Transient Heat Transfer 1d Simulations for Electrical Vehicle Battery Using Openmodelica Software Package

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Publicat de

Universitatea Tehnică „Gheorghe Asachi“ din Iaşi,

Tomul LVII (LXI), Fasc. 2, 2012

Secţia

CONSTRUCŢII DE MAŞINI

TRANSIENT HEAT TRANSFER 1D SIMULATIONS FOR

ELECTRICAL VEHICLE BATTERY USING OPENMODELICA

SOFTWARE PACKAGE

BY

VLAD MARȚIAN1,2

, MIHAI NAGI1 and CIPRIAN FLUIERAS

1

1University „Politehnica” Timişoara,

Department of Mechanical Engineering 2 RAAL S.A.,

Research and Development

Abstract. Increasing demand for clean energy consumptions, and also the continuously

rising of gasoline prices, forced the car manufacturers to consider the electric driven

cars (EV) and hybrid traction cars (HEV), as a solution to this problem. The main

challenge in this field is to develop new batteries that have high power and high storage

capabilities, but this comes at the price of increased heat generation in the battery, heat

that must be evacuated so the battery doesn’t suffer any damage. The present article

presents the simulation of 1D thermal model of a battery using the OpenModelica

software package. The aim of this simulation is to develop the cooling system for an

electric vehicle.

Key words: heat transfer, electrical battery, electrical vehicles, hybrid vehicles,

simulation.

1. General Considerations

Electric energy seems to be the future of the vehicles driving power. Due

to continuously rising prices of petrol witch some forecast place a figure of 300

$/barrel in 2035 (Paier, 2011), and due to the growing need for a cleaner

Corresponding author: [email protected]

mailto:[email protected]

Vlad Marţian et al.

environment, more and more car manufacturers are beginning to develop

electrical powered (EV) and hybrid (HEV) vehicles. The advantages of this type

of powered vehicle are obvious, and apart from the clean energy consumption

there is also the advantage of efficiency which for the electric engine is around

80% -90%.

The main obstacle in producing on a mass scale this type of vehicles is

represented by the storing capacity of the electrical energy i.e. the batteries.

Actually the storing capacity isn’t enough, so one of the main directions of

research is to improve the storing capacity of the batteries. This increase in

energy density and also the need for drawing high powers form the batteries has

another side effect such as increasing the temperature of the battery. The

working temperature of the battery is a very important parameter, for example

for a Li-ion cell an increase in temperature of 15 °C will reduce the life of the

cell by about 50% (Asakura, Shimomura, & Shodai, 2003). The temperature

has also another effect on the charge/discharge of the battery and also on the

storage capacity of the battery. These parameters i.e. charge/discharge and

storage capacity is quantified by using the term SOC (State of charge). In the

work of Zheng Popov and others (Zheng, Popov, & White, 1997) an optimum

temperature for a battery is around 25 °C, even if now there are batteries that

can have a maximum temperature of 85 °C (Winston, 2011). The current

discharge/charge rate grows as the temperature approaches the optimum due to

increased ion mobility and also due to modifications of internal resistance of the

battery, but after the optimum the current charge/discharge rate stats to decrease

due to oxidations that happen inside battery. Increasing the temperature over the

functioning domain make the batteries to have a catastrophic failure, and not

only the performance of the battery will be diminished but also irreversible

oxidations occur and the battery becomes useless (Jiangang, et. al., 2006).

For these reasons, toghether with RAAL S.A., we began to investigate the

necesity of a cooling system for batteries equiped in EV and HEV. This paper

presents the first step from many that includes battery modelling, the modelling

of cooling modules, the modelling of an automatic driver, experimental tests of

the cooling modules, and thermal test on the battery pack, etc.

2. Battery Models

The literature has many models which vary in complexity. There are

complex models that use quantum mechanics for describing the battery at

chemical reaction level (Parthasarathy M Gomadam, et. al. , 2002), (Aron,

Girban, & Pop, 2010), finite element models that describe the spatial dynamics

in the battery (Sievers, Sievers, & Mao, 2010),electrochemical models,

electrical equivalent circuit (Matthias, Andrew,et al., 2005), Dynamic Lumped

parameters models, tabulated battery data models.

Bul. Inst. Polit. Iaşi, t. LVII (LXI), f. 1, 2011

To model the battery as close to the reality as possible every model has to

take into account the parameters on which the battery depends on, and these

parameters are a few. One of the most important parameter that the battery has

is the so called state of charge, SOC, or the electrical energy stored in the

battery. This parameter depends on other parameters of the battery as the

current drawn from the battery, the time that the current has been drawn, and the

capacity of battery, and can be express in mathematical form as:

C

tISOC

1 . (1)

C

dttItSOC

t

0

)(1)(

(2)

where I –the current drawn (A), t –time (s), C –the battery capacity (A.s)

Other parameters of the battery include the temperature of the battery, the

internal resistance and the open circuit voltage.

