A Study of Battery Modeling Technologies for Vehicle System Simulations

Takayuki Sekisue Technical Division, Electrical Business Unit.

ANSYS Japan K.K. Tokyo Japan

takayuki.sekisue@ansys.com

Koichi Shigematsu Model Based Development Promotion Division

CYBERNET SYSTEMS CO., LTD Nagoya AICHI, Japan

k-shige@cybernet.co.jp

Takashi Abe Division of Electrical Engineering and Computer Science

Graduate School of Engineering Nagasaki University Nagasaki Japan

abet@nagasaki-u.ac.jp

Thanh-Son Dao Application Engineering Division

Maplesoft Waterloo, Canada

tdao@maplesoft.com

Abstract— The goal of this research is a proposal of a standard model for vehicle system simulations. Recently, the CO2 reduction and efficiency improvement of the energy consumption are important subjects in development of the vehicle systems. The new technologies related to vehicle development have continued to increase in complexity. For these reasons, the energy management simulation by the coordinated design of an electric system and vehicle system is required. The electrical behavior of the batteries becomes important to improve the energy management in the vehicle systems. The battery modeling technologies and the application example for vehicle system simulation are reported.

Keywords-Battery Modeling; Vehicles; System Simulation; Standard Model

I. INTRODUCTION (HEADING 1) Recently, a reduction in CO2 emission and an improvement

of fuel consumption are an important subject in development of the vehicle systems. The new technologies has been applying to vehicle systems, for example, the no idling control, the energy regeneration of HEV and PHEV, the weight saving and high efficiency by electrical power-train, and thermal recycle technology. Therefore, vehicle systems have continued to increase in complexity, the simulation technology is essential on the planning and development stage. A number of papers have reported about the fuel consumption and optimum design using vehicle system simulation [1]-[3]. But, the vehicle system is a multi-domain that requires many branches of science and engineering. The energy management simulation by the coordinated design of an electric system and vehicle system is required. The electrical behavior of the batteries becomes important to improve the energy management in the vehicle system [4]. Furthermore, the standard battery model which can be defined the model parameters are required by system design engineers. The standardization of simulation

model is considered by VDA (Verband der Automobilindustrie), which is Germany Automobile Manufacturers Association, a new report is shown as the library for system simulation [5]. This research has made it possible to easily build the whole model of vehicle system. On the other hand, the particular model which can be analyzed in greater detail is developed for system simulation, so that evaluation and examination can be performed at the multi-level suitable for the purpose of the simulator.

This paper reports several battery standard models for vehicle system simulation, and discusses the electrical behavior of the batteries needed for the energy management. Furthermore, the application examples for vehicle system simulation are reported.

II. BACKGROUND AND PRESENT MODEL OF BATTERIES Generally batteries are expressed using an equivalent

circuits [6] or chemical reaction equations [7][8], and many results of research have been reported. The models using an equivalent circuit is simple and easy handling. On the other hand, in order that there are no relations between the circuit parameters and the physical constants of an actual battery, weak points that difficulty of fitting of the characteristics and less flexibility are exists. Furthermore the battery model expressed by the equivalent circuit is classified into what simulates an AC impedance characteristic or simulates the nonlinear DC internal resistance depending on a battery charge state (SOC; State of Charge) and a charge-and-discharge current value. On the other hand, the model based on an electrochemistry reaction is easy to take correspondence with physical constants of actual battery and model parameters however model parameters become detailed and they are difficult to understand/determine for electric engineers.

III. THE LEAD ACID BATTERY MODEL FOR VEHICLE SYSTEM SIMULATIONS

Recently, the whole vehicle system simulation for improving fuel consumption is being put in practical use. The functions of battery which required are the charge-and-discharge performance in a partial charge state and detection of overcharge, and several 10[ms] or less cycle behavior should be simulated. Moreover, the simulation should take into consideration the voltage drop according to a charge state until over 10[min] of time range.

A method to derive parameters from a general measurement examination using the equivalent circuit which consists of minimum elements which simulate the function required as a lead acid battery model in which a system design engineer can determine parameters easily is investigating. An equivalent circuit model is shown in Fig. 1. Variation of the electromotive force E and the resistance Ri according to SOC obtained by current integration is measured from the charge-and-discharge characteristic. The result of which the parameters Ri and E for simulating the lead acid starter battery type of 55D23 from 5 hour rate electric discharge characteristic is shown in Fig. 2. And the result of having simulated RC parameter from the transient characteristic acquired from JIS light load endurance test is shown in Fig. 3.

