A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter

Applied Energy 190 (2017) 740–748

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter q Min Ye a,⇑, Hui Guo a, Binggang Cao b a b

National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an 710064, China Electric Vehicle and System Control Institute, Xi’an Jiaotong University, Xi’an 710049, China

h i g h l i g h t s
Propose an improved adaptive particle swarm filter method.
The SoC estimation method for the battery based on the adaptive particle swarm filter is presented.
The algorithm is validated by the case study of different aged extent batteries.
The effectiveness and applicability of the algorithm are validated by the LiPB batteries.

a r t i c l e

i n f o

Article history: Received 18 October 2016 Received in revised form 8 December 2016 Accepted 27 December 2016

Keywords: Electric vehicles Lithium-ion battery Particle swarm filter Improved adaptive particle filter State of charge

a b s t r a c t Obtaining accurate parameters, state of charge (SoC) and capacity of a lithium-ion battery is crucial for a battery management system, and establishing a battery model online is complex. In addition, the errors and perturbations of the battery model dramatically increase throughout the battery lifetime, making it more challenging to model the battery online. To overcome these difficulties, this paper provides three contributions: (1) To improve the robustness of the adaptive particle filter algorithm, an error analysis method is added to the traditional adaptive particle swarm algorithm. (2) An online adaptive SoC estimator based on the improved adaptive particle filter is presented; this estimator can eliminate the estimation error due to battery degradation and initial SoC errors. (3) The effectiveness of the proposed method is verified using various initial states of lithium nickel manganese cobalt oxide (NMC) cells and lithium-ion polymer (LiPB) batteries. The experimental analysis shows that the maximum errors are less than 1% for both the voltage and SoC estimations and that the convergence time of the SoC estimation decreased to 120 s. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Using a battery management system (BMS) is critical for electric vehicles [1,2], especially those with a lithium-ion battery (LIB). Based on the foundation of BMS control topology, accurate model estimations including the parameters, the capacity and the state of charge (SoC) of the battery are important for the safety, power and economic performance of the vehicle. Currently, most BMSs for electric vehicle use the static equivalent circuit model to estimate the battery condition [3]. For example, in the Rin and RC [4], Thevenin [5], Partnership for a New Generation of Vehicles (PNGV) [6] and nonlinear equivalent circuit models [7], the battery parameters are tested using the offline hybrid pulse power characterization q The short version of the paper was presented at REM 2016 on April 19–21, Maldives. This paper is a substantial extension of the short version. ⇑ Corresponding author. E-mail address: [email protected] (M. Ye).

http://dx.doi.org/10.1016/j.apenergy.2016.12.133 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

(HPPC) experiments. However, the model structure and the model parameters will vary largely for the entire BMS lifetime. As a result, these models cannot reflect the effects of the working current, SoC, state of health (SoH), temperature or the self-discharge on the internal characteristics of the battery [8]. Another drawback of this modeling method is that the model parameters are identified using offline data. Therefore, the battery parameters cannot dynamically change over the lifetime of the battery. The variances in the battery model parameters that follow its degradation and varying operation conditions are neglected. Thus, the reliability and applicability of these models should be discussed further. LIBs have become the dominant battery type for electric vehicles due to their many merits. Compared with other types of batteries, LIBs have outstanding energy density, charging velocity, robust health conditions and use cycles. SoC is a crucial index for LIBs but is difficult to measure directly due to the electrochemical process that occurs during working operation. Considerable effort has been expended to investigate the estimation methods, and

