Pedagogical study of an electric bike with low energy consumption

Arnaud Sivert, Franck Betin, Thierry Lequeu
Pedagogical study of an electric bike with low energy consumption,
management and dimensioning of onboard energy : eco marathon
(1) Institut Universitaire de Technologie de l’Aisne Département Génie Electrique SOISSONS
Laboratory for Innovative Technologies (L.T.I), Team Energy Electric and Associated System
(2) Institut Universitaire de Technologie de Tours, Département GEII, 37200 TOURS.
Abstract: - The electric bike is a very good educational system because it can be used by all students without
problem of safety. When pedaling on the electric bike, the student can identify with the motor drive and understand the meaning of torque, speed and power. This educational system uses many modules of Electrical Engineering: power converter, battery, motor, controller, electronics, lights, instrumentation, sensors, mathematical
modeling, mechanics...
Thus, many technologies can be presented. These vehicles have a difficult compromise between weight, power,
battery life, and price. These vehicles could be implemented using new composite materials and new Lithium
batteries. But to increase the lifespan of the batteries, which represent 35 % of the electric vehicle price, we will
demonstrate the benefits of a control with constant power through the motor, compared to a control with a constant force. This paper will outline the resistive power, as a function of vehicle speed and the state of energy
consumption. A comparison of energy prices between different kinds of electric vehicle will be presented. The
advantages and disadvantages of using super capacitors will be presented, as well as energy management on
board the motor speed controller. Then, an overview of the regulation of a fast charger with current control and
voltage control will be presented. Finally, many educational applications will be presented around the electric
vehicle realized.
Key-Words - Challenge Eco Marathon, motor control constant power, Lithium battery, motorized electrical
cycle, project-based teaching, battery charger, super capacity, energy management.
We will now define the vehicle mathematically to
understand its characteristics (maximum speed,
size, acceleration...). For the sake of simplicity,
we will not go into detail regarding the mechanical losses of the engine, the control (speed control
and/or current), the power electronics...
Firstly, we will briefly present the resistant power
as a function of the vehicle speed and then present
the dimensioning of the vehicle, the control of
electric motors and finally the cost of this transportation way.
Vehicles with low electric power consumption [1,
2, 3, 4] are becoming new actors for transport in
our congested cities. This type of vehicle meets
the demand of minimizing the production of CO2
and responds also to the future energy transitions.
We will see that it is possible to build vehicles
traveling at 80 km/h maximum with a engine
power of less than 4000 W. We will see that the
energy consumption can reach a value of 560
Wh/100km at an average speed of 50 km/h, with a
autonomy of 180km, so a consumption of 1600
km with the equivalent of a liter of petrol.
The electric bike is a very good educational system because it can be used by all students without
problem of safety. When pedaling, the student can
identify with the motor drive and understand the
meaning of torque, speed and power. This educational system uses many modules of Electrical
Engineering: power converters, battery, motor,
controllers, electronics, lights, instrumentation,
sensor, mathematical modeling, mechanics...
E-ISSN: 2224-3410
The resistive force [5] depends on the rolling resistance, the gradient of the road and air resistance. Their respective equations are:
Fresistive ( N) = FRolling + Fslope + FAir
FSlope ( N) = M (kg ) ⋅ g ⋅ Slope(%)
FAir ( N) = f air ⋅ [S(m / s) + S wind ]
= ⋅ ρ ⋅ S ⋅ Cx ⋅ (S + Swind ) 2
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Arnaud Sivert, Franck Betin, Thierry Lequeu
tors is 90 %, while the petrol vehicles are around
30 %.
Therefore, the streamlined tricycle, called velomobile [14], has low energy consumption with
respectable speeds. In addition, the streamlining
reduces the impact of bad weather conditions and
insulates during cold winters.
This type of vehicle is made for challenges such
as the Eco-Marathon [15, 16] but with low average speeds (30 km/h) and ergonomics that do not
allow daily use. In this Challenge, electric motors
have supplanted combustion engines with a record
consumption of 7000 km for the equivalent of one
liter of petrol.
We will see the dimensioning of a streamlined
electric tricycle that can be used daily and find out
whether muscular strength is relevant. To conduct
this dimensioning, we must answer the following
• What is the mass of the vehicle and what will it
• What speed and maximum acceleration will
the vehicle have? (this will determine the power of the motor)
• What is the objective of vehicle autonomy and
consumption? (which defines the energy capacity of the battery and hence its weight)
• What is the budget for the designed vehicle?
The rolling forces depend on the kind, and width
of tires and of kind the road. They are represented
by the coefficient krolling. But, the width of the tire
depends on the maximum speed, acceleration, and
braking of the vehicle mass.
