A New Battery Model for use with Battery Energy Storage Systems and Electric Vehicles Power Systems

H.L. Chan, D. Sutanto Department of Electrical Engineering,

The Hong Kong Polytechnic University, Hung Hom. Hong Kong.

eesritantG3ii)oolvu edu hk FCZX : (852) 2330-1514

Abstract: This paper will initially present a review of the several battery models used for Electric Vehicles and Battery Energy Storage System applications. A model will be discussed which takes into account the non-linear characteristics of the battery with respect to the battery’s state of charge. Comparisons between simulation and laboratory measurements will be presented. The effects of high frequency switching on the battery performance will also be discussed. A strategy to reduce the high frequency charging and discharging curre‘nt will be proposed.

Keywords: Battery Model, Battery Energy Storage Systems, Electric Vehicles, Battery Management.

I. INTRODUCTION

The development of electric vehicle has been accelerated by the recent “California Initiative” which has required increasing proportions of new vehicles in Los Angeles area to be Zero Emission vehicles. Similar legislation has now been passed in several other US states. This has impelled car manufacturers throughout the world to have Electric Vehicles ready for the market when the legislation is enforced. General Motors, for example, has recently released the new EV 1 in USA. The possibility of large amounts of Electric Vehicles on the road, has also created interest in making better use of the spare batteries that each Electric Vehicle must have. It has been suggested that a Battery Charging station be made available by the electric utilities, so that cars can come into the charging station and have they batteries replaced in a short time.

While extensive research has been carried out to develop new types of batteriks and converters to convert the batteries output into useful work, very little work has been done in modeling the battery itself. The fact that most power converters are now switched at relatively very high frequency (much higher than 50Hz), will require new model of the batteries to take into account the operation of the battery under this high switching mode. This paper will initially present the current state-of-the art of battery modeling for use in Electric Vehicles and Battery Energy Storage System. A new model will be introduced which takes into account the response of the batteries to high frequency switching in the converter. Impact of battery chargers will be also be discussed. Comparisons between simulation and laboratory measurements will be presented. Some of the issues that will be considered are given below.

11. FACTORS DETERMINING BATTERY CAPACITY

To have better performance of EV, the energy utilization of battery capacity must be ensured. The following factors are critical to determine battery capacity and must be considered in any battery model:

1. Internal Resistance Self-discharge Resistance which takes account of resistances in (a) electrolysis of water at high voltage and (b) slow leakage across the battery terminal at low voltage. This resistance is more temperature-sensitive and inversely proportional to the temperature change. Resistances for Charge and Discharge: These are the resistances associated with electrolyte resistance, plates resistance and fluid resistance, however all these resistances can be different in charging and discharging. Overcharge and Overdischarge Resistance: When the battery is overcharged or overdischarged, the internal resistance will be increased significantly due to the electrolyte diffusion.

2. Discharge Type: - - _ Continuous Discharging: When battery continuously delivers energy to load without rest, and the battery capacity is dropping continuously. Intermittent Discharging: When a battery drives a load for a period and is disconnected from the load for some time, then voltage recovery will be took place in the battery to increase its voltage with some amount. When the battery is operating in this intermittent manner, it will give a longer discharge time.

3. Discharge Mode: Constant Load: When a battery delivers energy to a load of constant resistance, so the load current is decreasing as battery voltage does. Constant Current: Current drawn from a battery is kept constant to a load that continuously reduces its resistance, the discharge duration in this mode is shorter due to the average current is higher. The voltage drops more faster than that in constant load. Constant Power: A constant electrical power is drawn by load from a battery, such that the load current will be increasing to compensate for the decreasing battery voltage. This mode has the shortest discharge time.

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4. Rate of Charge/Discharge: To extend the service life of battery the rate of charge and discharge can not be too high. Excessive overcharging and over-discharging can reduce battery life. Further, the frequency of switching needs to be taken into account, particularly now when the EV or BESS batteries are subjected to high switching frequency associated with the converters in the control system.

111. BATTERY MODEL

In the following section, six battery models will be described briefly. One of these is found to be simple and yet represents many of the important features of the EV batteries.

A. Simple Battery Model

The most commonly used battery model is shown in Figure 1. This model consists of an ideal battery with open-circuit voltage Eo and a constant equivalent internal series resistance ESR. Vo is the terminal voltage of battery.

