Abstract:
A regeneration method to rapidly and efficiently desorb ions after the ions are absorbed to electrodes in a deionization apparatus to eliminate ion components in a fluid (liquid and gas) is disclosed. A plurality of cells including a plurality of electrodes to absorb ions included in a fluid are connected to configure a stack. In a capacitive deionization (CDI) apparatus including at least two stacks, if 0 V is applied as a method of desorbing the ions and regenerating the electrodes after the ions are absorbed to the electrodes, and the cells or the stacks are connected in series in a state in which the cell units and the stack units obtained by connecting the cells are electrically disconnected from a power source, the capacitance of the entire system is reduced, a discharging time is shortened, and the ions are rapidly and efficiently desorbed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of Korean Patent Application No. 2008-82174, filed on Aug. 22, 2008 in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
       BACKGROUND 
       [0002]    1. Field 
         [0003]    A deionization apparatus eliminates ion components in a fluid (liquid and gas) and a method controls the same, and, more particularly, a deionization apparatus rapidly and efficiently desorbs ions after the ions are absorbed to electrodes, and a method controls the same. 
         [0004]    2. Description of the Related Art 
         [0005]    Water and, more particularly, underground water includes a large amount of minerals such as calcium and magnesium. A numerical value representing a total amount of calcium and magnesium is called hardness. Water having high hardness is called hard water, and water having low hardness is called soft water. 
         [0006]    If hard water, that is, water having high hardness, is used in an electronic appliance such as a washing machine or a dish washer, detergency deteriorates due to reaction with a detergent. In addition, since a large amount of scales accumulates on a channel in which water flows, the reliability of a product deteriorates. 
         [0007]    To solve this problem, a water softener using ion exchange resin has conventionally been suggested. 
         [0008]    The water softener using the ion exchange resin softens water while Ca +2  and Mg +2  ions, which are hard water components included in the water, are exchanged with Na +  obtained from NaCl injected into the ion exchange resin. Such a water softener using the ion exchange resin is disadvantageous in that NaCl should be periodically injected, and the ion exchange resin should be replaced due to impurities included in the water. Since a method of using the ion exchange resin should use an acidic or basic solution when the resin is reproduced and uses a large amount of polymer resin and chemicals to treat a large amount of water, this method is uneconomical. 
         [0009]    Recently, to solve this problem, research into a capacitive deionization (hereinafter, referred to as CDI) technology is actively conducted. 
         [0010]    The CDI technology is realized based on a simple principle that power is applied to two porous electrodes to electrically absorb negative ions to a positive electrode, and positive ions to a negative electrode, such that ions included in a fluid such as water are eliminated. In addition, if the absorption of the ions to the electrodes is saturated, the polarities of the electrodes are reversed, or the power is disconnected so that the ions absorbed to the electrodes are detached (desorbed), thereby facilitating the regeneration of the electrodes. Since the CDI technology does not uses a cleaning solution such as an acidic or basic solution as is done in the ion exchange resin method, or a reverse osmosis method for the regeneration of the electrodes, a chemical waste is not secondarily generated. In addition, since corrosion or contamination of the electrodes does not occur, the life span of the electrodes is semi-permanent. Furthermore, since the CDI technology has an energy efficiency that is higher than that of other treatment methods, energy is conserved by a factor of 10 to 20 times that of the other treatment methods. 
         [0011]      FIG. 1  is a view showing a structure of a unit cell of a general CDI technology. If a DC power source  20  is supplied to a collector  13  having two parallel electrodes  11  and  12  (carbon electrodes) of the unit cell  10 , negative ions are electrically absorbed to the positive electrode  11 , and positive ions are electrically absorbed to the negative electrode  12  so that the ions are eliminated in a fluid (liquid and gas). 
         [0012]      FIG. 2  is an electrical circuit diagram obtained by modeling the power source connection of  FIG. 1 . The two parallel electrodes  11  and  12  are modeled by connecting two capacitances C 1  and C 2  in series. The two capacitances C 1  and C 2  may be expressed by a capacitance Cp [Cp=C 1 ·C 2 /(C 1 +C 2 )]. Rp denotes the sum of parasitic resistances of a conducting wire, the collector  13  or a contact resistance. 
