- Email: [email protected]

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

A novel approach of remaining discharge energy prediction for large format lithium-ion battery pack Xu Zhang, Yujie Wang, Chang Liu, Zonghai Chen* Department of Automation, University of Science and Technology of China, Hefei 230027, PR China

h i g h l i g h t s Remaining discharge energy is initiated for battery pack. Temperature is taken into consideration in battery pack model description. Battery inconsistency is considered to analyze the battery usage efﬁciency. The accuracy and robustness of the method is veriﬁed by dynamic proﬁles.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 October 2016 Received in revised form 9 January 2017 Accepted 11 January 2017

Accurate estimation of battery pack remaining discharge energy is a crucial challenge to the battery energy storage systems. In this paper, a new method of battery pack remaining discharge energy estimation is proposed using the recursive least square-unscented Kalman ﬁlter. To predict the remaining discharge energy precisely, the inconsistency of the battery pack caused by different working temperatures is taken into consideration and the degree of battery inconsistency is quantiﬁed based on mathematical methods of statistics. In addition, the recursive least square is applied to identify the parameters of the battery pack model on-line and the unscented Kalman ﬁlter is employed in battery pack remaining discharge energy and energy utilization ratio estimation. The experimental results in terms of battery states estimation under the new European driving cycle and real driven proﬁles, with the root mean square error less than 0.01, further verify that the proposed method can estimate the battery pack remaining discharge energy with high accuracy. What's more, the relationship between the pack energy utilization ratio and the degree of battery inconsistency is summarized in the paper. © 2017 Elsevier B.V. All rights reserved.

Keywords: Remaining discharge energy Degree of battery inconsistency Recursive least square-unscented Kalman ﬁlter Battery pack model

1. Introduction The lithium-ion battery has been widely used in distribution energy storage system and electric vehicle [1,2]. To meet the demands of high voltage and more energy storage, a battery pack is usually composed by hundreds or thousands of batteries. Unfortunately, although the batteries are rigorously selected, different of battery actions caused by working conditions will lead to the battery inconsistency. Therefore, battery management systems (BMS) are designed to monitor the single cells and control the process of battery pack discharge/charge. One of the most important issues of the BMS is to estimate the battery pack state parameters, including state-of-charge (SOC),

state-of-energy (SOE), state-of-power (SOP), remaining useful life (RUL) and state-of-health (SOH). Conventionally, the battery SOE is deﬁned by the ratio of the residual energy to the maximum available energy, which is directly related to the battery terminal voltage and the load current [3]. Meanwhile, difference of battery load proﬁles will lead to different results of SOE estimation caused by the energy dissipation in battery resistance. Therefore, to evaluate the energy storage in battery, the remaining discharge energy (RDE), which is the unused energy stored in the battery, is proposed as shown in Eq. (1).

Zt2 ERDE ¼

UOCV $I$dt ¼ t

* Corresponding author. E-mail address: [email protected] (Z. Chen). http://dx.doi.org/10.1016/j.jpowsour.2017.01.054 0378-7753/© 2017 Elsevier B.V. All rights reserved.

SOC Z t

ZCt UOCV dI t ¼ CN Ct2

UOCV dSOC

(1)

SOCt2

In Eq. (1), the ERDE is the RDE of the single battery, which

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

represents the cumulative energy from the time t to t2. At time t, the SOC of the battery is SOCt and the residual battery capacity is Ct. At time t2, the battery reaches the lower cut-off voltage, and the SOC is SOCt2 , the battery capacity is Ct2 . CN is the maximum available capacity. UOCV is the open circuit voltage (OCV) of the battery which is the function of SOC. According to Eq. (1), when the battery voltage reaches the lower cut-off voltage, the battery SOC is regarded as 0. Therefore, the battery remaining discharge energy is directly related to the battery OCV and current SOC. The prediction of RDE, which is applied to evaluate the energy storage in the battery and the ability of battery discharge, is very important and challenging in battery usage. There exist few studies on battery energy estimation. In Ref. [4], Liu et al. used a coupled prediction of future battery state variation based on the predictive control theory to enhance the RDE accuracy. Wang et al. [5] proposed a joint estimation based on particle ﬁlter to predict the available energy batteries and SOC concurrently. Wei et al. [6] analyzed the discharge behaviors of primary alkaline batteries, and the concept of draining the remaining energy by stacking up multiple used batteries was demonstrated to be feasible. Kim et al. [7] used the interpolation of lookup tables which allowed for battery temperature and battery voltage to estimate the battery residual energy. Besides, in Ref. [8], the ambient temperature, battery discharge/charge current rate and cell aging level were analyzed and a moving-window energyintegral technique was incorporated in battery maximum available energy estimation. Wang et al. [9] proposed the Bayesian learning technique in SOE estimation and presented the implementation of remaining energy prediction based on the mC/OS-II real time operating system. Bayram et al. [10] used the adaptive neural fuzzy inference system to predict the battery remaining storage energy. Fares et al. [11] proposed a simpliﬁed equivalent model to estimate the battery energy. As shown in Eq. (1), to precisely estimate battery remaining discharge energy, the accurate prediction of SOC is obbligato. Various kinds of battery SOC estimation methods have been introduced in literature. Zhang et al. [12] proposed the method of the extended Kalman ﬁlter and unscented Kalman ﬁlter (EKF-UKF) in battery pack SOC estimation. The battery pack inconsistency was taken into consideration and the mean absolute percentage error of the prediction estimation was less than 0.04. Dong et al. [13] adopted a linearized battery model and used the Kalman ﬁlter in battery SOC estimation under various scenarios. In Ref. [14], the adaptive extended Kalman ﬁlter and particle ﬁlter were employed in SOC estimation. The proposed method was veriﬁed with high accuracy at different temperatures and under dynamic current. Zhang et al. [15] adopted the method of recursive least squareunscented Kalman ﬁlter in SOC estimation. Besides, other methods in SOC estimation included coulomb-counting algorithm [16], unscented Kalman ﬁlter [17,18], unscented particle ﬁlter [19,20]. All of the above methods have their own advantages and can estimate battery states with high accuracy. However, most of the above methods only can be used in single cell and do not take the battery working temperatures into consideration. Meanwhile, the estimation of battery pack RDE is different from single cell, which is inﬂuenced by the battery inconsistency. In practice, the cells in battery pack are usually placed in a small space which lead to the battery with different heat dissipation conditions and different working temperatures. Therefore, in this paper, we analyze the battery performance inﬂuenced by temperatures and propose a novel approach of battery pack RDE and the maximum RDE estimation. In addition, the mathematical methods of statistics are used to deﬁne the degree of battery inconsistency based on accurate estimation of battery SOC. In order to analyze the inﬂuence of temperature, the data-driven model is employed and the

