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					     Series connection of supercapacitors, with an active device
                     for equalizing the voltages

                     Philippe Barrade                Serge Pittet              Alfred Rufer
                                     Laboratory of Industrial Electronics
                               Swiss Federal Institute of Technology Lausanne
                                   CH-1015 Lausanne EPFL, Switzerland
                                        philippe.barrade@epfl.ch

  Abstract — The paper presents an active shar-                The aim of such an association is to profit of the
ing device, for equalizing the voltages across a            advantages of each devices : that kind of system
series connection of supercapacitors. This en-              is able to provide a high energy storage density
sures an optimal value for the stored energy.               (batteries) and a high instantaneous power delivery
Based on a buck–boost topology, this device is              capability [4] [5].
designed and controlled to propose a high effi-
ciency.                                                        Using supercapacitors enforces a series connec-
                                                            tion of them in order to reduce the related power
  Keywords — energy storage, supercapacitors,               losses in the associated power electronic converter.
active voltage sharing.                                     Due to difference of values of each supercapacitor,
                                                            the total voltage will not be equally distributed be-
                  I. Introduction                           tween the different capacitors. A local over-voltage
                                                            could appear over one or several supercapacitors,
   An energy storage system is usually based on             and the stored energy would not be optimized.
batteries. Such components offer a big amount of
                                                               This paper presents an active device for voltage
energy, but with a limited instantaneous power.
                                                            sharing on each supercapacitor, which ensures no
   Compared to batteries, supercapacitors repre-
                                                            over-voltage, a maximum energy stored with a high
sent one of the most interesting new developments
                                                            efficiency.
in the field of energy storage [1]. Supercapacitors,
also called ultracapacitors, are electrochemical dou-
ble layer capacitors. They can be used for electrical        II. Series connection of supercapacitors
storage devices because of their high energy stor-             Because of the technology limits, the maximum
age density, even if their energy density is 10 times       voltage of a supercapacitor when charging is low,
lower than a battery. But supercapacitors propose           near 2.5V . As the supercapacitors are used for en-
a high instantaneous power delivery capability.             ergy storage, the efficiency of the associated power
   Various energy storage systems have been de-             electronic must be as high as possible. In order
signed using both batteries and supercapacitors [2]         to reduce the power losses in the static converter
[3]. An illustration of such a system, developed            when charging and discharging, a series connection
in the Laboratory of Industrial Electronics is given        of several supercapacitors is needed to increase the
Fig. 1.                                                     operating voltage and decrease the charging and
                                                            discharging current value as shown Fig. 2 for 2 su-
                                                            percapacitors.



                                                                                        +      7   ? 




                                                                        1
                                                                                                          7


                                                                                        +       7   ?




Fig. 1. Energy storage device with batteries and superca-
pacitors                                                    Fig. 2. Series connection
   Due to differences in the values of each superca-    voltage across C1 is 2V , and the total voltage is
pacitor, the total voltage over a series connection    only 4.5V instead of 5V . As a result, the stored
will not be equally distributed between the differ-     energy is 28% lower than the ideal case (d = 0%).
ent supercapacitors. It can lead to an unsymetrical      The third case take into account a device, con-
voltage share between the capacitors. If this effect    nected across each supercapacitor, which allows the
is not compensated for a local over-voltage could      sharing of the two voltages Uc1f and Uc2f . Even if
appear over one of several supercapacitors with a      the stored energy is still lower than 6.25kJ (because
risk of destruction of this component.                 of C1 and C2 values), this energy is 20% bigger
   We can consider e.g. the series connection of two   than the case where d = −20% without any volt-
supercapacitors Fig. 2, associated with a current      age sharing device. The main advantage of a volt-
source in order to charge and discharge this system.   age sharing device is to keep the voltages across
   Introducing d the relative difference between C1     each supercapacitor on their nominal values with
and C2 values (d is expressed in percent), we can      no over-voltage. The stored energy is in that case
define the values of C1 and C2 compared to the          at its maximal possible value, taking into account
ideal reference value C :                              the values of C1 and C2 .
                                 d + 100
         C1 = C    and C2 = C                  (1)                                 III. Voltage sharing devices
                                    100
                                                          A common way to equalize the voltages in a se-
  Because the voltages across the supercapacitors
                                                       ries association of capacitors is to connect a resistor
must be limited to 2.5V , the series connection is
                                                       across each of them. The values of the resistors are
considered charged when the total voltage is 5V .
                                                       fixed by various criteria. The main criteria to con-
Under this condition and if the initial voltage is
                                                       sider is to fix a dynamic of the voltage sharing equal
zero, we can establish :
                                                       to the dynamic of the charge process of the super-
                                                       capacitors. This allows to avoid any overshoot of
           d + 100                      100            the individual voltages.
  Uc1f =           Uf   and Uc2f =            Uf
           d + 200                    d + 200             As an illustration, we propose Fig. 3 a simula-
                                                 (2)   tion result dealing with a series connection of five
  Where Uc1f and Uc2f are the voltages across C1       supercapacitors : four of them are 1000F , the fifth
and C2 at the end of charging and Uf is the to-        is a 800F supercapacitor. We propose the balance
tal voltage (5V ). According to those relations, we    of the energy at the end of a charging process from
can consider two extreme cases for C = 1000F .         0V to 12.5V , using a voltage sharing device. The
The first one is related to ideal supercapacitors       final stored energy in the supercapacitors is 15kJ.
(d = 0%). The second case is related to a bad          We will compare this reference energy to the energy
supercapacitor C2 (d = −20%, C1 = 1000F ,              given by the charging device.
C2 = 800F ). The results are given in Tab. I.
                                                                               4
                                                                           x 10
                                                                   14