         [0013]    The CDI technology has a treatment capacity that is relatively lower than that of the ion exchange resin method. However, to solve this problem, a CDI stack  100  is configured by connecting several unit cells  10  in parallel, as shown in  FIG. 3 , such that a large amount of ions that are included in water is absorbed when hard water is introduced. Thus, the amount of soft water treated is increased. 
         [0014]      FIG. 4  is an electrical circuit diagram obtained by modeling the power source connection of  FIG. 3 . Cp 1 , Cp 2 , Cp 3 , . . . denote capacitances of the respective CDI cells  10  and Ct (Ct=Cp 1 +Cp 2 +Cp 3 + . . . ) denotes a total capacitance of the CDI stack  100  including the several CDI cells  10 . 
         [0015]      FIG. 5  is an electrical circuit diagram obtained by modeling the power source connection of a conventional CDI apparatus including at least two stacks. Ct 1 , Ct 2 , Ct 3 , . . . denote capacitances of the respective CDI stacks  100  and Cs (Cs=Ct 1 +Ct 2 +Ct 3 + . . . ) denotes a total capacitance of the CDI apparatus, including the at least two CDI stacks  100 . 
         [0016]    If the ions are absorbed by the CDI stack  100  of  FIG. 4  or the CDI apparatus of  FIG. 5  (ion absorption mode), a switch is connected to a node A such that the DC power source  20  is supplied to the CDI cells  10  and the CDI stacks  100 . While Cp, Ct and Cs are charged, the ions are absorbed to the electrodes  11  and  12  when hard water is introduced. Thus, the water is softened. In contrast, if the ions are desorbed (ion desorption mode), the switch is connected to a node B. Then, while Cp, Ct and Cs charged by the voltage of the DC power source  20  are discharged via Rp, the ions absorbed to the electrodes  11  and  12  are desorbed and are discharged together with the water. Thus, the electrodes  11  and  12  are regenerated. 
         [0017]    If the switch is connected to the node B in the ion desorption mode, Cp, Ct and Cs are discharged via Rp. At this time, a discharging voltage Vc(t) is calculated by Equation 1. 
         [0000]        Vc ( t )= Vi·e−t/τ   Equation 1 
         [0018]    where, Vc(t) denotes a discharging voltage according to a time t, Vi denotes an initial charging voltage, Rp denotes a resistance component, Cs denotes a total capacitance of the CDI apparatus, e denotes 2.718928, and τ denotes a time constant (Rp·Cs). 
         [0019]    As the number of the CDI cells  10  or the CDI stacks  100  is increased, the total capacitance Cs which is the total sum of the capacitances electrically connected in parallel is increased (Cs 1 &lt;Cs 2 &lt;Cs 3 ). In addition, as the treatment capacity is increased, a discharging time is increased as shown in  FIG. 6 . Thus, in the CDI apparatus, a time consumed for desorbing the ions after absorbing the ions to the electrodes  11  and  12  is increased. If the ion desorption time is increased, the amount of water which should be discharged is increased, and thus the waste of the water is increased. Accordingly, there is a need for a CDI apparatus that minimizes the waste of the water while increasing the treatment capacity. 
       SUMMARY 
       [0020]    Therefore, it is an aspect of the invention to provide an electrical configuration to rapidly and efficiently desorb ions absorbed to electrodes in a CDI apparatus, including at least two stacks, and to provide a regeneration method thereof. 
         [0021]    Additional aspects and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the invention. 
         [0022]    In accordance with the invention, the above and/or other aspects may be achieved by the provision of a deionization apparatus including: a plurality of stacks including electrodes to which ions included in a fluid are absorbed; a circuit unit to connect at least a portion of the plurality of stacks in parallel or in series; and a switch unit to switch at least the portion of the plurality of stacks to a serial connection or a parallel connection. 
         [0023]    The switch unit may be controlled to connect the plurality of stacks in parallel in an ion absorption mode and may be controlled to connect at least the portion of the plurality of stacks in series in an ion desorption mode. 
         [0024]    The deionization apparatus may further include a power source unit to supply power to the plurality of stacks, and the switch unit may further include a switch to switch power source lines connected between the power source and the plurality of stacks. 
         [0025]    The switch unit may be controlled to supply the power to the plurality of stacks in the ion absorption mode and may be controlled to disconnect the power from the plurality of stacks in the ion desorption mode. 
