Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy
Effectiveness of Battery-Supercapacitor
Combination in Electric Vehicles
S. Pay, Member, IEEE, and Y. Baghzouz, Senior Member, IEEE
Abstract—This paper investigates the application of a
supercapacitor bank when used as a power buffer to smooth
rapid power fluctuations in and out of the battery of an electric or
hybrid vehicle. The study considers the simple case where the
supercapacitor bank is connected directly in shunt with the
battery as well as the case where it is connected through a DC/DC
converter that is necessary to achieve optimal performance. The
work is illustrated through computer simulations during vehicle
acceleration and deceleration. Partial experimental data on a
prototype circuit is also shown. Proper design of such a hybrid
electrical energy storage system is expected to result in
substantial benefits to the well being of the battery bank.
Index Terms—electric and hybrid vehicles, supercapacitors,
deep-cycle batteries, regenerative breaking, power transients,
DC/DC converters.
I. INTRODUCTION
A
significant portion of energy is dissipated in the brakes
when driving conventional gasoline-powered vehicles in
urban areas, where periodic acceleration-deceleration cycles
are required. Therefore, recovering this energy through
regenerative breaking is an effective approach for improving
vehicle driving range and this can only be accomplished by
electric vehicles (EV) or hybrid-electric vehicles (HEV).
Regenerative breaking in these vehicles captures some of the
kinetic energy stored in the vehicle’s moving mass by
operating the vehicle’s traction motor as a generator that
provides braking torque to the wheels and recharge the
batteries [1].
The battery bank of an EV is sized for peak power demand,
and this often compromises the desired weight and space
specifications. On the other hand, The auxiliary power unit
(APU) of an HEV is designed to provide the normal average
power required by the vehicle, while the battery is sized to
provide power surges needed during acceleration and hill
climbing and to accept momentary powers during breaking.
While EVs and HEVs are more efficient than conventional
vehicles in urban areas, the electric load profile consists of
This work was supported in part by the U.S. Department of Energy,
Nevada Operations Office, through the Nevada Environmental Research Park
(NERP) Program.
S. Pay is with Harris Engineering Consultants, Las Vegas, NV 89119,
USA, (e-mail: spay@lvcm.com).
Y. Baghzouz is with the Department of Electrical and Computer
Engineering, University of Nevada, Las Vegas, NV 89154 USA (e-mail:
eebag@ee.unlv.edu).
0-7803-7967-5/03/$17.00 ©2003 IEEE
high peaks and steep valleys due to repetitive acceleration and
deceleration. The resulting current surges in and out of the
battery tend to generate extensive heat inside the battery,
which leads to increased battery internal resistance – thus
lower efficiency and ultimately premature failure [2], [3]. The
problem of battery overheating and loss of capacity is more
acute when batteries are near full state-of-charge (SOC) since
they cannot accept large busts of current from regenerative
breaking without degradation at this stage.
Supercapacitors (also referred to as ultracapacitors or
electrochemical capacitors) have much greater advantage over
batteries when capturing and supplying short bursts of power
due to their higher power density limits, and ability to charge
and discharge very quickly. Hence adding a supercapacitor
bank will assist the battery during vehicle acceleration and hill
climbing, and with its quick recharge capability, it will assist
the battery in capturing the regenerative braking energy. This
significant advantage a battery-supercapacitor energy
storage/supply system gained attention in recent years in
transportation systems [4]-[8] as well as other applications [9],
[10]. Applying supercapacitors also allows for a smaller
battery size, and there is almost no limit to number of their
charge-discharge cycles (since there are no chemical reactions
involved in their energy storage mechanism). Furthermore
these devices require no maintenance and do not use toxic
materials.
Special considerations must be taken into account when
integrating such a hybrid energy storage system to achieve
optimal performance. While direct connection of the
supercapacitor across the battery terminals does reduce
transient currents in an out of the battery, the best way to
utilize the supercapacitor bank is to be able control its energy
content through a power converter. The paper reviews the
direct supercapacitor-battery shunt connection, after a short
section addressing component modeling issues. The desired
connection is then addressed by using a DC/DC converter in
the boost mode when discharging, and in the buck mode when
charging the supercapacitor bank. The analysis is illustrated by
computer simulations of an actual system. Part of the
simulations is verified by experimental data on a prototype
model.
II. COMPONENT MODELING
This section reviews the modeling of the main power
system components in an electric vehicle; namely, the battery
bank, the supercapacitor bank, and the electrical load. More
details on electrical component modeling can be found in
power electronics textbooks such as Ref. [11].
A. Battery Bank
Batteries are quite difficult to model as they undergo
thermally-dependent
electrochemical
processes
while
delivering and accepting energy. Thus the electrical behavior
of a battery is a nonlinear function of a number of constantly
changing parameters, such as internal temperature, state-ofcharge, rate of charge/discharge, etc … The capacity of a
battery depends on the discharge rate as wells as temperature.
