State Estimation Method of Lithium-ion Battery Based on

3rd Joint International Conference on Energy, Ecology and Environment and Electrical Intelligent Vehicles (ICEEE 2019/ICEIV 2019) ISBN: 978-1-60595-641-1

State Estimation Method of Lithium-ion Battery Based on Electro-thermal Model and Strong Tracking Particle Filter

Chunyu Wang, Naxin Cui, Changlong Li

School of Control Science and Engineering, Shandong University, Jinan 250061

help improve battery utilization efficiency, extend

battery life and predict vehicle operating range.

In order to accurately monitor the battery state, a

battery model is required to describe battery dynamics.

Because battery is a complex electrochemical system

with coupled electro-thermal characteristics, battery electro-thermal model is more practical in industrial

context and studied widely [3] [4]. The entropy variation coefficient is an important parameter, which is

proportional to the entropy changes due to

electrochemical reactions. The classical method to

obtain entropic heat is potentiometric method. In this

method, the OCV variations under different

temperatures are measured at given SOC to calculate

entropy variation coefficient [5]. It requires a very long

test cycles. In this paper, a calorimetric method is

presented for the fast estimation of the entropy variation coefficient.

Lithium-ion battery is a strong nonlinear system. SOC is an internal state which cannot be measured

directly, so accurate estimation of SOC is a challenging

task. PF based estimation method, with the ability to deal with nonlinear problems, has been applied to

estimate SOC [6] [7]. However in the operation of

electric vehicles, especially starting, climbing and

regenerative braking, abrupt currents is ubiquitous, and

the conventional PF have the poor ability to track

saltatory states. STF method is robust to model errors

and has strong tracking ability for saltatory state [8] [9].

By introducing STF into PF, an estimator based on

STPF is proposed to improve the accuracy and

robustness of battery state estimation.

In this article, a battery electro-thermal model is

adopted to describe the dynamic behaviors of battery. A calorimetric method is proposed to fast determine

entropy variation coefficient. The estimator based on STPF is proposed to realize SOC estimation. The

performances of battery model and estimation method

are verified by experiments under dynamic characterization schedules.

Abstract

Accurate estimation of battery state is crucial for

battery management system. Lithium-ion battery is a

complex electrochemical system with coupled electro-

thermal characteristics and strong nonlinearity.

Therefore a state estimation method based on electro-

thermal model and strong tracking particle filter is proposed in this article. The calorimetric method is

employed to realize fast identification for thermal model

parameter. By introducing strong tracking filter into

particle filter, an estimator based on strong tracking

particle filter is proposed to improve the estimation

accuracy and tracking capability of saltatory state. The

simulation and experiments are conducted to verify the

performance of proposed method under dynamic

characterization schedules.

Keywords: battery management system, lithium-ion

battery, electro-thermal model, state estimation, strong tracking particle filtering

State of Charge

Open Circuit Voltage

Particle Filter

Strong Tracking Filter

Strong Tracking Particle Filter

Battery Management System

Nomenclature

Abbreviation

SOC

OCV

PF STF

STPF

BMS

1. Introduction

Lithium-ion batteries have become the most

promising power sources in electric vehicles and hybrid

electric vehicles due to their high energy and power

density, low self-discharge rate, long cycle life and lack

of memory effect[1]. In order to improve the safety and

reliability of battery system, the BMS is required to be

well-designed[2]. Accurate estimation of battery state is

one of the most critical indexes for BMS, which can

177

Paper ID: ICEIV2019-89

2 Copyright © by ICEIV

2. Battery electro-thermal model

2.1 Electrical dynamics The second-order RC equivalent circuit model is

adopted to describe the battery electrical behavior, as shown in figure 1. A voltage source is used to describe the battery’s OCV. A resistance R0 represents ohmic resistance in the battery. The two RC parallel-connected networks consist of electrochemical polarization capacitance C1 and resistance R1, concentration polarization capacitance C2 and resistance R2, which reflect the dynamic property of battery.