         [0026]    The switch unit may be controlled to connect the plurality of stacks in series in the ion desorption mode and may be controlled to connect a portion of the plurality of stacks in parallel and connect the remaining portion of the plurality of stacks in series, in the ion absorption mode. 
         [0027]    Each of the stacks may be obtained by connecting a plurality of cells including the electrodes and may further include a circuit unit to connect at least a portion of the plurality of cells in parallel or in series, and the switch unit may further include a switch to switch at least a portion of the plurality of cells to the serial connection or the parallel connection. 
         [0028]    The switch unit may be controlled to connect the plurality of cells in parallel in the ion absorption mode and may be controlled to connect the plurality of cells in series in the ion desorption mode. 
         [0029]    The switch unit may be controlled to connect the plurality of cells in series in the ion desorption mode. 
         [0030]    The switch unit may be controlled to connect a portion of the plurality of cells in parallel and connect the remaining portion of the plurality of cells in series, in the ion absorption mode. 
         [0031]    In accordance with an aspect of the invention, there is provided a deionization apparatus including: a plurality of cells including electrodes to which ions included in a fluid are absorbed; a circuit unit to connect at least a portion of the plurality of cells in parallel or in series; and a switch unit to switch at least the portion of the plurality of cells to a serial connection or a parallel connection. 
         [0032]    The switch unit may be controlled to connect the plurality of cells in parallel in an ion absorption mode and may be controlled to connect the plurality of cells in series in an ion desorption mode. 
         [0033]    The switch unit may be controlled to connect the plurality of cells in series in the ion desorption mode. 
         [0034]    The switch unit may be controlled to connect a portion of the plurality of cells in parallel and connect the remaining portion of the plurality of cells in series, in the ion absorption mode. 
         [0035]    In accordance with another aspect of the invention, there is provided a method of controlling a deionization apparatus including a plurality of stacks, the method including: connecting the plurality of stacks in parallel in an ion absorption mode; and connecting at least a portion of the plurality of stacks in series in an ion desorption mode. 
         [0036]    In accordance with another aspect of the invention, there is provided a method of controlling a deionization apparatus including a plurality of cells, the method including: connecting the plurality of cells in parallel in an ion absorption mode; and connecting at least a portion of the plurality of cells in series in an ion desorption mode. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0037]    These and/or other aspects and advantages of the invention will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which: 
           [0038]      FIG. 1  is a view showing an embodiment of a structure of a unit cell of a general CDI technology; 
           [0039]      FIG. 2  illustrates an embodiment of an electrical circuit diagram obtained by modeling a power source connection of  FIG. 1 ; 
           [0040]      FIG. 3  is a view showing an embodiment of a structure of a CDI stack obtained by connecting several unit cells of  FIG. 1 ; 
           [0041]      FIG. 4  is an electrical circuit diagram obtained by modeling a power source connection of  FIG. 3 ; 
           [0042]      FIG. 5  is an electrical circuit diagram obtained by modeling a power source connection of a conventional CDI apparatus; 
           [0043]      FIG. 6  is a graph showing a discharging time according to a total capacitance Cs of the conventional CDI apparatus; 
           [0044]      FIG. 7  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus according to an embodiment of the present invention; 
           [0045]      FIG. 8  is a table showing switch operations according to modes of the CDI apparatus according to an embodiment of the present invention; 
           [0046]      FIG. 9  is an electrical circuit diagram of a power source connection state in an ion absorption mode of the CDI apparatus according to an embodiment of the present invention; 
           [0047]      FIG. 10  is an electrical circuit diagram of a power source connection state in an ion desorption mode of the CDI apparatus according to an embodiment of the present invention; 
           [0048]      FIG. 11  is an electrical circuit diagram obtained by modeling a power source connection of a conventional CDI apparatus including two stacks; 
           [0049]      FIG. 12  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus including two stacks, according to an embodiment of the present invention; 
           [0050]      FIG. 13  is a graph showing a difference between discharging times according to discharging voltages of the CDI apparatus according to an embodiment of the present invention and the conventional CDI apparatus; 
           [0051]      FIG. 14  is a graph showing a difference between discharging times according to conductivities of the CDI apparatus according to a first embodiment of the present invention and the conventional CDI apparatus; 
           [0052]      FIG. 15  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus including six stacks, according to another embodiment of the present invention; and 
           [0053]      FIG. 16  is a table showing switch operations according to modes of the CDI apparatus according to another embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0054]    Reference will now be made in detail to embodiments of the invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. The embodiments are described below to explain the invention by referring to the figures. 
