,no. 5, pp. 398–409, Oct. 1992.

[9] J. C. A. Antón, P. J. G. Nieto, C. B. Viejo, and J. A. V. Vilán, ‘‘Supportvector machines used to estimate the battery state of charge,’’ IEEE Trans.Power Electron., vol. 28, no. 12, pp. 5919–5926, Dec. 2013.

[10] B. Xiong, J. Zhao, Y. Su, Z.Wei, andM. Skyllas-Kazacos, ‘‘State of chargeestimation of vanadium redox flow battery based on sliding mode observerand dynamicmodel including capacity fading factor,’’ IEEETrans. Sustain.Energy, vol. 8, no. 4, pp. 1658–1667, Oct. 2017.

[11] B. Xia, C. Chen, Y. Tian, W. Sun, Z. Xu, and W. Zheng, ‘‘A novel methodfor state of charge estimation of lithium-ion batteries using a nonlinearobserver,’’ J. Power Sources, vol. 270, pp. 359–366, Dec. 2014.

[12] K. S. Ng, C.-S. Moo, Y.-P. Chen, and Y.-C. Hsieh, ‘‘Enhanced coulombcounting method for estimating state-of-charge and state-of-health oflithium-ion batteries,’’ Appl. Energy, vol. 86, no. 9, pp. 1506–1511,Sep. 2009.

[13] K.-S. Ng, C.-S. Moo, Y.-P. Chen, and Y.-C. Hsieh, ‘‘State-of-chargeestimation for lead-acid batteries based on dynamic open-circuit volt-age,’’ in Proc. IEEE 2nd Int. Power Energy Conf. (PECon), Dec. 2008,pp. 972–976.

[14] H. Chaoui, C. C. Ibe-Ekeocha, andH. Gualous, ‘‘Aging prediction and stateof charge estimation of a LiFePO4 battery using input time-delayed neuralnetworks,’’ Elect. Power Syst. Res., vol. 146, pp. 189–197, May 2017.

[15] P. Singh, R. Vinjamuri, X. Wang, and D. Reisner, ‘‘Design and implemen-tation of a fuzzy logic-based state-of-charge meter for Li-ion batteries usedin portable defibrillators,’’ J. Power Sources, vol. 162, no. 2, pp. 829–836,2006.

[16] I. H. Li, W. Y. Wang, S. F. Su, and Y. S. Lee, ‘‘A merged fuzzy neuralnetwork and its applications in battery state-of-charge estimation,’’ IEEETrans. Energy Convers., vol. 22, no. 3, pp. 697–708, Sep. 2007.

[17] X. Hu, S. E. Li, and Y. Yang, ‘‘Advanced machine learning approachfor lithium-ion battery state estimation in electric vehicles,’’ IEEE Trans.Transport. Electrific., vol. 2, no. 2, pp. 140–149, Jun. 2016.

[18] G. O. Sahinoglu, M. Pajovic, Z. Sahinoglu, Y. Wang, P. Orlik, andT. Wada, ‘‘Battery state-of-charge estimation based on regular/recurrentGaussian process regression,’’ IEEE Trans. Ind. Electron., vol. 65, no. 5,pp. 4311–4321, May 2018.

[19] C. Zou, X. Hu, Z. Wei, and X. Tang, ‘‘Electrothermal dynamics-consciouslithium-ion battery cell-level charging management via state-monitoredpredictive control,’’ Energy, vol. 141, pp. 250–259, Dec. 2017.

[20] C. Zou, X. Hu, S. Dey, L. Zhang, and X. Tang, ‘‘Nonlinear fractional-order estimator with guaranteed robustness and stability for lithium-ionbatteries,’’ IEEE Trans. Ind. Electron., vol. 65, no. 7, pp. 5951–5961,Jul. 2018.

[21] C. Zhang, W. Allafi, Q. Dinh, P. Ascencio, and J. Marco, ‘‘Online esti-mation of battery equivalent circuit model parameters and state of chargeusing decoupled least squares technique,’’ Energy, vol. 142, pp. 678–688,Jan. 2018.

[22] P. Malysz, J. Ye, R. Gu, H. Yang, and A. Emadi, ‘‘Battery state-of-powerpeak current calculation and verification using an asymmetric parameterequivalent circuit model,’’ IEEE Trans. Veh. Technol., vol. 65, no. 6,pp. 4512–4522, Jun. 2016.

[23] J. H. Meng, G. Z. Luo, and F. Gao, ‘‘Lithium polymer battery state-of-charge estimation based on adaptive unscented Kalman filter andsupport vector machine,’’ IEEE Trans. Power Electron., vol. 31, no. 3,pp. 2226–2238, Mar. 2016.

