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发布时间:2014-07-01 15:15:12  

Simulation of a commercial electric vehicle: dynamic aspects and


h,k,i DEEC AC-Energia and CIEEE, Instituto Superior Técnico, TU Lisbon

j CIEEE, Instituto Superior Técnico, TU Lisbon and ESTSetúbal/IPS J. M. Terrash, D. M. Sousak, A. Roquej, A. Nevesi

Av. Rovisco Pais, 1 – 1049-001 Lisboa

Lisboa, Portugal

Tel.: +351 – 21 841 74 29.

Fax: +351 – 21 841 71 67.

E-Mail: h josemterras@gmail.com, k duarte.sousa@ist.utl.pt,

j antonio.roque@estsetubal.ips.pt, i and.f.neves@gmail.com

URL: http://www.ist.utl.pt, http://www.cieee.org


Authors thank the CIEEE – “Center for Innovation in Electrical and Energy Engineering” of Lisbon and POSC – “Programa Operacional da Sociedade do Conhecimento” for financial support IST/TU

this work. of


?Electric vehicle?, ?Simulation?, ?Modelling?, ?Electrical drive?, ?Power converters for ?Control methods for electrical systems?. EV?,


The introduction of electric propulsion chains in automobiles has been contributing to improve efficiency and to reduce the local pollutant emissions. In this paper, the dynamic behavior their

commercial electric vehicle is simulated and analyzed in order to compare the dynamic behavior of a

performance of an available electric vehicle (“Fiat Seicento Elettra”) using two simulation and

The vehicle was simulated using two different approaches to the mechanical modeling: one using models.

detailed approach for the mechanical parameters and forces applied to the vehicle chassis a

other, only based on the typical forces applied to a body representing this type of vehicle. The and the

obtained results allow analyzing the dynamic behavior of the electric power chain, the autonomy, the state charge of the batteries and the power balance for typical operation modes: start, braking, of

and slowing down together with pathways of variable slope. acceleration,

From the two models, in addition to the dynamic aspects and performance of the electric vehicle, also possible to analyze other factors that are related with the design of an electric vehicle. it is

several Among factors and different operation modes of an automobile, it can be performed, for example, balance of torques (including the static friction torque, aerodynamic friction torque, viscous the

torque and the torque related with the weight of the car). In addition to the electromechanical friction

the implemented model also allows estimating the car power consumption and their costs (electric aspects,

energy) and the pollutant gas emissions (mainly CO2). In this paper, the values obtained commercial electric vehicle used as a reference are compared with those estimated to an for the

car, which is equipped with an internal combustion engine. equivalent


Electric vehicles (EVs) will be gradually launched in the market in the coming years and contribute to change the daily life of urban regions [1]. EVs can be a solution to prevent will to

pollution and to overcome the fuel dependency. Having as attributes the zero local emissions the air

silent driving, EVs will contribute to restore some quality of life in cities. Comparatively and the

to the

internal combustion engines (ICE), EVs can present a similar performance with less expensive costs it will be shown in this paper. as

Under this context, a commercial car (“Fiat Seicento Elettra”) is simulated and investigated “Matlab/Simulink” software. This vehicle is a lead-acid battery electric vehicle based and using

with an induction motor supplied by a voltage inverter and controlled by field orientation. This equipped

part of a project, where the models described in this article include the ability to perform work is

balance, calculate pollutant emissions and estimate the autonomy for different configurations the power

electric as, for instance, having photovoltaic panels or using different types of batteries. of an vehicle

context, the integration of the developed routines was done using the “Matlab/Simulink” In this


Characteristics of the System

The available commercial electric vehicle is characterized by owning a group of 18 lead-acid grouped in series [2]. The batteries are connected to a voltage inverter, able to operate with batteries

voltage and frequency and controlled by field orientation (Fig. 1). The output of the variable

connected to an induction motor (15 kW; water cooled; length of 360 mm; diameter of 196 mm). inverter is

Fig. 1: Block diagram of the control system (field oriented control principle) M – mutual

inductance, – rotor inductance, rr – rotor resistance and W = Lr/ rr are parameters of the induction (where, Lr

machine; T is the torque; \pp is the number of pole pairs; Z is the reference speed; r is the rotor flux; ref

Z r PI is the rotor speed on the reference frame; Zm is the motor speed; Ze is the reference frame speed; is the controller; is1, is2 and is3 are the motor stator currents; T is the rotation isDangle; and isQ are the currents in the DQ reference frame)

The classical control methods of induction motors are based on steady state models, which inadequate when high dynamic performance is required. The field orientation control method are

control is a principle that can fulfill the control and dynamic operation requirements of an electric equipped with an induction machine. vehicle