M. Ye et al. / Applied Energy 190 (2017) 740–748

the advantages of each are reviewed in [9–12]. The ampere-hour (A h) integral algorithm is a very precise and low-cost approach if the initial SoC is accurate and if the current measurement electronics have high fidelity. However, the strong dependence on model corrections and the trade-off between model complexity and estimation accuracy are concerning. In addition, some intelligent algorithms [13,14] have been used to estimate the SoC. For example, the sliding mode method [3], proportional-integral (PI) method [15], and Kalman filter method can somewhat reduce the error of SoC estimation. Although these models can achieve desirable results, the necessary a priori knowledge is their primary weakness. The model error of the battery defines the accuracy of the SoC estimation. The system error, which is caused by the variation in the internal parameters of the battery, is not considered. A novel online method that can estimate the SoC and can dynamically and adaptively follow the parameter variation of the battery was then proposed. To overcome the abovementioned shortcomings, a previous study used the uncertainty quantification method to innovatively solve the uncertainty modeling problems of a dynamic battery system [16]. With an accurate battery pack model and an adaptive filter based on the battery SoC estimator, the SoC of the battery group can be accurately estimated. Then, a novel battery temperature field forecasting method was proposed for an online LIB, including the electrochemical impedance and the internal battery characteristics [1]. This novel method is a key contribution to excellence in BMS energy research. Furthermore, the authors of [17] proposed a novel systematic state-of-charge estimation method that considers both the open circuit voltage (OCV) and the SoC of the batteries. This method can be used to not only predict the state of a single battery cell but also accurately model the battery pack; furthermore, this method can be used to balance the energy flow of the hybrid energy system (HES) of an electric vehicle in order to optimize the energy efficiency of the HES. The above cases [16,1,17] have made some progress in the SoC estimation for a single LIB in a pack of batteries. However, the inconsistency of the battery is neglected. Thus, the above cases are can handle flat noise with a zero average value, but their weakness is attenuating disturbance in the uncertainty of the battery model and parameters. This paper presents an improved adaptive particle swarm filter (improved-APF) that can achieve better convergence performance and robustness under outer/inter disturbance than the abovementioned methods. Not only can the estimation performance be guaranteed but lower computation cost can also be realized; in particular, the improved-APF method has less hardware requirements. 1.1. Contributions of the paper A data-driven adaptive SoC estimator was built by combining the particle swarm filter and the adaptive estimation method. The effectiveness and feasibility of this method have been verified using different battery loading profiles. The applicability of the algorithm has been further verified using different types of batteries, particularly lithium-ion polymer batteries (LiPB). In the proposed SoC estimator, the error analysis method is added into the adaptive particle filter method, and the improved-APF is embedded. The improvedAPF algorithm can improve the robustness and the convergence speed by adaptively updating the model parameters. The proposed method can deal with the model variation with both a random time series and random white noise covariance. 1.2. Organization of the paper The outline of the paper is as follows: The introduction is presented in Section 1. Section 2 describes the fundamental battery

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model and some intelligent estimation methods. In Section 3, the particle swarm optimization (PSO) based on the online parameter identification method is presented. Then, an error analysis method for the state estimation of the batteries is proposed. In Section 4, a data-driven adaptive SoC estimator using the APF algorithm is presented. To verify the proposed approach, 3.6 V/2 A h lithium-ion polymer battery (LiPB) cells with different ages are used to execute the characteristic test; this experiment is described in Section 5. Section 6 verifies the proposed adaptive SoC estimator using the Urban Dynamometer Driving Schedule (UDDS) test and DTS test on a LiPB battery and discusses the analysis in detail. Section 7 provides conclusions and suggestions. 2. Lithium-ion battery model Section 2.1 presents the lumped parameter battery model in detail, which allows for the optimization of the proposed APF algorithm. Section 2.2 elaborates each step of the PSO algorithm. 2.1. Lumped parameter battery model To model the dynamic characteristics of the battery under the variable working mode, the Thevenin model is adopted in this paper, as shown in Eqs. (1) and (2). The equivalent electrical circuit of a battery can be simplified as a resistor R0 and a capacitor C0 in parallel; then, the RC network is connected to the OCV in series. However, the battery parameters will change with time and working conditions, so the diffusion resistance Rp and diffusion capacitance Cp are used here to dynamically respond to the battery characteristics.

