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Electric Bicycle Using Batteries and Supercapacitors

D. M. Sousa♣, P. J. Costa Branco♠, J. A. Dente♥

♣ DEEC AC-Energia /CAUTL, Instituto Superior Técnico, TU Lisbon

♠,♥ DEEC AC-Energia, Instituto Superior Técnico, TU Lisbon

Av. Rovisco Pais, 1 – 1049-001 Lisboa

Lisboa, Portugal

Tel.: ♣+351 – 21 841 74 29, ♠+351 – 21 841 74 32, ♥ +351 – 21 841 74 35.

Fax: +351 – 21 841 71 67.

E-Mail: ♣pcdsousa@mail.ist.utl.pt, ♠ pbranco@alfa.ist.utl.pt, ♥ edentepc@ist.utl.pt

URL: http://www.ist.utl.pt

Keywords

«Electric vehicle», «Energy storage», «Supercapacitor», «Power converters for EV», «Electrical drive».

Abstract

In this paper, a traction system useful for an autonomous Electric Vehicle of individual use is described.

The developed system is constituted in a first approach by two different power sources: one is constituted

by batteries or by fuel cells, and the other by supercapacitors. This paper describes a technical solution

joining and accomplishing the usage of two energy storage systems in the same traction system. In the

developed system, the supercapacitors run as element that store energy temporarily and that can be used to

retrieve energy.

Starting from the functional characteristics of typical electrical vehicles and characterization of a typical

routing profile, the energy consumption is obtained.

In order to characterize and design the system, this is described in detail, namely the supercapacitors

models, the battery, the power converters and the implemented strategy of control.

According to the obtained results, a control strategy that allows an effective management of the stored

energy in the system regarding the vehicle’s optimal functioning and increasing its autonomy is also

presented and discussed.

Based on experimental and simulation results, the advantages and disadvantages of the proposed solution

are presented.

Introduction

In the modern societies, the increasing needs of mobility means sometimes increasing the number of

vehicles circulating. Ambient concerns, as for instance local pollutant emissions for the atmosphere,

influence also, in nowadays, the technical decisions related with all kind of vehicles. In this context, new

alternatives to the existing internal combustion engines are mandatory. So, vehicles with electric

propulsion seem to be an interesting alternative [1, 2, 3].

Starting from this context, this research describes a solution that was developed and studied to be applied

in electric vehicles of individual use as bicycles. The solution proposes the combination of two sources of

energy, batteries and supercapacitors, and two DC-DC converters. On board, batteries and supercapacitors

store the energy. Anyway, the proposed topology considers that fuel cells should be used in two ways:

replacing the set of batteries or to charge the batteries and the supercapacitors.

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As it is well known, in the typical electric traction systems the batteries drive the high currents and in the

worst situation drive the current peaks demanded by the load. As it is well known, this type of operation

decreases strongly the autonomy of the vehicles for individual use. The continuous and random operation

of electrical vehicles requires and claims for systems improving the autonomy and the performance of the

available ones. In this situation, a solution to improve the battery behaviour and its time life is to replace

temporarily the battery by another power source or, as in the developed solution, to supply the system

using other power source when undesired and transient situations occur [4]. In this case, the load is

supplied by the complementary energy source avoiding, at least, deep discharges of the battery. The

adopted solution uses supercapacitors, which drive the peaks of power required by the load.

Requirements of the system

The first step in order to project the system is to establish the objectives of the work according to the

energy consumption and the performance of the vehicle for individual use. To estimate the power required

by this type of vehicles, we have considered that the forces applied to the vehicle are, as represented in

figure 1, the following:

aM

Fa

⋅=

θ

sin

⋅⋅=

gM

Fg

1

2

tv

AC

M

F

fD air

⋅⋅⋅⋅⋅=ρ

(1)

(2)

)(

2

(3)

θ

cos

⋅⋅⋅=

C

gM

F

R

r

(4)

Where: Fa is the resulting force; Fg is the gravitational force; Fair is the air friction force; and Fr is the

wheels friction force; parameter ρ is the air density (1.29 kg/m3); Af is the frontal area of the vehicle; CD is

the air friction coefficient (tipically 0.9 for a scooter and 0.8 for a bicycle); and CR is the wheels friction

coefficient (usually between 0.008 and 0.014).