              d = 0%     d = −20%     d = −20%
                         no sharing    sharing                     12



   Uf (V)         5          4.5           5                       10

  Uc1f (V)       2.5          2           2.5
                                                          Energy (J)




  Uc2f (V)       2.5         2.5          2.5                          8


   E (J)        6250        4500         5625
                                                                       6


                    TABLE I
                                                                       4
        Voltage sharing and stored energy

                                                                       2
  In the case of same values for each supercapacitor
(d = 0%), the stored energy is 6.25kJ.                                 0
  When d is −20%, the voltages across each ca-                             0       50   100   150   200    250

                                                                                                          t (s)
                                                                                                                  300   350   400   450   500



pacitor are not equally distributed. In order to
avoid any over-voltage across a supercapacitor, the    Fig. 3. Energy cost : voltage sharing with resistors
charging process is ended as soon as one capacitor
reaches is maximum voltage (2.5V ). In that case,         The solution using resistors generates too much
the charging process is ended when C2 is 2.5V . The    losses. The values of the resistors (0.1Ω) have been
chosen to have a good dynamic of voltage sharing.
                                                                                                                                                                                     1    ? 
But this dynamic is not quick enough : the charging
                                                                                                 1       A G
                                                                                                                                                 +                                                 7         ? 
process is ended in 40s, but it takes 400s to equalize
the voltages of all the capacitors. As a consequence,                                                                                        1           A G
the charging device has to provide nearly 120kJ to                     1                                                                                                        )                                       7
store 15kJ in the capacitors. The global efficiency
                                                                                                                                                                                     1    ?
is too low : 12.5%. The main disadvantage of this                                                    1   A G                                     +                                                  7         ?
solution is the power dissipated in each resistor.
   A second solution consists in the use of zener
diodes, which are connected across each superca-
pacitors. Those zener diodes have to limit the volt-                Fig. 5. Principle of the active sharing
ages of the capacitors, in order to fix the maximum
value to 2.5V . There is no power dissipation as
far as all the voltages are less than the limit volt-               tors during the charging or discharging process, the
age (2.5V ). But the power dissipation can be im-                   value and the sign of the sharing current Ieq should
portant if many supercapacitors reach their limit                   be chosen in order to obtain a dynamic of voltage
voltages, as shown Fig. 4.                                          sharing identical to the dynamic of the charging or
                                                                    discharging process.
              18000
                                                                      To respect this design criteria, we can establish :
              16000

                                                                                                                          d
              14000                                                                      Ieq = I                                                                                                                            (3)
                                                                                                                       d + 200
              12000
 Energy (J)