217

parameters of the model are identiﬁed by the algorithm of recursive least square (RLS). To estimate SOC, the unscented Kalman ﬁlter (UKF) is applied, and the RLS and UKF are working successively. The proposed method is veriﬁed by the experiment under the new European driving cycle (NEDC) [21] conditions and the real electric vehicle driven proﬁles. This paper is organized as follows: In section 2, the introduction of battery pack available energy and the degree of battery inconsistency are deﬁned. In section 3, we introduce the battery pack model and elicit the state space equations of battery pack estimator, then present the algorithm of RLS-UKF, meanwhile give the implement ﬂowchart of the proposed method. Section 4 describes the test bench and test methods used in experiments, meanwhile analyzes the experimental results. Section 5 gives the conclusions.

2. Battery pack remaining discharge energy and the degree of battery inconsistency 2.1. Battery pack remaining discharge energy According to Eq. (1), the battery pack RDE can be deﬁned as the cumulative energy from the current condition to the state that one of the batteries in the battery pack reaches the lower cut-off voltage. For a time-series process, the battery pack RDE can be built as follows:

EPRDE ðtÞ ¼

n X

CNi

i¼1

i SOC Z t

i UOCV ðSOCÞdSOC

(2)

SOCti 1

where EPRDE(t) is the battery pack RDE at time t, CNi is the maximum available capacity of the ith battery, n is the number of cells in the battery pack connected in series, SOCti is the SOC of the ith battery at time t, and SOCti1 is the SOC of the ith battery at time t1 when one of the batteries in the battery pack reaches the lower cut-off voltage. Unfortunately, due to the inconsistency in battery pack, the cells cannot reach the cut-off condition concurrently. And then, the pack energy utilization ratio is proposed and can be deﬁned by the ratio of the cumulative energy from the current state to the state of one of the cells reaching the lower cut-off condition to the cumulative energy that all cells reach the lower cut-off condition simultaneously. The battery maximum RDE is shown in Eq. (3) and the battery energy utilization ratio is shown in Eq. (4).

EmaxPRDE ðtÞ ¼

n X i¼1

i SOC Z t

CNi

i UOCV ðSOCÞdSOC

(3)

0

EUR ¼ EPRDE =EmaxPRDE

(4)

where EmaxPRDE(t) denotes the maximum RDE at time t, EUR is the pack energy utilization ratio, EPRDE is the battery pack RDE.

2.2. The degree of battery inconsistency To quantify the degree of the battery pack, the battery pack SOC, SOC variance are usually employed to measure the inconsistency:

218

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

8 > min SOC i C i > > 1in > > SOCPACK ¼ > > < min SOC i C i þ min 1 SOC j C j 1in 1jn > > > n > X 2 > 1 2 > > SOC i SOCPACK :d ¼ n i¼1

(5)

where SOCPACK denotes the SOC of battery pack, min ðSOC i C i Þ is the 1in minimum of remaining cell capacity, min ðð1 SOC j ÞC j Þ is the 1jn minimum charging capacity, i; j are the battery number. The SOC variance d2 , which embodies the degree of deviation between the cell SOC and the battery pack SOC, represents the degree of battery inconsistency, n is the number of cells in the battery pack connected in series. 3. Battery pack model description and the proposed method

where Uti is the terminal voltage of ith cell in the battery pack. Upi represents the polarization voltage of RC network of the ith series i cell. Udiff denotes the diffusion voltage of RC network of the ith series cell. Rio is the ith series cell electrical resistance. Cp , Cdiff , Rp , Rdiff are battery parameters which reﬂect the battery dynamic i response and capacity. UOCV is the OCV of the ith series cell. n is the number of battery in the battery pack connected in series. The OCV can be represented by the function of SOC based on the combined electrochemical model shown as follows:

