Peak power prediction for series-connected LiNCM battery pack based on representative cells

Journal of Cleaner Production 230 (2019) 1061e1073

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Peak power prediction for series-connected LiNCM battery pack based on representative cells Zhongkai Zhou a, Yongzhe Kang a, Yunlong Shang a, b, Naxin Cui a, Chenghui Zhang a, Bin Duan a, * a b

Shandong University, Jinan, China San Diego State University, San Diego, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 January 2019 Received in revised form 4 May 2019 Accepted 13 May 2019 Available online 16 May 2019

Accurate power prediction for a battery pack is of great importance for efficient and safe operation of electric vehicles. However, a battery pack typically consists of dozens of cells connected in series, and how to accurately predict its peak power in practical applications has always been a challenging issue. This paper proposes a low-complexity peak power prediction method for a series-connected battery pack, where the peak power of battery pack is predicted depending only on representative cells. Firstly, considering state of charge and voltage limits for power prediction, the representative cells are selected by using two easily available variables, namely characteristic voltage and ohmic resistance. Secondly, the state of charge and voltage of the representative cell are estimated accurately by the dual adaptive extended Kalman filter algorithm. Finally, the multi-parameter limited method for battery pack is developed to predict the peak power under Urban Dynamometer Driving Schedule test at different temperatures. The experimental results verify the feasibility and robustness of the proposed selection method, and the peak power of battery pack is predicted with low complexity and high accuracy. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Battery pack Peak power Battery inconsistency Representative cells Multi-parameter limited method

1. Introduction Electric Vehicle (EV) is considered a sustainable solution to replace conventional internal combustion engine vehicle in the future (Casals et al., 2019; Saw et al., 2016). Lithium-ion batteries have become the optimal energy storage choice in EVs because of their high energy and power density and excellent cycling performance (Jiang et al., 2018; Rahman et al., 2016). In order to provide sufficient energy, a battery pack often consists of hundreds or thousands of battery cells (Cheng and Sun, 2017). To ensure the safety, optimize the energy usage and extend the lifespan of the battery pack, a battery management system (BMS) is designed to provide accurate multi-state estimation, efficient equalization and real-time fault diagnosis of the battery pack (Wang et al., 2019). The multi-state parameters include peak power/state of power (SoP), state of health (SoH) and state of charge (SoC) (Fleischer et al.,

* Corresponding author. E-mail addresses: [email protected] (Z. Zhou), [email protected] (Y. Kang), [email protected] (Y. Shang), [email protected] (N. Cui), [email protected] (C. Zhang), [email protected] (B. Duan). https://doi.org/10.1016/j.jclepro.2019.05.144 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

2014a, 2014b), which are the basic performance characteristics of the battery pack. Peak power indicates the maximum charge and discharge power that the battery can maintain for a short time without exceeding the pre-set battery limits (including SoC, voltage, design current and design power), which is closely related to the acceleration, regenerative braking and gradient climbing power requirements of EVs (Malysz et al., 2016; Zhang et al., 2015). It is extremely important for battery operation and even passenger safety to provide accurate peak power. The predicted peak power above the true value probably causes the battery pack overcharge or over discharge, which may shorten the battery pack lifespan irreversibly by damaging the electrode materials and even cause battery safety problems. On the other hand, the predicted peak power below the true value may incur a conservative control strategy, which in turn affects the driver's operation to EV and even threatens the safety of passengers. 1.1. Review of the peak power prediction method The existing methods for peak power prediction can be divided