For the speed superior at 25 km/h, the rolling
forces are very small compared to the aerodynamic force of the air, which depends on the surface
area S, turbulence and therefore Cx.
To model the resistive power of a vehicle, it is
easier to use the speed (S in km/h) with the following equation:
Presistive ( W ) = k aero ⋅ S3 + (k rolling + k slope ) ⋅ S(km / h ) (4)
With kslope in Watt/(km/h) and kaero in Watt/(km/h)3
The order of magnitude of these coefficients for
the vehicles tested is:
Type de cycle / coef
kaero krolling weight kg
Mountain e-bike
0,0066 7,30
0,0051 7,50
e-Bent rider
0,0040 5,00
e-Velomobile [12]
0,0018 4,06
Small car
0,05 100,00
Table 1 : power coefficient of vehicles [12]
With of low value coefficients, there are of low
Due to the slope force caused the weight of the
vehicle, the energy consumption will increase in
daily use.
From the typical energy consumption of vehicles,
the graph in Figure 1 shows the average speed as a
function of energy consumption per 100km and
per person.
Finding the perfect compromise is not an easy
thing, because all these specifications are related.
For example, if you want to go faster then the
motor power will be larger, so the engine will be
heavier. You will have to use more energy for
your battery capacity or more efficient technologies and your budget will increase. We will impose a specification for the vehicle, which is to
use city and country roads without interfering
with traffic.
The vehicle shall carry a person who weighs 80
kg and is 1.8 m tall, with 15 kg of luggage (volume 20 liters) on the classic road. The vehicle
must be less than 50 kg when empty and have a
low consumption. The maximum speed it will
reach is 80 km/h, with a range of 200 km.
The dimensions of the vehicle must be less than
2.7 m in length, a width of 0.8 m and a height of 1
Fig. 1. Average speed based on energy consumption
per 100 km and per person [12].
Figure 1 shows us that only light vehicles lead to
low energy consumption. Similarly, electric vehicles have a lower consumption than those of
petrol because the efficiency of the electrical mo-
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Volume 11, 2014
m. The ergonomics of the vehicle will allow of
pedaling for long journeys and easy entry.
From the coefficients in table 1, the power versus
a speed can be seen in the following figure:
S(m / s) =
bike 0%
slope 5% 150kg
slope 0%
speed (km/h)
E(J) = Ekinetic + Eforce resistive = Fm (t) ⋅ S(t) ⋅ dt
Fig. 2. Motor power vs the speed and the slope. [10,11]
For example, during acceleration, the energy required (7) is equal to:
In this figure, we can see that the fairing allows
very low power consumption of a velomobile
compared to a regular bike, but requires 40 kg
extra. Therefore, for a power of 3 kW and a slope
of 5%, the consumption is identical to 40 km/h.
The average power of a person pedaling is 150 W
to 300 W at a pedal speed of 30 rev/min to 100
However, on the flat, for a velomobile up to 50
km/h, resistive power is 430 W, so muscle power
human can provide 50% of the power required.
Therefore, muscle power human strongly increases autonomy and provides exercise. However,
muscle power is derisory on uphill roads.
Now that the resistive power is known, it is necessary to know the power required for respectable
acceleration. The motors are often controlled using constant force. We will look at the vehicle
performance with this type of command [6].
S t2
⋅ )⋅
E ( W.H) = ( M ⋅ S 2 + Fresis tive ⋅
t acc 2 3600
= 4,7Wh
It may be noted that the energy recovered during
deceleration corresponds almost to the energy of
acceleration to the resistance force nearly.
It may be noted in figure 3a, the high peak current
supplied by the battery during acceleration and
during regeneration.
Fig. 3a. Limiting the motor current at 80A.
Constant motor force during dynamic phases is
ensured by limitation of the motor current, which
in our case is 80 A. Therefore, the driving force
during acceleration will be 328 Nm, since the
torque constant of our engine is 4.1 Nm/A. With a
72 V battery, the maximum power is 5700W this
voltage allows us to reach the speed of 17.5 m/s or
63 km/h.
Constant force causes a constant acceleration and
linear speed increase corresponding to the following equation if we neglect the air resistive force:
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(Fm − Fresis tive )
⋅ t + S( t = 0)
M(kg )
With Fm(N) representing the motor force, t the
time (s).
During acceleration, operation at constant force
causes a significant peak of current to be supplied
from the batteries.
For a vehicle mass of 100 kg, and flat road, the
acceleration and deceleration will be 6 seconds
both to reach 17.5 m/s and get back to stationary.
