Patent Publication Number: US-2023163374-A1

Title: Charge and discharge control device and charge and discharge control method

Description:
FIELD 
     The present disclosure relates to a charge and discharge control device and a charge and discharge control method for controlling a battery system in which a plurality of batteries having different characteristics from each other are present. 
     BACKGROUND 
     With the increase in vehicles using batteries such as electric vehicles and hybrid electric vehicles, methods for reusing batteries having used in such vehicles and therefore being degraded and batteries having different characteristics in module configurations, battery materials and the like depending on the vehicle types have been considered. For example, ways for reusing batteries that can no longer be used in electric vehicles with large outputs, as batteries for stationary applications with small outputs have been considered. Under present situation, however, use of such batteries remains within applications of batteries with equivalent characteristics such as batteries with substantially equal degradation levels, or batteries of the same types. Thus, in order to reuse various batteries, there has been demand for development of a control method for effectively and efficiently using batteries having different characteristics from each other. 
     Patent Literature 1 teaches a technology of a power supply control device, which is mounted on a vehicle including a plurality of battery devices and controls charging and discharging of the battery devices, calculating and comparing losses during charging and discharging, assigning power when a loss is small, and adjusting the charge states, that is, the states of charge (SOCs). 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: Japanese Patent Application Laid-open No. 2019-187148 
     SUMMARY 
     Technical Problem 
     According to the related art technology, however, powers are not assigned and the SOCs are not adjusted when losses are large during charging or discharging, which is problematic in that the efficiency of the battery system may be lowered. In particular, in a case where batteries having different characteristics from each other are present in one battery system and there are significant differences in capacity, resistance, and the like between the batteries, the characteristics of the battery system are limited to those of a battery with a small capacity or those of a battery with a large resistance, which lowers the efficiency of the battery system. 
     The present disclosure has been made in view of the above, and an object thereof is to provide a charge and discharge control device capable of reducing or preventing decrease in the efficiency of a battery system including battery modules with different characteristics. 
     Solution to Problem 
     To solve the above problem and achieve an object, the present disclosure is directed to a charge and discharge control device to be connected to a battery system including a plurality of battery modules. The charge and discharge control device includes: an obtaining unit to obtain information on states of the battery modules; an estimation unit to estimate a parameter indicating each of the states of the battery modules by using the information on the states of the battery modules obtained by the obtaining unit; and an output control unit to compare the parameters of the battery modules estimated by the estimation unit, and control division of output among the battery modules so as to reduce difference between charge states of the battery modules on the basis of a result of comparison. 
     Advantageous Effects of Invention 
     According to the present disclosure, a charge and discharge control device produces an effect of being capable of reducing or preventing decrease in the efficiency of a battery system including battery modules with different characteristics. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a diagram illustrating an example of a configuration of a charge and discharge control system according to an embodiment. 
         FIG.  2    is a diagram illustrating an example of a configuration of a charge and discharge control device according to the embodiment. 
         FIG.  3    is a diagram illustrating an example of a configuration of a direct current (DC)-DC converter according to the embodiment. 
         FIG.  4    is a diagram illustrating the relation between an output of a battery module and an output of a DC-DC converter in a battery system according to the embodiment. 
         FIG.  5    illustrates graphs of an example of discharge curves in a case where battery modules having different characteristics are used with outputs equal to each other as a comparative example. 
         FIG.  6    is a first diagram explaining a method for dividing output among the battery system constituted by m battery modules performed by the charge and discharge control device according to the embodiment. 
         FIG.  7    is a second diagram explaining a method for dividing output among the battery system constituted by m battery modules performed by the charge and discharge control device according to the embodiment. 
         FIG.  8    is a table illustrating an example of division of output performed by an output control unit of the charge and discharge control device according to the embodiment in a case of pattern 1: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≥R n . 
         FIG.  9    is a graph illustrating an example of a discharge curve of a battery module  111 - 1  in a case where output is divided in pattern 1 by the output control unit of the charge and discharge control device according to the embodiment. 
         FIG.  10    is a graph illustrating an example of a discharge curve of a battery module  111 - n  in a case where output is divided in pattern 1 by the output control unit of the charge and discharge control device according to the embodiment. 
         FIG.  11    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 2: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≤R n . 
         FIG.  12    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 3: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≥R n . 
         FIG.  13    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 4: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≤R n . 
         FIG.  14    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 5: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≥R n . 