The lead acid battery model was applied and calculated to the electrical load transition during an idling stop run of a measured vehicle, and the simulation model of the automobile electric power system including power generation with an alternator. The behaviors of battery voltage as the result of 12[V] electric system passenger car and simulation model are

Figure 1. Equivalent circuit model.

Figure 2. Discharge curve of 55D23.

Figure 3. Light load endurance test for lead-acid battery.

shown in Fig.4. In all the running time, sufficient accuracy were obtained to the increasing rate of the voltage by the charge from alternator (3%) and voltage drop at the time of the electric power supply by engine stop (6%). On the other hand, the difference is shown as 5 to 20% of the voltage drop at the time of engine starting. This is the reason of shortage of modeling of the discharge current dependence at the large current being consumed, and expression of voltage at the time of starting is a problem to be solved.

IV. CHEMISTRY-BASED NI-MH BATTERY MODEL There are currently several different approaches for car

battery modeling, the most popular of which can be categorized into: (1) Circuit-based approach in which battery behaviors are presented as an electrical circuit such as in the works done by Salameh et al.[9].and Chen and Rinćon-Mora[10]. The circuit-based approach results in a conceptually simple model. However, the actual physical parameters are hidden and there is no explicit relationship between the model parameters and battery parameters, making remodeling difficult as a different battery is used. (2) Chemistry-based approach that captures the actual chemical reactions and other electrochemical processes in a battery. The chemistry-based approach can be seen in the works done by Newman et al., and Wu et al.. In this paper, the chemistry-based approach allows us to vary battery physical parameters for the design and control purposes to match the requirements for the HEV.

Due to its dominance in almost all hybrid vehicles, a Ni-MH battery has been chosen for the HEV model in this paper. Figure 5 shows a diagram of the cell sandwich used in a battery model A porous negative electrode made of a MH material is shown on the left, and a porous positive electrode made of Ni(OH)2 deposited on a nickel foam is shown on the right.

(a) Power network simulation model.

(a) Idling stop system simulation result

Figure 4. Verification test result of 12V vehicle simulation.

The Ni-MH battery model presented is a modified version of the battery model proposed. For simplicity, the effects of side chemical reactions and thermal effects have been ignored. The two main chemical reactions on the two electrodes of the battery are:

−⎯⎯⎯ →⎯

⎯⎯ ⎯←− +++ OHNi(OH)eOHNiOOH 22

discharge

charge (1)

discharge

2chargeMH OH M H O e− ⎯⎯⎯⎯⎯→ −

←⎯⎯⎯⎯+ + + (2)

where the metal M in the negative electrode is an inter-metallic compound, usually a rare earth compound.

The electromotive force in the battery is defined by the two open-circuit voltage equations (i.e., Nernst equations) for cathode and anode:

( ) H ,max H

c pos 0e H

lnpos c cU RTU T TT F c c

φ+ +

+

−⎛ ⎞∂= + − + ⎜ ⎟⎜ ⎟∂ ⎝ ⎠

(3)

( )

( )MH

MH,max

4a neg 0 e

28.057 4

2MH MH,max

ln 9.712 10

2.7302 100.237240.010768

neg

cc

U RTU T T cT F

ec c

φ −

−−

∂= + − + + ×

∂

×+ −+

(4)

In these equations, CH+ and CH

+,max are the current and

maximum concentrations of Ni(OH)2; CMH and CMH,max are the current and maximum concentrations of MH; Ce is the concentration of the KOH electrolyte; Upos and Uneg are the standard open-circuit potentials on cathode and anode, respectively.