þ K5 lnð1 SOCÞ

It is difﬁcult to obtain an accurate model to describe the relationship between the battery terminal voltage and battery states, since the performances of battery are impacted by the complex physical and chemical reactions. However, a battery model is required for estimating battery states. Many models have been proposed in literature [22e25], which are used in different appli-

n X

(6)

UOCV ðSOCÞ ¼ K0 þ K1 SOC þ K2 SOC 2 þ K3 =SOC þ K4 lnðSOCÞ

3.1. Battery pack model

EPRDE ðkÞ ¼

8 1 1 i > i > > U_ p ¼ i i Up i Ib > > R C C > p p p > > < 1 1 i i Udiff i Ib ði ¼ 1; 2; …; nÞ U_ diff ¼ i > i > > R C C > diff diff diff > > > > : Ui ¼ Ui i i i t OCV þ Ro Ib Up Udiff

(7) where Ki (i ¼ 0, 1, …, 5) are six polynomial coefﬁcients which are the functions of the battery temperature (T). Combining with Eq. (7), the discrete equation of Eqs. (2) and (3) can be written as:

2 3 CNi ðK0 K4 K5 ÞSOCki þ 1=2K1 SOCki þ 1=3K2 SOCki þ K3 In SOCki þ K4 SOCki In SOCki

i¼1

i SOCk þK5 SOCki 1 In 1 SOCki i

(8)

SOCend

EmaxPRDE ðkÞ ¼

n X

2 3 CNi ðK0 K4 K5 ÞSOCki þ 1=2K1 SOCki þ 1=3K2 SOCki þ K3 In SOCki þ K4 SOCki In SOCki

i¼1

þK5 SOCki

i SOCk i 1 In 1 SOCk

(9)

0

cations and test conditions. A common used model based on the data-driven model [26,27] is shown in Fig. 1, which contains n OCVs i UOCV , n resistors Rio , n polarization RC networks and n diffusion RC networks. The electrical behavior of battery pack model can be described as:

Fig. 1. Schematic diagram of the battery pack model.

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

where EPRDE(k) is the battery pack RDE at the kth sampling time, SOCki represents the SOC of the ith series cell at the kth sampling i time, SOCend is the SOC of the ith series cell that one of the batteries reaches the lower cut-off voltage, EmaxPRDE(k) denotes the maximum RDE at the kth sampling time. Deﬁning ap ¼ expðDt=Rp Cp Þ, adiff ¼ expðDt=Rdiff Cdiff Þ, according to Eq. (6), the discrete state space equation of battery pack can be expressed by:

i i i i i Udiff ;k ¼ adiff Udiff ;k1 1 adiff Rdiff Ib;k1 ði ¼ 1; 2; …; nÞ > > > i i i : Ui ¼ Ui þR I U U o b;k

OCV;k

i

(10) i i where Up;k and Up;k1 represent the polarization voltage of the ith i i cell at the kth and (k-1)th sampling time. Udiff and Udiff ;k ;k1 represent the diffusion voltage of the ith cell at the kth and (k-1)th sampling time. Dt is the sampling interval. Ib,k and Ib,k-1 represent i represents the the current at the kth and (k-1)th sampling time. Ut;k i terminal voltage of the ith cell at the kth sampling time and UOCV;k represents the OCV of the ith cell at the kth sampling time.

3.2. Model parameter identiﬁcation based on RLS algorithm The transfer function of the cell in the battery pack based on Eq. (6) in the frequency domain can be obtained as:

Gi ðsÞ ¼

Rio s2 þ Ri C i R1i p

p

Ci diff diff

T i 4ik Pk1 ¼ T i 4ik l þ 4ik Pk1

þ

i Rip Cpi Ridiff Cdiff

sþ

(18)

(19)

qik ¼ qik1 þ Kki eik

(20)

i , 4i and qi are the data input matrix and the where yik is equal to Ut;k k k model coefﬁcients matrix of the ith cell at the kth sampling time, Pki is the covariance matrix at the kth sampling time of the ith cell, l is a forgetting factor. Then the algorithm of the RLS method can be

p

diff

diff

(11)

1 i Rip Cpi Ridiff Cdiff

bi þ bi4 z1 þ bi5 z2 Gi z1 ¼ 3 1 bi1 z1 bi2 z2 2 1 z1 T 1 þ z1

(12)

(13)

where z is the discretization operator. T is the sample interval, which is equal to 1 in this paper. b1, b2, b3, b4, b5 are ﬁve undetermined coefﬁcients. Then Eq. (6) can be rewritten as Eq. (14), which can be employed in the method of RLS.

i i i i Ut;k ¼ 1 bi1 bi2 UOCV;k þ bi1 Ut;k1 þ bi2 Ut;k2 þ bi3 Ib;k þ bi4 Ib;k1 þ bi5 Ib;k2

(17)

i i Kki 4ik Pk1 Pki ¼ l1 Pk1

p

i Rip Cpi þRidiff Cdiff

where Gi ðsÞ is the transfer function of the ith cell. The discretization calculation of Gi ðsÞ can be shown as the result in Eq. (12) by the method of bilinear transformation shown in Eq. (13).