                                                                      This relation shows that for a charging current
              10000
                                                                    I = 100A , if C1 = 1000F and C2 = 800F
               8000
                                                                    (d = −20%), the sharing current should be Ieq =
               6000                                                 −11.1A.
               4000
                                                                      The sharing current sources can be synthetized
                                                                    as proposed Fig. 6.
               2000


                  0
                      0   5   10   15     20    25   30   35   40
                                                                                                                                                                        I           c 1
                                        t (s)                                            T                         D
                                                                                             1                                 1         C           1                                          U       c 1


Fig. 4. Energy cost : voltage sharing with zener diodes
                                                                                                                       L           e q   2 I              e q
                                                                           I                                                                                        A                                               U
  The use of zener diodes offers a better efficiency
                                                                                                                                                                            I
than the resistor solution. The charging device pro-                                                                                                                                c 2

                                                                                         T                     D                         C                                                      U
vides 16.3kJ, for 15kJ finally stored in the super-                                           2                             2                         2                                                  c 2


capacitors, with a good dynamic of voltage sharing.
The efficiency is nearly 90%, but the main disad-
vantage of that solution is to use the zener diodes                 Fig. 6. Active sharing device
to dissipate power when maximum local voltages
are reached.
                                                                       The aim of using such a converter is to enable
                                                                    a voltage sharing by means of current deviation
              IV. Active device for equalising the
                                                                    created by the switching of the components of the
                              voltages
                                                                    active device. Compared to the previous defined
   In order to obtain a sharing of each voltages, with              solutions, this device should propose a better effi-
the best efficiency, we propose a new topology of                     ciency because its working principle is not based on
device, based on the topology given Fig. 5 for two                  a power dissipation.
supercapacitors.                                                       The proposed topology is a current reversible
   The principle of this solution consists in a current             buck-boost converter. That kind of structure al-
deviation of the main charging current I, by means                  lows the transfer of energy from C1 to C2 (or the
of two auxiliary current sources. Depending on the                  opposite), independently of the voltages Uc1 and
difference of voltages between the two supercapaci-                  Uc2 . Compared to the topology given Fig. 5, the
two current sources have been replaced by two tran-          sharing will be efficient whatever the voltages
sistors/diodes. But the principle stay identical if          Uc1 and Uc2 are, but the switching frequency
the current in the inductor is two times bigger than         f has to vary in a large range.
the current Ieq previously established.
   In order to optimize the efficiency of such a de-         The topology Fig. 6 and the established design
vice, it is recommended to drive this converter to      criteria (4) are valid for a two supercapacitors series
obtain a discontinous conduction mode working.          connection, but can be extended for a n superca-
Two different cases should appear. When a positive       pacitors series connection, as shown Fig. 7 for a 5
current 2Ileq is needed (Uc1 > Uc2 ), the transistor    supercapacitors series connection.
T2 is turned off, and T1 is turned on and off with a
given frequency. At the opposite, when a negative                  D           1                  D               2                      D               3                      D               4


current 2Ileq is needed (Uc1 < Uc2 ), the transistor
T1 is turned off, and T2 is turned on and off with               T       1
                                                                                   L   1
                                                                                             T            2                         T            3
                                                                                                                                                                 L   3
                                                                                                                                                                           T            4


the same switching frequency. The switching pro-
cess is started as soon as a significant difference of           C           1                 C                2                     C                3                     C                4                     C        5

voltage has been detected between C1 and C2 . The                                                                         L   2                                                                         L   4

                                                                                                      D               '                      D               '                      D               '                  D           '
switching process is stopped when the two voltages                                                                2                                      3                                      4                              5