The rate of chemical reaction on each electrode is defined by the Butler-Volmer equation which relates the current density Ji to the over-voltage ηi by:

0.5 0.5

0,i i

F FRT RT

i ij i e eη η−⎛ ⎞

= −⎜ ⎟⎝ ⎠

(5)

where i = pos (positive) for cathode and i = neg (negative) for anode, F is the Faraday constant, R is the gas constant, T is the battery temperature, and io,j is the exchange current density given by:

0.5 0.5 0.5

,maxe0, 0, ,ref

,ref e,ref ,max ,ref

i iii i

i i i

c cc ci i

c c c c⎛ ⎞ ⎛ ⎞ ⎛ ⎞−

= ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟−⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (6)

where Ci=CH+ for cathode and Ci=CMH for anode, and i0,j,ref is

the exchange current density at a reference reactant

concentration. The charge and discharge characteristics of the battery for four different rates from 1 C (3.4 A) to 1/8 C (0.425 A) are shown in Fig. 6. The battery voltage drops/rises more quickly as the discharge/charge current is increased.

Figure 5. Cell sandwich schematic for Ni-MH battery.

Figure 6. Discharge(left) and charge(right) characteristics.

V. SERIES-HEV MODEL The series-HEV model presented in this paper is illustrated

in Fig. 7. The mathematics-based modeling of HEVs is complex because it requires the associations of devices in different domains with very different dynamics and characteristics. The vehicle uses an ICE to generate power for an electric generator which, in turn, converts mechanical work into electricity to charge a Ni-MH battery pack whenever the battery state of charge (SOC) drops below a minimum charge level. A power controller is used to determine how much current to be drawn from the battery in order to turn the wheels according to the speed requirement. When the driver reduces vehicle speed by stepping on the brake pedal, the DC motors are put into the reverse mode and act as electric generators to charge the battery pack. The detail of each components are shown in [11].

τ,V i

,V i

,V i

Figure 7. Series-Hybrid Electric Vehicle Model.

A. Mean-Value ICE Model The engine model is composed of three main subsystems:

the throttle, intake manifold, and engine power generation from the fuel combustion. The rate of air mass flowing into the engine is determined based on the geometry and position of the throttle valve set by a simple PID controller which closes the loop between the actual and desired engine speeds. The intake manifold has a significant effect on the gas flow and pressure to the engine cylinders. The pressure of the air/fuel mixture in the intake manifold can be calculated based on the ideal gas equation:

( )mm thr e

m

RTP m m

V= − (7)

where R is the gas constant, Tm and Vm are the temperature and volume of the intake manifold, thrm is the throttle mass flow rate, and em is the throttle mass outflow.

The HEV components consisting of an ICE, a battery pack, controllers, a multibody vehicle, and a motor/generator are developed in MapleSim.

B. HEV dynamics Model The vehicle and tire models are formulated using the graph-

theoretical method developed by McPhee et al.[12]-[14]. This results in a compact and efficient set of system equations. The entire system equations are organized into a set of DAEs across multiple domains, namely mechanical domain (vehicle, tire, motor, generator), electrical domain (motor, generator, power converter), chemical domain (battery), and hydraulic domain (ICE) as:

( ), ,T t+ =Mp C f b q p (8)

( ), t =Φ q 0 (9)

( ), ,t=q h p q (10)

Equation (8) contains differential equations involving the generalized speeds p . The matrix M contains the coefficients of p in the system’s dynamic equations. The portion of M that corresponds to mechanical variables may be thought of as a mass matrix, whereas the portion corresponds to electrical variables may be thought of as an inductance/capacitance matrix, and electrochemistry coefficients for chemical variables. The column matrix f contains variables related to the system’s constraint equations in the form of constraint forces and the matrix C gives the coefficients of f in the dynamic equations. Equation (9) contains algebraic constraint equations involving the zeroth-level derivative modeling variables q. Equation (10) describes kinematic transforms relating the derivatives of the coordinates q to the generalized speeds p, coordinates q, and time t.

C. Simulation The initial vehicle speed of 15 m/s and the initial battery

SOC of 80% are used in the simulations. In the first test, the vehicle is controlled to follow a simple drive cycle. The durations of acceleration and deceleration are both 20 s. Since the initial speed is 15 m/s, the vehicle has to slow down first and put the DC motor into the reverse mode, charging the battery due to the regenerative braking effort and causing the battery SOC to rise from 80% to the high 85%. The drive cycle used in the second test is the FTP-75 drive cycle (see Fig. 8(a)), which is currently used for emission certification of light duty vehicles in the U.S. This cycle has three phases: cold start phase, transient phase, and hot start phase. Since the cold start phase and hot start phase are the same in simulation, the model is only simulated from the beginning of the cold start phase until the end of the transient phase. The battery is initially pre-charged to 60%. The time history of the battery SOC is plotted in Fig. 8(b), which shows the charge and discharge processes as the vehicle follows the drive cycle.