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into two groups: methods based on characteristic maps and on dynamic battery models (Burgos-Mellado et al., 2016; Farmann and Sauer, 2018; Waag et al., 2013a), which is shown in Fig. 1. Specifically, the method based on characteristic maps uses the static interdependence between battery peak power, state parameters (e.g., SoC and SoH) and working conditions (e.g., voltage, current and temperature) (Zheng et al., 2016). To obtain the accurate mapping between them, a lot of test procedures need to be conducted out at different SoCs, temperatures and aging levels in the laboratory. Then, for vehicle applications, the multidimensional characteristic map has to occupy high memory size, which is usually not feasible on a low-cost microcontroller. The other power prediction method is based on dynamic battery models, which mainly focuses on two aspects, one improving the accuracy of battery model and the other considering the multiparameter constraints. A comparative study of seven dynamic ECMs on-board SoP prediction was carried out in (Farmann and Sauer, 2018), where the dependence of SoP prediction accuracy on prediction time horizon, SoC, temperature and applied current was examined comprehensively. If battery model can accurately describe the dynamic battery behavior, the prediction accuracy of power capability will be greatly improved. In (Wang et al., 2014), a dynamic matrix control algorithm was proposed to simplify the identification of battery model parameters. The battery voltage predicted was in good agreement with that measured with the maximum difference of 3.7%. In (Malysz et al., 2016), two modelbased SoP algorithms were proposed based on an asymmetric parameter equivalent circuit model. In order to reduce the impact of model error on SoP prediction, the one resistor-capacity (RC) circuit model was improved by adding a moving average noise (Feng et al., 2015). To achieve accurate power prediction for longer time, the equivalent-circuit model with a nonlinear resistance was proposed to address the diffusion effect of battery (Wang et al., 2012). To describe the dependency of the polarization resistance on the discharge or charge current, a non-linear dynamic model was proposed to estimate the available power (Waag et al., 2013a). As an improvement to (Waag et al., 2013a), the effects of SoC and current on polarization resistance were considered in (BurgosMellado et al., 2016), and accurate power prediction was achieved based on the improved model. The model-based method also focuses on the impact of multiparameter constraints on power prediction. In order to avoid peak power being over-predicted, multiple parameter constraints should be considered, including SoC, voltage, design current and design power according to the definition mentioned above. The SoC and voltage constraints were first taken into account for battery power estimation in (Plett, 2004a). Although the battery model used is still simple, only comprising the open circuit voltage (OCV) and the internal resistance, his work helps a lot for later researches. A parameter and power estimator was presented using a dual extended Kalman filter based on a Thevenin model with one RC branch in (Pei et al., 2014). However, only voltage and current

constraints are considered, and SoC constraint is neglected. Sun and Xiong et al. did a series of studies about power prediction. A modelbased SoC and peak power joint estimator was achieved in an online manner, and SoC, voltage and current were simultaneously taken into account to predict the peak power (Sun et al., 2012, 2014; Xiong et al., 2013a, 2013b). In addition, based on the multiparameter constraints, the effects of temperature and aging on battery peak power were discussed in (Hu et al., 2014; Pan et al., 2017; Zhang et al., 2015). Moreover, for automotive applications, a joint estimator for SoC and state of function of batteries based on Kalman filter (KF) was proposed in (Dong et al., 2016). The OCV was a linearized function of SoC so that the KF based SoC estimation was achieved. Compared with extended Kalman filter, unscented Kalman filter and particle filter, KF could greatly reduce the computational complexity. The methods described above make an important contribution to the power prediction for the single cell. However, there are few publications about the power prediction for the series-connected battery pack. In fact, to meet the requirements of high-power applications, a battery pack generally consists of dozens of cells connected in series. If a battery pack is treated as “a big cell”, the predicted peak power may be inaccurate due to the neglect of the inconsistency among the in-pack cells and even cause some cells to be overcharged or over discharged. Therefore, the inconsistency problem should be paid enough attention about the peak power prediction of the battery pack. A straight-forward approach is mentioned in (Waag et al., 2013a), where the maximum discharge and minimum charge power (negative) for each cell are predicted to calculate the available power of the total battery pack. In addition, an online parameter identification method based on ratio vectors reflecting cell difference is proposed to extract the parameters of each in-pack cell in (Jiang et al., 2017). And the peak power of battery pack was predicted based on the inconsistency analysis of cell parameters. Although the two methods can predict the peak power of battery pack effectively, they need large amount of computational time and memory space because the state parameters of each cell need to be calculated. Therefore, there is an urgent need for a low-complexity and accurate peak power prediction method for battery pack in practical applications. 1.2. Contribution of the paper From the perspective of practicality in EVs, this paper has developed a peak power prediction method for series-connected battery pack with high accuracy and low complexity and has the following original key contributions. Firstly, to reduce the computational cost, this paper proposes a peak power prediction method based on the representative cells, the complexity of which is compared with that of the straight-forward method. Secondly, considering the SoC and voltage limits, the selection method for the representative ones is proposed, the feasibility of which is verified by Urban Dynamometer Driving Schedule (UDDS) test at different temperatures. Thirdly, the multi-parameter limited method for battery pack is proposed to achieve accurate peak power prediction. 1.3. Organization of the paper

Fig. 1. Existing methods for peak power prediction.

As SoC and voltage are the key parameters for predicting the peak power, in Section 2, an equivalent circuit model (ECM) is presented to simulate the dynamic behavior of LiNCM cell. Moreover, the dual adaptive extended Kalman filter (AEKF) algorithm is employed to extract model parameters and estimate the SoC of cell. In Section 3, the selection method for the representative cells is proposed and analyzed in detail. Subsequently, the multi-

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073

parameter limited method is proposed to predict the peak power of the battery pack. In Section 4, the proposed selection method is verified by UDDS test at different temperatures. And the experimental results are provided and discussed in detail. Finally, the conclusions and future work are given in section 5.