become the same.
                                                                                           T 2'                                   T 3'                                   T 4'                                   T 5'
   A soon as the difference of voltages is less than
the forward voltage of the diodes, and if the switch-   Fig. 7. Active sharing device for 5 supercapacitors
ing of T1 and T2 is defined by a 50% duty cycle, the
buck-boost converter works in discontinuous con-
duction mode. Under those conditions, we can es-           The series connection is divided in associations
tablish the main design criteria of such a topology,    of two supercapacitors. A buck-boost converter is
taking into account the relationship which gives the    associated for each pair of capacitors. The con-
value of the needed sharing current Ieq as a func-      verter T1 D1 T2 D2 allows the voltage sharing of C1
tion of the main current I :                            and C2 . The converter T2 D2 T3 D3 allows the volt-
                                                        age sharing of C2 and C3 , etc.
                                                           The same design criteria is applied for each con-
              1 d + 200           Uc1                   verter. If the main current I is 100A, for d = 20%,
   Leq f =              Uc1 1 +                  (4)
             16 I  d            Uc2 + Ud                the values of all the inductors must be 3µH if the
                                                        switching frequency is 10kHz. As an illustration,
   Where f is the switching frequency, Leq the value
                                                        we propose some simulation results, dealing with a
of the inductor, and Ud is the forward voltage of the
                                                        5 supercapacitors series connection. Each of them
diodes.
                                                        is a 1000F capacitors, except one which is 800F .
   This relationship ensures the choice of the induc-
tor and the switching frequency values for a main          The first result Fig. 8 shows the voltages across
current I given, and for a relative difference d of      each capacitor during the charging process. Even
C1 and C2 given.                                        if the sharing is not instantaneous, all the voltages
   Once the value of Leq has been fixed, there are       are equal at the end of the process, with no over-
two ways for determining the switching frequency        voltage on the supercapacitors.
f :                                                        The second result Fig. 9 shows the voltage ap-
                                                        plied to an inductor, and the current in that induc-
  • f can be fixed once for all. The maximum val-        tor once a process of voltage sharing is decided.
    ues for Uc1 and Uc2 have to be considered in
                                                           The considered converter works in discontinuous
    order to limit the sharing current value. Dur-
                                                        conduction mode. That means that the current
    ing the charging and discharging process, this
                                                        peak should be important to have a mean value as
    value should change as a function of Uc1 and
                                                        fixed by the used design criteria.
    Uc2 . As a consequence, the voltage sharing
    will be the most efficient when Uc1 and Uc2              Finally, we can compare values of the energy
    will reach their maximum value.                     given by the charging source and the energy finally
                                                        stored in the supercapacitors, taking into account
  • f can vary as a function of Uc1 and Uc2 . This      power losses in the semiconductors. This show a
    closed loop working mode ensures a constant         97% efficiency, witch is the best obtained compared
    value for the sharing current. The voltage          to other sharing solutions.
                              2.5                                                                                             serial resistor.
                                                                                                                                As described in the theoretical study, the transis-
                                2
                                                                                                                              tors are controlled by pairs to share the voltages on
                                                                                                                              each associated pairs of supercapacitors. The con-
   Voltages (V)




                                                                                                                              trol structure for two transistors is given Fig. 10.
                              1.5


                                                                                                                                                                                     C       k


                                1
                                                                                                                                                                                                           d riv e r   G a te
                                                                                                                                                                             D -la tc h          N a n d
                                                                                                                              U       re f
                                                                                                                                                                     + 1 V                                  M O S        T 1
                                                                                                                                             -   1 0 0 H z   x 2 0
                              0.5                                                                                                 U     c
                                                                                                                                                                                                           d riv e r   G a te
                                                                                                                                                                             D -la tc h          N a n d
                                                                                                                                                                     -1 V                                   M O S        T 2

                                0
                                    0          5         10         15      20       25         30         35            40
                                                                                                                                                                                 C       k
                                                                           t (s)
                                                                                                                              Fig. 10. Control structure
Fig. 8. Simulation results

                                2                                                                                               The switching frequency is constant during the
                                                                                                                              charge and discharge process. The sharing current
   Inductor Voltage (V)




                              1.5

                                1

                              0.5
                                                                                                                              varies to be maximum when the voltages across the
                                0                                                                                             supercapacitors are maximum.
                          −0.5

                              −1
                                                                                                                                This structure provides a good precision ( about
                          −1.5
                                    6    6.2       6.4        6.6    6.8     7     7.2    7.4        7.6    7.8          8
                                                                                                                              ±20mV ) and is not noise-sensitive while the volt-
                                                                           t (s)                                     −4
                                                                                                                  x 10        age information on the supercapacitor is taken be-
                               10                                                                                             fore that the transistor turns on.
       Inductor Current (A)