In Figure 3b, the speed and energy consumption
can be observed without neglecting the force of
air resistance. This energy is composed of the
kinetic energy and the energy required by the
resistive force. The energy corresponds to the
following equation:
Power motor (Watt )
Mountain bike
110 kg slope 5%
Arnaud Sivert, Franck Betin, Thierry Lequeu
Fig. 3b. Speed performance and energy consumption
with constant force control.
Volume 11, 2014
But all batteries are
charge currents and
damage. So there is
desired performance
lowed by the battery.
types of batteries
58 F/75 V
Super capa 30S
1600F/75 V 45Wh
Super capa 30S
50F/75 V
The following table shows the price of batteries
according to discharge rates and their type [12].
limited by the rate of disthe charging rate to avoid
a compromise between the
and maximum current al-
li-po 20 Ah 18S
li-po 20 Ah 18S
Li-fer 20 Ah 22S
Super capa 30S
Arnaud Sivert, Franck Betin, Thierry Lequeu
Size & Volume cm3
(0.8*20.6*10) 3000
(1*22*10) 3960
(0.8*22.8*16) 6600
(Ø4*7.6) 3650
(Ø6.0*8.5) 9100
(Ø1.8*4) 400
7.5 kg
9 kg
11 kg
3.7 kg
620 €
1000 €
650 €
900 €
Rate charge
20 A = 1C
50A = 2.5C
20 A = 1C
20 A
10.5 kg 1100€
0.6 kg
90 €
Table 2 : Comparison of different types of batteries 72V/20Ah
S(m / s) =
D( m ) =
+ FRe sis tan t
2 ⋅ Pm lim it
2 ⋅ Pm lim it
⋅ t1/ 2
2 3/ 2
1 mΩ
5 mΩ
10 mΩ
6 mΩ
( 1440Wh)
When the battery power is limited, the engine will
run at constant power Pm limit. To establish the
performance of the vehicle, it is necessary to solve
the differential equation (8). Neglecting the resistive force, the resolution of the equation (8) gives
the speed (9) and displacement (10):
Pm lim it
With the resistive force not neglected, the differential equation cannot be solved analytically and
will be simulated.
During acceleration, if the power is limited to
2880 W (72 V, 40 A) corresponding to the average power in Figure 3a, it will take 6 seconds to
reach the speed of 17.5 m/s. The energy consumed
will therefore be identical between the two control
methods (fig. 3b and 4b).
But, with constant power control, the distance
travelled is 70 m instead of 55 m (fig. 5c). Indeed,
velocity versus time at constant power is greater
than that of the constant driving force, as can be
seen in fig. 5b.
In this table, it can be observed that the weight,
the volume and, especially the price, increase
when the rate of discharge is large. In addition,
the regeneration current must be limited by the
rate of battery charging.
We can observe that the price of super-capacitors
is relatively high compared to batteries. Supercaps
can withstand a very large current discharge and
charge but they have low energy content. They
accept a large number of cycles of charge and
discharge 1000 times more than a battery.
To minimize the discharge and charge battery
current, we will see that constant power control is
more appropriate than constant force.
rate discharge
60 A = 3C
360 A = 15 C
60 A = 3C
200A max
20 A
1240 A max
70 A max
14 A
Fig. 4a. Constant power with battery current limitation.
Fig. 4b. Speed and power
for a constant power control.
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Volume 11, 2014
Monitoring the temperature of the motor is required for correct operation of this command.
With constant power control, the current limit of
the motor is 2 to 3 times the rated current. Warning: it is possible to exceed the maximum motor
power when the gradient of the road is high and
therefore destroy it, as well as the batteries. Thermal monitoring is also necessary to protect the
motor, but we also use temperature sensors to
monitor the batteries.
Battery energy (W.H)
Constant power control
constant force control
speed (m/s)
Constant power
To minimize the rate of discharge of the battery, it
is possible to use super capacitors.
Indeed, it is interesting to combine the advantage
of super-capacitors that can provide a lot of power
and advantage batteries with high energy capacity.
We must find a compromise between size, weight
and acceptable price. But, it is also necessary to
manage the charging and discharging of the two
energy sources. Therefore, specific converters
must restrict outgoing and incoming current to the
batteries and super capacitors. These converters
must also monitor and limit the maximum voltage
of each cell of the battery and super capacitors
through a BMS (Battery Management System).
One solution is that the battery and super capacitors provide energy to a continuous DC bus via
two reversible powers switch current (power
switch 1 and 2). The DC bus provides power to
the drive motor vehicle.
Constant Force
Distance (m)
70 m
constant power
55 m
Constant force
Fig. 5. Energy, speed, distance control to the power and
force with constant M = 100 kg.
So, the speed performance is greater with constant
power during the acceleration, and the current in
the battery is constant at 40 A without never
reaching 80 A (Fig. 3a).