s¼

Kki

h i Ri þRi þRi i Rio þ Ridiff Rip Cpi þ Rio þ Rip Ridiff Cdiff s þ RioC i Rpi Cdiff i s2

(16)

i 4ik qk1 eik ¼ Et;k

diff ;k

p;k

(15)

The process of RLS can be implemented as follows:

yik ¼ 4ik qik þ eik

8 i i > > ¼ aip Up;k1 1 aip Rip Ib;k1 Up;k > < t;k

8 yi ¼ 4i qi > i hk k < ki i i i 4k ¼ UOCV;k ; Ut;k1 ; Ut;k2 ; Ib;k ; Ib;k1 ; Ib;k2 > iT h : i qk ¼ 1 bi1 bi2 ; bi1 ; bi2 ; bi3 ; bi4 ; bi5

219

(14)

To identify the model parameters of battery with RLS method, Eq. (14) can be written as:

used for model parameters identiﬁcation. The parameters of the battery model can be calculated by following equations:

8 > bi3 þ bi4 bi5 > > Rio ¼ > > > 1 þ bi1 bi2 > > > > rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ > > 2 > > i > > bi2 þ 3bi2 bi1 1 þ b2 þ > > i i > > R C ¼ p p > > > 2 1 bi1 bi2 > > > > > rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ > < 2 i bi2 þ 3bi2 bi1 1 þ b2 > i i > R C ¼ > > diff diff > > 2 1 bi1 bi2 > > > > > > > > bi5 bi3 > Ri Ri C i þ Ri C i i > þ Ridiff Rip Cpi þ Rip Ridiff Cdiff ¼ > o p p diff diff > > 1 bi1 bi2 > > > > > > > bi3 bi4 bi5 > i i i > > : Ro þ Rdiff þ Rp ¼ 1 bi1 bi2 (21)

220

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

Table 1 Process of UKF ﬁlter. Step 1: Initialization 8 1;þ 1;þ 1;þ T b > x ¼ E x10 ; S1;þ x10 b x0 x0 x10 b > x;0 ¼ E < 0 « > n;þ > n;þ n;þ T :b xn0 b x0 x0 xn0 b x 0 ¼ E xn0 ; Sn;þ x;0 ¼ E

(24)

3 2 SOC where x ¼ 4 Up 5. Udiff for i ¼ 1; /; n, computer the state of cells in battery pack, where n is the number of series battery in the battery pack. Step 2: The process of UKF 1) Calculate sigma points: 8 > > >

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ < i;þ i;ðjÞ i;ð0Þ i;ð0Þ i;ðjÞ i;ð0Þ xk ¼ b x k1 xk ¼ xk ðm þ kÞSi;þ ðm þ kÞSi;þ ; j ¼ 1; /; mxk ¼ xk þ ; j ¼ m þ 1; /; 2m x;k1 x;k1 > > > : where m is the dimension of battery state.k ¼ a2 ðm þ lÞ m. a is determined by the distribution of the sigma points around state, l is a secondary scaling parameter. In this paper, m ¼ 3,a ¼ 0:8, l ¼ 0. 2) Compute the weights: 8 ðmÞ > W ¼ k=ðm þ kÞ > < 0 ðcÞ W0 ¼ k=ðm þ kÞ þ 1 a2 þ b > > ðcÞ : ðmÞ Wj ¼ Wj ¼ 1=½2ðm þ kÞ; j ¼ 1 2m where b is the distribution of state, which is equal to 2 in this paper. 3) Update the battery state according to Eq. (23): 8 i;ðjÞ i;ðjÞ > x ¼ f xk1 ; uik1 ; qik > < kjk1 2m X i; ðmÞ i;ðjÞ > Wj xkjk1 xk ¼ > :b

(25)

(26)

(27)

j¼0

4) Calculate the battery state covariance 2m X i; i; T ðcÞ i;ðjÞ i;ðjÞ ¼ Wj xk xk xkjk1 b xkjk1 b Si; x;k j¼0

(28)

5) Calculate measurement by posteriori estimation 8 i;ðjÞ i;ðjÞ > y ¼ g xkjk1 > < kjk1 2m X i; ðmÞ i;ðjÞ > Wj gkjk1 yk ¼ > :b

(29)

j¼0

6) Calculate the measurement covariance and the UKF gain 2m X i; i; T ðcÞ i;ðjÞ i;ðjÞ Wj yk yk ykjk1 b ykjk1 b Siy;k ¼ Sixy;k ¼

j¼0 2m X

ðcÞ

Wj

i;ðjÞ

i;

xk xkjk1 b

i;ðjÞ

Lix;k

i; T

yk ykjk1 b

j¼0

1 ¼ Sixy;k Siy;k

(30)

(31) (32)

7) Update the state and error covariance i;þ i; i; b x k þ Lix;k yik b yk xk ¼ b T ¼ Si; Lix;k Siy;k Lix;k Si;þ x;k x;k