θ

cos

⋅⋅⋅=

C

gM

F

R

r

θ

sin

⋅⋅=

gM

Fg

)(

2

1

2

tv

AC

M

F

f

D

air

⋅⋅⋅⋅⋅=ρ

Fig. 1: Forces applied to the vehicle

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Considering that the vehicle runs with a speed v, the power required by the system is:

⇔+++=

PPPPP

r airgaVE

θρθ

cos)(

)(

2

1

sin)()()(

3

⋅⋅⋅⋅+⋅⋅⋅⋅⋅+⋅⋅⋅+⋅⋅=⇔

tv

C

gM

tv

A

C

MtvgMtvtaM

P

RfDVE

(5)

Assuming that the vehicle speed is equal to the angular speed ω of wheels with radius R, torque of the

traction system can be estimated as:

⇔+++=

TTTTT

r airga VE

θρθ

cos)(

)(

2

1

sin)(

3

2

⋅⋅⋅⋅⋅+⋅⋅⋅⋅⋅⋅+⋅⋅⋅+⋅⋅=⇔

tv

C

RgM

R

tv

A

C

MRgMRtaM

T

RfD VE

(6)

Anyway, to analyze and compare the performance of different vehicles for individual use, operating

conditions in terms of speed and autonomy should be used. So, based on the Portuguese standards (NP EN

1986-1), a typical urban cycle (Figure 2), repeated 10 times, with the total duration of 1180 s should be

fulfilled by the traction system in terms of torque and speed and by the power sources on board in terms of

energy stored.

Fig. 2: Profile of the used urban cycle

To fulfill the cycle above and taking into account the physical dimensions of a bicycle or a scooter, the

nominal power required by this type of system stays in the range of 2 kW to 2.5 kW. So, based on the

premises and conditions above, a traction system is proposed aiming the autonomy, efficiency and

performance of this type of vehicles.

Global system

The main elements constituting the global system are two power converters, two energy storage systems

(in the basic implementation, batteries and supercapacitors) and the traction motor [5].

With the proposed solution, the most important objective is to increase the capacity of storing energy and

vehicle autonomy, avoiding deep discharges of the batteries.

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In order to achieve this goal, the global topology represented in figure 3 was investigated.

VSC

iSC'iSC

Vdc

iC

DC-DC 1DC-DC 2

ia

Va

idc

L

Fig. 3: Global system

The power converters

The proposed topology uses two power converters. Their main functions are:

• The power converter DC-DC 1 (operating as buck or book converter (figure 4), in agreement

with the level of charge of the supercapacitors) transfers energy from the supercapacitors to the

battery.

• The DC-DC 2 converter adjusts the supply voltage of the traction motor (in this case, a DC

motor) to control its speed.

VSC

iSC'L

S1

S2

iSC

Vdc

iC

LOAD

idc

Fig. 4: Converter topology of the used DC-DC power converters

The traction motor

The implemented traction system is based on a DC motor, which dynamic behaviour can be represented

by:

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−⋅⋅=⋅

⋅⋅+⋅+⋅=

⋅+⋅=

Ti

k

dt

d

J

k

dt

i

d

L

i

r

U

dt

i

d

L

i

r

U

Load

a

a

aaaa

f

f

f

f

f

φ

ω

ωφ

(7)

To project and analyse the system, knowledge of motor parameters is mandatory. In particular, the

electrical time constant and the starting current allowed by the system, which according to experimental

tests are, respectively:

L

a

a

30

≈=

τ

ms

r

a

(8)

A

r

U

i

a

a

start

20

≈≈

(9)

The supercapacitors model

The nominal voltage of each supercapacitor available is lower than the rated voltage of typical electric

traction systems (12 V or 24 V, for instance) [6]. Therefore, in order to fulfill the rated voltage of these

systems, it is mandatory to connect supercapacitors in series and in parallel modes. Anyway, to investigate

the dynamic behaviour and the performance of the global system it is important to know the

supercapacitor model, which electric equivalent model is represented in figure 5.

Fig. 5: Equivalent model of a supercapacitor

The supercapacitor model is constituted by an inductance L, a resistance Ri and an impedance Zp

connected in serie. The impedance Zp can be calculated using the expression:

ωτ

τ

ω

j

C

ωτ

j

j

)coth(

)(

Zp

⋅=

(10)

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To the available supercapacitors (2.5 V; 200F ±30% (at 20ºC)), the parameters of the model were

obtained by electrochemical impedance spectroscopy, which simulated and experimental spectra are

shown in figure 6 [7, 8].