In the remaining paper I will only describe the electrical circuit models

which are the base for the model in this article, for other model types you can

see (Gomadam, Weidner, Dougal, & White, 2002).

2.1. Simple model

The simplest model used consists of a constant resistance Rb in series

with an ideal voltage source E0, sketched in Fig. 1.

Fig. 1–Simplest model

Even this is very simple form electrical point of view; this model doesn’t

take into account the true internal resistance of the battery, which is highly

related to the state of charge (SOC). In this case the draw of energy is unlimited.


Another drawback of this model is that it doesn’t take into account the thermal

energy generated during discharge.

There are other, improved, electrical models, some of which modify the

internal resistance according to the SOC, and also include other parameters that

take into account the dynamics of the electrical current during discharge. One of

this improved a model that is worth mentioning it is the Thervein model.

2.2. Thervein model

This is another basic battery model which describes a battery with an

ideal voltage source (E0), internal resistance R and a capacitance C0 which

represents the actual capacitance of the battery, and also an over-voltage

resistance R0 (Ziyad & Salameh, 1992). The main disatvantage of this model is

that all the components are constant, whereas in reality all these characteristics

are dependent of the SOC, and the dicharge current. The circuit diagram can be

seen in the Fig. 2. below:

Fig. 2 Thervein Model

2.2. Non linear Dynamic model

A more realistic model has been created by extending the Thervein

model. This new model takes into account the nonlinearities in the components

of the Thervein model. As I said earlier the internal resistance of the battery

R+R0 and the open circuit voltage E0 are dependent on the SOC of the battery,

and also on the temperature T of the battery.

Since we are interested in how the temperature of the battery changes in

time I will use a modification of this later model, which can be seen in a

simplified version in Fig. 3.

In this model different form Thervein model I have included the internal

resistance in the overvoltage resistance, for simplification purpose, and the


internal resistance R and the open circuit voltage E0 are dependent on some

function of SOC.

Fig. 3 Non Linear Dynamic model

3. Modeling Implementation

If we want to know how the current and the voltage in the battery are

modified in time we have to solve a system of equations that include first order

differential equations and also algebraic equations. Doing it by hand it takes a

long time, and if one of the parameter is changed we will have to do it again.

There is a faster and error free method anyway doing this with the help of the

computer.

In the following I will present the modeling implementation steps with

the help of the OpenModelica (OpenModelica, 2012) software package.

The first step in modeling the battery was to model the equivalent electric

circuit of tha battery. Since OpenModelica has a diagram development

interface, and because the Modelica language (Modelica, 2012) is an equation

based language, the implementation of the electrical model was straithforward.

In the Fig. 4 can be seen the end result of the model.

The battery model is composed from different components, which are

electrical components represented by:

Voc that implements a signal voltage source,

Rint that implements a variable resistor, the internal rezistor of the

battery

C that implements a capacitor

ISens that implements a measuring sensor for curent drawn


To complete the battery model it was necesarry to include non electric

components such as:

mCp implements a heat capacitor

Temp implements a temperature sensor

Soc implements the SOC parametter acording to equation (2)

ExpDataVoc,ExpDataR implements experimental functions for

open circuit voltage and respectively for internal rezistor of the

battery

Fig. 4 Battery model.

The battery model is linked with the rest of the circuit by three

connectors: a positive (p) and negative (n) electric connectors, and a heat

connector (heatPort)

Let us explain the thermal part of the battery:


It is well known that the energy conservation law stipulates that the

energy that is stored in a domain must equal the energy that comes in minus the

energy that goes out plus the energy generated inside the domain. The equation

form per unit time, of this law can take the form:

dt

dE

dt

dE

dt

dE

dt

dE goutinst (3)

And in the case of a solid domain as the battery, and where we do not have

phase change the equation (3) becomes:

][)(2

int ambTThAtiRdt

dTCpm (4)

where m –mass of the battery, Cp –specific heat capacity of the battery, T –

battery temperature, Rint –internal battery resistance, h –thermal convection

coefficient with the outside medium, A –exchange surface of the battery, and

i(t) –the current intensity.

The equation (4) is implemented in the battery model as in Fig. 5, except the

Temp sensor, which it is used for linking the temperature to the other

components

Fig. 5 Thermal model

4. Simulations

For simulations we have choose a Winston Li-ion battery (Winston,

2011) with a capacity of 60 Ah. The internal resistances and the open circuit

voltage where determined by fitting the charts form the manufacturers data. The

capacitor value was taken to be 4.047kF (Valerie, Ahmad, & Thomas, 2000).