Therefore, the current demands of the battery is
lower. With a constant power control, the maximum current of batteries is never exceeded in the
mountain road. But, there is a high motor current
at low speeds and therefore the transistors must be
highly oversized (therefore, 2 transistors IRF4110
able to support 180A have been mounted in parallel).
The use of two transistors minimizes the size of
the cooler. The PIC 18F6520 microcontroller regulates the battery current, but there is also the
measurement of the motor current which allows
the determination of motor heating in order to
protect it (numeric thermal relay). The command
of the brushless motor is made without sensors to
increase the reliability of the vehicle but the motor
drive loses a little acceleration torque compared to
a control with a sensor.
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Arnaud Sivert, Franck Betin, Thierry Lequeu
Power Stage 1
Power Stage 2
Fig. 6. Presentation of the "hybrid power"
battery and super capacity [1,6,17].
Both the converters have to adapt the level of
voltage between the DC bus and the battery voltage and the voltage of the super capacitors.
Indeed for super capacitors, the switch power
allows to adapt the variation of the voltage (∆V)
related to the unavoidable variation energy ∆W
which corresponds to the following equation:
Volume 11, 2014
∆W ( Joule) = C SC Vmax 2 − Vmin 2 = ⋅ C SC ⋅ ∆V 2
We will now see how the controller handles the
control of a motor cycle.
with, Csc as the value of the super capacitor.
The principle behind the control of the 2 switch
power is to maintain constant voltage on the DC
bus which supplies the drive of the vehicle. Regulation of the two switch power can be done with a
cheap microcontroller using simple fuzzy logic
controller [8].
The brake levers are equipped with switches to cut
off the motor, control the choppers and the rear
brake light. When the mechanical front brakes are
activated, there is an electric braking of 10A (1C
for 10Ah batteries and a recovery of 720W).
If the throttle handle is at 0%, without pedaling
there is light electric braking of only 5A (360W)
on the batteries. All our motorized cycles are rear
wheel drive (rear motor) which does not allow
high braking at the rear. Indeed, we must provide
70% braking at the front and 30% rear, otherwise
over steer is assured (rear drift). If you’ve just
fully charged the batteries and begin a long descent, the battery will be soon be full, and BMS
stops regeneration. There won’t be any braking in
these circumstances; this is detrimental to driving.
Therefore, super capacitors will be size only to
minimize the rate of discharge to 20A when the
battery also provides 20A. The voltage of the supercaps was chosen to be 24V to minimize the
price and size, with 9 supercaps in series of 500F.
The acceleration phase energy is 4.7Wh from
equations (6 and 7). With hybrid power, the supercaps will recharge as soon as the battery current is less than 20A and will depend on the speed
that you go at. The problem of managing the super
capacitors is that after an initial acceleration of
2880W, it takes some time for them to be charged
to 100%. So the driver sometimes has slower acceleration and this is also problematic for driving.
Another, much simpler, solution than hybrid power is to put 2 super capacitors in parallel on each
battery element. Indeed, in recent years the price
of super capacitors has declined sharply with internal resistances much lower than that of the
battery. Therefore, the peak current will be provided by super capacitors. Note: the super capacitor voltage will never be exceeded due to the voltage threshold of the battery cells which is much
lower than the voltage of 2 super capacitors in
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Arnaud Sivert, Franck Betin, Thierry Lequeu
Our electric prototypes cycles are equipped with
engines with a constant 3000 W power control [7,
9] which provides a wide speed range. A 72 V 20
Ah (1440 Wh) battery gives an acceptable autonomy.
Fig. 7. Different prototypes of electric vehicles
(Left to right) bent rider, tricycle, go kart, velomobile.
You can see in the following figure the dynamic
of speed for the velomobile, which weighs 140 kg
with its driver and 10 kg of luggage.
Motor power
speed 75km/h
Battery whithout
super capacity
temps (s)
Fig 8: Acceleration and deceleration of the velomobile
versus time (on flat ground, without pedaling)
with M = 140 kg.
In Figure 8, the power and intensity battery is
constant throughout the acceleration.
Then there is power going to match the resistant
power. Finally, we can observe the mechanical
brake and a significant deceleration.
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Arnaud Sivert, Franck Betin, Thierry Lequeu
The resulting power of 3000 W for a 140 kg mass
provides an acceleration of 4 m/s2, identical to a
car, which allows this velomobile to blend into
city traffic.
To model the vehicle performance, it is possible
to use the simple first order Broida identification,
even though the differential equation of the vehicle is non-linear.
In the figure 8, we can observe the use of a constant power control avoids peak current from the
battery during transients. This control is made by
managing the current on the battery and not on the
current of motor.
tronic circuit called BMS that will prevent charging in this case.