2.2. Parameters identification and SoC estimation Defining qk ¼ ½ð1  a1 ÞUoc;k ; a1 ; a2 ; a3 T , the state-space expression for the dynamics of the model parameters can be constructed as follows according to Eqs. (2) and (3).



2. Battery model and SoC estimation

qkþ1 ¼ qk þ rk

Ut;k ¼ gðX k ; ik ; qk Þ þ ek In order to accurately predict peak power, the SoC and voltage of cell should be firstly estimated. Accordingly, the 1st-order ECM is applied to describe the dynamic behavior of cell. Based on the battery model, the dual AEKF algorithm is used to identify the model parameters and estimate the SoC successively. 2.1. Battery model The schematic diagram of the used model is illustrated in Fig. 2 (a), where Uoc is the OCV; R0 is the ohmic resistance; R1 and C1 denote the electrochemical polarization resistance and capacitance, respectively; U1 is the voltage across C1 and R1; i is the working current which is positive in discharge and negative in charge; Ut represents the terminal voltage of the battery model. The electrical behavior of the 1st-order ECM can be written as

8 > < U ¼ Uoc  U1  iR0 dU1 i U > ¼  1 : C1 C1 R1 dt

(1)

The discretization calculation of Eq. (1) can be expressed as

(

Ut;k ¼ Uoc;k  U1;k  ik R0

  U1;kþ1 ¼ U1;k eT=t þ ik R1 1  eT=t

(2)

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(5)

where rk is the process white noise, which represents the inaccuracy of the parameter change; ek is the measurement white noise, which represents the inaccuracy of the model output. gð $Þ is the output equation of the battery model, which is described in detail in Eq. (9). The ampere-hour counting is commonly used to calculate the true SoC, which can be written as

ðt z ¼ z0  hidt=Cmax

(6)

0

where z denotes the SoC; z0 is the initial SoC; h is the columbic efficiency, and Cmax is the maximum available capacity of battery. Then the discrete-time form of Eq. (6) can be written as

zkþ1 ¼ zk  ik ðhT=Cmax Þ

(7)

where zk and ik are the SoC and the current at the kth sampling time, respectively. The relationship between OCV and SoC can be achieved by the following polynomial model (Pattipati et al., 2014; Lin et al., 2017).

Uoc ðzÞ ¼ Κ 0 þ Κ 1 z þ Κ 2 z2 þ Κ 3 z3 þ Κ 4 z4 þ Κ 5 z5 þ Κ 6 z6

where Uoc,k, Ut,k, U1,k and ik are the OCV, the terminal voltage, the polarization voltage and the load current at the kth sampling time, respectively; T is the sampling interval, and t is the time constant (t ¼ R1 C1 ). In order to identify the model parameters online, Eq. (2) can be rewritten as

where Ki (i ¼ 0, 1, …, 6) are eight constants chosen to make the model parameters fit test data well. According to Eqs. (5) and (7), the system state-space equations can be achieved by

Ut;k ¼ ð1  a1 ÞUoc;k þ a1 Ut;k1 þ a2 ik þ a3 ik1

(

(3)

The parameters a1, a2 and a3 can be calculated by Eq. (4).

8 T  2R1 C1 > > a1 ¼  > > T þ 2R1 C1 > > > > < R T þ R1 T þ 2R0 R1 C1 a2 ¼  0 > T þ 2R1 C1 > > > > > R T þ R1 T  2R0 R1 C1 > > : a3 ¼  0 T þ 2R1 C1

(8)

X kþ1 ¼Ak X k þBk ik þwk Ut;k ¼gðX k ;ik ; qk Þþvk

(4)

Fig. 2. Schematic diagram of battery model: (a) 1st-order equivalent circuit model; (b) Rint equivalent circuit model.

Z 3 8   > # " #" # 2 " > T= t < zkþ1 5ik þwk zk hT =Cmax R1 1e 1 0 ¼ þ4 T= t > U1;k 0e > : U1;kþ1 Ut;k ¼Uoc;k U1;k R0 ik þvk (9) where Xk is the state vector and Xk ¼ [zk, U1,k]T; wk is the process white noise, which is used to explain current sensor error and inaccuracy of the state equation; vk is the measurement white noise, which is used to explain voltage sensor error and inaccuracy of the output equation. Based on Eqs. (5) and (9), the dual AEKF algorithm is used to identify the model parameters and estimate battery state. Compared with EKF, AEKF presents better performance in state estimation and parameter identification by updating the covariance iteratively with the innovation sequence (Deng et al., 2016). What's more, the battery SoC and the model parameters can be obtained in real time by the dual AEKF algorithm. The specific steps of the dual AEKF algorithm are described in Table 1.