U t ¼ U ocv ðzÞ  IR0  U d

ð1Þ

U d ¼ expðDt=ðRp C p ÞÞU d þ Rp ð1  expðDt=ðRp C p ÞÞÞI

ð2Þ

where Ut represents the terminal voltage of the battery that changes with time, as shown in Eq. (1), Uocv is the diffusion voltage, and Ud is the resistance dependency. Furthermore, the diffusion voltage Ud can be represented by an exponential function. According to the authors of [17], Uocv can be induced from the electrochemical equation of the battery and can be written as

OCV ¼ K 0 þ K 1 z þ K 2 z2 þ K 3 z3 þ K 4 =z þ K 5 logðzÞ þ K 6 logð1  zÞ ð3Þ where Ki (i = 0, 1, . . . , 6) are seven parameters that can accurately depict the OCV of the battery under different battery SoCs. For different types of battery, these parameters can be polyfitted by the current and voltage of the experimental results. 2.2. Parameter identification method for the battery model Eqs. (1) and (2) of the battery state are in the continuous form. To identify the SoC of the battery, the algorithm must be implemented in a digital processor. The state equations should be discretized by linear transformation, as shown in Eqs. (4) and (5).

U d;kþ1 ¼ expðDt=sÞU d;k þ Rp ð1  expðDt=sÞÞIk

ð4Þ

U t;k ¼ U ocv ðzk Þ  Ik R0  U d;k

ð5Þ

where Dt is the sampling time interval, which is a constant value here; the subscript k represents the sampling moment, which is an integer number; the subscript d represents the diffusion voltage and t represents the time variable. Other parameters can be indexed in Eqs. (1) and (2). Ud,k+1 denotes the terminal diffusion voltage at the sampling time interval k + 1, and s is a time constant that can be calculated from the RC circuit, s = Rp  Cp.

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The PSO algorithm is a type of evolutionary computation technology that was first proposed by Dr. Eberhart and Dr. Kennedy in 1995. The PSO is a parallel searching optimization method with origins in the food scavenging behavior of a bird flock. The algorithm can animate the bird flock to establish a simple optimization model based on intelligent populations. In the early optimization process, the searching process is disorder. Gradually, every individual becomes ordered and proceeds to the optimized solution. The PSO is similar to the simulated annealing algorithm and gene algorithm. The optimization process is started randomly; then, the solution is renewed by iterations, and the solution performance is evaluated by the fitness function. However, the PSO is simpler than the gene algorithm as there are no crossover or mutation operations during optimization. The PSO is outstanding in its simple execution, high accuracy and fast convergence velocity and has been widely used for the parameter identification of batteries [3,14–16,1,17]. In this paper, the conventional PSO fitness function is presented in Eq. (6) to estimate the SoC of the battery.

min f ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xk ðU err;i Þ2 i¼kw w

the RMSE is the variance of the normal distribution (see Eqs. (7) and (8)):

l¼

k 1 X ðU r;i  U t;i Þ w i¼kw

r ¼ min f

ð7Þ ð8Þ

where Ur,i is the observed value and Ut,i is the output value of the dynamic model. In this paper, all the errors are considered to be inside the interval when the confidence value is 95%. Ua is the normal upper quantile when a = 0.05. Therefore, we consider Eq. (9) to be the bound of the model error.

U ebound ¼ l  rU a

ð9Þ

In the state estimation process, when the model error Ue is in this bound, it is considered normal error or model-caused error. When it is outside this bound, it is considered abnormal error or error caused by the initial state.

ð6Þ 4. An improved adaptive particle filter state of charge estimator

where Uerr,i is the battery terminal voltage error at sampling time i; w can determine the length of the identification interval; and f is the cumulative error of the voltage. Here, the terminal voltage of the battery is selected using the root mean square error (RMSE).

3. An error analysis method for state estimation After the parameters are identified, we can obtain the parameter optimization results from Eq. (6). We approximately assume that the model error obeys a normal distribution, that the average of the model error is the mean of the normal distribution, and that

This section describes the process for building a data-driven adaptive SoC estimator for achieving accurate SoC estimation at different battery ages and loading profiles. Section 4.1 defines the SoC calculation; the numerical implementation of the recursive derivative computation of the data-driven adaptive SoC estimator is presented in Section 4.2. 4.1. State of charge definition This study uses the traditional definition for the battery SoC, which is the ratio between the remaining capacity and the

Table 1 The detailed calculation method of the improved-APF.  The state-space equations of the batteries: Step 1