To control the motor of an electric motor cycle
without assistance, there are several strategies,
such as:
- Limiting the motor current (motor control with
a constant force during acceleration);
- Limiting of the current from the battery (motor
control with constant power during acceleration);
- Speed control and battery current limiting with
electrical braking.
Fig 9. Third Strategy: Speed control with battery current
limiting of 30A with a 48V battery [7,10]
13 km/h
throttle handle 100%
Intensity brake
Now that we have seen the feasible performance
of the vehicle and the different strategies for the
control of the motor, we will look at its consumption and autonomy.
The third strategy can easily incorporate an assisted sensor placed on the pedal as specified below:
On the flat road, without pedaling, the velomobile
consumption is 285 Wh per 100 km at an average
speed of 35 km/h. This consumption corresponds
to 3157 km for the equivalent of one liter of petrol.
But use in our gently undulating region with pedaling, consumption goes up to 540 Wh for 100
km. There is almost a factor of 2 between favorable conditions (flat road, no wind, low acceleration) and daily use. This factor is also found for an
average speed of 50 km/h.
Variety Flat road Variety Flat
Speed average 35 km/h 35 km/h 50km/h
bent rider
(Wh/100 km,
180 km 245 km
- If pedaling between 0 to 0.1 rev/s, the motor is
coasting regardless of the action of the throttle. So
the reference speed for the controller is 0 km/h.
- If there is low rate pedaling between 0.1 to 0.15
rev/s, even if the hand throttle is 100%, the speed
reference will be only 13 km/h, allowing acceleration, but not allowing you to go quickly.
- If there is pedaling greater than 0.15 rev/s, the
speed reference will be a certain percentage of the
hand throttle.
- Electric braking will be invoked only with the
throttle handle to 0% above the speed of 13 km/h.
below this speed, the motor is freewheeling.
(Wh/100 km,
We can see in the figure below, the implementation of the third strategy with a safety sensor on
the pedal. The battery current is limited to 30 A.
The 48V battery allows us to reach a speed of 43
km/h. We can observe the speed control management during acceleration and braking.
Energy recovery is dangerous if the Li-Po batteries are 100% charged. Therefore, the level of
charge of the battery must be known in order to
allow electric braking. It is the role of the elec-
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Speedmax 43 km/h
266 km
500 km
Table 3 : consumption vs average speed
and variety road with of slope.
The difference in autonomy is due to the consumer requested by acceleration but especially due to
the slopes of the road. This consumption is nevertheless very low compared to an electric scooter
with 45kWh/100km at 50 km/h.
Our costs of transport are not only linked to the
consumption of energy. We must take into ac-
Volume 11, 2014
count the cost of manufacturing and obsolescence
recycling batteries.
Therefore, the following table shows the energy
costs of a vehicle to do 100 km at an average
speed of 50 km/h, with an electricity price 0.12
€/kWh (French domestic rate in 2013).
Arnaud Sivert, Franck Betin, Thierry Lequeu
The design of a charger requires constant current
charging then constant voltage to not exceed the
maximum voltage of each cell as shown in following figure:
Battery Voltage
Full energy
per 100km
Renting =
battery price,
Cost of
4 years
25 kg
0,48 €
Electric 50 kg
Electric vehicle
500 €/1.4 kWh
500 €/1.4 kWh
50 €/mois
4000 €/10Wh
2000 €
6000 €
8000 €
1,00 €/100 km
0,81 €/100 km
5,60 €/100 km
15 €+52 €
1,80 €+135 €
59 €+166 €
Twizy 450 kg
0,60 €
Max voltage
Fig. 10. The working steps of a battery charger [8]
The model parameters of an electrochemical converter vary depending on the volume, the area of
the electrodes, the type of electrodes, the state of
the charge process, the number of cycles, the temperature and the age. The simplest model is an
electromotive force (EMF) noted EB in series with
a resistor noted RB. But the model of a battery is
much more complex with, notably, a high level of
capacity at its terminals. The charger must work
with different kind of battery whose energy capacity and technology, Li-ion, Li-Po or LiPoFe are
also different. Thus, there is no need to consider a
complicated model. The choice has been fixed
here to use an EFM denoted by EB in series with a
resistor denoted by RB and with switch power step
Table 4 : Cost of different electric vehicles
In this table the depreciation of the vehicle was
determined over 4 years with use of 1500 km per
month. Therefore, the cost per month is split between the two values (consumption and vehicle
depreciation). It can be seen that the renting of the
battery is relatively expensive compared to the
cost of the battery.
One can also note that the cost of electricity consumption is very low compared to that of a petrolengine scooter whose cost per month over 4 years
is 112 € +52 €.