ESR '--i.-4

I v0 -- Eo

0

Figure I . Simple Battery Model

Vo can be obtained from the open circuit measurement and ESR can be obtained from both the open circuit measurement and one extra measurement with load connected at the terminal when the battery is fully charged. While this model has been extensively used, it does not take into account the varying characteristic of the internal impedance of the battery with the varying state of charge, electrolyte concentration and sulfate formation. Such a model is only applicable in some circuit simulations where the energy drawn out of the battery is assumed to be unlimited or where the state of charge is of little importance. Clearly, for electric vehicle applications, this model is not appropriate.

B. Modified Battery Model

Jean Paul Cun [I ] proposed an improved battery model based on the configuration given in Figure 1. In this battery model, the battery's state of the charge is taken into account, by making the ESR of battery no longer constant, but varies in accordance with its state of charge. A common formula is to set ESR = Ro/Sk, where Ro = initial battery internal resistance calculated when the battery is full charged and S = 1 - Ah/Clo, where Clo is the ten-hour capacity (Ah) at the reference temperature (this value varies as the battery ages). S varies from 0 (battery discharged) to 1 (battery charged). k is a coefficient that is a function of the discharge rate, calculated on the basis of kl, k2, and k3. kl. k2 and k3 are coefficients determined using the curves provided by the manufacturers. They correspond to three discharge rates.

This model has been used by many battery manufacturers for battery monitoring purposes.

C. Thevenin Battery Model

The other commonly used model is the Thevenin battery model, which consists of an ideal no-load battery voltage (Eo), internal resistance (R), capacitance (CO) and overvoltage resistance (Ro). CO represents the capacitance of the parallel plates and Ro represents the non-linear resistance contributed by the contact resistance of plate to electrolyte.

CO

I "O

Figure 2. Thevenin Battery Model

The main disadvantage of the Thevenin battery model is that all the elements are assumed to be constant, but in fact all the values are functions of battery conditions.

D. Dynamic Battery Model [7-91

An empirical mathematical model is developed in [7,8] to model lead-acid traction battery:

K e t b = - (Rb +=litb

where etb = battery terminal voltage V, = charge dependent open circuit voltage RI, = battery terminal resistor, typically OAohm K = polarization constant, typically 0.1 ohm i,b = battery discharge current, amps SOC = state of charge

The improvement of this model is to account for the non- linear characteristic of both the open circuit voltage and internal resistance represented by the WSOC component.

E. Fourth Order Dynamic Model [ 1 I ]

Giglioi [ I I ] proposed a dynamic model shown in Figure 3. The battery model is comprised of two parts: (a) current I p

flowing through RP (electrolyte reaction), Rd (Ohmic effect) and its associated leakage capacitance Ca and RW (waste of energy) and its associated leakage capacitance CW; (b) current Is flowing through RS (self discharge).

Although this model is sophisticated and accurate for simulation purpose, it still has some drawbacks in that: (a) a longer time is required for computation due to the high order of model; and (b) modeling procedure is too complicated because it involves a lot of empirical data.

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F. Over-Current Battery Model [IO]

Figure 4 shows a SPICE battery model. It has a variable current source, a variable voltage sources, a variable resistor and a capacitor.

L I . Figure 3. Fourth Order Dynamic Model

t+ - I T J E m L

Gb

Evb A * -

vb Y 4-

Figure 4. Over-Current Battery Model

where Gb =variable current source to model the battery current and

is defined by Peukert relationship: Battery Capacity,

EVb= variable voltage source to model the battery voltage and is defined by Nernstian relationship: Battery Voltage,

ERI,= variable voltage source characterizing voltage drop across the battery, it is actually modeled as the internal resistance, R

R = internal resistance including RI, R2 and Rs RI = resistance of grid, group bar and lug material, which is a

constant AI R2 = resistance of electrolyte=Az/C R3 = resistance of plate surface sulfation=AJ*(l-C) Cb =capacitor, the voltage across Cb which is scaled to 1V

when 100% of SOC and OV when 0% of SOC Vb =current sensor of zero voltage for SPICE simulation A,-, are constants and obtained by experiments.

C = A ~ x I*'

VOC =Ad+As+log(C)

This model provides a good representation of both variable internal drop in the battery and changes in the output voltage due to the state of charge. However one of its drawbacks is that too many parameters are required.