3.3. UKF based state observer UKF is widely applied in nonlinear system states prediction. The key of this algorithm is unscented transformation which the sigma points are chosen through the system state function, the new states are updated through the newly estimated mean and covariance based on their distribution. According to Ref. [28], the SOC is deﬁned as:

(33) (34)

SOCk ¼ SOCk1 þ Ik Dt=CN

(22)

where SOCk and SOCk-1 denote the SOC at the kth and (k-1)th sampling, Ik represents the current at the kth sampling, Dt represents the sampling period, CN is the maximum available capacity. Combining Eq. (10), and Eq. (22), the battery pack state equations can be written as follows:

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

88 0 > > > >> Dt > > > > > 1 > B 1 0 10 > >0 1 1 1 >> > C B > SOCkþ1 1 0 0 SOCk > N > > B > > > >B C B CB C B > > > > B B B C C C B > > > 1 > B 1 C B C B 1 > >B 0 C > CB Up;k C B 1 a1 R1 B Up;kþ1 C ¼ B 0 ap;k >> > > > B B B C C C B > p;k p;k > > >@ A @ [email protected] A B > > > > B > > 1 > 1 > 1 B >> 0 0 adiff ;k Udiff ;k > >> @ > Udiff ;kþ1 > > > >> > 1 a1diff ;k R1diff ;k > > >> > > > >> < > > > < « > > > > > 0 > > > Dt > >> > > > n > > 0 0 1 1 > B > 0 1 n n > C >> N 1 0 0 SOCk B > > > SOCkþ1 > > > > B B C B C B > > B C > > B B C C > > C > n > B n C B 0 an C B > > 0 CB Up;k > > B Up;kþ1 C ¼ B CB p;k > > B B 1 anp;k Rnp;k CB > > B B C C > > [email protected] > > A @ A B > >@ B > > > n n n > B > > a 0 0 U U > > diff ;k @ diff ;k diff ;kþ1 >> > > > > > > > 1 andiff ;k Rndiff ;k > >: > > > > > > > i i i i i : Ui t;kþ1 ¼ UOCV;k Up;k Udiff ;k þ IL;k Ro;k þ nk ; ði ¼ 1; …; nÞ

where u and n are the measurement noise matrix and process noise matrix, respectively. Based on Eq. (20), the process of UKF is shown in Table 1. 3.4. RLS-UKF applied in battery pack state estimation From above analysis, the RLS-UKF is employed in battery pack states estimation. The RLS is applied to estimate the slowly timevarying cell parameters caused by the different battery working conditions and initial battery states, while the UKF is employed to estimate battery SOC. In the process of the proposed method, the RLS provides accurate real-time model parameters for battery state estimation as shown in Fig. 2, which can be divided into three parts, including online battery pack model parameters identiﬁcation

221

1 C C C C C C CIL;k þ u1k C C C C A

1

(23)

C C C C C CIL;k þ un k C C C C A

based on RLS, single battery SOC observer based on UKF and the battery pack states estimation. Part 1: online battery pack parameters identiﬁcation. The realtime battery terminal voltage, cell working temperatures and load current are measured by BMS, and the online parameters of the battery pack model can be identiﬁed by the RLS based on the real-time data provided by BMS. Part 2: single cell battery SOC observer. With the parameters provided by the RLS, the UKF is applied in single cell SOC observer. In the process of UKF, the ﬁrst step is the state initialization by random and covariance approximated by sigma points selected. The second step is to predict the states through the state transition function, the predict mean and covariance need to be computed at the same time. Finally, the battery states are updated through

Fig. 2. Diagram of the process of RLS-UKF.

222

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225 Table 2 The main parameters of a Li(Ni1/3Co1/3Mn1/3)O2 battery. Nominal capacity Nominal voltage Upper/lower cut-off voltage Operation condition of temperature

38AH 3.7 V 4.2 V/2.7 V 20 Ce60 C

Fig. 3. Battery test bench.

calculating the UKF gain and the error of battery voltage observation. Part 3: the battery pack states estimation. According to above processes, the single battery states are achieved. The degree of battery inconsistency, the battery pack remaining discharge and energy utilization ratio can be calculated by Eq. (5), Eq. (8) and Eq. (4). 4. Experiment and veriﬁcation To acquire the measurement data such as cell voltages, load current, cell temperatures and charge/discharge capacity, the test bench is built as shown in Fig. 3, which contains a BMS used to monitor the cell voltages, the battery working temperatures and the load current, a Digatron battery test system used to provide programmable test schedule on the Li(Ni1/3Co1/3Mn1/3)O2 battery pack, a programmable temperature chamber which is applied to provide different working temperature conditions. They communicate with each other through TCP/IP or CAN. All of the proposed equipment is controlled by personal computer (PC). The parameters of Li(Ni1/3Co1/3Mn1/3)O2 single battery produced by Tianjin EV Energies Co., Ltd are shown in Table 2. 4.1. OCV-SOC-temperature test To acquire the relationship between SOC and OCV at different working temperatures as shown in Eq. (7), a series of experiments are conducted on a Li(Ni1/3Co1/3Mn1/3)O2 battery. The process of test schedule is designed as follows: ﬁrstly, the battery is fully charged; secondly, the battery is discharged as the capacity of 10% of the maximum available capacity and rested for 8 h; thirdly, repeat the second step till the battery reaches the lower cut-off voltage. The test procedures are conducted under the working temperature of 20 C, 0 C, 15 C, 25 C and 45 C. The test result is shown in Fig. 4 (a). Ki (i ¼ 0, 1, …, 5) in Eq. (7) are identiﬁed by the RLS as shown in Table 3. 4.2. The maximum available capacity To achieve the maximum available capacity, the experiments are done under the temperatures of 20 C, 0 C, 15 C, 25 C and 45 C.