It may be noted that the number of charge cycles
per month is much lower than what can a battery
is capable of performed. Indeed, a battery can
have 1000 to 1500 charge and discharge cycles
during its cycle life.
For this moment, the manufacture of velomobiles
is artisanal, so prices should drop with industrialization.
The price of a 3 kW electric bike kit is 1200 €
with a 72V/20Ah battery in 2013. This battery
provides a range of about 200 km, which allows a
distance of interesting uses.
In addition, it is not recommended to fully discharge a lithium battery which will reduce its
service life. A reserve of 20% energy capacity is
LiPo batteries require excellent current and voltage control charger so as not to destroy the cells.
We will see the educational use of charger regulation.
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L et RL
Fig 11a :switch power supply of charger battery
The battery types such as lead acid and Li-Po are
first charged by a constant current, then at a constant voltage and finally either by a holding voltage or disconnected. The battery’s voltage must
not exceed a critical threshold voltage. So the
voltage must be precisely regulated to avoid battery damage. The charging current level must be
modified according to the current energy capacity.
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Arnaud Sivert, Franck Betin, Thierry Lequeu
The next section focuses on the current control
process, followed by the control of the voltage
Ci(p)=(εi(p).ki)/p will cancel the static error without obtaining any overshoot. The first order transfer function of the current is given by:
9.1 The battery current and voltage control
I B ( p) = (
With Ic reference current, A=
The average voltage at the terminals of a battery is
given by the following equation for a step down
switch mode power fig 11.a:
UB moy = U input ⋅ (α / 216 ) − R L ⋅ I B
U B moy − E B
Uc (V)
Reference current
U input
of voltage
if UB > UB max
∆α ⋅ A
1 ⋅ 26V
= 16
=0.2 Α
2 ⋅ (0.001 + 0.001)
1 − Z −1
Feedback current
Bi = 9,4
Fig. 12: Control scheme of the corrector.
Fig. 11.b: The control scheme for current and voltage
The algorithm for the corrector is given by the
following statements where ε denotes the error.
if error ε > 0 then ∆C(z)= Te/(1-z -1)
if error ε < 0 then ∆C(z)= -Te/(1-z -1)
if ε < ε s = 0 then ∆C(z)= 0 /(1-z -1)
9.2 Current regulation with an integral
The electromotive force of the battery provokes a
static error. A pure integral corrector
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The step response integral corrector no longer
depends on the current measurement but only on
the sign of the error. To prevent a wide output
variation, the increment is chosen to be equal to
one step according to the sampling period Te as
shown on following figure.
9.3 Current regulation with a unit
integral corrector
UB (V)
Feedback voltage
Due to low resistance values, only a 16 bit PWM
is suitable when the current measurement is conditioned with an analog filter. As some perturbation always exists, this kind of regulator with a
following unit integral corrector is thus preferred.
The L/R time constant is very much higher than
the PWM period but L/R is very much smaller
than the sampling period of the control which has
been arbitrarily set to 2 ms. Therefore, the battery
current will have to reach its steady state level at
each sampling period, so that the inductance could
be neglected. The model of the current and voltage control can be represented by the following
Bv = 10
A ⋅ Bi
where p is the Laplace variable and R = R B + R L
k i ⋅ U input
Where Rmini=RL=1mΩ and Bi = 9,4 is the feedback coefficient.
The time constant depends on RB. Moreover this
classic control method depends on the current
measurement. With low values of the resistors RB
and RL, a current measurement error can cause
large output current variations. A minimal unit
change of the duty cycle ∆α will cause a current
variation given by the equation:
R + L.p
ki is the integration gain. The time constant of the
loop is defined by:
where Uinput is supply Voltage (26V) and α
equals the duty cycle of the PWM (Pulse width
modulation) with a 16 bit range. The 72V battery
is divided into 3 modules of 26V which is recharged by 3 chargers.
The resistance RL of the chopper filter inductance
L will not be neglected given that the charge current may reach 20 A in our application. The equation for the battery current is given as follows:
I B ( p) =
IC E B ⋅ p
Bi A ⋅ Bi 1 + p ⋅ τ
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(Battery Management Security) and to make technical choices.
Indeed, the electric vehicle is an excellent teaching aid to developing the electric converter and
programming the microcontroller that controls the
brushless motor. There is also all the electronics
of the onboard instrumentation: speed and distance measurement, measurement of current and
voltage in order to determine the energy capacity,
% of regeneration....
The current required by the motor creates electromagnetic disturbances, so the study of this aspect must be considered. Therefore, the currents
must be filtered both digitally and analogically.