G. Improved Battery Model [2,4]

Figure 5 shows a battery model that we believe is the simplest and at the same time meets all the requirements for a good battery model. It takes into account most nonlinear battery elements characteristics both during charging and during discharging as well as their dependence on the state of charge of the battery.

fiji Current Sensor

I I 1 ' 2

Battery Voltage

Figure 5 . Improved Battery Model

All the elements included in this model are functions of the open-circuit voltage of battery, which in turn relates to state of charge. The characteristic of these elements are described as below:

Self-Discharge Resistance (Rp): It takes account of resistances in (a) electrolysis of water at high voltage and (b) slow leakage across the battery terminal at low voltage. This resistance is a function of the open circuit voltage. Resistances for Charge and Discharge (Rc and Rd): These are the resistances associated with electrolyte resistance, plates resistance and fluid resistance, however all these resistances can be different in charging and discharging. Overcharge and Overdischarge Resistance (Rco and Rdo): When the battery is overcharged or overdischarged, the internal resistance will be increased significantly due to the electrolyte diffusion. Battery Capacity (Cb): A battery delivering or storing energy behaves as a large capacitor. However, it i s modeled as a voltage source, VOC in SPICE model which is function of state of charge.

The following table tabulates the relationships of the battery elements described above as VOC changes and extracted from [2] and manufacturer's data.

Because the model takes into account the variation of the elements with the open circuit voltage. and these relationships are obtained either from measurements or data sheet, the model is very accurate, and errors between actual tests and simulation will be minimised. Therefore, it provides a relatively simple but accurate structure.

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Table I . Parameters of Battery Elements - 3% 0.000 5.450 5.700 5.8 IO 6. I87 6.406 6.718 3.437

--

voc I Rp n voc I Rc I voc I Rd I soc, O.OOoc( 195.d O.OO@ 0.1164 4.0000( 4 . 0 4 0.d

poood 0.d I I

IV. SIMULATION

To test the model, a PSPICE simulation program using the improved battery model was carried out and the results are compared with the laboratory experiment. In the laboratory, a 6V sealed lead-acid battery is used and is subjected to (a) 1.5 hours of constant current discharge at 1.5A. then (b) 15 minutes of rest, and (c) another 1.5 hours of constant current charge at 1.5A. The experimental set-up is discussed in the next Section. The results from the simulation are shown in Fig. 6. The non-linear characteristics of the battery terminal voltage during charging and discharging can be clearly observed.

1.

voltage of the battery, the constant current supply and provide constant current discharging of battery.

Microcomputer m Load i [ . l .......... , ,

Constant Chent

Figure 7. Battery Testing System

The results obtained from laboratory measurement are shown in Figure 8 which is identical to that in Fig. 6. This can be expected as the variations of the model with the state of charge are now well represented both from measurements and manufacturer's data sheet.

However, it should be noted that the battery tests carried out in both simulation and experiment are under constant DC condition. in order to verify the battery performance under high frequency switching condition, a possible application of EV battery as an active filter and power factor correction is simulated, first using the ideal battery model with constant voltage and then withthe proposed battery model.

'I

*mm 0" ,mm I" 2" *" Tine

Figure 8. Experiment Result

VI. BESS PROVIDING ACTIVE FILTERING AND POWER FACTOR CORRECTION

V. EXPERIMENT

The experimental set-up is shown in Figure 7. It comprises a microcomputer, a constant current supply. a constant current load demand, circuit selector, current and voltage sensors. The microcomputer is used to control and record the current and

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A PSPICE simulation of an active filter using a Battery Energy Storage system is shown in Figure 9.

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.............................................. 8

Active Filter

Figure 9. Active Filtering System

The current drawn from the non-linear load contains a lot of harmonics, it will definitely degrade the power factor of electricity supply if the active filter is not installed. The Battery energy. storage system is used to provide alternating positive and negative current to ensure that the input current source will have a perfect sinusoidal waveform and in-phase with the supply voltage. The circuit configuration is shown in Figure 9. The Capacitor in parallel with the battery is intended to provide filtering in that it will take most of the high frequency component of the switching devices allowing the battery to experience low frequency charging and discharging.. The active filter was implemented with hysteresis control strategy[3], where the input source current is controlled within a tolerance band or hysteresis band. The switching frequency is as high as several kHz.

Two studies were carried out for comparison, the first case using an ideal battery as energy storage and the second one made use of the improved battery model. Both two cases were simulated using PSPICE.

VII. ACTIVE FILTER USING IDEAL BATTERY

Figure 10.a shows the supply current (Is), load current (IL) and active filter current (IF). The non-linear load demanded a current containing high harmonics and the active filter current was controlled by referencing the ideal sinusoidal supply current, such that the actual supply current is IS = I t - IF. However, it can be seen from Figure 1O.b that the battery voltage remains constant and no current flows through the capacitor. The high frequency component is absorbed by the battery, a very undesirable situation as this will shorten the battery life.