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Table 1 Summary of dual AEKF algorithm for state estimation and parameter identification. 

(

qkþ1 ¼ qk þ rk

Ut;k ¼ gðX k ; ik ; qk Þ þ ek

and



X kþ1 ¼ Aqk X k þ Bqk ik þ wk Ut;k ¼ gðX k ; ik ; qk Þ þ vk

dUoc j 1 dz z¼zk 1. Initialization: For k ¼ 1, set Definitions: C qk ¼



(10)

and Dqk ¼  R0 T

þ bþ bþ Parameter initialization: b q 1 ¼ E½q1 ,P þ q;1 ¼ E½ðq1  q 1 Þðq1  q 1 Þ 

b þ ¼ E½X ,P þ ¼ E½ðX  X b þ ÞðX  State initialization: X 1 1 1 1 1 X;1

T b þÞ  X 1

Computation: For k ¼ 2, 3, …, compute: 2. Time update: Time update for parameter estimator:   b q kþ1 ¼ qþ ¼ P þ þ Pb k , Pb b q ;r q ;kþ1 q ;k

(11) (12)

(13)

Time update for state estimator:  bþ b ¼ A X ¼ Ak P þ ATk þ P b X k k þ Bk ik , P b kþ1 b X ;w X ;kþ1 X ;k

(14)

3. The adaptive law: Error innovation: εk ¼ Ut;k  gðX k ; ik ; qk Þ Adaptive law-covariance matching: 1 Xk Hk ¼ ε εT i¼kM¼1 k k M For parameter estimator:

(15)

T T  ðC qk Þ , Pr ¼ Lqk Hk ðLqk Þ Pe ¼ Hk  C qk Pb q ;k T

where U is defined as the characteristic voltage; R0 is the ohmic 0 resistance; i is the working current which is positive in discharge 0 and negative in charge; U t represents the terminal voltage of the battery model. d is introduced to reduce the influence of measurement noise. The characteristic voltage U is approximately equal to the OCV and is not affected by the ohmic resistance. More importantly, it can be obtained by simple calculation, which is suitable for vehicle applications.

4. Measurement update for parameter estimator: 1

b  þ Lq ε bþ ¼ q Parameter update: q k k k k

(19) (20)

 Covariance update: P þ ¼ ðI  Lqk C qk ÞPb b q ;k q ;k

(21)

5. Measurement update for state estimator: T

T

X  X  Kalman gain matrix: LX ðC X k Þ ½C k P b ðC k Þ þ Pv  k ¼ Pb X ;k X ;k X b  þ Lb bþ ¼ X State update: X k k k εk

Covariance update: P

þ

b X ;k

¼ ðI 

1

X  LX k C k ÞP b X ;k

0

(17)

X ;k

T T   ðC qk Þ ½C qk Pb ðC qk Þ þ Pe  Kalman gain matrix: Lqk ¼ Pb q ;k q ;k

0

U ¼ U t þ i R0 þ d

(18)

T

0

(16)

For state estimator: X  X X Pv ¼ Hk  C X k P b ðC k Þ , Pw ¼ Lk Hk ðLk Þ

terminal voltage are often selected as the ones with the highest and lowest SoC. This method may lead to erroneous results when the inconsistency among in-pack cells is weak. In fact, the terminal voltage is widely used to avoid overcharge or over discharge of battery (Sun et al., 2016), and is not suitable for selecting in-pack cells with different SoC levels. Due to the differences in ohmic resistance among in-pack cells, especially with the aging of battery pack, the SoC level of each cell is difficult to be judged by the terminal voltage. In fact, the battery SoC is typically estimated based on the relationship between the SoC and the OCV, and the OCV can be used to determine the SoC level. However, it is difficult to measure the OCV, and it is usually estimated by various algorithms. Therefore, it is a good choice to find an easily accessible variable instead of the OCV. In this paper, we introduce a characteristic voltage to judge the SoC level of cell based on the Rint (internal resistance) model (Plett, 2004b), which is shown in Fig. 2 (b). It can be expressed as

(22) (23) (24)

3. Peak power prediction for battery pack In order to provide sufficient power and energy for electric vehicles, a battery pack usually contains dozens of cells connected in series. Due to limited memory storage and computing speed of embedded controllers employed in BMS, it is difficult to calculate the peak power of battery pack by predicting the peak power of each cell. Therefore, it is necessary to select several cells that can represent the whole behavior of battery pack to calculate its peak power. Similar to the single cell, the peak power of battery pack is also limited by the voltage and SoC of in-pack cell. Specifically, the peak charge power of battery pack depends on the two cells respectively with the highest SoC and highest voltage, and the peak discharge power depends on the two cells respectively with the lowest SoC and lowest voltage. Therefore, the four cells, namely the representative cells, are selected to predict the peak power of battery pack. 3.1. Selection method for the representative cells 3.1.1. Cell selection considering SoC limit To obtain the cells with the highest and lowest SoC, the straightforward method can be applied, which is achieved by estimating the SoC of each cell. However, this method requires substantial computing power, which is hard to run on a low-cost microcontroller in EVs. Besides, the cells with the highest and lowest