[24] X. Chen, W. Shen, M. Dai, Z. Cao, J. Jin, and A. Kapoor, ‘‘Robust adaptivesliding-mode observer using RBF neural network for lithium-ion batterystate of charge estimation in electric vehicles,’’ IEEE Trans. Veh. Technol.,vol. 65, no. 4, pp. 1936–1947, Apr. 2016.

[25] H. Pan, Z. Lü, W. Lin, J. Li, and L. Chen, ‘‘State of charge estimation oflithium-ion batteries using a grey extended Kalman filter and a novel open-circuit voltage model,’’ Energy, vol. 138, pp. 764–775, Nov. 2017.

[26] G. Dong, J. Wei, and Z. Chen, ‘‘Kalman filter for onboard state of chargeestimation and peak power capability analysis of lithium-ion batteries,’’J. Power Sources, vol. 328, pp. 615–626, Oct. 2016.

27626 VOLUME 6, 2018


[27] Q. Zhu, X. Hu, N. Xiong, and G.-D. Hu, ‘‘H∞-based nonlinear observerdesign for state of charge estimation of lithium-ion battery with polynomialparameters,’’ IEEE Trans. Veh. Technol., vol. 66, no. 12, pp. 10853–10865,Dec. 2017.

[28] C.-Z. Liu et al., ‘‘A state of charge estimation method based on H∞observer for switched systems of lithium-ion nickel–manganese–cobaltbatteries,’’ IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 8128–8137,Oct. 2017.

[29] B. J. Wang, Z. Liu, S. Li, S. Moura, and H. Peng, ‘‘State-of-chargeestimation for lithium-ion batteries based on a nonlinear fractional model,’’IEEE Trans. Control Syst. Technol., vol. 25, no. 1, pp. 3–11, Jan. 2017.

[30] X. Hu, F. Sun, and Y. Zou, ‘‘Estimation of state of charge of a lithium-ionbattery pack for electric vehicles using an adaptive Luenberger observer,’’Energies, vol. 4, no. 9, pp. 1586–1603, 2011.

[31] G. L. Plett, ‘‘Extended Kalman filtering for battery management systemsof LiPB-based HEV battery packs: Part 3. State and parameter estimation,’’J. Power Sources, vol. 134, no. 2, pp. 277–292, 2004.

[32] G. L. Plett, ‘‘Sigma-point Kalman filtering for battery management sys-tems of LiPB-based HEV battery packs: Part 2: Simultaneous state andparameter estimation,’’ J. Power Sources, vol. 161, no. 2, pp. 1369–1384,2006.

[33] S. Sepasi, R. Ghorbani, and B. Y. Liaw, ‘‘A novel on-board state-of-charge estimation method for aged Li-ion batteries based on model adap-tive extended Kalman filter,’’ J. Power Sources, vol. 245, pp. 337–344,Jan. 2014.

[34] S. Peng, C. Chen, H. Shi, and Z. Yao, ‘‘State of charge estimation of batteryenergy storage systems based on adaptive unscented Kalman filter with anoise statistics estimator,’’ IEEE Access, vol. 5, pp. 13202–13212, 2017.

[35] H. Aung, K. S. Low, and S. T. Goh, ‘‘State-of-charge estimation oflithium-ion battery using square root spherical unscented Kalman filter(Sqrt-UKFST) in nanosatellite,’’ IEEE Trans. Power Electron., vol. 30,no. 9, pp. 4774–4783, Sep. 2015.

[36] Y. Zou, X. Hu, H. Ma, and S. E. Li, ‘‘Combined state of charge and stateof health estimation over lithium-ion battery cell cycle lifespan for electricvehicles,’’ J. Power Sources, vol. 273, pp. 793–803, Jan. 2015.

[37] C. Zou, C. Manzie, D. Nešić, and A. G. Kallapur, ‘‘Multi-time-scaleobserver design for state-of-charge and state-of-health of a lithium-ionbattery,’’ J. Power Sources, vol. 335, pp. 121–130, Dec. 2016.

[38] X. Hu, S. Li, and H. Peng, ‘‘A comparative study of equivalent circuitmodels for Li-ion batteries,’’ J. Power Sources, vol. 198, pp. 359–367,Jan. 2012.

[39] G. Bai, P. Wang, C. Hu, and M. Pecht, ‘‘A generic model-free approachfor lithium-ion battery health management,’’ Appl. Energy, vol. 135,pp. 247–260, Dec. 2014.