Clearly such a result is not realistic and does not reflect the true performance of the battery.

0 I . ' I , 0 1 , * .

Tim (nu)

Figure 10.a Active Filter Using Ideal Battery

I I

------+ 4

4 1 0 2 . ' I

Tinu! (nu)

Figure 10.b Active Filter Using Ideal Battery

VJII. ACTIVE FILTER USING IMPROVED BATTERY MODEL

Using the improved battery model instead of the ideal model, the PSPICE simulation generated quite a different result illustrated in Figure 1 1 .a and 1 1 .b.

Nevertheless, the battery voltage and capacitor current shown in Figure 10.b are not the same as those shown in Figure 10.b. The capacitor now absorbs most of the high frequency component and the battery only needs to absorb or generate the low frequency component.

IX. CONCLUSION

The paper has presented a review of several battery models used in the industry. One particular model was found to best represent the non-linear characteristic of the battery elements with respect to the state of charge very well. The battery model is then used to simulate the application of BESS as an active filter. Super-capacitor was used to take care of the high frequency component. The use of the proposed model of the battery allows a better understanding of the battery behaviour when used in conjunction with Electric Vehicle or Battery Energy Storage System.

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4 1 I D , . . I W I I ~ .

Tinw(mr)

Figure 1 1 .a Active Filter Using Improved Model

The supply current, load current and filter current in Figure 10.a follows similar pattern as before.

rm- i m

t-

0 2 4 . , m * 2 , . 7 6

T k (m)

Figure 1 I .b Active Filter Using Improved Model

X. ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial contributions of the Hong Kong University Grants Committee and the Hong Kong Polytechnic University to the project and to Mr. Jim McDowall, Chair, PES Stationary Battery Committee for his comments on the abstract of the paper.

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XI. REFERENCES

[ I ] Jean Paul CUN, Jean No FIORINA, Michael FRAISSE, Henri MABBOUX, "The Experience of a UPS Company in Advanced Battery Monitoring", MGE UPS Systems, Grenoble, France,'http://www- merlin-gerin.eunet.fr/news/techpap/tp02us.ht'

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Ziyad M. Salameh, Margaret A. Casacca and William A. Lynch, "A Mathematical Model for Lead-Acid Batteries", IEEE Trans. on Energy Conversion. Vol. 7, No. 1, March 1992 C. E. Lin, M. T. Tsai, Y. S. Shiao and C. L. Huang, "An Active Filter for Reactive and Harmonic Compensation Using Voltage Source Inverter", IEE Int'l Conference on Advances in Power System Control, Operation and Management, November 199 1, Hong Kong. Margaret A. Casacca and Ziyad M. Salameh, "Determination of Lead-Acid Battery Capacity Via Mathematical Modeling Techniques", IEEE Trans. on Energy Conversion. Vol. 7, No. 3, Sept. 1992 "Rechargeable Batteries Applications Handbook", TK294 I .R43 1991, Technical Marketing Staff of Gates Energy Products, Inc. David Linden, "Handbook of Batteries" Second Edition, TK290 1 .H36 1994, McGraw-Hill, 1994 Jayne, M.G., and Morgan , C., "A N e w Mathematical Model of a Lead Acid Battery for Electric Vehicles", Eighth Int'l Electric Vehicle Conference, Washington, D.C., October 1986. Sims, R.I., Carnes, J.C., Dzieciuch, M.A. and Fenton, J.E., "Computer Modeling of Automotive Lead Acid Batteries", Ford Research Laboratories Technical Report SR-90- 154, Sept., 25, I990 Jayanths, M.S., Hayhoe, G.F., and Henry, J.J., "Modeling and Digital Computer Simulation of an Electric Vehicle", Technical Report, Pennsylvania Transportation Institute, Pennsylvania State University, University Park Pennsylvania, August, 1979. Robbins, T.; Hawkins, J. "Battery model for Overcurrent Protect ion Simulat ion of DC Di s t r i but i o n System S", I N T E L E C . S i x t e e n t h Internat ional T e l e c o m m u n i c a t i o n s Energy Conference, p307- 14. Giglioli R., Cerolo P., "Charge and Discharge Fourth Order Dynamic Model of the Lead Battery", 10Ih Int'l Electric Vehicle Symposium, Hong Kong, 1990, p. 1-9.

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