Supercapacitors in power converter DC link
A short overview of design and application issues
B.Sc., E.E. Tihomir Čihak*, Ph.D., E.E. Željko Jakopović **
**
* KONČAR – Electrical Engineering Institute/Power Electronics and Control Department, Zagreb, Croatia
Faculty of Electrical Engineering and Computing/Department of Electric Machines, Drives and Automation, Zagreb,
Croatia
tcihak@koncar-institut.hr
Abstract - Very high values of efficiency in electric power
conversion, electric energy saving requirements and power
converter component optimization are priorities in design
and construction of any type of modern power electronic
converters. Moreover, if such power converters are
connected to battery power source or other "weak" power
source (as, for instance, fuel cells), additional design
problems appear in sense of (battery) power source
longevity, absorption of high peak power transients,
provision of on-demand power bursts for load and other.
EDLC, well known by their commercial name as
Supercapacitors, are one of the possible solutions for
aforementioned problems.
Key words - Supercapacitors, ultracapacitors, EDLC, power
converters, energy recovery, efficiency, energy saving,
energy storage.
I.
INTRODUCTION
Capacitor as a component that enables storage of
energy is known since 18th century, when Leyden jar has
been invented. Principles of capacitor operation, in other
words electrostatic mechanism of energy storage has soon
been explicitly defined. As a component, in essence two
metal plates separated by dielectric material, capacitor has
not been changed from the day of its invention.
Only in 1957, with an invention by H. E. Becker [2], a
truly innovative component, electrochemical dual layer
capacitor, has appeared. In electrical view, this component
is also a capacitor, but it's characteristic that separates it
from the previously known capacitor types is its huge
capacity. In consequence, this innovative component has
extremely high specific power rating and specific energy
rating in the same order of magnitude as, in that sense,
weakest batteries.
This properties enable electrochemical dual layer
capacitors to be used as an energy buffer located in the DC
link in high power systems, in systems with battery power
source (or similar) as a component or a subsystem which
corrects drawbacks of a weak power source, and even as a
sole power source in the low power systems.
II.
an electrode is submerged into an electrolyte, on the
interface between electrode and electrolyte charge
separation occurs in immediate vicinity of the interface.
Since two electrodes are needed for connection to external
circuit, two of such interfaces appear. Looking more
closely at an interface, on electrode surface excess (or
deficiency on the other electrode) of electrons appears. To
achieve neutrality, this excess (or deficiency) is balanced
by electrolyte ions. Charge separation distance, or in other
words distance between electrode surface and the center
of the ions (possibly increased by a thickness of a
solvation sphere around the ions) that form a layer in the
near vicinity of the electrode is equivalent to the dielectric
thickness of a normal capacitor. Therefore at each of the
formed interfaces an equivalent to the capacitor appears,
and the resulting device is equivalent to a series
connection of two capacitors, which is shown in figure 1.
ELECTROCHEMICAL DUAL LAYER CAPACITOR
Electrochemical dual layer capacitor, EDLC in further
text, is based on a phenomenon for which is believed that
is observed for the first time by H. Helmholtz. In short, if
C =ε⋅
S
[F ]
d
(1)
Since this distance is on the order of a nanometer or
smaller, resulting capacitance is according to the (1),
where S is electrode surface and d is a distance between
charges, higher then a capacitance of an ordinary
capacitor. But, besides the "dielectric thickness", EDLC
have a very high specific capacitance due to electrode
material used in their construction. This material is (in
most cases) activated carbon which is a very porous
material, as shown in picture 2. Due to its porous nature it
has high effective surface area (on the order of 1000m2/g
[1], but some manufacturers state surface are of over
2000m2/g and even 3000m2/g [44][45]). Also, carbon
aerogels [10] and carbon nanotubes (shown in the picture
3) are used for EDLC construction for the same reason.
These characteristics result in devices with a specific
capacitance on the order of 250F/kg [1][17][31][34].
Typical EDLC is constructed, as shown in the figure 1
out of two metal plates, current collectors, on which
electrode material is deposited. Current collector type and
electrode material deposition can vary as shown in
literature [1][31]. This two electrodes are stacked together
and separated with a membrane which serves as an
electric isolator between two electrodes, but must allow
for electrolyte ions to pass through. An exploded view of a
commercial EDLC is shown in picture 4.