Fig. 4. (a) OCV-SOC-T test results under different working temperatures. (b)The maximum capacity test results under different working temperatures.

At each temperature, the battery is fully charged, then the battery is discharged under the current rate of 1C till the terminal voltage reaches the lower cut-off voltage. Above process is repeated three times. The results are shown in Fig. 4 (b). What's more, the relationship between the maximum available capacity and working temperatures are shown in Eq. (35).

CN ðTÞ ¼ 6:3987e 05T 3 6:9118e 03T 2 þ 0:3137T þ 34:5427

(35)

where T is the battery working temperature, CN(T) is the maximum available capacity at temperature of T. 4.3. Battery experimental veriﬁcation Before the experiments, the batteries in the battery pack are rigorously selected, which have the similar capacity within the error of 1% and the same relationship between SOC and OCV under different working temperatures. In experiments, the Li(Ni1/3Co1/ 3Mn1/3)O2 battery pack are connected with 18 series and 2 parallels and the sampling period is 1 s. 4.3.1. Test schedule A The NEDC is a typical vehicle test proﬁle used in Europe, which refers to the electric vehicle battery test procedures manual. The load current is shown in Fig. 5 (a). The temperatures of the 18 series

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

223

Table 3 Parameters of the OCV-SOC-T function UOCV(SOC). Parameters

Value

K0

ð3:2042e 07ÞT 4 ð9:1170e 06ÞT 3 ð3:6322 04ÞT 2 þ 0:0107T þ 3:7838

K1

ð5:9134e 07ÞT 4 ð1:0894e 05ÞT 3 þ 0:0011T 2 0:0278T 0:4590

K2

ð2:9688e 07ÞT 4 ð1:2625e 06ÞT 3 ð7:9574e 03ÞT 2 þ 0:0173T þ 0:9064

K3

ð1:4283e 12ÞT 4 ð5:1263e 11ÞT 3 ð1:2305e 09ÞT 2 þ 5:3955e 08T þ 7:2280e 07

K4

ð1:1944e 07ÞT 4 ð3:8177e 06ÞT 3 ð1:1579e 05ÞT 2 þ 0:0048T þ 0:0721

K5

ð1:2081e 09ÞT 4 þ 7:9476e 07T 3 ð6:8033e 06ÞT 2 þ 1:6540e 04T þ 0:0038

Fig. 5. Experimental results of the NEDC: (a) Load proﬁles. (b) Cell temperature. (c) Battery pack remaining discharge energy. (d) Energy utilization ratio and the degree of battery inconsistency.

Table 4 Performance of SOC and cell voltage estimation under NEDC proﬁles. Cell number

Cell voltage- RLSUKF(V)

Cell voltage- UKF(V)

MAE

RMSE

MAE

RMSE

Cell1 Cell2 Cell3 Cell4 Cell5 Cell6 Cell7 Cell8 Cell9 Cell10 Cell11 Cell12 Cell13 Cell14 Cell15 Cell16 Cell17 Cell18

0.0576 0.0569 0.0583 0.0572 0.0564 0.0517 0.0493 0.0514 0.0430 0.0415 0.0463 0.0445 0.0499 0.0505 0.0556 0.0561 0.0571 0.0587

0.0868 0.0907 0.0925 0.0913 0.0875 0.0879 0.0841 0.0870 0.0785 0.0747 0.0804 0.0752 0.0814 0.0822 0.0887 0.0901 0.0909 0.0918

0.0702 0.0710 0.0721 0.0714 0.0691 0.0679 0.0663 0.0676 0.0628 0.0620 0.0629 0.0617 0.0643 0.0669 0.0706 0.0727 0.0744 0.0735

0.1216 0.1228 0.1354 0.1207 0.0995 0.0991 0.0983 0.0987 0.0916 0.0907 0.0916 0.0912 0.0947 0.0986 0.1053 0.1342 0.1448 0.1376

Initial SOC

SOC-RLS-UKF

SOC-UKF

MAE

RMSE

MAE

RMSE

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.0052 0.0053 0.0054 0.0062 0.0052 0.0057 0.0056 0.0053 0.0045 0.0048 0.0044 0.0042 0.0044 0.0040 0.0059 0.0061 0.0052 0.0051

0.0072 0.0079 0.0080 0.0091 0.0076 0.0082 0.0079 0.0073 0.0062 0.0066 0.0062 0.0058 0.0060 0.0057 0.0085 0.0094 0.0080 0.0076

0.0065 0.0072 0.0074 0.0087 0.0071 0.0073 0.0075 0.0070 0.0057 0.0063 0.0054 0.0052 0.0054 0.0049 0.0064 0.0066 0.0075 0.0073

0.0091 0.0119 0.0120 0.0147 0.0123 0.0127 0.0128 0.0099 0.0097 0.0126 0.0102 0.0096 0.0101 0.0083 0.0106 0.0112 0.0111 0.0120

224

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

Fig. 6. Experimental results of the real driven proﬁles: (a) Load proﬁles. (b) Cell temperature. (c) Battery pack remaining discharge energy. (d) Energy utilization ratio and the degree of battery inconsistency.