The electric models simulated using the “Matlab/Simulink” software joins the following

parts: an electric model of energy storage systems (batteries, in this work), a voltage inverter electrical

and an induction motor [3]-[6]. The batteries were computational implemented using the block voltage

“SimPowerSystem” library. This block implements a generic model parameterized to represent of

most popular types of rechargeable batteries [7]-[8]. In Fig. 2 is presented the schematic of the

chain implemented. the power


Field Oriented ControlZref

Battery set 12V 60Ah



s nt rre cu or ot M


Load Torque







on rsi ve on dc ee Sp




Fig. 2: Main blocks of the electric vehicle global model

Vehicle Dynamic Model


Vehicle Model

To model the "Fiat" electric car it is necessary to establish the balance of torques that vehicle dynamic behavior. To determine each torque, it is necessary to identify and define the affects the

applied to the vehicle. There are forces applied to the "chassis" and on the driving wheels forces vehicle. of the So, it would be necessary to know each force and knowing that it is mandatory to analyze system the of forces when the vehicle is stopped and when it is in movement. There are several

considerations about the forces applied to the vehicle body and on the driving wheels of a vehicle should be taken into consideration. In [9] are identified the four major forces that affect that

dynamics: the the vehicle static friction force, the force of the viscous friction, the aerodynamic drag force vehicle weight assigned to each wheel motor (as it is well known, this force depends on the and the

slope, i.e, the inclination of the place where the vehicle is parked or vehicle moving).

Vehicle Dynamics and Mechanical System The available commercial electric vehicle has 3319 mm long, 1443 mm high, weights about 1300 kg, with a distribution of approximately uniform weight to all four wheels [2]. The distribution lead-acid batteries (20 kg each (approx.)) was done in order to avoid overloading of the front of the 18

the vehicle. The induction motor and controllers placed in the back of the vehicle weigh about rear of and 50 respectively [2]. If it is considered that the metal body of the vehicle has a uniform 42 kg kg,

distribution, the centre of mass of the vehicle will be located approximately in the centre of mass

near the bottom of the "chassis". Figure 3 illustrates the relative position of the centre of the vehicle

distance between the axles and the centre of mass. mass and the

In this work, it is assumed that the electric vehicle owns M a and the opposing forces to the mass vehicle motion are the static friction force Fae), the force of viscous friction ( Fas), the aerodynamic

T)). drag force (Fad ) and the weight assigned to each motor wheel with the slope variation P( (

The force of static friction, presented in the equation (1), is a component of the total ( imposed on a wheel MERwheel ) frictional force motor. This force is only dependent on the weight assigned to the and The (Pstatic friction coefficient changes depending on the ( of the static friction coefficient e) .

contact surfaces. In this work, it is considered one common case: rubber tires together asphalt. with dry

P (1) eeraegMF

Center of mass

Fas PsinT FadF T ae P Fig. 3: Illustration of the center of mass and the forces applied to the vehicle According to the ordinary speeds of a personnel car, the air motion, when the car is in movement subject to a force against the motion, the viscous friction force. This force, which corresponds is braking force imposed by the fluid (air), is proportional to the speed of the car body. The to a friction force, equation (2), is dependent on the linear velocity of a moving Vv) as well as the viscous coefficient of Stokes (ks) resulting from the contact of the vehicle body with the fluid vehicle ( (air). (2) VkFvsas When moving, the vehicle also moves a mass of fluid. This fluid is responsible by the vehicle force known as aerodynamic drag force. The aerodynamic drag force applied to a vehicle depends braking the fluid density (U), the drag coefficient specific to the CD ), the vehicle frontal area (Af) and on

the vehicle speed (??). The determination of the air density, the friction coefficient and the vehicle (

are illustrated in [9]. The specific drag coefficient of the vehicle is obtained through the use frontal area

information The calculation of the air density is given by the equation (3) and the frontal of specific [2].

equation (4). area by

§ . · § atm16288 (3) P. ·¨ ¨¨?16273 ??13251012251U r ??1 ? .T.

Where Patm represents the atmospheric pressure in (kPa) Tr the air temperature in ( and oC).

The area Af is given in squares meter (m2) and the mass M in (kg). Combining equations (3) and (4) is obtained the aerodynamic drag force equation (5) [9].

The weight of a vehicle interferes and influences strongly its dynamic characteristic. A vehicle, centre of mass is placed at the geometric centre, corresponds to a fair distribution of weight whose

the two car Anyway, if the car is placed or moving in an inclined plane a weight transfer between axles.

between axles occurs and need to be considered when analysing the vehicle dynamics. For the “Fiat” vehicle under study, is calculated the value of the weight supported by the rear Pr and considering that the weight is evenly distributed over the two wheels is possible to determine the axle

component of that affects the behaviour of the vehicle on an inclined P(T plane )). horizontal weight (

TT2 (6) )sin(P)(Pr 1U (5) 2 VACFvfDad 2 ??M..Af7650005606 (4) 1??