[40] Z. Wei, K. Tseng, N. Wai, T. Lim, and M. Skyllas-Kazacos, ‘‘Adaptiveestimation of state of charge and capacity with online identified batterymodel for vanadium redox flow battery,’’ J. Power Sources, vol. 332,pp. 389–398, Nov. 2016.

CHAO HUANG (S’16–M’17) received the B.Eng.degree in electrical engineering and automationfrom the Harbin Institute of Technology, China,in 2011, the M.S. degree in intelligent transportsystem from theUniversity of Technology of Com-piègne, France, in 2013, and the Ph.D. degreein systems engineering and engineering manage-ment from the City University of Hong Kong,Hong Kong, in 2017.

He was appointed as a Post-Doctoral Fellowwith the Department of Systems Engineering and Engineering Management,City University of Hong Kong. He is currently a Lecturer with the Schoolof Automation, Guangdong University of Technology. His research interestsinclude photovoltaics, lithium-ion battery, machine learning, and computa-tional intelligence.

ZHENHUA WANG received the Ph.D. degreein engineering from China AgriculturalUniversity, China, in 2014. He conducted thePostdoctoral research in soil hydrology with Penn-sylvania State University, Pennsylvania, USA,in 2016. He became a Ph.D. Supervisor of agri-cultural soil and water engineering in 2015.

He is currently the Deputy Dean of the Collegeof Water Conservancy and Architectural Engi-neering, Shihezi University, and also the Deputy

Director of the Key Laboratory of Modern Water-Saving Irrigation Corps.His research interests include the theory and technology of water-savingirrigation in arid area, and the theory and technology of drip irrigation waterand salt control.

ZIHAN ZHAO is currently pursuing the bache-lor’s degree in surveying and mapping engineer-ing with the School of Geosciences and Survey-ing Engineering, China University of Mining andTechnology, Beijing, China.

LONG WANG (S’16–M’17) received the M.Sc.degree (Hons.) in computer science from Uni-versity College London, London, U.K., in 2014,and the Ph.D. degree in systems engineering andengineering management from the City Universityof Hong Kong, Hong Kong, in 2017.

He is currently an Associate Professor withthe Department of Computer Science andTechnology, University of Science and Technol-ogy Beijing, Beijing, China. His research interests

include machine learning, computational intelligence, and computer vision.He was an awardee of the Hong Kong Ph.D. Fellowship in 2014. He servesas an Associate Editor for the IEEE ACCESS.

CHUN SING LAI received the B.Eng. degree(Hons.) in electrical and electronic engineeringfrom Brunel University London, U.K., in 2013.He is currently pursuing the D.Phil. degree inengineering science with the University of Oxford,U.K. He is currently a Visiting Research Fellowwith the School of Automation, Guangdong Uni-versity of Technology, China, and also a ResearchFellow with the School of Civil Engineering, Uni-versity of Leeds. He organized the IEEE SMC

Workshop on Smart Grid and Smart City in SMC 2017, Canada. His currentinterests are in data analytics and energy economics for renewable energyand storage systems.

VOLUME 6, 2018 27627


DONG WANG received the Ph.D. degree with theCity University of Hong Kong (CityU) in 2015.He was appointed as a Research Associate,a Senior Research Assistant, and a Post-DoctoralFellow with CityU from 2015 to 2018. He iscurrently a Research Fellow with CityU. He wasa recipient of the Hong Kong Ph.D. Fellowshipin 2012.

His research interests include statistical mod-eling, prognostics and health management, con-

dition monitoring, fault diagnosis, signal processing, data mining,and nondestructive testing. His researchworks appear inMechanical Systems

and Signal Processing, the Journal of Sound and Vibration, ASMETransactions on the Journal of Vibration and Acoustics, the IEEETRANSACTIONSONRELIABILITY, the IEEE TRANSACTIONSON INSTRUMENTATIONAND

MEASUREMENT, the Journal of Power Sources, andMeasurement Science andTechnology.

Dr. Wang was invited to be a Reviewer for 50 SCI-indexed journals.In recognition to his contributions to Elsevier and IEEE journals, he wasawarded Outstanding Reviewer Status 13 times. He was a lead guest edi-tor/guest editor for several SCI-indexed journals and a referee for theFONDECYT, Chile. He is an Associate Editor for the Journal of LowFrequency Noise Vibration and Active Control and an Associate Editor forthe IEEE ACCESS.

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Robustness Evaluation of Extended and Unscented Kalman ...eprints.whiterose.ac.uk/133918/1/08355786.pdf˝lter (EKF) and unscented Kalman ˝lter (UKF) for state of charge (SOC) estimation