Step 2

xk ¼ f k ðxk1 ; uk1 ; hk1 Þ þ wk yk ¼ hk ðxk ; uk ; hk Þ þ v k

The initialization process: For k = 0 (a) Set dmax, dmid and dmin as the maximum value, middle value and minimum value of the noise variance (b) Select initial particle s based on the clustering p(x0). Every particle can be represented as ^ xiþ 0 ði ¼ 1; 2; . . . NÞ ^i ¼ 1=Nði ¼ 1; 2; . . . NÞ (c) Compute the initializing weight: q The computation process: For k = 1, 2, . . . , compute the time series of the state equation: ^iþ ¼ f k ðx ; uk1 ; hk1 Þ (a) Compute the time update for the state: ^ xiþ k k1 (b) Update the measurement data: ^ik ¼ yk  hð^ xi Compute the error innovation: err ik ¼ yk  y k Þ n o P 1 2 1 N 1 i ffi exp ðerr k Þ 2R ; q  i ¼ qi  Compute and scale the weight: qi ¼ pffiffiffiffiffiffi i¼1 qi 2pR

Step 3

Step 4

Generate ^ xkiþ using the resampling method: P ^ Estimate the state: ^ xk ¼ N1 N i¼1 xkiþ ; Noise variance estimation: (a) Compute the demand value of the noise variance: P P  ec;k ¼ 1k ki¼kk jec;i j ¼ 1k ki¼kk j^ xc;i  f c;k ð^ xi1 ; ui1 ; hk1 Þj where c is one of the states in x and k is a constant such as w. (b) Forecast the noise variance for the next time step:  if ec;k > dc;k1 minð ec;k ; dc;mid Þ ^ dc;k ¼ maxðbdk1 ; dc;min Þ if ec;k 6 dc;k1 where b is the attenuation factor and dc,k is the noise variance of state c Error analysis and noise variance update: (a) Compute the error bound of the model: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P l ¼ w1 ki¼kw ðU ei Þ  0; r ¼ w1 ki¼kw ðU ei  lÞ2  min f ; e

U  Nðl; rÞ error bound ¼ ðl  rU a=2 l þ rU a=2 Þ  ðrU a=2 rU a=2 Þ where Ua/2 is the upper quantile of the standard normal distribution, a = 0.05. ^k ¼ hk ð^ xk ; uk ; hk Þ (b) Compute the estimated measurement: y ( ^c;k rUa=2 ; dc;max Þ if  ey P rU a=2 minðd n (c) Update the noise variance: dc;k ¼ ^ dc;k if  ey < rU a=2

(11)

(12) (13) (14) (15) (16)

(17)

(18)

(19)

(20) (21) (22) (23) (24)

M. Ye et al. / Applied Energy 190 (2017) 740–748

maximum capacity. Using discrete linear transformation, the SoC of a battery can be shown as in Eq. (10).

zk ¼ zk1  gi IL;k Dt=C n

ð10Þ

where zk and zk1 are the SoC at different sampling moments, the subscript k represents the sampling time, and gi is the Coulomb efficiency. The other parameters were previously defined in the equations above.

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mator based on the improved-APF is proposed for attenuating the parameter inconsistency and model perturbation. Furthermore, error analysis is added to the algorithm to provide more appropriate noise variance for increasing the robustness to offsets in the initial states and improving the convergence ability. The improved-APF algorithm is described in Table 1, and the corresponding flowchart is shown in Fig. 1.

4.3. Model-based SoC estimator

4.2. An improved adaptive particle filter Some battery parameters, such as the nominal power density and energy density, slowly change throughout the entire lifetime of the battery. However, other battery parameters, such as the SoC and OCV, change quickly. All these parameters increase both the micro-scale and macro-scale complexity of state estimation for a battery. Based on the traditional successful application of the PSO method for a nonlinear system, PSO has been successfully used for battery parameter identification [17]. However, the inconsistency of the battery and the flat noise with zero average value are neglected in the traditional PSO method. The particle filter (PF) and APF methods depend on the noise variance to achieve accurate estimation and to converge; however, the traditional PF and APF cannot adjust the noise variance very well, especially when the initial error is very large or variable. In this paper, an esti-

To accomplish the SoC estimation, Eq. (1) must be transformed to a discrete form, as shown in Eq. (25), by combining Eqs. (1)–(5).