(25) 0

3.1.2. Cell selection considering voltage limit About peak power prediction, peak current can reach high rate in the next short time period. When the battery pack is discharged at a small current, the in-pack cell with the highest voltage may not be the representative cell for power prediction due to the measurement error, nor is the in-pack cell with the lowest voltage. According to the impedance analysis of 1st-order ECM, the terminal voltage of battery is mainly affected by the voltage over the ohmic resistor in a short time. Especially for high rate current, the small ohmic resistance difference may cause a large voltage difference. Therefore, for the in-pack cells with good consistency, we can select the cell with the biggest ohmic resistance as the one with the highest and lowest voltage. 3.2. Multi-parameter limited method for peak power prediction of battery pack In order to predict the peak power accurately, the multiparameter limited method for battery pack is introduced in this section. As the cells selected above can represent the SoC and voltage levels of battery pack, the peak power of battery pack is limited by their SoCs and voltages. Besides, the design limits of single cell about current and power should also be taken into account. 3.2.1. SoC limit of representative cell There is a reasonable operating range for cell SoC. Based on Eq. (7), the SoC-limited current can be expressed as follows.

8 zk  zmax > cha;SoC > > < I min;N ¼ hNΤ=Cmax > dis;SoC zk  zmin > > : I max;N ¼ hNΤ=C max

(26)

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073

where I cha;SoC and I dis;SoC max;N are the minimum (negative) charge curmin;N rent and the maximum discharge current under the SoC limit, respectively; zmax and zmin represent the maximum SoC and the minimum SoC, respectively; N is the number of the sampling interval.

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The first-order residual oð $Þ has little influence on Uoc ðzkþN Þ if the variation of SoC is small (Sun et al., 2014), thus the term oð $Þ could be neglected. Then the peak currents under the voltage limit can be obtained from the kth sampling time to the (k þ N)th sampling time based on Eqs. (28) and (29).

3.2.2. Voltage limit of representative cell Through Eq. (5), the terminal voltage of the 1st-order ECM can be obtained from the kth sampling time to the (k þ N)th sampling time.

 N 8 Uoc;k ðzk Þ  U1;k eT=t  U max t > cha;vol > > I min;N ¼ > N1 > N1j X > dUoc > > eT=t jz¼zk þ R0 þ R1 ð1  eT=tÞ ðhNT=Cmax Þ > > > dz < j¼0 > > > > > > > Imax; Ndis;vol ¼ > > > > :



Uoc;k ðzk Þ  U1;k e ðhNT=Cmax Þ





T=t

e

N1j

N

(30)

 Utmin

N1 N1j X dUoc eT=t jz¼zk þ R0 þ R1 ð1  e  T=tÞ dz j¼0

T=t

Ut;kþN ¼ Uoc;kþN  U1;k e N 1  X

T=t

N

0

3.2.3. Design limits about current and power Considering the design current limit, the minimum (negative) charge current I cha min;pack and the maximum discharge current I dis max;pack of series-connected battery pack can be expressed as follows.

   ik @R0 þ R1 1  eT=t

1 A

j¼0

(27) where Ut;kþN is the terminal voltage at the (k þ N)th sampling time. To calculate the minimum charge current, the terminal voltage should be equal to the upper cutoff voltage of cell. To calculate the maximum discharge current, the terminal voltage should be equal to the lower cutoff voltage of cell. Therefore, the equations are as follows.

 ¼ max Imin;cell ; I cha;SoC min;N  dis;SoC : Idis ¼ min I ; I max;cell max;N max;pack 8 < Icha

high

min;pack

low

cha;vol ; I min;N

dis;vol ; I max;N

high

low



 (31)

cha;SoC high dis;SoC low where I min;N and I max;N are the minimum (negative) charge current of cell with the highest SoC and the maximum discharge current of cell with the lowest SoC under the SoC limit, high dis;vol low respectively; I cha;vol and I max;N are the minimum (negative) min;N charge current of cell with the highest voltage and the maximum discharge current of cell with the lowest voltage under the voltage

0 1 8  N   N1 N1j > X > > cha;vol T= t T= t T= t A ¼ U max > Uoc;kþN  U1;k e e  I min;N @R0 þ R1 1  e > t > < j¼0 0 1 >  N   N1 N1j X > > > @R0 þ R1 1  eT=t A ¼ U min eT=t Uoc;kþN  U1;k eT=t  I dis;vol > t > max;N :

