State of Health Estimation Using SMO for EVs

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 105 (2017) 4383 – 4388

The 8th International Conference on Applied Energy – ICAE2016

Lithium-ion Battery State of Charge/State of Health Estimation Using SMO for EVs Cheng Lina, Jilei Xinga , Aihua Tanga,b* a

National Engineering Laboratory for Electric Vehicles and Collaborative Innovation Center of Electric Vehicles in Beijing, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China b Sichuan Provincial Key Lab of Process Equipment and Control, School of Mechanical Engineering, Sichuan University of Science & Engineering, Zigong 643000, China

Abstract Advanced battery management systems (BMS) in electric vehicles (EVs) require immediate and accurate battery state, such as State-of-Charge (SoC) and State-of-Health (SoH) for efficient monitoring and control. To improve the state estimation performance of battery, an electrochemical model is applied in this paper. First, the electrochemical model is reduced to describe the instantaneous Li-ion concentration dynamics of each electrode sufficiently without main information loss. Second, two separate sliding mode observers (SMOs) combined with reduced order electrochemical model are designed to identify SoC/SoH of lithium-ion cell from external measured voltage and current value. An estimation scheme which is comprised of two subestimators is designed. They work jointly: one separate sliding mode observer (SMO) for SoC estimation using Li-ion solid-electrolyte concentration and the other observer for cell contact resistance adopting Lyapunov’s stability theory. Finally, in order to demonstrate the performance of proposed scheme, the simulations are verified by experiments from a 2.3Ah high-power LiFePO4/graphite cell used in EVs. The results indicate that the proposed estimation scheme with the SMO algorithm performs well with initial error values. The maximum SoC and SoH estimation error are less than 3% and 2.5% under Urban Dynamometer Driving Schedule (UDDS) drive cycles. © Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2017 2016The TheAuthors. Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy.

Key words: electric vehicles (EVs); State-of-Charge (SoC); State-of-Health (SoH); sliding mode observers (SMO); electrochemical model

Introduction At present, Li-ion cells has become one of the very attractive candidates in EV’s application since they were featured by high-power density, high-energy density, long service life, non-memory effect and * Corresponding author. Tel.: +86-106-891-3992; fax: +86-106-891-3992. E-mail address: [email protected].

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.931

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environmental friendliness, etc.[1]. However, Li-ion cells for EVs must operate within a safe and reasonable range, and improper operating conditions such as exceeding the specified restrictions of temperature and voltage windows can accelerate attenuation processes and even result in the failures. Thus, for safety and reliability of Li-ion batteries, it is required to monitor the batteries operate at reliable operation range through the adoption of model-based BMS in EVs. The core of a BMS is a battery model which identifies the relationship between measured voltages and currents at battery terminals [2].Unfortunately, the main technical challenge for SoC/SoH estimation of Li-ion cell comes from the weak observability and the effects from the intricate electrochemical processes in EV application [3]. The main challenge in SoH estimation exists in the lack of established existing SoH evaluation indictors. Recent literatures have proposed a number of indicators (charge capacity [4], internal resistance [5], etc). This paper attempts to study the joint estimation of SoC/SoH for individual battery cells. In this paper, we derived SPM from P2D model and validated it in order to evaluate the accuracy considering the application of SPM in next step. Moreover, we analyzed the state space properties of the SPM. Next, we designed a combined SoC/SoH estimation scheme applying sliding mode theory, where the SoC is calculated according to Li-ion solid-electrolyte spatial concentrations and the SoH is characterized by the contact resistance estimation. The intention of adopting SMO derives from its intrinsic property of processing uncertainty problem. Then, schematic diagram for the offline identification of the joint SoC/SoH estimation in Li-ion cell is designed in this paper. Finally, an evaluation of the tracking accuracy, complexity and computation, and convergence ability against uncertainty with initial SoC values is implemented. 2.Li-ion cell electrochemical model 2.1.Single particle model As illustrated in Fig.1 [6, 7], a Li-ion cell model composes of a negative electrode, a separator, a positive electrode and two current collectors at the ends of the two electrodes. Generally, a grain structure of quasi-spherical active particles comprise electrode in μm scale. The Li-ions travel inside/outside the active particles via diffusion and migration within the active particles along the r-axis, which is called solid phase diffusion. The SPM is a physics-based, order-reduced model of P2D where the current density is supposed to be LiFePO4 Carbon uniform in each electrode, and all of the active Separator material particles are distributed parallel in  cs (r ) Discharge cs (r )  separate manner. Mathematically, the SPM is Li r r composed of two linear solid-state diffusion Electrolyte PDEs for each electrode’s concentration Positive Negative c s 0 c s1 dynamics, where current inputs as Neumann c sM boundary conditions (1), a nonlinear output r R r 0 voltage function of the state values at the Fig. 1 Schematic diagram of single particle of a Li-ion cell model boundary and the input current deduced from Bulter-Volmer kinetics (4). The details of SPM are given as follows.