The total resistive force (FAT) applied to the vehicle movement is the sum of the forces previously presented. The total force is also the result between the resistive forces applied to the wheels (Fwheel ) and to the vehicle metal structure body (Fbody). motor drive

?? )(PFFaewheelT? 2 (7)

Combining equations (7) and (8):

So, the load torque in the motor referential (TeRW) results from the set of vehicle motion resistive forces (FAT ) applied to a wheel of radius, RW .

? (10) FRTATWeRW? (9) FFFbodywheelAT ? (8) FFFadasbody

Considering the transmission gearbox ratio (kdif) (i.e., the ratio between the speed of the motor and the speed of the wheels), the load torque in the vehicle referential TeRV) can be obtained using the following expression: (

TT eRWeRV (11)

k dif

The dynamic behavior of a rotating mechanical system is represented by the following equation:


dt ? Z (12) TT eRWm

Where, Tm represents the motor torque (N.m) and Z m represents the angular motor speed (rad/s). The total inertia associated to the vehicle Jv), is given by the equation (13), being the sum of the moments ( of inertia of the electric machine (Jm) , wheel ( Jw) and the one associated with the vehicle that is

function of the road characteristics [9]. a

§ w · ¨ ? 12121¨ dif ? 1 22 § w · ¨??? ¨ dif ? 1 J v ?? . (13) ???sMkRMkRJJverwmv

Where, Mw represents the mass of the wheel and sv is the slip of the wheel [9].

About the slip of the wheel, it is important to note that it depends on the adhesion coefficient wheel and floor. The simulations were performed using mainly the coefficients corresponding to between

dry asphalt floor and to and wet asphalt floor. the

Characteristics of the Electric Model

The commercial electric vehicle “Fiat Seicento Elettra” under study is characterized by electric vehicle powered by a group of 18 lead-acid batteries grouped in series. The batteries being an

connected to a voltage inverter, able to operate with variable voltage and frequency and controlled are

a field orientation method. The output of the inverter is connected to an induction motor (15 by

water cooled (manufactured by “Siemens”; model/reference: 1LH5118-4AA9-Z) [2]. kW)

The electric model simulated using the “Matlab-Simulink” software joins the following

parts: an electric model of energy storage systems (batteries, in this work), a voltage inverter electrical

and an induction motor. voltage

One of the issues related with the available motor, was to know the electrical

induction motor on board of commercial electric car. The method used to determine the induction parameters of the the

motor equivalent circuit parameters is presented in [10]-[12]. Only with the results of [11] possible implement in the “Matlab/Simulink” the dynamic model of the induction motor. it was to

The control methods of induction motors commonly used are based on steady state models, which inadequate when hard dynamic control is required. The field orientation control method is a are

principle that can fulfill the control and dynamic operation requirements of an electric control

equipped with an induction machine [3]-[12]. vehicle

The batteries were computational implemented using the block of “SimPowerSystem” library of “Matlab/Simulink”. This block implements a generic model parameterized to represent the the

popular most types of rechargeable batteries [7]. In the study case, there are 18 lead-acid batteries Volts and 60 Ah, connected in series. with 12


The dynamic model of a vehicle owns a very high degree of complexity, combined with the change parameters when the vehicle is running (weather, road, tires pressure and usage, and so of

Some complex models are available [13]-[18], which can be adapted to any road vehicle, being on).

necessary to provide generic characteristics of the vehicle, as for instance, the weight of the only

relative position of center of mass. In addition, to take advantage of this model in order car or the

detailed and rigorous analysis of the behavior of a vehicle, it is necessary to define specific to obtain parameters. mechanical

In this work, based on the theoretical approach of the mechanical model of a car, i.e, forces the vehicle, a distinct model was implemented considering the most important parameters applied to

influence the dynamic behavior of the vehicle under study and based on a different approach from that

models described in [13]-[18]. The “dynamic model”, representing the mechanical parts of the the (“Sub-model 2”) (Fig. 5), is simpler than the model of [14]-[15] (“Sub-model 1”) (Fig. vehicle

represent the system to be simulated with accuracy as it can be demonstrated by the simulation 4) but can results.





To Workspacetime


Teta0Switch Acel1



Vehicle Dynamics




Switch Acel











Motor + Control

Bat +

Bat -






Ir / Is

RpmWm (rad/s)

? ? ?