(28)

j¼0

where I cha;vol and I dis;vol max;N are the minimum (negative) charge current min;N and the maximum discharge current under the voltage limit, respectively; U max and U min are separately the upper voltage and t t the lower cutoff voltage of cell. According to Eq. (8), Uoc is the and I dis;vol function of the SoC. Therefore, in order to calculate I cha;vol max;N min;N

limit, respectively; Imin;cell and Imax;cell are the minimum (negative) charge current and the maximum discharge current of cell obtained from battery manufacturer, respectively. Considering the design power limit, the peak power of battery pack can be expressed as follows.

in Eq. (28), Uoc should be linearized and its Taylor-series expansion is expressed as

Uoc ðzkþN Þ ¼ Uoc ðzk  ik ðhNT = Cmax ÞÞ ¼ Uoc ðzk Þ  ik ðhNT = Cmax Þ

dUoc j þ oðzk ; ik ðhNT = Cmax ÞÞ dz z¼zk

(29)

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Fig. 3. Battery test bench.

Table 2 Characteristics of the battery tester. Characteristic

Measurement inaccuracy

Measurement range

Voltage for cell Voltage for battery pack Current Temperature

±0.02% FSR ±0.1% FSR ±0.1% FSR ±1  C

0 V-5 V 10 V-100 V 100 A-100 A 200  C -þ200  C

  ¼ n * max Pmin;cell ; I cha min;pack * Ut;kþN   dis : P dis max;pack ¼ n * min Pmax;cell ; I max;pack * Ut;kþN 8 < P cha

min;pack

(32)

dis where P cha min;pack and P max;pack are the minimum (negative) charge power and the maximum discharge power of battery pack, respectively; Pmin, cell and Pmax, cell are the minimum (negative) charge power and the maximum discharge power of cell obtained from battery manufacturer, respectively; n represents the number of in-pack cells.

4. Experimental verification and discussion 4.1. Test bench The battery test bench mainly includes the Arbin battery tester (BT-MP 100V-200A) for charging and discharging LiNCM battery pack, a computer for programming and storing experimental data (including voltage, current and temperature), a data collector for collecting experimental data, a thermal chamber for controlling different test temperatures and a battery pack consisting of eight cells connected in series. The experimental setup is shown schematically in Fig. 3. The characteristics of the battery tester are specified in Table 2. The brand-new LiNCM cell produced by Lishen Battery CO., LTD of China is selected for all experiments, whose specification is shown in Table 3.

Fig. 4. Experimental procedure and current profiles: (a) flowchart of battery experiment; (b) current profile for one UDDS cycle; (c) charge current curve for seriesconnected battery pack.

4.2. Experimental procedure and test results The flowchart of battery experiment is showed in Fig. 4 (a). First of all, the capacity test for eight cells is conducted to obtain their maximum available capacities, which consists of constant currentconstant voltage (CC-CV) charge and constant current (CC) discharge. Secondly, the OCV test is conducted to obtain the relationship between SoC and OCV. The fully charged cell is discharged

Table 3 Specifications for the test cell. Items

Parameters

Nominal capacity Nominal voltage End-of-charge voltage End-of-discharge voltage

32.5 Ah 3.6 V 4.2 V 3.0 V

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073

Fig. 5. Experimental test results: (a) capacity test results at three temperatures; (b) SoC results at three temperatures.

by constant current pulses until its voltage reaches the lower cutoff value. Finally, to verify the proposed method, UDDS cycle is used to simulate the real operating scenarios of the seriesconnected battery pack, whose current profile is shown in Fig. 4 (b). The battery pack is charged in multi-step CC mode, whose current curve is shown in Fig. 4 (c). For the pack-level test, to ensure that eight cells have the same initial SoC, each one is fully discharged and then connected in series. The above tests are repeatedly conducted in the different ambient temperatures (10  C, 25  C and 45  C) and the surface temperature of each cell is collected. Also, it is worth noting that before UDDS test is carried out, the battery pack is fully charged at 25  C and then rest for sufficient time to stabilize in the set temperature (10  C, 25  C or 45  C). Fig. 5 (a) illustrates the capacity test results at three temperatures. As the temperature decreases, the cell capacity also decreases. But they have the similar available capacities at the same temperature. Besides, the pack capacity is less than any one of the cell capacity, and the cell capacity remains relatively unchanged at 25  C and above. Fig. 5 (b) shows the SoC results at three temperatures when the battery pack is fully charged. Only one cell, # 3, is fully charged among the eight cells. 4.3. Verification and discussion 4.3.1. Verification of the selection method for the representative cells In order to verify the proposed selection method for the representative cells, UDDS test is conducted for the seriesconnected battery pack at different temperatures. Fig. 6 shows the characteristic voltage profiles and the numbers of the cells with the highest and lowest characteristic voltages in eight cells at 10  C, 25  C and 45  C. It is worth mentioning that the number of the cell with the highest or lowest characteristic voltage is recorded only