         [0055]      FIG. 7  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus according to an embodiment of the invention. The same portions as the conventional portions are denoted by the same reference numerals. 
         [0056]    In the CDI apparatus according to an embodiment of the invention of  FIG. 7 , n CDI stacks  100  are connected. Ct 1 , Ct 2 , Ct 3 , . . . denote capacitances of the respective CDI stacks  100 , Rp 1  and Rp 2  denote the sum of parasitic resistances, and SW 1  to SW 6  denote switches to switch the power source connection of the CDI apparatus in an ion absorption mode and an ion desorption mode. 
         [0057]      FIG. 8  is a table showing switch operations according to modes of the CDI apparatus according to an embodiment of the invention. The operations of the switches SW 1  to SW 6  are switched according to the ion absorption mode and the ion desorption mode and the power source of the CDI apparatus is connected according to the modes. 
         [0058]      FIG. 9  is an electrical circuit diagram of a power source connection state in the ion absorption mode of the CDI apparatus according to an embodiment of the invention. The capacitances Ct 1 , Ct 2 , Ct 3 , . . . , and Ctn corresponding to the respective CDI stacks  100  are connected in parallel according to the operations of the switches SW 1  to SW 6  in the ion absorption mode shown in  FIG. 8 , such that the total capacitance Cs (Cs=Ct 1 +Ct 2 +Ct 3  . . . +Cn) of the CDI apparatus is increased. 
         [0059]      FIG. 10  is an electrical circuit diagram of a power source connection state in an ion desorption mode of the CDI apparatus according to an embodiment of the invention. The capacitances Ct 1 , Ct 2 , Ct 3 , . . . , and Ctn corresponding to the respective CDI stacks  100  are switched from a parallel connection to a serial connection according to the operations of the switches SW 1  to SW 6  in the ion desorption mode shown in  FIG. 8  such that the total capacitance Cs (1/Cs=1/Ct 1 +1/Ct 2 +1/Ct 3  . . . +1/Cn) of the CDI apparatus is decreased. 
         [0060]    Accordingly, since a discharging time to reduce the voltage applied to the CDI stacks  100  to 0V is shortened, the ions absorbed to the ions  11  and  12  are rapidly and efficiently desorbed to rapidly regenerate the electrodes  11  and  12 . Accordingly, it is possible to suppress the waste of water by the shortened discharging time. 
         [0061]    In the CDI apparatus according to an embodiment of the invention, as the number of CDI stacks  100  is increased and treatment capacity is increased, the regeneration effect is more rapidly obtained.  FIGS. 11 to 13  show a difference between the invention and the conventional technology in the CDI apparatus including two CDI stacks  100 . 
         [0062]      FIG. 11  is an electrical circuit diagram obtained by modeling a power source connection of a conventional CDI apparatus including two stacks. In the ion absorption mode, a switch SW 7  is connected to a node E such that the DC power source  20  is supplied to two CDI stacks  100 . While the capacitance Ct 1  and Ct 2  corresponding to the two CDI stacks  100  are charged, ions are absorbed to the electrodes  11  and  12  when hard water is introduced. Thus, the water is softened. In contrast, in the ion desorption mode (electrode regeneration), the switch SW 7  is connected to a node F, while Ct 1  and Ct 2  charged by the voltage of the DC power source  20  are discharged via Rp 3 , the ions absorbed to the electrodes  11  and  12  are desorbed and are discharged together with the water. Thus, the electrodes  11  and  12  are regenerated. When the electrodes  11  and  12  are regenerated, Ct 1  and Ct 2  are connected in parallel, and thus the total capacitance Cs (Cs=Ct 1 +Ct 2 ) of the CDI apparatus is increased. 