" Dt # 8    Dt > < X ¼ U d;k ¼ f ðX ; u Þ ¼ e s U d;k1 þ ð1  e s ÞRp Ik k k k zk zk1  gi Ik Dt=C n > : Yk ¼ U t;k ¼ hðXk ; uk Þ ¼ U ocv ðzk Þ  Ik R0  U d;k

In Eq. (25), the X variables represent the state of the battery, which can be reflected by the resistance impendence, and Y is the output variable; here, the OCV of the battery is selected for Y. According to the calculation algorithm in Table 1, the detailed calculation steps are shown in Fig. 2. The four steps are online data measurement, data-driven parameter identification, adaptive PF SoC estimation and convergence judgment.

Noise variance estimation (traditional APF)

Randomly generate N particles

Compute the demand value of noise variance Noise variance Estimation of next Step

Time update for state Sate update

⎞ ⎟ +w xˆ i- = f ⎜⎛⎜ xˆ i +,u ,θ k k ⎝ k −1 k −1 k −1⎟⎠ k −1

Analysis of errors and update Noise variance Estimation of next Step Time update for state Estimated measurement computation

Error innovation Compute and scale the weight

The average error of the estimated measurement computation

Resampling step State estimation N

xˆ = ∑ wk ,i +1 xˆk ,i +1 k

ð25Þ

Noise convariance update

i =1

k=k+1

Fig. 1. The outline of the improved adaptive particle filter.

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M. Ye et al. / Applied Energy 190 (2017) 740–748


Step 4: Convergence judgment. According to the demand value of the noise covariance at the sampling time k  1, the noise variance is updated using the error analyses method, and the appropriate noise covariance can be generated to converge quickly.


Step 1: Online data measurement. During the DST profile test, the current and voltage of the charging and discharging battery are simultaneously obtained from the sensors. The collected data are stored and transmitted to the computer by a bus, and the algorithm is performed by the Matlab/Simulink software. Although the current and voltage are not used in real time to estimate the battery state, the time series are the same for the calculation process, especially for the parameter estimation.
Step 2: Parameter identification based on iteration. After the battery parameters are obtained and stored, the battery state equation can be established offline. During the modeling process of the battery, parameter iteration and identification are most important. First, the parameters are defined using the nominal battery parameter. After the sampling time, the current and voltage of the battery are transmitted to the computer by a bus. The OCV and SoC of the battery are then calculated according to the proposed algorithm, and the estimation error of the SoC can be limited to within a specified region. The sequence of the iteration process for the battery state is as follows: OCV, SoC and voltage.
Step 3: Adaptive particle swarm SoC estimator. To overcome the inconsistency of the battery with the flat noise with zero average value, the SoC estimator based on the improved-APF is proposed in this paper. The proposed method can dynamically attenuate the disturbance of the uncertainty of the battery model and parameters. When the battery parameters or voltage changes, this information is simultaneously transmitted to the model. The error between the old parameters and the new estimated parameters is calculated, and the improved-APF can dynamically adjust the error. After several iterations, the error becomes increasingly small until reaching zero. At this time, the adaptive optimization process can be stopped. The true and accurate SoC is obtained, which can be used to effectively optimize the BMS.

Stac Capacity Test

Efficiency Test

Characterisc Test (25 đ)

OCV_SoC Test

Loading profiles Test Aging Cycle Test(25 đ)

Fig. 3. Battery test process.

Table 2 Capacity values of the three NMC cells. Cells

Cell01

Cell02

Cell03

Capacity

2.045

2.097

2.113

Time update for state Sate update

(

)

i + ,u ,θ +w xˆ i - = f xˆ k k k −1 k −1 k −1 k −1

Online PSO based method for parameters identification

Noise variance estimation (traditional APF) Compute the demand value of noise variance Noise variance Estimation of next Step

Sample

Sample Measurement update for state Error innovation

Battery model +

oc v

Hybrid pules Test

Characterisc Test (40 đ)

Randomly generate N particle

Real-time measurment of battery voltage and current

Repeat 3 times

Characterisc Test (10 đ)

H

Compute and scale the weight

The error bound of Battery model computation Estimated measurement computation

Resampling step SoC estimation

Estimated voltage updated

Analysis of errors and update

xˆ = k

N

1 ∑ xˆ i+1 N i =1 k

The average error of the estimated measurement computation Noise variance update

k=k+1 Onboard data measurement

PSO based parameter identification Fig. 2. The data-driven adaptive SoC estimation method.