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when the battery pack is charged or discharged at a large current. From the figures at three temperatures, the characteristic voltages of the cells # 3 and # 6 are almost always the highest and the lowest, respectively. Fig. 7 shows the SoC estimation results and the numbers of the cells with the highest and lowest SoCs in eight cells at 10  C, 25  C and 45  C. Corresponding to the characteristic voltages, the SoCs of the cells # 3 and # 6 are almost always the highest and the lowest, respectively. The characteristic voltages of different cells can generally reflect their SoC differences. Even at different temperatures, this selection method is feasible. Table 4 summarizes the mean values of ohmic resistance for eight cells at three temperatures. The ohmic resistance of # 3 is always the biggest at 10  C, 25  C and 45  C. Therefore, the cell # 3 is selected as the one with the highest and lowest voltage at the beginning of discharge. Fig. 8 shows the voltage profiles and the numbers of the cell with the highest and lowest voltages in eight cells at 10  C, 25  C and 45  C. The blue dot and red dot indicate the number of the cell with the highest and lowest voltages respectively when the battery pack is charged or discharged at a large current. From the figures, the voltage of the cell # 3 indicated by yellow is always the highest or lowest at every large current point. And the zoom figures show this result clearly. From the experimental results in Figs. 6 and 7, the characteristic voltage can be used to decide the in-pack cell with the highest or lowest SoC. In fact, the characteristic voltage is approximately 0 equivalent to the OCV in the Rint model, i.e. U oc in Fig. 2 (b). Although the Rint model cannot describe the dynamic behavior of battery accurately due to the neglect of polarization characteristics, 0 U oc can reflect the SoC level of cell, which can be used to select the cells with the highest and lowest SoC. On the other hand, the cell with the biggest ohmic resistance may not the one with the highest or lowest voltage due to the fact that measurement noise plays a dominant role in small current condition. However, for peak power prediction, peak current can reach high rate in the next short time period, and the terminal voltage of battery is mainly affected by the ohmic voltage in a short time according to the 1st-order ECM. Therefore, it is reasonable that the ohmic resistance is used to decide the voltage levels of in-pack cells.

4.3.2. Voltage and SoC estimation for the representative cells In order to predict the peak power capability accurately, the voltage and SoC of cell should firstly be estimated. The dual AEKF algorithm is used to identify the model parameters and estimate the SoCs of the representative cells successively. Fig. 9 illustrates the estimation results at three temperatures (10  C, 25  C and 45  C), which include voltage estimation error, SoC estimation and SoC estimation error for the representative cells. The initial SoC are incorrectly set to 0.92 for analyzing the robust performance of the algorithm. Table 5 summarizes the mean absolute errors (MAEs) and root mean square errors (RMSEs) of estimation results. In general, the temperature significantly affect the estimation accuracy. Accordingly, the estimation errors of cell voltage increase with decreasing temperature. The estimation errors of cell SoC at 25  C are similar to that at 45  C, while the estimation errors at 10  C is significantly higher than them. At 10  C, the errors of the voltage estimation and the SoC estimation of # 3 are the highest, and their RMSEs are only 2.48 mV and 0.72%, respectively. It indicates that the dual AEKF algorithm is effective for estimating the terminal voltage and the SoC of cell accurately.

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Fig. 6. Characteristic voltage profiles and numbers of the cells with the highest and lowest characteristic voltages in eight cells under UDDS test: (a) 10  C; (b) 25  C; (c) 45  C.

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073

Fig. 7. SoC estimation results and numbers of the cells with the highest and lowest SoCs in eight cells under UDDS test: (a) 10  C; (b) 25  C; (c) 45  C.