In addition, the design of the display of low vehicle power consumption allows the use of power
LEDs for illumination. Hence the design of a
chopper circuit to convert the 72V battery voltage
to the current control for lighting.
This electric vehicle has to be charged daily and
fairly quickly, so you have to design rapid
72V/20A chargers, which are not yet available
commercially with a power factor near 1.
Thus all of the topologies of electric converters
can be implemented for this application.
All problems regarding output control (parameterization, performance, instability) can be observed
on the drive motor and the battery charger. In
addition, you must know how to program these
digital controllers.
The working student working enters the course of
the works construction of the technology institute.
From project specification, students must construct the system. The teacher carries out the technological choice and orders the equipment for a
successful project in the year of cursus.
The number of time about 150 hours throughout
the year, is followed by a single-teacher in our
small organization of 50 students in first and
second year.
But often students are passionate and come during
their free time and some weekends to finish their
tests and promote the project in different types of
Students are divided into pairs with different objectives (2 students website communication and
signaling (LED lighting prototype), 2 for the production of chargers, 2 for instrumentation and
measure vehicle dynamics et consumption, 2 to
achieve inverters, two for mounting and battery
test, 2 to an electrical circuit section and the wiring).
This corrector provides less dependence of the
output measurements on any variations of EB and
RB. Nevertheless, the output dynamics are very
slow and satisfy the following equations:
I B (n.Te) = (n ⋅ Te ⋅ A - E B ) / R B
With a sampling period of 2ms, EB=23V,
RB=1mΩ, it is necessary to wait 1.9s to reach the
reference 20A, but this time is negligible compared to the charging time. Therefore, there is no
need to ramp in the current demand.
The charger installation has been done on a PIC
16F6520 microcontroller where an LCD display
displays the main information from the charger.
The current is measured from the oscilloscope by
using a Hall Effect sensor and a difference amplifier.
The microcontroller monitors the voltage of each
cell and transfers all data to a PC, as can be seen
in the following figure.
Current 25A
Voltage 8 cells
Capacity energy en A.H
Fig. 13: Charging of 8 LiPoFe cells 40Ah to 25A (voltage, current, energy versus time) [13]
It can be seen in the previous figure, that when
one of the cells has reached 3.7V, the current decreases. But all cell voltages have not reached
their threshold voltages. So the charger will balance the cells with a current of 0.5A, routing the
current through a 2 Watt resistor. The charger
reacts like a BMS.
This educational system requires us to examine all
the possible motor technologies, with different
solutions for drives and for batteries. We need to
see the issues of on-board power management
E-ISSN: 2224-3410
Arnaud Sivert, Franck Betin, Thierry Lequeu
Volume 11, 2014
marathon challenge [16] that exploit this possibility.
Similarly, a hydrogen fuel cell battery may replace the battery. To minimize the peak current
during acceleration, super capacitors can be used.
The list of technical and educational possibilities
is very large.
Throughout the design of an electric vehicle, there
are as many studies in mechanics as there are in
electrics and therefore collaboration can be made
between these two fields. The design of an electric
vehicle motivates our students and gets them to
use their minds.
To help others who have the same project on the
implementation of electric vehicles, the students
completed a web site and communicated on forum
and blog [12,13,14,15]. In addition, there are numerous articles in the local press, all serving to
promote the university.
The cost for the construction of a prototype is
relatively large (7000€ for our case), but some of
these finances are returned through publicity in
the daily press to the university.
Upon completion, it is possible to develop other
types of vehicles, such as gokarts or a more standard car [13].
But often there is a mutual aid between pairs with
an organization star, so a methodology a little bit
“rock and roll”.
Indeed, the organization is based on the progress
of each student with the teacher who is the manager and conductor of the project.
Student assessment is carried out with a table that
considers each student on the following criteria
(self-organization, dynamism, initiative, involvement, teamwork, research resources, methodology, and final results). Then, students are graded on
a folder of 25 pages, a large poster and an oral
presentation of 15 minutes and 15 minutes for
In other universities that have a number of 150
students, there are several teachers who supervise
students in turn throughout the year and bring
their expertise.
The problem of students is often a prerequisite. So
there is 15 hours of study at the beginning of the
year for the whole class 50 students on how to
make choices to achieve homogeneous electric
During the competitions, students are very mature
and take a lot of initiatives in order to do their
The students were very proud of themselves enjoying their work "this is me and my colleagues
friends who make this prototype" but also explaining to competitors, their prototype.
Students have an excellent state team, with respect
for competitors.
On the return trip, the students do positive and
negative results of the prototype and think about
the future prospects.
For a new team and new teachers, the harder is to
start from scratch to make a prototype. This is
why a technical book was made to help people
wanting to make all electric vehicles [1].