         FIG.  15    is a graph illustrating an example of a discharge curve of a battery module  111 - 1  in a case where output is divided in pattern 5 by the output control unit of the charge and discharge control device according to the embodiment. 
         FIG.  16    is a graph illustrating an example of a discharge curve of a battery module  111 - n  in a case where output is divided in pattern 5 by the output control unit of the charge and discharge control device according to the embodiment. 
         FIG.  17    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 6: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≤R n . 
         FIG.  18    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 7: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≥R n . 
         FIG.  19    is a table illustrating an example of division of output performed by the output control unit of the charge and discharge control device according to the embodiment in a case of pattern 8: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≤R n . 
         FIG.  20    is a diagram illustrating an example of discharge curves of individual battery modules in a case where the output control unit of the charge and discharge control device according to the embodiment performs division of output in pattern 1. 
         FIG.  21    is a diagram illustrating an example of discharge curves in a case where the output control unit of the charge and discharge control device according to the embodiment does not switch the method of dividing output. 
         FIG.  22    is a diagram illustrating an example of discharge curves in a case where the output control unit of the charge and discharge control device according to the embodiment switches the method of dividing output. 
         FIG.  23    is a flowchart illustrating the operation of charge and discharge control performed by the charge and discharge control device according to the embodiment. 
         FIG.  24    is a first graph illustrating an effect produced by the charge and discharge control device according to the embodiment. 
         FIG.  25    is a second graph illustrating an effect produced by the charge and discharge control device according to the embodiment. 
         FIG.  26    is a diagram illustrating an example of a case where processing circuitry included in the charge and discharge control device according to the embodiment is constituted by a processor and a memory. 
         FIG.  27    is a diagram illustrating an example of a case where processing circuitry included in the charge and discharge control device according to the embodiment is constituted by dedicated hardware. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A charge and discharge control device and a charge and discharge control method according to an embodiment of the present disclosure will be described in detail below with reference to the drawings. 
     Embodiment 
       FIG.  1    is a diagram illustrating an example of a configuration of a charge and discharge control system  100  according to an embodiment. The charge and discharge control system  100  includes a battery system  110 , a charge and discharge control device  120 , and a device  130 . The battery system  110  includes replaceable battery modules  111 - 1  to  111 - m , and DC-DC converters  11 - 1  the number of which is m. “m” is an integer not smaller than 2. In the description below, each of the battery modules  111 - 1  to  111 - m  may be referred to as a battery module  111  when the battery modules  111 - 1  to  111 - m  are not distinguished from each other. The battery system  110  has a configuration in which units  115 , each of which includes a battery module  111  and a DC-DC converter  114  are connected with each other, are connected in series or in parallel with each other. Although not illustrated in  FIG.  1   , assume that the battery system  110  includes m units  115 . The battery modules  111 - 1  to  111 - m  may have different characteristic from each other. Thus, the battery system  110  is constituted by the replaceable battery modules  111  having different characteristic from each other. 
     As illustrated in  FIG.  1   , in the battery system  110 , voltages applied to the respective units  115  are represented by voltages V 1 , . . . , V m , and currents flowing through the respective units  115  are represented by currents I 1 , . . . , I m . The battery system  110  can indirectly control the voltages of the respective units  115 , that is, the respective battery modules  111  or the currents flowing to the respective battery modules  111  by controlling the voltage V 1 , . . . , V m  when the units  115  are connected in series or controlling the current I 1 , . . . , I m  when the units  115  are connected in parallel. In addition, as illustrated in  FIG.  1   , in the battery system  110 , outputs from the respective units  115  are represented by outputs P 1 , . . . , P m , the voltages applied to the respective battery modules  111  are represented by V 1b , . . . , V mb , and the currents flowing through the respective battery modules  111  are represented by I 1b , . . . , I mb . The output P 1 =V 1 ×I 1 , and the output P m =V m ×I m . 
     The battery modules  111  each include cells  112  and a battery management unit (BMU)  113 . The battery modules  111  each have a configuration in which cells  112 , a cell, being the smallest unit, are connected in series or in parallel with each other, and the cells  112  are connected with the BMU  113 . The cells  112  are chargeable and dischargeable secondary batteries, and the examples thereof include, but are not limited to, lithium-ion batteries, nickel-metal hydride batteries, and lead storage batteries. In each BMU  113 , thresholds such as an upper and lower limit, voltage, a maximum charge and discharge current, and a maximum cell temperature are set for the purpose of preventing overcharge, overdischarge, overvoltage, overcurrent, temperature anomaly, and the like of the cells  112 . The BMUs  113  each monitor the states of the cells  112 , by performing such as protective functions, voltage measurement, current measurement, power measurement, temperature measurement of the battery system  110 , full charge management, and remaining capacity management, using the aforementioned thresholds. 
     In the charge and discharge control system  100 , the device  130  refers to a load to which the battery system  110  discharges and refers to a power supply that supplies power when the battery system  110  is charged. Although not illustrated in  FIG.  1   , the charge and discharge control system  100  can include a plurality of devices  130 . 