This relationship is described by Peuket’s equation relating the
discharge current I (A) to the time t (hr) it takes it to discharge,
I = α√(β/t), where α and β are constants. Given the battery
capacity CTo at temperature To, the capacity at some other
temperature is computed by CT = CTo{1 + σ(T-To)} where σ is
a constant.
An approximate model that is often used for batteries is a
Thevenin equivalent circuit that consists of the open circuit
voltage in series with an effective internal resistance. Both
voltage and resistance values are functions of the battery SOC,
and these relations are generally supplied the manufacturer.
SOC is defined the percentage of energy left in a battery (after
supplying a certain amount of amp-hours) relative to its full
capacity.
The open-circuit voltage is often approximated by a linear
function of the SOC: Voc = a1+ a2 SOC, at some specific
temperature (e.g., 80o F). The battery internal resistance has
static and dynamic values that depend of battery SOC, whether
the battery is being charged or discharged and rate of
charge/discharge. In short duration studies, however, the
amount of amp-hours in and out of the battery is a small
fraction of the battery capacity. Hence it is fair to assume that
battery internal voltage is constant during such periods, and a
quasi-steady state model with fixed open-circuit voltage and
internal resistance constitutes an acceptable battery model
[12],[13]. Note that two resistance values are used in this case,
one during charging and another during discharging.
B. Supercapacitor Bank
As in conventional capacitors, the resistance and
inductance of the terminal wires and electrodes of
supercapacitors are represented by a series R-L circuit.
Further, non-perfect insulation between the device electrodes
results in leakage current that is represented by a large shunt
resistance. The difference between conventional and
supercapacitors is that the latter are much more efficient, i.e.,
the series resistance is a lot lower and the shunt resistance is
much higher in value. The self-discharge time constant of
supercapacitors several orders of magnitude larger than that of
conventional capacitors. More sophisticated models suitable
for dynamic studies are found in Ref. [14].
The study under investigation is a short-duration analysis of
the power (or current) distribution between the battery bank
and supercapacitor bank during acceleration and deceleration.
Hence, the leakage resistance can be ignored without much
error, and the supercapacitor bank can simply be represented
by a series R-C circuit.
C. Electrical Load
The electrical load in electric vehicles consists mainly of an
inverter-fed induction motor for motive power. During
regenerative breaking, the motor is turned into a generator by
reducing the frequency of its terminal voltage, thus reversing
power flow and producing braking torque. Detailed modeling
of inverter-fed motor drives is found in standard power
electronics and drives textbooks.
As far as the power source in concerned, power demand is
sufficient for analysis. Since the DC bus voltage is not allowed
to vary significantly from its nominal value, current demand
gives a good approximation of power demand. Thus the load
can be modeled simply by a time-varying current source that
reverses direction as the vehicle switches from coasting or
acceleration to regenerative braking.
III. DIRECT SUPERCAPACITOR CONNECTION
Supercapacitor integration with the battery-load circuit can
be challenging when trying to optimize the presence of this
additional sub-system. The simplest way is to connect the
supercapacitor directly in parallel with the battery bank, after
first pre-charging it to the battery terminal voltage. Such a
connection is shown in Fig. 1 where the load current denoted
by iL is defined to flow downward (i.e., positive during
acceleration and coasting, and negative during regenerative
breaking).
Fig. 1. Parallel connection of supercapacitor bank, battery bank, and
electrical load.
Given a certain load current profile representing some
short drive cycle, the battery current ib and supercapacitor
current ic are found by basic circuit rules such Kirchoff’s
voltage and current laws:
ic + ib = iL
v = vc − ic Rc = vb − ib Rb
ic = −C
dvc
dt
(1)
( 2)
( 3)
where vc and vb represent the internal capacitor and battery
voltages, respectively. Subsititution of (1) and (3) in (2) yields
the first order equation of vc:
dvc
+ α vc = α vb + β iL
dt
( 4)
where
α=
Rb
1
, β =−
C ( Rb + Rc )
C ( Rb + Rc )
(5)
The solution to (5) can be written as shown in Eqn. (6) below:
vc = Ke−α t + vb + β e−α t ∫ iL eα t dt
(6)
where K is determined by setting the initial value of vc to vb.
Note that it is not possible to control power flow in and out
of the supercapacitor bank in the circuit above since its
terminal voltage is forced to be equal to the that at the battery
terminals at all time. Current division between the battery and
supercapacitor bank is determined solely by the two branch
internal resistances and internal voltages.