         [0063]      FIG. 12  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus including two stacks, according to a first embodiment of the present invention. In the ion absorption mode, the switch SW 1  is turned on, the switch SW 2  is connected to a node C and the switch SW 3  is connected to a node A, such that the DC power source  20  is supplied to the two CDI stacks  100 . Then, while Ct 1  and Ct 2  are charged, ions are absorbed to the electrodes  11  and  12  when hard water is introduced. Thus, the water is softened. In contrast, in the ion desorption mode (electrode regeneration), the switch SW 1  is turned off, the switch SW 2  is connected to a node D and the switch SW 3  is connected to a node B. Accordingly, while Ct 1  and Ct 2  charged by the voltage of the DC power source  20  are discharged via Rp 3 , the ions absorbed to the electrodes  11  and  12  are desorbed and are discharged together with water. Thus, the electrodes  11  and  12  are regenerated. When the electrodes  11  and  12  are regenerated, Ct 1  and Ct 2  are connected in series, and thus the total capacitance Cs (1/Cs=1/Ct 1 +1/Ct 2 ) of the CDI apparatus is decreased. 
         [0064]    In  FIGS. 11 and 12 , if it is assumed that Rp 1 =Rp 2 =Rp 3 , Ct 1 =Ct 2 , the initial charging voltages of the CDI stacks are Vi to simplify the equation, the total capacitance Cs of the conventional CDI apparatus shown in  FIG. 11  becomes 2*Ct 1 , and the total capacitance of the CDI apparatus according to an embodiment of the invention shown in  FIG. 12  becomes Ct 1 /2. 
         [0065]    Accordingly, the discharging time to reduce the voltage to 0 V by Equation 1 is shown in  FIG. 13 . 
         [0000]        Vc ( t )= Vi·e−t/τ   Equation 1 
         [0000]    where, Vc(t) denotes a discharging voltage according to a time t, Vi denotes an initial charging voltage, Rp (Rp 1 , Rp 2  and Rp 3 ) denotes a resistance component, Cs denotes a total capacitance of the CDI apparatus, e denotes 2.718928, and τ denotes a time constant (Rp·Cs). 
         [0066]      FIG. 13  is a graph showing a difference between discharging times according to discharging voltages of the CDI apparatus according to an embodiment of the invention and the conventional CDI apparatus. 
         [0067]    In  FIG. 13 , when the electrodes  11  and  12  are regenerated, the voltage Vi charged in the two CDI stacks  100  is reduced to 0 V with time. It may be seen that the time to reduce the voltage to 0 V in the conventional regeneration method shown in  FIG. 11  is about three times that in the regeneration method according to an embodiment of the invention shown in  FIG. 12 . As the number of CDI stacks  100  is increased, the total capacitance Cs of the conventional regeneration method shown in  FIG. 11  is gradually increased to n*Ct 1  by the number of CDI stacks  100 . However, the total capacitance Cs of the regeneration method according to an embodiment of the invention is gradually decreased to Ct 1 /n by the number of CDI stacks  100 . Accordingly, while the discharging time may be gradually decreased, the ions absorbed to the electrodes  11  and  12  may be rapidly and efficiently desorbed. If the ion desorption time is decreased, the amount of water to be discharged is decreased, and thus, the waste of the water is decreased. Therefore, it is possible to realize a CDI apparatus that minimizes the waste of water while increasing treatment capacity. 
         [0068]    In a CDI water treatment apparatus according to an embodiment of the invention, the effect of the reduction of a regeneration time consumed for desorbing the ions absorbed to the electrodes  11  and  12  after absorbing the ions and sending soft water to a place where the soft water is used is shown in  FIG. 14 . 
         [0069]      FIG. 14  is a graph showing a difference between discharging times according to conductivities of the CDI apparatus according to an embodiment of the invention and the conventional CDI apparatus. 
         [0070]    In  FIG. 14 , when the DC power source  20  is applied to the two parallel electrodes  11  and  12  when water flows into the CDI apparatus at a predetermined flow rate (A Liter/min), ions included in hard water are absorbed to the electrodes  11  and  12  by the capacitances of the two electrodes  11  and  12  and soft water is discharged to the place where the soft water is used while the conductivity is reduced. In the ion desorption mode, 0 V (short circuit) is applied before the ions are saturated in the electrodes  11  and  12 , energy charged in the CDI stacks  100  is discharged, and the ions absorbed to the electrodes  11  and  12  are desorbed and are discharged to a water distribution side together with water. At this time, the faster the energy charged in the CDI stacks  100  is discharged, the faster the ions are desorbed from the electrodes  11  and  12 . Accordingly, the discharging time is significantly important. It may be seen that the electrode regeneration time may be shortened by Δt due to the technical difference between the CDI apparatus according to an embodiment of the present invention and the conventional CDI apparatus. If Δt is B min, since the flow rate is A Liter/min, A*B liters of water is conserved during one cycle of the CDI apparatus. If a total of 1000 cycles are operated, a total of 1000*A*B liters of water can be conserved. 