-10

0

10

20

30

40

50

24,5 25,224,724,224,1 24,425,126,328,3 31,735,937,5

Re(Z) [mOhm]

- Im ag(Z) [m O hm ]

Exp

Simul

Fig. 6: Spectra of a supercapacitor impedance

Experimental and Simulation Results

In a first approach to the problem, the supercapacitors were connected in parallel with the battery, as

represented in figure 7 [9, 10]. To study and analyse the performance of such system, both experimental

and simulation results were obtained. The implemented model (simulated using the @Matlab/Simulink)

includes dynamic models to the used battery and supercapacitors [11, 12, 13].

ia

Va

VB

Rb

ib

VSC

Rsc

isc

Fig. 7: Circuit connecting in parallel the supercapacitors and battery

The electrical equations representing the circuit are in a first approach the following:

+

=

i

v

v

bbb SCSC

⋅−=

⋅−=⋅

d

−=

dt

v

C

i

RivR

i

i

ia

SC

SC

b

SC

(8)

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A prototype of this circuit was implemented in the laboratory, with a set of batteries (12V, 7Ah each one),

a DC motor and a five supercapacitors in series (Ctotal = 200/5 = 40 F). To a random load diagram, the

experimental and simulation results obtained are shown in figures 8 and 9. From these results, it is

important to point out that current peaks are driven by the supercapacitors, thus avoiding deep discharges

of the batteries. Furthermore, when the motor is braking the supercapacitors are charged.

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

30.00

060 120 180240300360420

Tempo [s]

Time (s)

Battery

Corrente [A]

CargaBateria SC

Current (A)

Load Supercapac.

Fig. 8: Experimental results

Current (A)

Time (s)

BatteryLoadSupercapac.

Fig. 9: Simulation results

A reasonable agreement between the experimental results and the simulation ones is observed, leading that

the assumption that the developed models constitute a good approach and the circuit behaves as foreseen

analytically.

Anyway, the above operating principle is only valid if an effective control of the energy transit between

the supercapacitors and the battery is reached.

The control strategy

The first approach to the problem of energy management is based on the calculation of an average value

of the current iDC demanded by traction system. The average current should be supplied by the main power

supply, which can be the set of batteries or a fuel cell [3, 14, 15]. The difference between the

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instantaneous value of the load current ia and the average value of iDC will be the current supplied by the

supercapacitors, iSC.

When the current iSC is positive and the total voltage of the supercapacitors is higher than the energy

availability, the break level Vα, a duty-cycle is applied to the semiconductor S1 (figure 4) running the DC-

DC 1 converter as a boost converter. On other hand, if the supercapacitors does not have energy available,

that is, the set of supercacitors is discharged or their voltage is under the break level, converter DC-DC 1

is switched off and the main power supply supplies the traction system. For negative values of iSC and if

the supercapacitors do not have the maximum load Vβ, converter DC-DC 1 runs as buck converter. When

the supercapacitors voltage reaches the value Vβ , converter DC-DC 1 remains in its stand-by mode.

Anyway, if a fuel cell is used as the main power supply, condition iDC <0 cannot occur. If for instance, iDC

is negative and the supercapacitors are fully load, to guarantee the protection of the fuell cell, converter

DC-DC 2 is switched off, that is, the power supply and load are disconnected.

The flow chart representing the algorithm of control is represented in figure 10.

Fig. 10: Flow chart of the algorithm of control

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Conclusion

In this paper an electronic converter using two power sources connected through two DC-DC converters is

described having potential application in electric bicycles or in other vehicles for individual use without

internal combustion engines.

The proposed system uses in its basic topology a set of batteries and a bank of supercapacitors to supply

the traction system but is also designed to replace the batteries by fuel cells. The conception of the

proposed system is also the first step to investigate the solutions and systems that allow to charge

electrical vehicles in remote places or when the infinite power nets are not available. In this case, fuel cells

can be used to store energy and to restore the energy of these types of autonomous vehicles.

With the proposed solution, it is expected to increase the autonomy of electrical vehicles as electric

bicycles or scooters and to avoid high current peak and fast discharges of the batteries. Therefore, a

control algorithm managing the energy stored on board and the running of the proposed system is

described.

From the experimental and simulation results obtained it is important to point out that the proposed system

has an appropriate performance in hard situations like high loads avoiding deep discharges of the batteries.

Furthermore, it is also possible to adequate the algorithm of to the profile of the course and maximize the

energy recovering. It is also important to refer that the running of the DC-DC converter either as buck or

boost converters does not introduce perturbations in the system dynamics, in particular the vehicle speed

remains constant.

This work reflects also the real perspective of integration of multi energy storage systems in a unique

traction system. The proposed solution reveals advantages from the point of the viewpoint of the traction

system concerning overload situations and avoiding an unnecessary over dimensioning of all system.

In the further work, the implemented power circuit (figure 3) will be analysed taking into account the

amount of energy stored for unit of weight in the storage systems available and useful to these type of

small vehicles.

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