The basic controls for the static power converter in Fig. 2
can be summarized as follows: prior to vehicle use, the
supercapacitor must charged by the battery bank or by an off
board power supply. During the initial stages of vehicle
acceleration, power flow out of the supercapacitor should be
matched to that of the load demand as long as the device
current rating is not exceeded. This requires the controller to
adjust the ON state pulse with of S1 accordingly. As the
capacitor continues to discharge, the battery current should
gradually increase and ultimately reach the load current when
the energy stored in the capacitor reaches low levels. During
regenerative breaking, the supercapcitor should be charged at
the maximum possible rate (by modulating switch S2) so that a
small fraction of the load current flows into the battery bank.
The current injected by the load is then diverted slowly into
the battery as the capacitor approaches full charge.
IV. SUPERCAPACITOR CONNECTION THROUGH
POWER CONTROLLER
The above straight connection clearly indicates that
optimal use of the supercapacitor bank requires a power flow
controller between the two energy storage subsystems. The
objective is to maintain the battery current as constant as
possible with slow transition from low to high current during
transients to limit battery stress. On the other hand, the
supercapacitor ought to charge as fast as possible without
exceeding maximum current from regenerative breaking, and
to discharge most of its stored energy during acceleration.
Energy flow in and out of the supercapacitor can be
controlled with a pulse-with-modulated (PWM) DC/DC
converter with a simple topology as shown Fig. 2 [7], [8]. The
supercapacitor is discharged during acceleration at a rate
controlled by modulating switch S1. In this boost mode, energy
is delivered to inductor Lf when S1 is turned ON (State 1), then
transferred to the load through diode D2 when S1 is OFF (State
2). During deceleration, the supercapacitor is charged at a rate
controlled by modeling switch S2. In here, energy is transferred
to Lf when S2 is turned ON (State 3), then to the supercapacitor
through diode D1 when S2 is turned OFF (State 4).
The analytical expression of the supercapacitor current can
be determined by the second order differential equation
d 2ic Rc dic
1
+
+
ic = f (t )
2
dt
L f dt CL f
(7)
where f(t) = 0 in States 1 and 4, and
f (t ) =
Rb di L
L f dt
(8)
in States 2 and 3. The power controller governs the flow of
energy in and out of the supercapacitor only during
fluctuations in power demand. Consequently, quasi-steadystate relations between the converter input and output
parameters do not exist in this case, and one has to resort to
circuit simulation software such as PSpice.
Fig. 2. Supercapacitor integration through power flow controller.
IV. NUMERICAL ILLUSTRATION
To illustrate the analysis in the sections above, the
performance of supercapacitor bank that was recently designed
and installed as part of the energy storage system of a series
hybrid-electric bus is investigated by computer simulations.
The APU of this hybrid vehicle is a hydrogen-powered internal
combustion engine [15]. But for simplicity, the analysis
simulates the vehicle power circuit with the APU shut off, thus
representing the vehicle engine status when the battery bank is
at or near full charge. The battery system consists of two
banks connected in parallel, and one of the banks is shown in
Fig. 3 along with the supercapacitor bank. A short description
of the battery and supercapacitor subsystems follows.
Each of the two battery banks consists of 28 deep-cycle
valve-regulated-lead-acid (VRLA) battery units connected in
series. Each unit is rated at 12 V, and a capacity of CTo = 85
Ah @ C/3 (at To = 80o F). Other battery parameters are listed
below.
• static internal resistance during charging: 4 mΩ for
SOC ≤ 80%, and 10 mΩ at SOC = 90%
• recharge current limit: 400 A,
• Peukert’s equation constants: α = 1.33 and β = 256,
• capacity-temp. dependence parameter: σ = 0.004,
• Voc vs. SOC parameters: a1 = 11.80, a2 = 1.32,
• battery subsystem rating: 336 VDC, 170 Ah@C/3.
The supercapacitor consists of a string of 150 cells. Each cell
is rated at 2.5 V and 2,500 F. Additional data follows:
• cell series resistance = 1 mΩ,
• cell leakage resistance: 300Ω,
• cell peak voltage: 2.7 V,
• cell rated current: 400 A,
• supecapacitor subsystem rating - rated voltage: 375 V,
peak voltage: 405 V, capacitance: 16.67 Farads, energy
storage capability: 1.2 MJ.
Since no capacitor cells are alike, they need to be
balanced as the voltage distribution becomes a function of
internal parallel resistance and cell capacitance. To
distribute the total stack voltage evenly across the capacitor
bank, bypass resistors sized to dominate the leakage current
are placed in parallel with each cell. The battery pack,
however, is not equipped with a charge equalizer. The
battery condition are monitored with a data acquisition
system that logs terminal voltage and internal temperature
of each cell and alerts the operator in case of excessive
heating or out-of-range voltages.
acceleration and deceleration. The following test procedure
was conducted:
•
Pre-charging the supercapacitor string and connecting
it in parallel with the battery unit.