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Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073 Table 4 Mean values of ohmic resistance for eight cells at three temperatures. Temperature Ohmic resistance (mU)

# # # # # # # #

1 2 3 4 5 6 7 8

4.3.3. Peak power prediction for battery pack Based on the accurate voltage and SoC estimates, the peak power of battery pack is predicted for 20 s, generally between 1 s and 20 s in EVs (Waag et al., 2013b), using the multi-parameter limited method mentioned in Section 3. The design limits are listed in Table 6 according to battery manufacturer. Fig. 10 (a), (b) and (c) show the charge/discharge current of the representative cells based on the SoC, voltage and design current

10  C

25  C

45  C

4.13 3.76 4.58 3.90 3.78 4.41 3.92 4.03

3.52 3.14 4.10 3.31 3.20 3.97 3.38 3.41

2.83 2.53 3.57 2.64 2.58 3.28 2.65 2.74

limits. From the overall view, the peak current of the representative cell depends on the voltage limit over a wide range of SoC. Only near the upper and lower limits of the SoC, the peak current is limited by the SoC. Moreover, the peak charge current depends on the cells with the highest voltage and the highest SoC, i.e. # 3, and the peak discharge current depends on the cells with the lowest voltage and the lowest SoC, i.e. # 3 and # 6. Fig. 10 (d) shows the peak power of battery pack under UDDS test at three temperatures. With the increase of temperature, the power capability increases from the relationship between battery operating temperature and power capability. The reason for this is the difference of model parameters at different temperatures. Table 7 summarizes the mean values of model parameters for the representative cells at three temperatures. The mean values of the model parameters obviously decrease with the increase of temperature, which makes the peak current and power capability increase according to Eq. (30). To compare the complexity of the proposed method with that of the straight-forward method, the computational time of both methods is evaluated by the Matlab functions tic and toc in a computer with i7-4790 CPU and 4.00 GB RAM. Table 8 lists the comparison of the complexity of the proposed method and straight-forward method. The proposed method takes about 786 ms, and its algorithm occupies about 5.3 KB memory size, while the straight-forward method takes more computational time and needs about 1420 ms, and its algorithm occupies about 17.6 KB memory size. It is evident that the proposed method has lower complexity. Furthermore, as the number of series-connected cells increases, the straight-forward method requires more computational time and occupies more memory size, which is difficult to use in BMS. On the contrary, the complexity of the proposed method does not increase with the number of cells, which only depends on the representative cells. Therefore, the proposed method is promising for vehicle applications. 5. Conclusions

Fig. 8. Voltage profiles and numbers of the cells with the highest and lowest SoCs test in eight cells under UDDS: (a) 10  C; (b) 25  C; (c) 45  C.

This paper proposes a peak power prediction method for a series-connected battery pack with low complexity and high accuracy. Firstly, considering the SoC and voltage limits, the selection method for the representative cells is proposed, which greatly reduces the computational complexity. The experimental results verify the feasibility and robustness of this selection method. Secondly, the voltage and SoC of the representative cell, which are the key parameters of peak power prediction, are estimated using the dual AEKF algorithm based on the 1st-order ECM. The experimental results show that the maximum RMSEs of the voltage and SoC estimation are only 2.48 mV and 0.72% under UDDS test, respectively. Finally, based on the accurate voltage and SoC estimation, the peak power of battery pack is reliably predicted by the multiparameter limited method at different temperatures.

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073

Fig. 9. Voltage and SoC estimation results of the representative cells under UDDS test: (a) 10  C; (b) 25  C; (c) 45  C.

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Table 5 Voltage and SoC estimation errors at three temperatures. T (ºC)

10

Representative cell

3#

6#

3#

6#

3#

6#

0.87 2.48 0.55 0.72

0.66 1.49 0.49 0.61

0.50 0.99 0.39 0.55

0.49 0.99 0.40 0.55

0.36 0.82 0.43 0.59

0.35 0.81 0.41 0.51

Voltage SoC

MAE (mV) RMSE (mV) MAE (%) RMSE (%)

25

45

Table 6 Design limits for the test cell. Charge current

Discharge current

Charge power

Discharge power

120 A

180 A

400 W

600 W

Fig. 10. Peak current of the representative cells and peak power of battery pack under UDDS test at three temperatures: (a) 10  C; (b) 25  C; (c) 45  C; (d) peak power of battery pack.

Z. Zhou et al. / Journal of Cleaner Production 230 (2019) 1061e1073 Table 7 Mean values of model parameters for the representative cells at three temperatures. T (ºC)

10

Representative cell

#3

#6

#3

25 #6

#3

45 #6

R0 (mU) R1 (mU) C1 (F) t (s)

4.58 4.81 12,411 59,696

4.41 4.13 12,192 50,352

4.10 3.22 13,849 44,594

3.20 3.40 13,906 47,280

3.57 2.21 17,336 38,313

2.58 2.15 17,443 37,502

Table 8 Comparison of the complexity of the proposed method and straight-forward method.

The proposed method The straight-forward method

Occupied memory size (KB)

Computational time (ms)

5.3 17.6

696 1420

The future work will focus on the effect of aging on the power prediction of battery pack. Acknowledgment This work is supported by the National Natural Science Foundation of China (No.61527809, U1764258, 61633015), National key R&D program of China and Shandong Province (No. 2018YFB0104000, 2016ZDJS03A02). References
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