     Each of the DC-OC converters  114  converts voltage output from the battery module  111  or the device  130 , and outputs the converted voltage. For example, the DC-DC converter  114  connected with the battery module  111 - 1  converts the voltage V 1b  and the current I 1b  into voltage V 1  and current I 1 , respectively, and outputs the voltage V 1  and the current I 1  at the time of discharging. Furthermore, the DC-DC converter  114  converts the voltage V 1  and the current I 1  into the voltage V 1b  and the current I 1b , respectively, and outputs the voltage V 1b  and the current I 1b  at the time of charging. 
     The charge and discharge control device  120  is connected with the battery system  110 . The charge and discharge control device  120  obtains information on the individual battery modules  111 , divides an output required for a load that is a device  130 , among the battery modules  111  at the time of discharging, and divides power input from a power supply that is a device  130 , among the battery modules  111  at the time of charging. The charge and discharge control device  120  transmits output commands to the individual battery modules  111 , and controls division of output among the battery modules  111 . A configuration of the charge and discharge control device  120  will be described in detail.  FIG.  2    is a diagram illustrating an example of a configuration of the charge and discharge control device  120  according to the embodiment. The charge and discharge control device  120  includes a current obtaining unit  121 , a capacity obtaining unit  122 , a voltage obtaining unit  123 , an SOC estimating unit  124 , a resistance estimating unit  125 , a remaining capacity estimating unit  126 , and an output control unit  127 . In the charge and discharge control device  120 , the current obtaining unit  121 , the capacity obtaining unit  122 , and the voltage obtaining unit  123  constitute an obtainment unit  128 . In addition, the SOC estimating unit  124 , the resistance estimating unit  125 , and the remaining capacity estimating unit  126  constitute an estimation unit  129 . 
     The obtainment unit  128  obtains information on the states of the battery modules  111 - 1  to  111 - m  included in the battery system  110 . 
     Specifically, in the obtainment unit  128 , the current obtaining unit  121  obtains information on current I b  in the battery module  111  measured by an ammeter in the corresponding DC-DC converter  114  from battery information transmitted from each of the DC-DC converters  114 . In the description below, current I b  obtained by the current obtaining unit  121  from a DC-DC converter  114  connected with a battery module  111 - n  may be referred to as current I nb . Note that n is an integer satisfying 1≤n≤m. The voltage obtaining unit  123  obtains information on voltage V b  of the battery module  111  measured by a voltmeter in the corresponding DC-DC converter  114  from the battery information transmitted from each of the DC-DC converters  114 . In the description below, voltage V b  obtained by the voltage obtaining unit  123  from a DC-DC converter  114  connected with a battery module  111 - n  may be referred to as voltage V nb . 
     The capacity obtaining unit  122  estimates the capacity of each of the battery modules  111  on the basis of the battery information transmitted from the individual DC-DC converters  114 . Note that the capacity of a battery module  111  which the capacity obtaining unit  122  estimates, is assumed to be a full-charge capacity (FCC). The full-charge capacity is a sum of currents when a battery module  111  is charged within a control range of the battery module  111 , such as within a voltage range of 2.5 V to 4.2 V of the cells  112 , for example. When replaceable battery modules  111  are used, a battery module  111  having a different full-charge capacity from that of a battery module  111  before replacement may be connected after the replacement in the battery system  110 . Because the full-charge capacity may vary depending on a battery module  111  to be replaced with, the capacity obtaining unit  122  estimates the full-charge capacities of the individual battery modules  111 . In a method of estimating the full-charge capacity of a battery module  111 , the capacity obtaining unit  122  may obtain a sum of currents when the battery module  111  is charged within a control range of the battery module  111 , such as within a voltage range of 2.5 V to 4.2 V of the cells  112 , for example, or may use information on the full-charge capacity transmitted from the BMU  113 . When information on the SOC can be obtained from the BMU  113 , the capacity obtaining unit  122  can also estimate the full-charge capacity of a battery module  111  on the basis of the change in the amount of current and the change in the SOC. In the description below, the full-charge capacity of a battery module  111 - n  obtained or estimated by the capacity obtaining unit  122  may be referred to as FCC n . 
     The estimation unit  129  estimates a parameter indicating a state of each of the battery modules  111 - 1  to  111 - m  by using information on the respective states of the battery modules  111 - 1  to  111 - m  obtained by the obtainment unit  128 . 
     Specifically, in the estimation unit  129 , the SOC estimating unit  124  estimates the SOC of each battery module  111  by using the information on the current I b  obtained by the current obtaining unit  121  and the full-charge capacity estimated by the capacity obtaining unit  122 . The SOC is a parameter indicating the charge state of a battery module  111 , SOC=0 means a state in which a battery module  111  has fully discharged, and SOC=1 means a state in which a battery module  111  is fully charged. A method for estimating the SOC by the SOC estimating unit  124  may be a common method. In the embodiment, a method of calculating the SOC by using a current integration method will be described. The SOC estimating unit  124  can calculate the SOC by integrating current flowing into a battery module  111  from estimation start time as expressed by formula (1). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                         
                     1 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     SOC 
                     ⁡ 
                     ( 
                     t 
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         FCC 
                       