         [0071]    Accordingly, in the CDI apparatus according to an embodiment of the invention, as the number of CDI stacks  100  is increased, and the treatment capacity is increased, the electrode regeneration time is decreased. Accordingly, a large amount of water may be conserved. 
         [0072]    Hereinafter, another embodiment of the invention will be described. 
         [0073]    In the CDI apparatus according to an embodiment of the invention, since the initial charging voltage Vi may be increased by connecting the CDI stacks  100  in series, an electrical configuration to connect at least two CDI stacks  100  in series or in parallel may be utilized. 
         [0074]      FIG. 15  is an electrical circuit diagram obtained by modeling a power source connection of a CDI apparatus including six stacks, according to an embodiment of the invention. Ct 1 , Ct 2 , Ct 3 , Ct 4 , Ct 5  and Ct 6  denotes capacitances of the six CDI stacks  100 , Rp 1  and Rp 2  denote the sum of parasitic resistances, and SW 1  to SW 6  denote switches to switch the power source connection of the CDI apparatus in the ion absorption mode and the ion desorption mode. 
         [0075]      FIG. 16  is a table showing switch operations according to modes of the CDI apparatus according to an embodiment of the invention. The operations of the switches SW 1  to SW 6  are switched according to the ion absorption mode and the ion desorption mode, and the power source of the CDI apparatus is connected according to the modes. 
         [0076]    In the CDI apparatus of  FIG. 15 , in the ion absorption mode, the switches SW 1 , SW 2  and SW 4  are turned on, the switch SW 3  is connected to a node A, the switch SW 5  is connected to a node C, and the switch SW 6  is turned off such that the DC power source  20  is supplied to the six CDI stacks  100 . Then, while Ct 1 , Ct 2 , Ct 3 , Ct 4 , Ct 5  and Ct 6  are charged, ions are absorbed to the electrodes  11  and  12  when hard water is introduced. Thus, the water is softened. In contrast, in the ion desorption mode (electrode regeneration), the switches SW 1 , SW 2  and SW 4  are turned off, the switch SW 3  is connected to a node B, the switch SW 5  is connected to a node D, and the switch SW 6  is turned on. Accordingly, while Ct 1 , Ct 2 , Ct 3 , Ct 4 , Ct 5  and Ct 6  charged by the voltage of the DC power source  20  are discharged via Rp 2 , the ions absorbed to the electrodes  11  and  12  are desorbed and are discharged together with water. Thus, the electrodes  11  and  12  are regenerated. When the electrodes  11  and  12  are regenerated, Ct 1 , Ct 2 , Ct 3 , Ct 4 , Ct 5  and Ct 6  are connected in series and in parallel, and thus the total capacitance Cs (1/Cs=1/(Ct 1 +Ct 2 )+1/(Ct 3 +Ct 4 )+1/(Ct 5 +Ct 6 )) of the CDI apparatus is decreased compared with the total capacitance (Cs=Ct 1 +Ct 2 +Ct 3 +Ct 4 +Ct 5 +Ct 6 ) when the stacks are connected in parallel. In addition, the initial charging voltage Vi may be decreased compared with the case where the stacks  100  are connected in series. 
         [0077]    Although a portion of the stacks  100  is connected in parallel in  FIG. 15 , the stacks  100  may be changed to the serial connection or the parallel connection as shown in  FIG. 7 . Alternatively, a portion of the stacks  100  may be connected in parallel and the remaining portion of the stacks may be connected in series. 
         [0078]    Although the plurality of stacks  100  is switched between the serial connection and the parallel connection in an embodiment of the invention, the invention is applicable to a circuit to connect a plurality of cells  10  configuring one stack  100  or is simultaneously applicable to a circuit to connect a plurality of cells  10  in one stack  100  and a circuit to connect a plurality of stacks  100 . 
         [0079]    Although a few embodiments of the invention have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.