• Inject a constant current of 200 A until the voltage
reaches the maximum allowed value of 14.2 V, then
reduce the current to maintain this voltage for 10
seconds.
• Shut of the load for 30 seconds.
• Connect a 200 A load for 10 seconds, then stop.
The measured load current, battery current, capacitor
current and system voltage are shown in Fig. 4(a). Note that
the presence of the supercapacitor led to significant reduction
of battery current, especially during the initial seconds of
imposing load current. Fig. 4(b) shows the corresponding
current and voltage profiles calculated by Eqn. (1)-(7) where
-1.25 t
- e-0.16 t)
the load current is approximated by iL = 320(e
A for 0 < t ≤ 10 sec., and iL = -205 A for 40 < t ≤50 sec.
The graphs of both figures are nearly perfect duplicates.
(a)
(a)
(b)
Fig. 3. (a) Supercapacitor bank, (b) battery bank.
To validate the performance of the supercapacitor-battery
system during charge and discharge, a prototype model
consisting of one 12 V battery cell in parallel with a string of 6
supercapacitor cells of the same model and make described
above, was tested using special equipment that can both
generate and absorb specific current profiles that simulate
(b)
Fig. 4. Battery and supercapacitor currents during charging and
discharging, (a) experimental data, (b) calculated data.
Testing with a power controller to govern the energy flow
from the supercapacitor was not conducted due to lack of
converter availability, and only computer simulations using
PSpice are performed at present. To show the performance of
the hybrid system with a DC/DC controller, a vehicle
acceleration cycle is simulated by a load current having a
waveshape that increases from 0 to 300 A within 10 seconds,
then decreases exponentially for 1.5 seconds, then stays
constant at 66 A for 9.5 seconds. The converter parameters are
set as follows: Lf = 100 mH, Rf = 10 mΩ, fsw = 1 kHz, Cf = 100
mF, the switch duty ratio is set to increase in discrete steps
every 1.5 seconds as long as the load current is rising.
Figure 5 below shows the simulated supercacitor and
battery currents and terminal voltages. Note that the power
controller allowed the supercapacitor to discharge from 360 V
down to 135 V (i.e., its energy content dropped to nearly 14%
of the initial charge). This made the supercapacitor an
effective energy buffer as delivered the most significant
portion of the load current during the first 10 seconds of
acceleration, and the battery bank current made a relatively
smooth transition for vehicle stand-still to constant speed.
For comparison purposes, Fig. 6 shows the corresponding
currents and voltages when the battery and supercapacitor
banks are connected without a power controller. Some of the
additional remarks that can be made include the following
when comparing both figures:
a) The battery peak current is reduced by 40%.
b) The DC bus voltage regulation is improved by 30%.
c) The supercapacitor’s SOC is 3.5 times lower with
than without the power controller after acceleration.
(a)
(b)
Fig. 6. Simulated battery and supercapacitor (a) currents and (b)
voltages during acceleration (w/o power converter).
V. CONCLUSIONS
(a)
Adding a supercapacitor bank to a battery- or fuel celldriven vehicle makes sense and advantages by far outweigh the
disadvantages. A direct parallel connection will reduce battery
stress by assisting with transient currents during acceleration
and deceleration, but will not make full use of the
supercapacitor as a true power buffer. Optimal use of the
supercapacitor requires a power controller that requires only
two static power switches, two power diodes, an inductor and
filter capacitor, but the best control strategy is not fully
developed due challenging control issues.
Future work will report on the development of the power
converter that is currently in the design stages and on
experimental data from actual vehicle driving cycles.
VI. ACKNOWLEDGEMENT
The work reported in this paper was funded by a grant from
the U.S. Department of Energy, Nevada Operations Office,
through the Nevada Environmental Research Park (NERP)
program.
VII. REFERENCES
(b)
Fig. 5. Simulated battery and supercapacitor (a) currents and (b)
voltages during acceleration (with power converter).
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VIII. BIOGRAPHIES
Steven Pay received his B.S. and M.S. degrees in electrical engineering from
the University of Nevada, Las Vegas in 1994, and 2000, respectively.
He is currently an electrical engineer with Harris Consulting Engineers, Inc.
His interests include power systems analysis, distribution system design and
power quality. His is a registered Professional Engineer in the State of
Nevada.
Yahia Baghzouz received is B.S., M.S. and Ph.D. degrees in electrical
engineering from Louisiana State University, Baton Rouge, LA, in 1981,
1982 and 1986, respectively.
He is currently professor of Electrical Engineering, and Associate Director of
the Center for Energy Research at the University of Nevada, Las Vegas. His
interests are in power quality, power electronics and renewable energy. He is
a registered Professional Engineer in the State of Nevada.