Because we wanted only to test the model, first we have simulated the model

without any cooling and with a constant resistor taken to be the load on the

battery. You can see the modeling in the Fig. 6

Fig. 6 Battery without cooling

The simulation was done for a time of 1 hour in which the battery has

been drained for almost the entire energy. In the following charts you can see

the most important parameters of the battery function of time:

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Time [min]

Bat

tery

Te

mp

era

ture

[°C

]

Fig. 7 Battery Temperature


As it is observed from the Fig. 7 the temperature is rising and in an hour

of using the battery with a constant load the temperature rises with almost 40 oC.

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70

Time [min]

Cu

rre

nt

Inte

nsi

ty [

A]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Bat

tery

Vo

ltag

e [

V]

Current Intensity Battery Voltage

Fig. 8 Current Intensity & Voltage

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1 1.2

SOC

Eoc

[V]

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09R

int

[Ω]

Open circuit voltage Internal Resistance

Fig. 9 Battery internal parameters


Chart in Fig. 8 show the current intensity and voltage evolution in time

and Fig. 9 show the battery parameters, Open Voltage Eoc and internal

resistance Rint function of the battery state SOC.

Another simulation done was with a simple cooling of the battery, and

with a variable load resistor which changes the current drawn over time

Fig. 10 Second Simulation

Here we used a convection model to remove the heat from the battery and

an ambient temperature of 20 oC.

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Time [min]

Tem

pe

ratu

re [o

C]

0

0.2

0.4

0.6

0.8

1

1.2

SOC

Temperature SOC

Fig. 11 Temperature and SOC


0

5

10

15

20

25

30

0 10 20 30 40 50 60Time [min]

Tem

pe

ratu

re [o

C]

0

20

40

60

80

100

120

Cu

rre

nt

inte

nsi

ty [

A]

Temperature Intens i ty

Fig. 12 Temperature and Current Intensity

In Fig. 12 can be seen that the temperature and the current intensity are

connected but there is a slight shift between the current maximum and the

temperature maximum, this can be explained if we look at Fig. 11 and Fig. 9. In

Fig. 11 can be observed that the maximum temperature is near a SOC of 0 and

from Fig. 9 we can see that at SOC near 0 the internal resistance rises so more

heat will be generated.

Another fact that can be observed is that due to current intensity the

battery drains out more rapidly, which is in concordance with the reality.

5. Conclusions and Future work

This research’s main objective was to model the battery to include the

heat generated and to extract information from it.

As can be seen in the first simulation in Fig. 7 the Li-ion battery will need

a cooling system to maintain its temperature at an optimal value. Without it the

battery’s temperature can raise above the maximum temperature and it will

damage the battery

The OpenModelica is a great tool that can help us in creating what if

scenarios and we rapidly can take decisions about the dynamics of any physical

system.


Even OpenModelica helped us to see the extent of the heat generation in

the battery we still need to do experiment and to determine if we took all the

parameters in this model, so the next phase will be to determine experimentally

the battery’s coefficients and to validate the model.

Acknowledgements. The authors would like to thank University

“Politehnica” of Timisoara, and also to RAAL S.A. Company for the support in

this endeavor.

REFERENCES

Aron, A., Girban, G., & Pop, C. (2010). About the solution of a battery

mathematical model. Int. Conf. of Diff. Geom. and Dynamical Systems

(p. 10). Bucharest: Balkan Society of Geometers, Geometry Balkan

Press.

Asakura, K., Shimomura, M., & Shodai, T. (2003, June). Study of life

evaluation methods for Li-ion batteries for backup application. Journal

of Power Sources, Volumes 119-121 , 902-905.

Gomadam, P. M., Weidner, J. W., Dougal, R. A., & White, R. E. (2002).

Mathematical modeling of lithium-ion and nikel battery systems.

Journal of Power Sources , 110, 267-284.

Jiangang, L., Xiangming, H., Maosong, F., hunrong, W., Changin, J., &

Shichao, Z. (2006). Capacity fading of LiCr0.1Mn1.9O4/MPCF cells at

elevated temperature. Ionics , 12, 153-157.

Matthias, D., Andrew, C., Sinclair, G., & McDonald, J. (2005). Dynamic model

of a lead acid battery for use in. Journal of Power Sources , 161 (2),

1400-1411.