Improved APF SoC estimater

745

M. Ye et al. / Applied Energy 190 (2017) 740–748 Table 3 The optimal OCV parameters. Parameters

K0

K1

K2

K3

K4

K5

K6

Cell01 Cell02 Cell03

10.6205 11.1220 10.5783

15.3250 16.4477 15.1172

13.2636 14.2546 12.9449

4.7734 5.1719 4.6220

0.2171 0.2366 0.2253

3.3655 3.6227 3.3935

0.0127 0.0143 0.0123

Lithium nickel manganese cobalt oxide (NMC) cells are selected to verify the effectiveness of the proposed approach. Section 5.1 presents the organization of the experiments and the outline of the test equipment; then, the test schedule is presented in Section 5.2.

of the battery is tested three times to reduce the error. After the static capacity test is complete, the efficiency test, the hybrid pulse test, the OCV-SoC and DST loading profile tests are conducted, and all the current, voltage and SoC data are obtained by the test equipment. The charging current is selected as 0.1 C for the NMC cells,

Voltage error (V)

5. Dataset of lithium-ion battery cells

5.1. Experimental platform

0.08 0.03 0 -0.03 0

20

40

(a)

Cell03

Nominal capacity (A h) Actual capacity (A h) Rated voltage (V) Cutoff voltage (V)

2.0 2.045 3.6 4.1/3.0

2.0 2.097 3.6 4.1/3.0

2.0 2.113 3.6 4.1/3.0

40

0.4

50

100

150

Time(min)

200

250

120

140

SoC error (%)

0.1 0.05 0.01 0 -0.00 -0.05 0

(c)

20

40

60

80

100

120

140

Time(min)

Fig. 5. The estimation results of the voltage and SoC for NMC cell01 under the DST loading profiles: (a) the voltage error; (b) the SoC; (c) the SoC error.

6

4

3.5

4 2 0 -2

3 0

100

Improved-APF APF

0.15

0.2 0

80

0.2

Current (A)

Voltage (V)

SoC (%)

0.6

60

Time(min)

1 0.8

140

0.2

Table 4 The main specifications of the three NMC cells. Cell02

120

0.4

The battery experiments are presented in Fig. 3. First, the batteries are tested at a temperature of 10 °C; then, the surrounding temperature is increased to 25 °C and then further increased to 40 °C. Finally, the temperature is decreased to 25 °C. The temperature is controlled by a constant temperature battery experimental chamber. At every given temperature condition, the static capacity

Cell01

100

0.6

(b)

Cells

80

Reference Improved-APF APF

20

5.2. Battery test

60

Time(min) 0.8

SoC (%)

Experiments are conducted to test the validity and effectiveness of the proposed improved-APF. To simulate the actual running condition of the battery, an experimental platform is established that considers different initial SoCs and running temperatures for validation. An Arbin BT2000 is used to simulate two different battery running styles: the UDDS and the DTS. Voltage and current sensors are integrated into the equipment and have measurement errors that are limited to ±0.05%. The test region for the current sensor is [100 A 100 A]; the test region for the voltage sensor is [0 V 5 V]. The equipment can transmit data to a computer or controller using a TCP/IP bus; the transmission velocity is sufficiently high for the software to estimate the battery state. To simulate temperature variations, a constant temperature control unit from the Landian Company is selected. The unit can contain at least ten cells in a single test, and the temperature can be controlled within the range of 55 °C to 85 °C. Here, only three temperature conditions are selected: 10 °C, 25 °C and 40 °C. Two different battery types are tested: the NMC cell and the LiPB cell.

Improved-APF APF

0.12

50

100

150

200

250

50

Time(min) Fig. 4. The experimental current and voltage and calculated SoC profiles of the NMC cells.

100

150

Time(min)

200

250

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M. Ye et al. / Applied Energy 190 (2017) 740–748

which is a nominal value of 1 A. In every aging cycle, the battery is charged or discharged until reaching the maximum or minimum voltage. Here, we select the datasheets for three different health states of NMC cells from the experimental data, and the capacity values of these three NMC cells are listed in Table 2. The OCV curves under different available capacities and SoCs are plotted in Fig. 6. The corresponding polyfitted parameters of Eq. (17) are shown in Table 3, which represents the optimal state of the battery used to calculate the OCV.