Participating in challenges is always a great adventure that requires us to surpass ourselves.
Work on electric vehicle low consumption allows
it to be useful to society in our world or energy
transition of petrol will be inevitable.
In addition of the technology, it is possible to add
solar panels to have more autonomy. But a panel
of 1.5 m2 can only provide 300 W in full sunlight
and weighs 6 kg for Semiflexs [3]. For the moment, the price of photovoltaic panels doesn’t
allow them to be considered.
And yet, there are different challenges in Europe
such as the "Sun Trip", the "Solar Event", the
"World Solar Challenge" in Australia or the eco-
E-ISSN: 2224-3410
Arnaud Sivert, Franck Betin, Thierry Lequeu
The design and construction of an electric vehicle
is a very good teaching project for our students of
bachelor to Electrical Engineering and Mechanical Engineering.
The constant power control method protects the
battery. This control method has long been used
for electric traction railways. The benefits of constant power control are obviously applicable to all
electric vehicles; however, many manufacturers
only offer variable speed constant torque drives.
We also proved that it was possible to make motorized cycles with respectable speeds and autonomy. Some of our students enjoy extreme vehicles
with a high acceleration. In this article, we have
also demonstrated that the consumption of electrical energy depends greatly on the vehicle mass
and Cx. If the price of electricity is low, one must
take into account the cost of production and the
life of the batteries in order to determine the overall running cost of our vehicles.
The electric velomobile will definitely be one of
our alternative transport means in future of energy
Volume 11, 2014
[13] Web site : Construction of Electric Vehicle: (03.2014)
[14] (03.2014)
[15] Site web : eco-marathon competition.
[16] (03.2014)
E. Hoang, G. Feld, B. Revol, D. Penard, « Eléments d'étude
d'un système de stockage de l'énergie électrique : le
supercondensateur, La revue 3E.I, N°49, juin 2007, pp. 15-21
The students are very motivated by this subject
because they feel useful in responding to a demand of our society to minimize our impact on
the planet. In addition, participation in the adventure of a challenge can motivate students and
teachers on the completion of the project.
[1] A. Sivert, T. Lequeu “ I build my electric vehicle ”, Publishing
book french Dunod, 2013, 144 pages.
SHYUE-BIN CHANG “The Torque Control with MultiObjective Performance for E-Bike Systems with Human
and CONTROL, volume 6 october, 2011 pp361 to 370.
[3] M. S. Carmeli, F. Castelli Dezza, G.Galmarini, M. Mauri and L.
Piehari, “A vehicle with very low fuel consumption;
realization, analysis and optimization”, in XIX International
Conference on Electrical Machines, Rome, Italy, 2010.
[4] José Fernández Ramos1, Juan Jesús Fernández Lozano 2,
Alfonso Gago Calderón “Design of Electric Racing Vehicles:
An experience of interdisciplinary project-based education in
engineering” EVS 27, octobre 2013
[5] A. Sivert “Le vélo électrique » Revue des départements Génie
électrique & informatique GESI N°80, décembre 2012, pp 2633.
[6] A. Sivert, F. Betin, S. Carriere “Difference force and constant
power control applied to electrical bike”, EVER ecologic vehicles & renewable energies de MONACO, mai 2012.
[7] A. Sivert, F. Betin, J. Becar “An Electrical Bike For Project
Based Learning Platform”, EVER ecologic vehicles & renewable energies de MONACO, avril 2011.
[8] A.Sivert, F.Betin, J.Becar “A Fuzzy Logic Application for
charger of batteries : go-kart”, Conference EVER ecologic vehicles & renewable energies de MONACO, Avril 2011.
[9] S. Viollin « le vélo à assistance électrique » les cahiers de
l’instrumentation N°9, Chauvin Arnoux, octobre 2010
[10] A.
ligne :
2011 (03.2014)
[11] Forum bentrider : (03.2014) 2013.
[12] Etude de la consommation énergétique d’un vélo-mobile :
E-ISSN: 2224-3410
Arnaud Sivert, Franck Betin, Thierry Lequeu
Arnaud.sivert was born in France.
He obtained a Ph.D. degree from the
University of Picardie Jules Verne, Soissons, France, in 2000.
In 1994, he joined an Institute University
of Technology in the Department of
Electrical Engineering, as an Assistant
Professor. His major research interests are
the advanced control techniques for electrical machines and drives, especially
using fuzzy logic algorithms and variable
structure control.
Another interest is in producing many electric vehicle prototypes
since 2008 and participating in the international challenge of electric
go karts ( In addition, since 2011, he participated in the Challenge of French National Electric Bike and Challenge Eco- marathon.
Volume 11, 2014