Table 5 Performance of SOC and cell voltage estimation under real driven proﬁles. Cell number

Cell voltage- RLSUKF(V)

Cell voltage- UKF(V)

MAE

RMSE

MAE

RMSE

Cell1 Cell2 Cell3 Cell4 Cell5 Cell6 Cell7 Cell8 Cell9 Cell10 Cell11 Cell12 Cell13 Cell14 Cell15 Cell16 Cell17 Cell18

0.0173 0.0192 0.0198 0.0181 0.0187 0.0169 0.0174 0.0165 0.0176 0.0169 0.0167 0.0171 0.0178 0.0171 0.0171 0.0175 0.0178 0.0169

0.0221 0.0256 0.0248 0.0228 0.0229 0.0215 0.0222 0.0211 0.0226 0.0223 0.0217 0.0215 0.027 0.0225 0.0219 0.0229 0.0232 0.0221

0.0249 0.0271 0.0268 0.0253 0.0249 0.0244 0.0252 0.0237 0.0252 0.0242 0.0237 0.0245 0.0237 0.0244 0.0245 0.0250 0.0251 0.0294

0.0310 0.0322 0.0320 0.0314 0.0312 0.0295 0.0307 0.0293 0.0322 0.0306 0.0273 0.0307 0.0275 0.0313 0.0305 0.0316 0.0323 0.0341

batteries in the battery pack are plotted in Fig. 5 (b). The battery pack RDE and the maximum RDE are shown in Fig. 5 (c). The degree of battery pack inconsistency and the energy utilization ratio are plotted in Fig. 5 (d). The numerical results of the mean absolute error (MAE) and the root mean square error (RMSE) of SOC and cell voltage estimation of the 18 series batteries are listed in Table 4. According to Table 4, the maximum of the MAE and the RMSE of the cell voltage estimation based on the proposed method in the pack are 0.0587 V and 0.0925 V, respectively. In contrast, the results based on UKF are 0.0744 V and 0.1448 V, respectively. Meanwhile the maximum of the MAE and the RMSE of the cell SOC estimation

Initial SOC

SOC-RLS-UKF

SOC-UKF

MAE

RMSE

MAE

RMSE

0.58 0.58 0.59 0.58 0.59 0.58 0.58 0.59 0.58 0.59 0.59 0.58 0.58 0.59 0.59 0.58 0.59 0.58

0.0024 0.0023 0.0026 0.0022 0.0022 0.0022 0.0023 0.0020 0.0022 0.0020 0.0021 0.0022 0.0021 0.0023 0.0021 0.0022 0.0023 0.0021

0.0035 0.0033 0.0034 0.0032 0.0034 0.0033 0.0034 0.0030 0.0033 0.0030 0.0031 0.0033 0.0032 0.0033 0.0031 0.0032 0.0033 0.0030

0.0041 0.0031 0.0049 0.0032 0.0033 0.0032 0.0032 0.0028 0.0039 0.0033 0.0036 0.0037 0.0039 0.0040 0.0040 0.0040 0.0046 0.0037

0.0056 0.0049 0.0061 0.0043 0.0051 0.0047 0.0045 0.0041 0.0048 0.0045 0.0051 0.0053 0.0051 0.0055 0.0056 0.0053 0.0059 0.0048

based on the proposed method in the pack are 0.0062 and 0.0091, respectively. The MAE and RMSE of the UKF method for SOC estimation are 0.0087 and 0.0147, respectively. The results show that the proposed method can estimate the battery state with high accuracy compared with the UKF method. In Fig. 5 (c), due to the energy dissipation in battery resistance and battery inconsistence, the battery pack RDE is always lower than the maximum RDE. According to Fig. 5 (d), we can ﬁnd that the battery pack energy utilization ratio and the degree of battery inconsistency change with the load proﬁles. Meanwhile, the increasing of the degree of battery inconsistency leads to the pack energy utilization ratio