I

Uocv

R0

R1 R2

C1 C2

Figure 1 Second order RC equivalent circuit model

Based on the second-order equivalent circuit model, the state space equation of a lithium-ion battery can be expressed as：

1

2

1

2

1

1, 1 1,

2, 1 2,

1

2

1 0 0

0 0

0 0

(1 )

(1 )

k k

t

k k

t

k k

N

t

k k k

t

z z

U e U

U e U

t C

e R I W

e R

(1)

, 1 1, 1 2, 1 0t k ocv k k k kU U U U I R V (2)

Where z represents SOC; is the coulombic efficiency; CN is the maximum available capacity; t is the sampling interval; k is discrete time variable;

1 ,

2 are the time constants; 1 1 1R C ,

2 2 2R C ; k is

noise drive matrix; Wk and Vk are process and measurement noise, the noises covariance are Q and

R respectively.

2.2 Thermal dynamics

q

Rth

Cth

Ta

T

Figure 2 lumped thermal model

A lumped thermal model is established in this paper, as shown in figure 2. The temperature and heat generation within the cell are assumed to be uniformly distributed. T represents battery temperature and Ta represents ambient temperature. Rth is thermal resistance, Cth is thermal capacitance,

th represents thermal time constants,

th th thR C . q is the rate of heat generation.

According to the energy conservation law, the temperature change can be expressed as:

ath

th

T TdTC q

dt R

(3)

The battery temperature at (k)th sampling time can be conducted from equation (3):

1 (1 )k k a

th th th th th

t t t qT T T

C R C R C

(4)

The heat generation rate q is determined by electrical dynamics as

( ) ocvt ocv

Uq U U I I T

T

(5)

where, ( )t ocvU U I accounts for resistive dissipation, whereas ocvU T I T is reversible entropic heat.

ocvU T is entropy variation coefficient. The heat generation rate q is affected by battery electrical model parameters. Then the electrical model parameters change according to battery temperature.

3. SOC estimation based on STPF method An estimator based on STPF is designed to realize

the SOC estimation. According to the battery model (1) and (2), the system input, state and output variables can be defined as k ku I ,

1 1 1,k 1 2,k 1k kx z U U

1 , 1k t ky U , respectively. Then the process of STPF algorithm can be summarized as follows.

(1) Initialization: k=0, randomly generate N particles based on gauss distribution 0 0 0( P )ix ~ N x ，， initial weights are defined as 1/N。

(2) Time update, For k=1:T For i=1:N, STF is employed to update particles and produce importance densities. (3) Update particles

1

ˆ ˆ( , ) ( ,P )i i i i

k k kk k k k k kx q x x y N x

(6)

(4) Calculate the weights

2

1 22

ˆ( )1(y ) exp( )

22

i i i k kk k k k

y yw w p x

RR

(7)

(5) Normalize the weights

178



1

Ni i j

k k k

j

w w w

(8)

(6) Residual resampling method is employed to resample, and the weights be reset to 1/N

(7) State estimation

1

ˆN

i i

k k k

i

x x w

(9)

4. Experimental results A 18650-type NMC ternary lithium-ion battery with

3.6V nominal voltage and 2.5Ah nominal capacity was used in experiments. The experimental setup consists of battery test system, isothermal calorimeter, temperature chamber, and host computer. The UDDS cycle is used to verify the accuracy of battery model and estimation algorithm. The current of the UDDS is shown in figure 3.

Figure 3 The current of the UDDS

4.1 Thermal model parameter identification A calorimetric method is presented here for the fast

determination of the entropy variation. According to equation (5), the entropy variation of battery can be expressed as:

1

( )ocvt ocv

Uq U U I

T I T

(10)

Battery testing system and isothermal calorimeter are used to record battery current, voltage and heat generation. The battery is tested in isothermal calorimeter at 25℃ and discharged with constant current. The discharge current is set as 1/5C to improve the proportion of reversible entropic heat. The heat generation rate q is accorded by isothermal calorimeter. Then the entropy variation can be calculated according to equation (22), as shown in figure 4.

The thermal model parameters (Rth and Cth) are determined by genetic algorithm. The UDDS cycles are

utilized to verify the battery thermal model. Battery working current is taken as an input and battery temperature as an output. The thermal model prediction result is shown in figure 5. The results illustrates that the proposed battery thermal model can describe battery temperature characteristics under dynamic condition. The model error increases at the end of discharge, and the maximum model error is 1.2℃.