A simple on-off controller is used to determine when to close/open the throttle valve of the ICE based on the battery SOC. In this model, the throttle valve is adjusted to only allow minimum air flow into the intake manifold, causing the ICE to rotate at an idle speed of 1000 rpm when the battery SOC is higher than a minimum level of 50%. Once the battery SOC drops below this minimum SOC level, the throttle valve is regulated to allow more air flow into the intake manifold, driving the electric generator to charge the battery up to 80%.

(a) Vehcle Speed.

(a) Battery SOC.

Figure 8. Vehcle Speed and Battery SOC.

VI. CONCLUSION This paper has reported the standard battery model and the

application example for vehicle system simulation. The procedure for determining of model parameters is a very important subject for not only electric engineers but also engineers in other field. On the other hand, the more detailed and high accuracy models suitable for the purpose of design are required, and they are necessary to be used on the same simulation platform. The investigation of multi-level modeling is also an important development in this search. In future studies, we hope to establish the standard model of each element for vehicle system simulation. Also, an approach to modeling a series-HEV based on a mean-value ICE, a chemistry-based Ni-MH battery pack, and a multibody dynamic vehicle has been proposed.

REFERENCES [1] K. Shigematsu, T. Sekisue, K. Tsuji : “Auto-motive System Simulation

(Japanese only)”, 2006 National Convention Record IEE Japan IAS, Vol.1, No.S9-3, pp.1-6 (2006)

[2] T. Abe, S. Takayama, T. Higuchi, K. Tsuji, K. Shigematsu : “Vehicle Fuel Consumption Simulation Model using VHDL-AMS”, Proc. of the 14th European Conference on Power Electronics and Applications, pp.1-9(CD-ROM), (2011)

[3] K. Tsuji, Y. Kido, T. Abe : “A Study of Vehicle Energy Management during Warming up Process Using VHDL-AMS Multi-domain Simulation”, IEEJ Trans, IA, Vol.131, No.8, pp.985-991 (2011)

[4] Investigating R&D Committee on Technologies for Automotive Integrated Electric Power Supply Systems : “Technologies for

Automotive Integrated Electric Power Supply Systems”, IEEJ-IA, No.1202 (2010)

[5] AK30 http://fat-ak30.eas.iis.fraunhofer.de/index_en.html [6] Chen, M. and Rinćon-Mora, G.A., “Accurate electrical battery model

capable of predicting runtime and i-v performance”, IEEE Trans-On Energy Conversion, Vol.21, No.2, pp.504-511 (2006)

[7] Saeedi, M., “A Mean Value Internal Combustion Engine in MapleSim”, MSc thesis, University of Waterloo, (2010)

[8] Newman, J. and Thomas-Alyea, K.E., “Electrochemical Systems”, 3rd ed, John Wiley & Sons Inc. (2004)

[9] Salameh, Z.M., Casacca, M.A. and Lynch, W.A., A, “mathematical model for lead-acid batteries”, IEEE Trans. On Energy Conversion, Vol. 7, No. 1, pp.93-98(1992)

[10] Chen, M. and Rinćon-Mora, G.A., “Accurate electrical battery model capable of predicting runtime and i-v performance”, IEEE Trans. On Energy Conversion, Vol. 21, No. 2, pp.504-511(2006)

[11] T.S. Dao, A.Seaman, J.McPhee and K.Shigematsu, “Development of a High-Fidelity Series-Hybrid Electric Vehicle Model using a Mathematics-Based Approach”, 1st International Vehicle Technology Conference 2011(2011)

[12] McPhee, J., On the use of linear graph theory in multibody system dynamics, Nonlinear Dynamics, Vol. 9, pp.73-90, 1996.

[13] McPhee, J., Schmitke, C., and Redmond, Dynamic modelling of mechatronic multibody systems with symbolic computing and linear graph theory, Mathematical and Computer Modelling of Dynamical Systems, Vol. 10, No. 1, pp.1-23, 2004.

[14] Schmitke, C., Morency, K., and McPhee J., Using graph theory and symbolic computing to generate efficient models for multi-body vehicle dynamics, Journal of Multi-body Dynamics, Vol. 222, No. 4, pp. 2041-3068, 2008.