                                0                                                                                               The schematic is suited for a bipolar voltage
                              −10                                                                                             source. The electronic circuitry has been matched
                              −20                                                                                             to unipolar source with auto supply, in order to
                              −30                                                                                             make the cells fully independent.
                              −40
                                    6    6.2       6.4        6.6    6.8     7     7.2    7.4        7.6    7.8          8
                                                                                                                                The supercapacitor’s voltage drop influences the
                                                                           t (s)                                     −4
                                                                                                                  x 10
                                                                                                                              equalizing current value. For that reason, it’s not
                                                                                                                              useful to equalize at the beginning of the charge.
Fig. 9. Simulation results
                                                                                                                              When the full cell voltage rises 3V (nearly 600mV
                                                                                                                              on each supercapacitor), an integrated boost con-
                                        V. The practical realization                                                          verter ensures a 15V source for control circuitry,
                                                                                                                              which can start equalizing.
   A 5 supercapacitors 12V stack has been designed                                                                              A photography of that device is shown Fig. 11.
to verify theoretical studies. Four of them are 800F
supercapacitors and one is 1000F to test the prin-
ciple with a dispersion d = 25%.
   The maximum voltage for each supercapacitor
has been fixed to 2.3V . As 12V cannot be reached
without equalizing (some capacitor voltage would
exceed 2.3V ) a lower voltage charge watchword has
been used for measurements.
   In order to obtain the best efficiency, the tran-
sistors of the active device should be chosen with a
Rdson as low as possible. We have chosen a 4mΩ
Rdson , 185A n-MOS transistor. For significantly
lower switching losses, ultra-fast and soft recovery
diodes are needed.
   To keep a high current with low frequency the                                                                              Fig. 11. Practical realization
inductor must be very low (about 5µH). A short
4mm2 flex with one turn over a ferrite will provide                                                                              A series connection of many of those stacks is
such a low inductance value with a low parasitic                                                                              possible. The sharing of the voltages in each stack
is assured. But because of their design, the voltage    crease the maximum instantaneous output power.
sharing is also assured from one stack to the others.   In order to increase the voltage across a superca-
This ensures a series connection of several stacks of   pacitor device, a series connection is needed. We
supercapacitors in order to obtain a high voltage       have defined an active voltage sharing device for
level for that energy storage system.                   5 supercapacitors, witch ensures an optimal stored
   The performances on such a device are shown          energy value with no over-voltage over any super-
Fig. 12, on which are represented the voltages          capacitor and an optimal efficiency.
across three of the five supercapacitors, without          Each stack of 5 supercapacitors with its active
and with voltage sharing.                               device becomes a elementary cell, which can be as-
                                                        sociated with other stacks in a series connection.
                                                        This defines an energy storage system with a high
                                                        output voltage level.
                                                          A prototype has been realized , for which a re-
                                                        quest for a patent has been suggested (Number of
                                                        registration SE9903153 − 6).

                                                                              References
                                                        [1] X. Andrieu, “Supercapacitors, CEC workshop on solid
                                                            lythium batteries,” January 1991.
                                                        [2] M. Schmid and A. Egger, “Double–layer capacitor
                                                            short–time storage device in a hybrid vehicle,” EPE’99,
                                                            pp. P.1–P.10, September 1999.
                                                        [3] A. D. Napoli, F. G. Capponi, and L. Solero, “Power con-
                                                            verter arrangements with ultracapacitor tank for battery
                                                            load leveling in EV motor drives,” EPE’99, pp. P.1–P.8,
                                                            September 1999.
            Figure 12(a) Voltage sharing
                                                        [4] A. Rufer and H. Ravokatrasolofo, “Static converter for
                                                            complementary energy storage with battery and super-
                                                            capacitor,” PCIM 99 Power Quality, 1999.
                                                        [5] A. Rufer, H. Ravokatrasolofo, and P. Barrade, “Le su-
                                                            percondensateur et la batterie se marient pour fournir
                                                                 e                                   e
                                                            de l’´nergie,” Electronique, pp. 81–84, F´vrier 2000.




     Figure 12(b) Current across an inductor

Fig. 12. Experimental results


  The results for the voltage sharing present also
the current in one equalizing device inductor. The
average value is as expected proportional to the
voltage drop on the supercapacitors. This ensures a
correct voltage sharing across each supercapacitor.

                   VI. Conclusion
  The use of modern supercapacitors allows a com-
plementation of normal batteries, in order to in-

				
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