wcsi wt

Dsi w § 2 wcsi · ¨r ¸ , for r  0, Rs r 2 wr © wr ¹

The initial conditions (2) and Neumann boundary conditions (3) are introduced :

(1)

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C si,0

, for C ! 0 at t

C

wcsi wr

0, r 0

wcsi wr

0 r   0, Rs 

r Rs

ji Dsi

(2) (3)

csi is the solid phase Li-ion concentration , Dsi is the solid phase diffusion coefficient inside solid particles, r is the radial coordinate, ji is the reactive ion current density ( ji ! 0 represent discharge) at the current collector boundary of positive and negative electrode, Rs is the radius of the particle, and i r represents positive/negative electrode. Where

The Bulter-Volmer equation is given:

ji

2ki cs ,i max (1  Ti )0.5 (Ti )0.5 c 0.5 sinh[

0.5F Ki ) RT

Where ki is the electrochemical reaction rate constant of positive / negative electrode, T i

(4)

c ssurf t ,i cs ,i ,max

is

the state of charge variable of positive / negative electrode, c surf  t is Li-ion concentration of particle s ,i

cs ,i max .is the maximum lithium ion concentration within active particles of positive / negative electrode, c is the Li-ion concentration of electrolyte, F is the faraday’s number R is the universal Gas constant, T is the temperature, and Ki is given as: surface,

Ki mi

2 RT ln( mi  mi2  1) F I Fki Si cs ,i ,max c 0.5 (1  Ti )0.5 (Ti )0.5

(5) (6)

Since the SPM ignores the reaction process related with the liquid phase diffusion, the potential of liquid phase at the electrode is zero. Therefore, the overpotential of the positive/negative electrode can be given:

Ki Ms ,i  Ui (cssurf ,i ) Where

Is,i

the solid is phase voltage and

(7)

U i (cssurf ,i ) is the open circuit voltage of the

positive/negative electrode. According to the internal physical characteristics of the battery, the difference between the positive electrode and the negative electrode is the battery terminal voltage, which is given:

V

Ms , p  Ms ,n ˄U p (T p )  U n (Tn )) ˄K p Kn )

(8)

2.2.Model validation and verification Fig. 2 compares the voltage responses between the simulations of SPM and experiments with 0.5C constant current charge/discharge process at 25ć ć ambient temperature for the 2.3 Ah LFP/gr cells. Where experiment and simulation are abbreviated as Exp and Sim. The lower and upper voltage limits for the cell experiments and simulations are between 2.95 V and 3.6 V. The simulation of SPM matches the experimental voltage response very well during charging stage within the mid SoC operating range. However, the SPM voltage responses at the end of

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discharge cycles do not match the experiment as well, which possibly can attribute to the simplifying assumptions in our reduced model. The battery voltage error is still acceptable with a maximum error of less than 30 mV. V(Voltage)

I(Current) Li-ion Cell V & I Measurement

ܴ෠݂

SOC Sliding Mode Observer

ܿƸ•

[Ĉs0,..,Ĉs•]

Contact Resistance Estimator

ܿƸ•

Li-ion Cell SOC / SOH determination

Fig. 2. Experimental and SPM voltage responses

Fig. 3. Scheme of model parameter identification

3.State estimation and parameter identification 3.1.State space model formulation The state space of the above reduced model can be re-written in the following:

x T Ax Ax  B Bu y

Where state vector x  R

M

h  xM , u  R f u

(9)

is the Li-ion concentrations in the negative electrode,

csM  R is the Li-ion surface concentration state of solid phase, T

Ds / '2  R is a scalar parameter referred to diffusion coefficient, R f  R is the contact resistance, u I  R is the mode input and y V  R are the input current and the output measured voltage of the cell respectively, and the tridiagonal matrices A and column vector B are derived from (8) and the scalar output function h is derived from (8). xM

3.2. Observer scheme design The schematic diagram for the offline identification of the combined SoC/SoH estimation of Li-ion cell is illustrated in Fig. 3. The initial values of the parameters cs 0 , cs 0 and R0 , R0 are presented. Then, the SoC observer estimate the Li-ion concentration states and the contact resistance estimator tracks

R f on

the basis of voltage and current measurements. The operating process of Fig. 3 can be divided into four steps: z Step 1: Data measurement. Dataset used here is offline data. z Step 2: Model parameter identification. The reasonable model parameter identification method is chosen according to the selected model. For example, parameters of all state-space based battery models can be identified offline (Fig. 3) based on the SMO method in this paper.