Figure 4. Construction of a commercial EDLC [24]
Figure 1. EDLC diagram
Figure 2. SEM images of activated carbon samples [18]
Figure 3. Single wall carbon nanotube based EDLC material [19]
III.
SUPERCAPACITOR MODELS
At the time of the writing, commercial supercapacitors
still have three downsides which result from the EDLC
design. Namely, low operating voltages, non-uniform
nominal parameters and non-linear characteristics. Low
operating voltages derive from its operating principles. Its
breakdown voltage cannot be, unlike the conventional
capacitor, easily "programmed", because, essentially, it
depends on the electrolyte type and extremely small
charge separation distance. Due to this problems EDLC
are limited to operating voltages of about three volts [1].
Two other problems are closely connected and cannot
be easily resolved. As shown in figure 2, typical electrode
material has heterogeneous surface with variable width
and depth of "valleys" which form the electrode surface
and along which electrode-electrolyte interface occurs.
For creating analytical model of such interface one should
now dimensions of each valley to approximate the
occurring process in electrical view [1][7]. Due to this,
EDLC are sometimes modeled as a transmission lines.
Furthermore, parameters and EDLC behavior depend on
temperature, state of charge, charge and discharge
intensity and frequency and other variables. To simulate a
part, and sometimes most of the behavior many models
where proposed [1][21][24].
Although these complex models show a good match
between estimated and measured values, such complexity
is not always needed. For instance, it has been noticed that
a complex MATLAB/Simulink model, incorporating
power electronics blocks, generator or motor blocks and
control blocks already suffers from bad performance, long
simulation times and other problems. Adding more
complexity creates only adverse effects.
Instead of developing already complex EDLC models,
in some cases it is more appropriate to start with the most
basic model and elaborate it up to the point where
acceptable results are acquired. A model development
sequence is shown in picture 5. A simple capacitor as a
model cannot be used because EDLC ESR values cannot
be ignored, and a series resistor-capacitor connection is
therefore the most basic EDLC model. For applications
where long term variables are observed (for instance, long
term storage of charged supercapacitors), self discharge
properties must be modeled and this model should be
further expanded with at least a leakage resistance as
shown.
Frequency domain analysis shows that a typical EDLC
shows different behavior in several distinct frequency
ranges, as shown in picture 6. To distinguish different
parameters in low and medium frequency ranges,
supercapacitor model is therefore expanded with a parallel
branch that contains an series resistor-capacitor
connection. This model type is known in literature [7] as a
"two branch model". For separation into more frequency
ranges, model is further expanded with another RC series
connection into "three branch model" [5]. Theoretically,
with this approach, EDLC model can be expanded
indefinitely [7]. Also, it is shown that such a linear RC
network can be transformed between a series, parallel and
Figure 6. Typical commercial EDLC frequency response [29]
Figure 5. EDLC models: A - ideal capacitor, B – series RC model, C
– model B with added leakage resistor, D – model C with added
high frequency inductance component, E – model D expanded with
n-branch RC circuits and voltage dependent main capacitance
transmission line network type [7]. For modeling in very
high frequency range, shown behavior is usually modeled
with a series connected inductance. It is stated that this
addition to the model should be used for pulse
applications [8].
EDLC capacitance is not constant and it is (among
other variables) dependent on the EDLC state of charge,
or in other words, on EDLC voltage. This capacitance
variation is not linear and can be seen on charge and
discharge graphs and cyclic voltammetry results. For
modeling this nonlinearity, main model capacitance is
variable, as shown, and it is usually split into two parts, a
constant and voltage variable part [21]. Charge-discharge
measurement results and Bode plots of aforementioned
models are given in pictures 7 and 8. There are other
variables that influence EDLC parameters, such as
temperature [16][33][35], and although they are not
considered within this work, they should be investigated
for practical implementations.
IV.