6.1.1. New cell The new cell from the factory is tested first using the DST loading profile. Constant current and power are used to impulse the battery to determine the battery characteristics. Then, different ages of NMC cells are tested; the age conditions of the different NMC cells are presented in Table 4. The actual capacity and nominal capacity are tested first; then, the estimation results are compared with the measured value. The maximum and minimum limited voltages are 4.1/3.0 V for all three types of cells. The amplitude curves of the current, voltage and SoC of the running style are shown in Fig. 4.

6. Validation and discussion The proposed adaptive SoC estimator is validated using two battery types in the UDDS test and DST test. Sections 6.1 and 6.2 verify the proposed SoC estimator with both loading profiles for NCM and LiPB battery cells, respectively. 6.1. NCM battery cell

Improved-APF

0.12 0.08

0.02 0 -0.02 0

20

40

(a)

60

80

100

120

0.2

(b)

80

100

120

Time(min)

40

60

80

100

0.6

0.4

0

20

40

60

80

100

SoC error (%)

0.02 0 -0.02 20

40

60

80

100

120

120

140

Time(min) 0.2

0.1

0

140

Reference Improved-APF APF

Improved-APF APF

APF

0.15

120

Time(min)

(b) Improved-APF

SoC error (%)

20

0.2

140

0.2

(c)

-0.02

0.8

0.4

60

0.02

0

SoC (%)

0.6

40

0.06

(a) Reference Improved-APF APF

20

APF

0.1

140

Time(min) 0.8

SoC (%)

Improved-APF

APF

Voltage error (V)

Voltage error (V)

In this section, two battery conditions are tested: a fresh battery cell that originates from the factory and one that is not new. All of the nominal parameters are defined in Table 4. The uncertainty of the battery should be considered in the SoC estimation. Both battery types can be used to test the validity and effectiveness of our proposed APF algorithm.

6.1.2. Considering the uncertainties due to aging To study the uncertain performance of the improved-APF algorithm due to the aging of the cells, three cells of different ages are used to verify the improved-APF algorithm; the specifications of these three cells are listed in Table 4. In this paper, the SoC is selected within the interval of 80% to 20%, and the initial SoC is 60%. The NMC experiments are conducted using the DST loading profiles. Fig. 5 shows the estimated voltage and SoC for Cell01; Fig. 6 shows those for Cell02; and Fig. 7 shows those for Cell03. The statistical analysis of the voltage estimation error after the system is stable is shown in Table 5. This table shows that the absolute value of the peak voltage error for each case using the improved-APF method is no greater than that for the case using the traditional APF method. Moreover, for the three cases, the volt-

Fig. 6. The estimation results of the voltage and SoC for NMC cell02 under the DST loading profiles: (a) the voltage error; (b) the SoC; (c) the SoC error.

0.1

0.01 -0.01 -0.05

140

Time(min)

0.15

(c)

0

20

40

60

80

100

120

140

Time(min)

Fig. 7. The estimation results of the voltage and SoC for NMC cell03 under the DST loading profiles: (a) the voltage error; (b) the SoC; (c) the SoC error.

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M. Ye et al. / Applied Energy 190 (2017) 740–748 Table 5 The analysis of the voltage estimation error. Cell

Algorithm

Convergence time (s)

Maximum (V)

Mean (V)

Standard deviation (V)

Cell01

APF Improved-APF

2224 239

0.025 0.025

0.0194 0.0069

0.0295 0.0167

Cell02

APF Improved-APF

1685 178

0.026 0.021

0.0131 0.0046

0.0249 0.0138

Cell03

APF Improved-APF

589 29

0.019 0.017

0.0035 0.0020

0.0067 0.0044

Table 6 The analysis of the SoC estimation error. Cell

Algorithm

Convergence time (s)

Maximum (%)

Mean (%)

Standard deviation (%)

