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Driving Characteristics for Hybrid Electric Drive with
Super-capacitor as Energy Storage Unit
D. Cundev and P. Mindl
Department of Electric Drives and Traction, Faculty of Electrical Engineering
Czech Technical University, Prague, Czech Republic
Abstract— This paper deals with calculation of the driving characteristics of the hybrid electric
drive which uses super-capacitor as energy storage unit. Results has been obtained thought
simulation of the driving regime of the experimental working stand for electric and hybrid car
drive research, which was developed in the research Centre Josef Bozek at the Technical University
in Prague. Computer program and algorithm for simulation of the drive regime is explained.
Results of the simulation define the driving characteristics of the entire working stand.
1. INTRODUCTION
In the Research Center of Engine and Automotive Engineering Josef Božek at CTU in Prague has
been realized project for development of hybrid electric drive. For that purpose, the experimental
working stand has been created at the Department of Electric Drives and Traction at the Faculty of
electrical engineering (FEE). Main characteristic of this hybrid drive is using of super-capacitor as
accumulation unit instead of chemical battery. Also, the energy transformation is done by means
of electrical power splitter (EPS).
As an instrument for further development of this type of hybrid drive with super-capacitor,
simulation computer program has been made. Main purpose of this task is calculation of every
essential value that characterizes the driving regimes of the hybrid drive. That represents complex
working system with many functional units like internal combustion engine, super-capacitor, traction electrical motor, power converters, microcontrollers etc. In such case it is essential to know
driving characteristics of this system for defined working regime.
2. LABORATORY MODEL OF THE HYBRID DRIVE
Model of the hybrid drive has been realized in laboratory at Department of electrical drives and
traction on FEE, CTU in Prague. The scheme of the experimental working stand is shown on
Fig. 1. Internal combustion engine (ICE) is simulated by a controlled electric AC induction motor.
Produced power Pice from ICE is divided to the mechanical power Pmech and electrical power Pel1 by
using electrical power splitter (EPS). EPS is special type of synchronous generator with permanent
magnets on the rotor and stator capable for rotation. Rotor is firmly coupled with the shaft of ICE
and stator of the EPS is firmly coupled with vehicle wheels and rotates with the speed proportional
to the vehicle velocity V . That technical solution enables internal combustion engine to operate
Figure 1: Experimental working stand of hybrid drive.
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with constant revolutions (with high efficiency) during entire driving regime without dependence
on actual vehicle speed. On the same shaft of the stator of EPS is inserted the induction traction
motor (TM). EPS and TM are electrically connected through DC circuit and two traction AC/DC
and DC/AC power converters. Traction load is simulated with another controlled AC induction
motor.
A super-capacitor (SC) is connected to the DC circuit via DC-DC converter. Energy Wsc
accumulated in SC is used to provide additional power Pel which is by means of TM transformed
to the mechanical power Pmech1 . After that Pmech1 is added to Pmech and resulting sum of powers
is directly transmitted to the vehicle wheels. Hybrid vehicle uses recuperative braking by changing
of TM operational regime from motor to generator. During that period TM decelerates the vehicle
and produced energy is accumulated in the super-capacitor SC.
3. CALCULATION OF THE DRIVING CHARACTERISTICS
Driving characteristics of the hybrid drive has been calculated by means of simulation program.
Simulation has been made by means of MATLAB programming interface. In programming has
been used the kinematical model described in publication [1]. Simulation starts with defining the
driving characteristic of the vehicle speed V as a function of the time t (See Fig. 2):
Figure 2: Driving characteristic of the vehicle speed V in function of time t.
By knowing the vehicle weight m and speed V , program calculates the car acceleration an ,
car trajectory distance Sn , needed acceleration force Fn , corresponding energy Wn . for each time
sub-interval (∆tn = tn − tn−1 ) of driving maneuver. By means of this calculated values, it can be
calculated the characteristic of the average acceleration power Pa (see Fig. 3). Compensation of
aerodynamics resistances has been performed by Equation (1) for additional power Pv :
Pv (t) = k1 · V 3 (t) + k2 V (t)
(1)
By that means is calculated the driving characteristic of the speed power Pv (Fig. 3):
Figure 3: Characteristics of Pa and Pv in function of time t.