HIGH POWER APPLICATION ISSUES
Unlike EDLC model, which is less important for
actual operation of supercapacitors in power electronic
systems, low operating voltages and non-uniform nominal
parameters create several implementation problems. For
high power applications, with power rating from tens of
kilowatts up to megawatt range, DC link voltage levels
from several hundreds of volts up to more then a kilovolt
are used. Even the simplest implementation solution
requires stacking (series connection) of several
supercapacitors. Main problem appears from the EDLC
parameter non-uniformity, in other words, non equal
Figure 7. Comparison of linear and nonlinear model in
charge/discharge test
Figure 8. Comparison of EDLC linear model frequency responses
capacitance of the used supercapacitors. Due to this,
voltage balancing circuits are required. Basic solution is
resistor or so called passive balancing [49]. This solution
is not optimal due to energy wasted in resistors, so active
voltage balancing circuits, for which many solutions are
proposed [50][51], are most common. Two basic
approaches are used for such circuits, centralized system
which monitors whole EDLC assembly and a distributed
solution where a number of voltage monitoring and
balancing circuits (each connected between two
supercapacitors from the stack) are used. One commercial
solution is shown in picture 9. Other common issue that
needs to be taken into account when designing
supercapacitor are EDLC rated values (ESR, capacitance
and value tolerances being the most important) and their
variation through usage. When these are observed, it can
be seen that all commercial EDLC-s have similar
problems [29][48]. Due to its construction and method of
operation, EDLC-s show notable aging through use which
cannot be bypassed (this is also one of the reasons for
comparison with batteries). Therefore, commercial EDLCs have actual capacitance higher or the same as rated and
ESR values lower or the same as rated. After the specified
number of cycles, these values inevitably change up to the
values defined with tolerances. In other words, high
tolerance values are necessity to insure that EDLC has
parameters within rated values after the rated number of
cycles. Furthermore, even higher tolerance values would
allow for longer operational lifetime. Also, it should be
noted that EDLC is not faulty after the rated number of
cycles, unlike batteries which are chemically changed and,
depending on the type, completely unusable after the rated
number of charge and discharge cycles or even sooner.
EDLC-s can be further used, but they must be retested and
new rated values must be computed
V.
Figure 9. Commercial EDLC active balancing circuit [47]
POWER CONVERTER TOPOLOGIES AND DESIGN
If EDLC assembly is used directly in power converter
DC link, passive as shown in picture 10-A, according to
(2) and (3), only a part of total available energy can be
used for performance improvements. Therefore, power
converter circuits are used as an interface between
supercapacitor banks and main DC link, as sketched in
figures 10-B and 10-C. It should be noted that passive
capacitor bank connection is nevertheless used in some
applications, as for instance in forklifts and other lowpower drives, where good results have been obtained.
EC =
U 2 ⋅C
2
∆EC = EC (U1 ) − EC (U 2 ) =
(2)
C
⋅ (U12 − U 22 )
2
(3)
When connecting EDLC banks to DC link through
converters, its nominal voltage is lower then DC link
voltage. Therefore, for discharging energy into DC link,
voltage needs to be stepped up, and for opposite energy
flow direction it needs to be stepped down. Power
converters for these operations are usually combined into
one circuit, and so far several different topologies are
presented, including converters using high frequency AC
link (shown in picture 10-C) and more exotic solutions as
stacked converters [13][14][20]. But, for high power
application, for instance tram traction, literature shows
that favored commercial solution is non-isolated buckboost converter, shown in pictures 10-B, 11 and 12.
Operation of such converter is straightforward, and it
is broken down into basic boost converter when power
switches are operated as shown in figure 11, and into buck
converter when operated as in figure 12. Usage of this
topology is understandable as all of the required power
electronic components are commercially available,
already combined as a half-bridge assembly which is
Figure 10. Connection of EDLC stacks to DC link: A passive, B - non-isolated DC/DC converter, C - converter
with galvanic isolation through medium frequency
transformer
widely used in traction and renewable energy applications
which cuts down production costs considerably. Also,
these assemblies can be easily paralleled allowing for
higher currents to be used in converters. Voltage and
current rating of these assemblies are also satisfactory and
they are suited for PWM controlled circuits.
For designing a supercapacitor system, rough
estimation on the power converter requirements needs to
be done first and from which supercapacitor parameters
assessment can be made. As a first step, rated voltage
levels of a whole supercapacitor system must be defined.