Electric Torque (Nm)








216 V 1080Ah Lead-Acid Battery




Fig. 4: Global model of the vehicle “sub-model 1” implemented in “Matlab-Simulink”




To Workspacetime_1



Ir / IsGoto1













Switch Acel


Bat +



RpmWm (rad/s)


Electric Torque (Nm)tetarpm2rad



Switch Teta









Motor + Control

Bat -






Up = 1 / Down = - 1


216 V 1080Ah Lead-Acid Battery


Fig. 5: Global model of the vehicle “sub-model 2” implemented in “Matlab-Simulink”

The vehicle dynamic behavior is analyzed, in a preliminary stage, changing the speed

(accelerator) and the terrain slope (Fig. 6). reference

Fig. 6: Speed evolution (0% Slope; Speed Ref.: variable)

A simple but important result is to observe the vehicle speed evolution when starting and when changes (Fig. 6). From Fig. 6 it can be observed that the “sub-model 2” has a faster transient speed occur

to the less complexity of the mechanical model implemented. The poor starting dynamics is due to due

weight the of the system and to limitations of the power sources (in this case, a battery

In Fig. 7, the state of charge of the battery set during the same simulation is shown. As it set).

and in accordance with the previous results, “sub-model 1” demands a little bit more power is expected

“sub-model 2”. Furthermore, the dynamic behavior observed can be important when analyzing than the

batteries life time and the autonomy of the investigated vehicle. As it can be observed in Fig. the

Fig. 7, both models give similar result having a steady-state error. The observed differences 6 and

the fact that, in “sub-model 2”, it is not considered the variation of the center of mass are due to

according to the of the vehicle characteristics of the route.

Simulation of the vehicle – “Speed change” - 0% Slope

Sub - Model 1Sub -

Model 2


ry s


he b et (

of t


e of

Stat cha

Fig. 7: SOC evolution (0% Slope; Speed Reference: variable)

Similar conclusions can be pointed out for the power consumption estimation. For the “sub-model and 1” “ sub-model 2” the power balance and the distance performed by the vehicle, under the same conditions, are presented in Table I and Table II, respectively. Although the distinct test

between models, their power balances differ only about 1.2%. complexity

Table I: Power Consumption for the “Sub-model 1” – 0% slope – Variable Speed

Time (s) [10,20] [20,40] [40,60] [60,80] [80,100]

Reference Speed (km/h) 50 30 20 40 60

Distance Performed (km) 0.138 0.1666 0.111 0.222 0.333

Mechanical Power (kW) 6.23 2.827 1.889 4.146 15.833

Electrical Power (kW) 7.239 3.325 2.222 4.877 18.627

Power Consumption (Wh) 20.35 18.475 12.34 27.09 103.47

Power Consumption per km (Wh/km) 147.46 111.295 111.171 122.027 310.72

Total Power Consumption 181.725

Total Distance Performed 0.971

Total Power Cons. per km (Wh/km) 187.152

Table II: Power Consumption for the “Sub-model 2” – 0% slope – Variable Speed

Time (s) [10,20] [20,40] [40,60] [60,80] [80,100]

Reference Speed (km/h) 50 30 20 40 60

Distance Performed (km) 0.138 0.1666 0.111 0.222 0.333

Mechanical Power (kW) 6.7023 3.393 2.073 4.524 14.137

Electrical Power (kW) 7.893 3.992 2.438 5.322 16.631

Power Consumption (Wh) 21.919 22.174 13.541 29.564 92.389

Power Consumption per km (Wh/km) 158.83 133.097 121.99 133.171 277.44

Total Power Consumption 179.587

Total Distance Performed 0.971

Total Power Cons. per km (Wh/km) 184.96

Other important results are the torque distribution (at starting, in Fig. 8 and in steady state, The greater complexity of the “sub-model 1” produces higher values of resistive torque in in Fig. 9).

situations. This higher value of resistive torque does not affect the speed evolution but extreme

different values of power consumption between the two models. corresponds to

2% Starting [0 s,20 s] - 50 Km/h , 0% Slope

13% 24%

Torque - Weight of the car

Torque - Static friction

61% Torque - Aerodynamic drag

Torque - Viscous friction

Fig. 8: Torque distribution (starting)

3% Load Torque distribution - 100 Km/h , 0% Slope


65% Torque - Static friction Torque - Aerodynamic drag

Torque - Viscous friction

Fig. 9: Torque distribution (steady state)

In addition to the comparative analysis among the referred models, it is also important to compare electric solutions with similar vehicles, which are equipped with internal combustion engines the

For a wide range of simulations (different routes and speeds), it was estimated that the energy (ICE).

an electric to perform an 100 km route, is about 46% of the energy costs of an ICE vehicle, costs of vehicle,

it is represented in Fig. 10. as

Energy costs/100 km

ICE Vehicle

EV - Sub-model 2

EV - Sub-model 1


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