                       ⁢ 
                       
                         
                           
                             ∫ 
                             0 
                           
                           t 
                         
                         Idt 
                       
                     
                     + 
                     
                       SOC 
                       ⁡ 
                       ( 
                       0 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In formula (1) SOC(t) is a parameter representing the SOC at certain time, FCC is a parameter representing the full-charge capacity, and SOC(0) is a parameter representing a charge amount at the start time charge amount estimation. In the description below, the SOC(t) of a battery module  111 - n  estimated by the SOC estimating unit  124  may be referred to as SOC n . 
     The resistance estimating unit  125  estimates the resistance R of each battery module  111  by using information on the current I b  obtained by the current obtaining unit  121  and information on the voltage V b  obtained by the voltage obtaining unit  123 . A method for estimating the resistance R of a battery module  111  by the resistance estimating unit  125  may be a common method. In the embodiment, a method of calculating the resistance R by using Ohm&#39;s law will be described. Upon obtaining the voltage V b  and the current I b  of a battery module  111  at certain time, the resistance estimating unit  125  calculates the resistance R by formula (2). Upon receiving the voltage V nb  and the current I nb  of the battery module  111 - n  at a certain time, for example, the resistance estimating unit  125  can calculate the resistance R n  by formula (2). 
       [Formula 2] 
       R=V b   /I   b (Ω)   (2)
 
     The remaining capacity estimating unit  126  estimates the remaining capacity Q of a battery module  111  by using the full-charge capacity of the battery module  111  estimated by the capacity obtaining unit  122  and the SOC of the battery module  111  estimated by the SOC estimating unit  124 . The remaining capacity estimating unit  126  calculates the remaining capacity Q by obtaining a product of the FCC and the SOC as expressed by formula (3). The remaining capacity estimating unit  126  can calculate the remaining capacity Q n  of a battery module  111 - n , for example, by obtaining a product of the FCC n  and SOC n  as expressed by formula (3). Alternatively, when the remaining capacity Q of a battery module  111  is transmitted from the BMU  113  of the battery module  111 , the remaining capacity estimating unit  126  may use the remaining capacity Q transmitted from the BMU  113 . 
       [Formula 3] 
         Q ×FCC×SOC   (3)
 