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z

Step 3: Parameter estimator. The SoC SMO estimates Li-ion concentration in face of known contact resistance and convergences in short time. Meanwhile, the contact resistance observer tracks R f based on measuring the output terminal voltage and input current of the cell. Step 4: Parameter and state update. The SMO-based SoC observer continually updates contact resistance information and the estimates of Li-ion concentration states within the operation range.

z

4.Simulation analysis In order to verify the proposed method, numerical simulation is carried out. The model parameters of the battery cell used in this study originate from [8] and experimental data from CALCE Battery Group Data. For the simulation, the state and parameter estimates are initialized at incorrect values to evaluate its convergence. The Urban Dynamometer Driving Schedule (UDDS) drive cycles is used to evaluate parameter estimation algorithms. In this paper, five consecutive UDDS cycles are applied to verify the offline estimation algorithm. UDDS test is performed with the current profiles shown in Fig. 4 and terminated by a lower cut-off voltage. The current, voltage and the evolution of the state and parameter estimate profiles are portrayed in Fig. 4. observer experimental data

3.6

0.2

Voltage error [V]

Voltage [V]

3.4

3.2

3

2.8

2.6

0.15

0.1

0.05

0

0

0.5

1

1.5

-0.05

2

Time [s]

x 10

4

0

0.5

1

1.5

Time [s]

(a) Terminal voltage

2 x 10

(b) Terminal voltage error

4

0.1

1 observer experimental data

0.9

0.08

0.8

SoC error

0.06

SoC

0.7 0.6

0.04

0.02 0.5

0

0.4 0.3

0

0.5

1

1.5

-0.02 0

2

Time [s]

(c) SoC estimation results and true SoC

x 10

0.5

1

1.5

Time [s]

4

2 x 10

4

(d) SoC estimation error 0.024

0.145

0.022

Resistance error [Ohm]

Resistance [Ohm]

0.14 0.135 0.13 0.125

0.02 0.018 0.016 0.014 0.012 0.01 0.008

0.12

0.006 0.115

0

0.5

1

Time [s]

1.5

0

2 x 10

(e) Estimation results and true profiles of cell contact resistance

0.5

1

1.5

Time (s)

4

(f) Estimation error of cell contact resistance

Fig. 4. Profiles of estimation results

2 x 10

4

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5.Conclusions This paper simplifies a Li-ion electrochemical mechanism model for the purpose of better application in EVs. An SPM is proposed for modeling the LiFePO4/graphite battery cell by ignoring the spatial distribution inhomogeneity of local volumetric transfer current density and the Li+ concentration in solidphase electrode and electrolyte. Furthermore, the offline identification approach of the model parameters is proposed by a SMO algorithm. For validation of the proposed observer scheme design, the simulation schedule is designed and carried out, and the offline model parameters are identified with UDDS test. The results are validated by experimental data. The proposed SMO-based offline parameter estimation identification method shows good performance in the accurate prediction of the terminal voltage and model parameters. The maximum voltage estimation error is within 1% and the SoC estimation error can converge to 2% under initial error SoC. Although the SP model exhibits less accuracy than the empirical model, it is an attractive candidate for application in EVs within an acceptable error range for its simple. Copyright Authors keep full copyright over papers published in Energy Procedia Acknowledgements The financial support from the National Natural Science Foundation of China (51575044) and SinaPolish collaborative research in e-mobility public transportaion (2015DFG81930) and from Sichuan Provincial Key Lab of Process Equipment and Control Foundation (GK201603). References [1] Xuebing Han, Minggao Ouyang, Languang Lu, Jianqiu. Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle. Part I: Diffusion simplification and single particle model. J. Power Sources 2015; 278: 802–813. [2] Yinyin Zhao, Song-Yul Choe. A highly efficient reduced order electrochemical model for a large format LiMn2O4/Carbon polymer battery for real time applications. Electrochimica Acta 2015; 164: 97–107. [3] K. B. Hatzell, A. Sharma, and H. K. Fathy. A survey of long-term health modeling, estimation, and control of Lithium-ion batteries: Challenges and opportunities. 2012 American Control Conference (ACC) 2012; 584-591. [4] K. S. Ng, C. Moo, Y. Chen, and Y. Hsieh. Enhanced coulomb counting method for estimating state-of-charge and state-ofhealth of lithium-ion batteries, Applied Energy 2009; 86: 1506-1511. [5] J. Remmlinger, M. Buchholz, M. Meiler, P. Bernreuter, and K. Dietmayer. State-of-health monitoring of lithium-ion batteries in electric vehicles by on-board internal resistance estimation. Journal of Power Sources 2011: vol; 196: 5357-5363. [6] S. Dey and B. Ayalew. Nonlinear Observer Designs for State-of Charge Estimation of Lithium-ion Batteries. American Control Conference (ACC) 2014. [7] M. F. Samadi, S. M. Alavi, and M. Saif. Online state and parameter estimation of the Li-ion battery in a Bayesian framework. American Control Conference (ACC) 2013; 4693-4698. [8] M. Safari, C. Delacourt. Modeling of a Commercial Graphite/LiFePO4 Cell. Journal of the Electrochemical SoCiety. 2011; 158 (5) :A562-A571.

Biography Aihua Tang is currently working toward the Ph.D. degree in vehicle Engineering with the Beijing Institute of Technology, Beijing, China.