Cell01

APF Improved-APF

3062 31

1.10 1.13

0.37 0.35

0.35 0.36

Cell02

APF Improved-APF

1689 170

1.49 1.25

0.77 0.46

0.72 0.67

Cell03

APF Improved-APF

1056 56

0.77 0.72

0.35 0.0020

0.59 0.0044

age estimation error is smaller for the improved-APF method than for the traditional APF method. Most important, the convergence time for the improved-APF is much shorter than for the traditional APF. The statistical analysis of the SoC estimation error after the system is stable is shown in Table 6. This table shows that the conver-

Table 7 The nominal parameters of the LiPB battery. Voltage (V)

Capacity (A h)

Limited maximum voltage (V)

Limited minimum voltage (V)

3.3

20

3.4

2.0

40

1

20 10

0.8

3

SoC (%)

Voltage (V)

Current (A)

30

2.5

0

0.6 0.4 0.2

2

-10 50

100

150

200

50

250

100

Time (min)

150

200

0

250

50

100

Time (min)

150

200

250

Time (min)

Fig. 8. Current, voltage and calculated SoC profiles of the LiPB cell for the UDDS test: (a) the current; (b) the voltage; (c) the SoC.

0.3

0.8

Reference improved-APF APF

SoC(%)

0.6

SoC error (%)

0.7

0.5 0.4 0.3

0.2 0.15 0.1 0.05

0.2

0

0.1

-0.05

0

50

(a)

100

150

improved-APF APF

0.25

200

0

(b)

Time(min)

50

100

150

200

Time(min)

Fig. 9. The estimation results of the LiPB cell under the UDDS loading profiles: (a) the SoC; (b) the SoC error.

Table 8 The statistical analysis of the SoC estimation error after the system is stable. Algorithm

Convergence time (s)

Maximum (V)

Mean (V)

Standard deviation (V)

APF Improved-APF

657 174

0.77 0.7

0.29 0.25

0.55 0.49

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M. Ye et al. / Applied Energy 190 (2017) 740–748

gence time for the improved-APF is much shorter than for the traditional APF and that the other indexes are similar for the two methods. 6.2. LiPB battery cell To study the uncertain performance of the improved-APF algorithm for different battery types, the test data for a LiPB battery cell are used to verify the algorithm. The main specifications for the LiPB cell are shown in Table 7. The UDDS loading profile was used to test the LiPB battery cell, and the experimental results are shown in Fig. 8. The experimental conditions for the battery include an initial SoC of 100% and constant charging/discharging currents and voltages. The currents, voltages and estimated SoCs are presented in Fig. 8. Fig. 9 plots the estimated SoC with an initial SoC error of 60%, and Table 8 lists the statistical analysis of the stable SoC estimation. Fig. 9 and Table 8 show that the absolute value of the SoC estimation error using the improved-APF is less than 1% after the system is stable and that this algorithm takes 120 s to converge to the accurate value. Although the SoC estimation error of the traditional APF is also less than 1%, it requires more than 600 s to converge. Because the initial SoC error is so large, the APF algorithm cannot generate appropriate noise variance to converge quickly; therefore, the improved-APF shows a clear advantage over the traditional APF. 7. Conclusions To improve the robustness and speed of convergence for SoC estimation, an improved-APF approach is presented in this study. Compared with traditional APF, the improved-APF uses an additional error analysis procedure to determine the origins of the SoC estimation errors. After the parameters are identified, this procedure calculates the error bound of the model and then compares the error bound with the estimated terminal voltage error that the estimated states feed back to the model; finally, the SoC estimation errors can be distinguished as coming from model error or initial SoC error. Thus, this algorithm can not only guarantee robustness but also increase the convergence speed to meet the demands of SoC estimation in BMS. To verify and evaluate the proposed adaptive SoC estimator, three different initial states of NMC cells are used to conduct a systematic system. The results show that the absolute value of the SoC estimation error using the improvedAPF is less than 1% after the system is stable and that this algorithm takes 120 s to converge to the accurate value. The experiments indicate that the proposed approach not only improves the robustness and the convergence speed for SoC estimation but also achieves somewhat more accurate SoC estimates. Therefore, the proposed method has good robustness and reliability for different battery ages and different battery types, and it can be widely used in the BMSs of online electric vehicles.

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