Figure 4 Entropy variation of battery

Figure 5 Thermal model prediction result

4.2 SOC estimation verification The UDDS cycle condition is used to verify the

accuracy and robustness of the estimator based on STPF. The experiment is conducted at 25℃. To verify the convergence of the method, the initial SOC is set as 0.8. The covariance of system process noise Q is set as 0.001 and the covariance of measurement noise R is set as 0.04. The reference battery SOC value is obtained by current integration method, based on the current value and sampling time which is recorded by the battery testing system.

0 1000 2000 3000 4000 5000 6000 7000

-4

-2

0

2

Time(s)

Cu

rren

t(A

)

0 0.2 0.4 0.6 0.8 1

-5

-4

-3

-2

-1

0

x 10-4

SOC

En

tro

py

var

iati

on

(V/K

)

Entropy variation sample

Entropy variation fitting curve

0 2000 4000 6000 800024

25

26

27

28

29

30

Time(s)

Bat

tery

tem

per

atu

re(

oC

)

Reference battery temperature

Prediction battery temperature

179



The SOC estimation result of PF and STPF is shown in figure 6 and the estimation errors comparison is shown in figure 7.

Figure 6 SOC estimation by two methods

Figure 7 SOC estimation errors of two methods

The experimental results show that the SOC curves estimated by PF and STPF converge rapidly to reference SOC curve. To further evaluate the estimation performance of two methods, the maximum absolute error (MAE), average absolute error (AAE) and root mean square error (RMSE) are listed in Table 1. It is shown that the MAE, AAE and RMSE of STPF are smaller than those of conventional PF.

Table 1 Comparison of SOC estimation errors

Method MAE(%) AAE(%) RMSE(%)

STPF 1.42 0.58 0.68

PF 4.07 1.26 1.58

5. Conclusion In this paper, a battery state estimation method

based on electro-thermal model and STPF is proposed. A battery electro-thermal model is adopted and a new thermal model parameter identification

method is proposed to reduce test cycles. The maximum error of thermal model is 1.2℃. The STPF based estimator is employed to solve the problem of nonlinear system state estimation and saltatory states tracking. The experiments under UDDS dynamic characterization schedules indicate that the proposed method can estimate battery accurately with RMSE less than 0.68%.

Acknowledgement This work was supported by the National Natural

Science Foundation of China (Grant No. 61633015, U1864205, 61527809, U1764258).

Reference [1] Zheng Y , Ouyang M , Han X , et al. Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles[J]. Journal of Power Sources, 2018, 377:161-188. [2] Lu L , Han X , Li J , et al. A review on the key issues for lithium-ion battery management in electric vehicles[J]. Journal of Power Sources, 2013, 226(none):272---288. [3] Motapon S N , Lupien-Bedard A , Dessaint L A , et al. A Generic Electrothermal Li-ion Battery Model for Rapid Evaluation of Cell Temperature Temporal Evolution[J]. IEEE Transactions on Industrial Electronics, 2017, 64(2):998-1008. [4] Mesbahi T , Rizoug N , Bartholomeus P , et al. Dynamic model of Li-Ion Batteries Incorporating Electrothermal and Ageing Aspects For Electric Vehicle Applications[J]. IEEE Transactions on Industrial Electronics, 2017:1-1. [5] Forgez C , Do D V , Friedrich G , et al. Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery[J]. Journal of Power Sources, 2010, 195(9):2961-2968. [6] Liu X, Chen Z, Zhang C, et al. A novel temperature-compensated model for power Li-ion batteries with dual-particle-filter state of charge estimation[J]. Applied Energy, 2014, 123(3):263-272. [7] Min Y, Hui G, Rui X, et al. A double-scale and adaptive particle filter-based online parameter and state of charge estimation method for lithium-ion batteries[J]. Energy, 2018, 144:789-799. [8] Li D , Ouyang J , Li H , et al. State of charge estimation for LiMn2O4 power battery based on strong tracking sigma point Kalman filter[J]. Journal of Power Sources, 2015, 279:439-449. [9] Li Y , Wang C , Gong J . A combination Kalman filter approach for State of Charge estimation of lithium-ion battery considering model uncertainty[J]. Energy, 2016, 109:933-946.

0 1000 2000 3000 4000 5000 6000 70000

0.2

0.4

0.6

0.8

1

Time(s)

SO

C

Reference

PF

STPF

0 1000 2000 3000 4000 5000 6000 7000

0

0.1

0.2

Time(s)

SO

C e

rro

r

PF

STPF

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State Estimation Method of Lithium-ion Battery Based on