X. Zhang et al. / Journal of Power Sources 343 (2017) 216e225

decrease. 4.3.2. Test schedule B To verify the proposed method with accuracy, the real driven proﬁle is tested at Anhui province Wuhu of China. The load current is shown in Fig. 6 (a). The cell temperatures are shown in Fig. 6 (b). The battery pack RDE and the maximum RDE are shown in Fig. 6 (c). Fig. 6 (d) shows the degree of battery inconsistency and the battery pack energy utilization ratio. The numerical results of the cell SOC and voltage estimations are listed in Table 5. The maximum of the MAE and the RMSE of the cell voltage estimation based on the proposed method are 0.0198 V and 0.0248 V, respectively. Meanwhile the maximum of the MAE and the RMSE of the cell SOC estimation are 0.0026 and 0.0035, respectively. And the results based on the UKF for SOC estimation are 0.0049 and 0.0061, respectively. These results suggest that the proposed method can estimate the cell state under uncertainty temperature and working proﬁles. According to Eq. (5), Eq. (8) and Eq. (9), the battery pack energy utilization ratio is bound up with the degree of battery inconsistency, which is veriﬁed in Fig. 5 (d) and Fig. 6 (d), and the battery pack energy utilization ratio will increase when the degree of battery inconsistency decreases. Meanwhile, the degree of battery pack inconsistency and energy utilization ratio change fast when the battery approach the lower cut-off conditions caused by the different battery performance. 5. Conclusion The battery remaining discharge energy is important in battery energy storage system. In this paper, to estimate the battery pack remaining energy with high accuracy, a novel algorithm of the RLSUKF is proposed, which the RLS is applied in the parameters of the battery pack model identiﬁcation, and the UKF is employed in the estimation of battery pack RDE and battery pack energy utilization ratio. Meanwhile, this paper proposes the deﬁnition of the degree of battery pack inconsistency by the mathematical methods of statistics based on the precise estimation of single cell SOC. The experiments under the NEDC proﬁles and the real driven proﬁles, with the RMSE of the battery SOC estimation less than 0.01, verify that the proposed method can precisely predict the battery pack

225

RDE and energy utilization ratio. In addition, the results of the experiments indicate that the battery pack energy utilization ratio decreases when the degree of battery inconsistency increases. Acknowledgement This work is supported by the National Natural Science Fund of China (Grant No. 61375079). The authors also wish to thank Tianjin EV Energies Co., Ltd for their valuable advices and providing the help in experiment test. References [1] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, J. power sources 226 (2013) 272e288. [2] P. Verma, P. Maire, P. Nov ak, Electrochimica Acta 55 (2010) 6332e6341. [3] C. Guenther, B. Schott, W. Hennings, P. Waldowski, M.A. Danzer, J. Power Sources 239 (2013) 604e610. [4] G. Liu, M. Ouyang, L. Lu, J. Li, J. Hua, Appl. Energy 149 (2015) 297e314. [5] Y. Wang, C. Zhang, Z. Chen, Appl. energy 135 (2014) 81e87. [6] C.-L. Wei, M.-F. Huang, Y. Sun, A. Cheng, C.-W. Yen, in: 2016 IEEE International Conference on Industrial Technology (ICIT), IEEE, 2016, pp. 230e233. [7] J. Kim, D.K. Noh, in: SENSORS, 2013 IEEE, IEEE, 2013, pp. 1e4. [8] L. Zheng, J. Zhu, G. Wang, T. He, Y. Wei, Appl. Energy 178 (2016) 1e8. [9] Y. Wang, Z. Chen, C. Zhang, Appl. Energy (2016), http://dx.doi.org/10.1016/ j.apenergy.2016.05.081. [10] B. Akdemir, S. Günes, I.T. Comlekciler, (2009) 779e783. [11] A.M. Fares, C. Klumpner, M. Sumner, in: Power Electronics and Applications (EPE'16 ECCE Europe), 2016 18th European Conference on, IEEE, 2016, pp. 1e10. [12] X. Zhang, Y. Wang, D. Yang, Z. Chen, Energy 115 (2016) 219e229. [13] G. Dong, J. Wei, Z. Chen, J. Power Sources 328 (2016) 615e626. [14] Y. Wang, C. Zhang, Z. Chen, J. power sources 279 (2015) 306e311. [15] J. Zhang, Y. Wei, H. Qi, Appl. Math. Model. 40 (2016) 6040e6050. [16] K.S. Ng, C.-S. Moo, Y.-P. Chen, Y.-C. Hsieh, Appl. energy 86 (2009) 1506e1511. [17] Y. Tian, B. Xia, W. Sun, Z. Xu, W. Zheng, J. power sources 270 (2014) 619e626. [18] F. Sun, X. Hu, Y. Zou, S. Li, Energy 36 (2011) 3531e3540. [19] Y. He, X. Liu, C. Zhang, Z. Chen, Appl. Energy 101 (2013) 808e814. [20] A. Tulsyan, Y. Tsai, R.B. Gopaluni, R.D. Braatz, J. Power Sources 331 (2016) 208e223. [21] M. Koot, J.T. Kessels, B. de Jager, W. Heemels, P. Van den Bosch, M. Steinbuch, IEEE Trans. Veh. Technol. 54 (2005) 771e782. [22] H. Dai, X. Wei, Z. Sun, J. Wang, W. Gu, Appl. Energy 95 (2012) 227e237. [23] H. He, R. Xiong, H. Guo, Appl. Energy 89 (2012) 413e420. [24] Y. Hua, A. Cordoba-Arenas, N. Warner, G. Rizzoni, J. Power Sources 280 (2015) 293e312. [25] G.L. Plett, J. Power Sources 161 (2006) 1369e1384. [26] R. Xiong, F. Sun, Z. Chen, H. He, Appl. Energy 113 (2014) 463e476. [27] R. Xiong, F. Sun, H. He, T.D. Nguyen, Energy 63 (2013) 295e308. [28] G.L. Plett, J. Power Sources 134 (2004) 277e292.