     As described above, the estimation unit  129  estimates the SOCs, which are charge states, the capacity values indicating the remaining capacities Q, and the resistances R of the battery modules  111 - 1  to  111 - m  as parameters indicating the states of the battery modules  111 - 1  to  111 - m.    
     The output control unit  127  compares the parameters of the battery modules  111 - 1  to  111 - m  estimated by the estimation unit  129 , and controls division of output among the battery modules  111 - 1  to  111 - m  on the basis of the comparison result so that the differences between the charge states of the battery modules  111 - 1  to  111 - m  become smaller. Specifically, the output control unit  127  compares the SOCs of the respective battery modules  111  estimated by the SOC estimating unit  124 , compares the resistances R of the respective battery modules  111  estimated by the resistance estimating unit  125 , and compares the remaining capacities Q of the respective battery modules  111  estimated by the remaining capacity estimating unit  126 . The output control unit  127  calculates an output of each of the battery modules  111  at discharge on the basis of the comparison results, and outputs an output command to each of the battery modules  111 . A method for comparing the parameters by the output control unit  127  will be described later. 
     A configuration of the DC-DC converters  114  will be described.  FIG.  3    is a diagram illustrating an example of a configuration of a DC-DC converter  114  according to the embodiment.  FIG.  3    illustrates a configuration in which the DC-DC converter  114  is connected with a battery module  111 - 1 . The DC-DC converter  114  has a function of stepping up or down the voltage V 1b  of the battery module  111 - 1 . While the DC-DC converter  114  in the example in  FIG.  3    is an isolated DC-DC converter, this is an example, and the DC-DC converter  114  is not limited thereto. The DC-DC converter  114  may be a non-isolated DC-DC converter. The DC-DC converter  114  includes a voltmeter  301 , an ammeter  302 , a capacitor  303 , a bridge circuit  304 , a transformer  305 , a bridge circuit  306 , a capacitor  307 , an ammeter  303 , a voltmeter  309 , and a controller  310 . The bridge circuit  304  includes switching elements SW 1  to SW 4 . The bridge circuit  306  includes switching elements SW 11  to SW 14 . 
     In the DC-DC converter  114 , the voltmeter  301  measures the voltage V 1b . The ammeter  302  measures the current I 1b . The ammeter  303  measures the current I 1 . The voltmeter  309  measures the voltage V 1 . The controller  310  obtains the voltage V 1b  measured by the voltmeter  301  and the current I 1b  obtained by the ammeter  302 , which are connected on the battery module  111 - 1  side. The controller  310  obtains the current I 1  measured by the ammeter  308  and the voltage V 1  measured by the voltmeter  309 , which are connected on the device  130  side. In addition, the controller  310  obtains battery control information from the battery module  111 - 1 . The controller  310  generates control commands for the bridge circuit  304  and the bridge circuit  306  and controls switching of the switching elements SW 1  to SW 4  and the switching elements SW 11  to SW 14  by using the obtained information. The controller  310  also transmits battery information including the voltage V 1b  measured by the voltmeter  301  and the current I 1b  measured by the ammeter  302 , to the charge and discharge control device  120 . The battery information may include information other than the voltage V 1b  and the current I 1b . 
     In the embodiment, if the units  115 , that is, the battery modules  111  are connected in series as the characteristics of the configuration of the battery system  110 , the sum of the voltages V 1  to V m  the DC-DC converters  114  connected with the respective battery modules  111  needs to be “V” that a total voltage required for the device  130  as expressed by formula (4). 
       [Formula 4] 
       V 1 + . . . +V m =V(V)   (4)
 
     On the other hand, if the units  115 , that is, the battery modules  111  are connected in parallel as the characteristics of the configuration of the battery system  110 , the sum of the currents I 1  to I m  of the DC-DC converters  114  connected with respective battery modules  111  needs to be “I” that is a total current required for the device  130  as expressed by formula (5). 
       [Formula 5] 
         I   1   + . . . +I   m   =I ( A )   (5)
 