Power that is needed to be provided to the hybrid vehicle Psum is sum (2) of acceleration power
Pa and speed power Pv :
Psum (t) = Pa (t) + Pv (t)
(2)
Driving characteristic of this value in time scale of the driving maneuver is presented in Fig. 4:
The power of the internal combustion engine Pice follows the needed driving power Psum for
each time interval ti (Fig. 4). Also Pice depends on actual energy volume Wsc accumulated in the
super-capacitor, which is determined from actual voltage Usc of SC:
Wsc =
2
C · Usc
2
(3)
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PIERS Proceedings, August 27-30, Prague, Czech Republic, 2007
Figure 4: Characteristics of Pice and Psum in function of time t.
In order to perform the better efficiency of ICE changes of output power Pice must be slow.
Therefore Pice follows the Psum according to predefined algorithm. That’s the main advantage of
hybrid electric drive that can’t be performed in classical cars in which the ICE must instantly and
rapidly changed the working regime according to the actual power demands. That results with
high fuel consumption and low efficiency.
Difference between the powers Pice and Psum defines the electrical power Pel which charges
or discharges the super-capacitor. That is needed electrical power from DC circuit, calculated in
accordance to relation (4) and in time scale is presented on Fig. 5.
Pel (t) = Psum (t) − Pice (t)
(4)
Figure 5: Characteristic of Pel in function of time t.
When Pel is positive (Pel > 0) SC is discharged, which means that driving regime demands
higher power then is produced in ICE (Psum > Pice ). In the case when Pel < 0 SC is charged,
which means that produced power is higher then the demanded (Pice > Psum ). That’s in the time
intervals when the voltage of SC is lower to the allowed minimal level and therefore ICE produces
higher power.
Also, SC is quickly charged by recuperation. During braking, kinetic energy of the vehicle is
transformed in to the electrical energy by TM which works in generator regime. It decelerates the
vehicle and produced energy is used for super-capacitor charging.
Pice provides power to drive the vehicle and also for charging the SC and keep the Usc above the
critical minimal level Usc min , which is half of the maximum SC voltage Usc max = 56 [V]. Driving
characteristic of the voltage output of the SC is presented on Fig. 6.
Figure 6: Usc in function of time t.
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According to the relation (3) output voltage of super-capacitor represents the accumulated
energy Wsc in SC. Therefore characteristic on Fig. 6 also represents the indicator of the amount of
accumulated energy in SC.
Knowing the actual voltage on SC (Usc ) and the needed electric power from SC (Pel ), the
charging or discharging current Isc of the SC can be calculated (Fig. 7). Isc must not exceed the
maximum allowed current in SC which is Isc max = 400 [A].
Figure 7: Characteristic of Isc in function of time t.
4. CONCLUSION
In this paper are presented the driving characteristics of specific driving regime. The simulation program enables to perform calculation of characteristics of any kind of driving regime. For calculation
is needed definition of vehicle speed. Program enable to taking into account other influences of the
driving regime like the weight of the vehicle and the number accumulative units (super-capacitors).
The calculated driving characteristic represents capabilities of the hybrid system during different
driving regimes. The work and the results presented in this paper gives contribution to the further
development of the hybrid electric drive.
Future works will be oriented to the calculation of the driving characteristics under different
conditions, like different weight of the vehicle, more accumulative units, different aerodynamic
characteristics etc. Simulation program can be adapted for more complex algorithms to perform
new calculated values in order to give more precise and realistic results. Modification of the program
will be in correspondence with the laboratory results gained from the experimental working stand
(Fig. 1).
ACKNOWLEDGMENT
Research described in the paper was supported by Josef Božek Research Center of Engine and
Automotive Engineering at the Department of electrical drives and traction, Faculty of Electrical
Engineering, CTU in Prague. Project is granted by the Czech Ministry of Education.
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