Modelica, A. (2012). Modelica. Retrieved May 5, 2012, from Modelica:

www.modelica.org

OpenModelica. (2012). OpenModelica. Retrieved April 5, 2012, from

OpenModelica: www.openmodelica.org

Paier, O. (2011). The E-Car Challenge. Kuli User Meeting. Steyr, Austria.

Sievers, M., Sievers, U., & Mao, S. (2010). Thermal modelling of new Li-ion

cell design modifications. Forschung im Ingenieurwesen , 74 (4), 215-

231.

Valerie, H. J., Ahmad, A. P., & Thomas, S. (2000). Temperature-Dependent

Battery Models for. 17th Electric Vehicle Simposium (p. 15).

Montreal,Canada: National Renewable Energy Laboratory.

Winston. (2011, May 5). GWL Power. Retrieved May 5, 2012, from GWL

Power: http://www.ev-power.eu/docs/GWL-LFP-Product-Spec-260AH-

7000AH.pdf


Zheng, G., Popov, N. B., & White, R. E. (1997). Effect of temperature on

performance of LaNi4.76Sn0.24. Journal of Applied Electrochemistry ,

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Ziyad, M., & Salameh, M. A. (1992). A mathematical model for lead-acid

batteries. IEEE Trans. Energy Convers , 7, 93-97.

SIMULARI 1D ASUPRA SCHIMBULUI TERMIC AL BATERIILOR

VEHICULELOR ELECTRICE FOLOSIND PACHETUL SOFTWARE

OPENMODELICA

Datorită creșterii nevoii de energie cu emisii zero, producătorii de

vehicule au fost forțați să caute soluții către zona vehiculelor electrice (EV) și a

vehiculelor hibride (HEV). Acestea folosesc pentru propulsie energie electrică,

energie cu emisii zero. Deși acest tip de locomoție nu este unul nou, încercări de

a realiza mașini electrice datând de la începutul secolului XX, realizarea

acestora fiind temperată de dificultăţile stocării acestei energi. Totuşi pe la

mijlocul secolului trecut, datorită nevoii de mobilitate au fost dezvoltate baterii

solide care pot stoca o densitate mai mare de energie, ceea ce a ajutat si la

dezvoltarea vehiculelor electrice.

Recunoscând importanța mare a acestui tip de locomție, RAAL S.A. a

inițiat un studiu aspura necesității răciri acestor baterii, această lucrare

reprezentând un prim pas in realizarea unor sisteme de răcire pentru bateriile

vehiculelor electrice.

În lucrarea de fata este prezentata o modalitate de realizare a unui model

de baterie, care să includă si influența temperaturii bateriei în performantele

acesteia, căt si pentru a vedea necesitatea unui astfel de sistem de răcire.

Modelul teoretic este implementat folosind pachetul software gratuit

OpenModelica. Avantajul acestui pachet software față de altele cum ar fi

Mathlab si Mathematica, in afara gratuității acestuia, este limbajul de

programare, care este un limbaj bazat pe rezolvarea ecuațiilor ceea ce ne

permite modelarea sistemelor fizice in limajul stiințific, făra ajutor din partea

unor specialiști in programare structurată.

Pentru exemplificarea avantajelor oferite, lucrarea prezintă rezultatele a

două simulari:

Prima simulare este realizată pe o celulă a bateriei folosind o încărcare

constantă, rezistor1 în Fig. 6, şi fără o răcire a bateriei. După cum se poate

observa din rezltatele acestei simulari Fig. 7, Fig. 8 şi Fig. 9, în funcţie de

curentul extras temperatura bateriei creşte cu 40 oC în timp de 1 oră. Scopul

acestei simulări a fost de a derermina necesitatea de răcire a unei astfel de

baterii.

Cel de al doi-lea exemplu este o simulare îm care se ia in considerare şi o

răcire a bateriei prin convectie şi o încarcare variabilă Fig. 13. Rezultatele


acestei simulări sunt prezentate în figurile Fig. 12 şi Fig. 11, aici se poate

observa termostatarea bateriei dar si a variaţiei temperaturii în funcţie de

puterea extrasă din baterie, putere reprezentată de curentul extras.

În concluzie se poate afirma că bateriile solide de tipul Li-ion necesită o

răcire, iar aceasta depinde de puterea extrasă.

Pachetul OpenModelica este un mediu de simulare util, care permite

crearea şi simularea, în diferite condiţii, a modelelor fizice uşor si cu evitarea

erorilor de calcul.

În continuare se va încerca dezvoltarea unor modele de răcire mai

complicate si care să reflecte căt mai aproape de adevăr realitatea.

Documents

Transient Heat Transfer 1d Simulations for Electrical Vehicle Battery Using Openmodelica Software Package