If using individual supercapacitors instead of
commercially available assemblies, any voltage level can
be chosen, but voltage balancing circuits must be used and
lifetime parameter degradation must be taken into
account. During EDLC discharge, voltage should fall up
to no more then a minimum predefined level. Minimum
voltage to operating voltage ratio is sometimes called
discharge voltage ratio [14][52] and it is given with (4).
For further design total amount of energy that needs to be
pumped from the supercapacitor storage into the DC link
must be known. In its simplest form, this will be equal to
the sum of products of the required DC link required
power during faults (voltage drop) and the corresponding
fault time periods for the worst case. Practically, required
power in these periods will usually be variable and not
constant, so energies must be computed through
integration. When the maximum energy that will be used
is known, from the equations (3) and (4), total amount of
energy that EDLC bank must have is given with (5).
du =
Vmin
⋅ 100 [%]
Vmax
Etot =
(4)
EC
d 
1−  u 
 100 
2
(5)
It is obvious that the total amount of energy is always
higher then the used amount of energy. For the buck mode
operation (DC overvoltage case), the equations are the
same, but care must be taken on choosing the EDLC bank
operating voltage prior to the fault. In other words, for the
worst case scenario, EDLC bank must be able to provide
total discharge energy and must be able to absorb total
amount of energy during DC overvoltages from the same
starting voltage level. Practically, this scenario almost
never occurs, as the charge and discharge cycles occur
alternately [9]. Therefore, EDLC bank size cannot be
efficiently designed unless converter operating cycles
(drive cycles for traction systems) are not known.
For chosen voltage levels, static duty cycles and the
duty cycle variation with EDLC voltage are given with (6)
and (7) for the boost and buck mode operation
respectively.
D = 1−
D=
Figure 11. Converter operation in boost mode – lower half bridge IGBT
is PWM controlled (switch B), and upper switch is constantly off.
UC
U (t )
⇒ D(U C ) = 1 − C
U DC
U DC
(6)
U (t )
UC
⇒ D(U C ) = C
U DC
U DC
(7)
 U C min,max ⋅ Dmax,min
Lmax = max
∆I L ⋅ f PWM




 U DC ⋅ Dmin,max ⋅ (1 − Dmin,max ) 

Lmax = max
∆I L ⋅ f PWM


(8)
(9)
For the chosen converter parameters, inductor size
must be chosen according to switching frequency and
required current ripple. Equations for this calculations are
given in (8) and (9) for the boost and buck mode
respectively (indicated min/max values are found from
input requirements on both converter operating extremes).
Care must be taken since, because of the electrical power
conservation rules, currents on both converter sides are
inverse proportional to voltage levels. Power electronic
components must also be chosen according to required
Figure 12. Converter operation in buck mode– upper half bridge IGBT
is PWM controlled (switch A), and lower switch is constantly off.
current ratings, and this step is rarely straightforward and
requires optimization between EDLC bank voltage
utilization ratio and the resulting EDLC bank, power
converter, inductor and cooling components size and
price. It should be mentioned that for high power
applications cooling becomes a great problem, especially
for the space restrained applications as for instance tram
on-board systems [11][13][15]. Also, supercapacitors are
not a high temperature enduring components, and besides
possible electrolyte deterioration when working in
prolonged overtemperature periods, EDLC lifetime
shortens considerably with temperature [16].
Simple design procedure shown here refers to a buckboost topology. It should be noted that there is more than
one correct solution to these design problems depending
on the application. Chosen solution must be validated,
both electrically (basic operation and component
requirements) and mechanically (space constrained
application), but also economically.
VI.
CONCLUSION AND FURTHER WORK
EDLC, or so called supercapacitors are relatively old
components, but their application is yet to become
widespread. For better understanding of these
components, an overview of EDLC design and
characteristics has been given. Furthermore, complex
behavior and accompanying simulation problems and
several examples have been displayed. Also, a series of
both positive and negative EDLC traits have been
mentioned. Simple design guidelines and important
practical implementation problems have also been
discussed.
Aforementioned design problems are one of the main
topics that will be elaborated in further work. Automated
procedure for defining optimal parameters for both
converter switching components and supercapacitor
assembly will be developed. This procedure will address
electrical variables, but also mechanical variables (for
instance, required supercapacitor assembly size for mobile
applications) and thermal variables. Also, measurements
and validations of given views on the usage of EDLC
models will be made.
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