     The relation between an output P 1b  of a battery module  111  and an output P 1  of a DC-DC converter  114  will now be described with reference to  FIG.  4   .  FIG.  4    is a diagram illustrating the relation between the output P 1b  of the battery module  111 - 1  and the output P 1  of the DC-DC converter  114  in the battery system  110  according to the embodiment.  FIG.  4    illustrates a configuration in which the DC-DC converter  114  is connected with the battery module  111 - 1 . When the conversion efficiency of the DC-DC converter  114  is represented by α, the relation between the output P 1b  of the battery module  111 - 1  and the output P 1  of the DC-DC converter  114  can be expressed as in formula (6). 
       [Formula 6] 
         P   1b   =αP   1 ( W )   (6)
 
     In addition, when the voltage of the battery module  111 - 1  is represented by V 1b , the current thereof is represented by I 1b , and the voltage and the current resulting from the conversion by the DC-DC converter  114  are represented by V 1  and I 1 , respectively, formula (6) can be expressed as in formula (7). 
       [Formula 7] 
       V 1b   I   1b =αV 1   I   1 ( W )   (7)
 
     Thus, the current I 1b  can be expressed as in formula (8) on the basis of formula (7). 
     
       
         
           
             
               
                 
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                     Formula 
                     ⁢ 
                         
                     8 
                   
                   ] 
                 
               
               
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                     I 
                     
                       1 
                       ⁢ 
                       b 
                     
                   
                   = 
                   
                     α 
                     ⁢ 
                     
                       
                         V 
                         1 
                       
                       
                         V 
                         
                           1 
                           ⁢ 
                           b 
                         
                       
                     
                     ⁢ 
                     
                       I 
                       1 
                     
                     ⁢ 
                         
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     As expressed by formula (8), the battery system  110  can indirectly control the battery module  111 - 1  by controlling the voltage V 1  and the current I 1  on the device  130  side of the DC-DC converter  114 . 
     While the DC-DC converter  114  has a voltage measuring function and a current measuring function in the embodiment, the DC-DC converter  114  is not limited thereto. Even when a battery module  111  performs measurement of voltage and current therein and sends the voltage and the current to the BMU  113 , it is sufficient that the charge and discharge control device  120  is capable of directly or indirectly obtaining information on the voltage and current measured in the battery module  111  from the BMU  113 . In addition, when the full-charge capacities of the battery modules  111  are known in advance, the charge and discharge control device  120  need not perform the estimation by the capacity obtaining unit  122  and need not obtain the full-charge capacities from the BMUs  113 . Note that the DC-DC converters  114  connected with the respective battery modules  111  are all assumed to have the same conversion efficiencies α. 
     Next, a method for comparing parameters performed by the output control unit  127  of the charge and discharge control device  120  will be described. The parameters compared by the output control unit  127  are the remaining capacities Q, the charge states SOC, and the resistances R of the individual battery modules  111  as described above. 
       FIG.  5    illustrates, as a comparative example, graphs of an example of discharge curves when battery modules  111  having different characteristics are used with outputs equal to each other. In  FIG.  5   , (a) on the left side is a discharge curve of the battery module  111 - 1 , where SOC 1 =80%, full-charge capacity=10 Wh, remaining capacity Q 1 =8 Wh, and resistance R 1 =10Ω. (b) on the right is a discharge curve of a battery module  111 - n , where SOC n =50%, full-charge capacity=5 Wh, remaining capacity Q n =2.5 Wh, and resistance R n =5Ω. When discharges are started with equal outputs, the battery module  111 - n  with the smaller remaining capacity Q n  and the smaller SOC n  can be completely discharged. However, the capacity of the battery module  111 - 1  that has the remaining capacity Q 1  and the SOC 1  larger than those of the battery module  111 - n  remains at the completion time of discharge of the battery system  110 , thereby lowering the efficiency of the battery system  110 . Furthermore, when the battery modules  111  are used with the outputs equal to each other, the loss or the battery module  111 - 1  that has a larger resistance R becomes large, thereby lowering the efficiency of the battery system  110 . 
     Thus, in the embodiment, the charge and discharge control device  120  controls division of output so as to resolve difference in the SOCs of the battery modules  111  and to reduce Joule heat. 
     A method for dividing output among the battery modules  111  performed by the charge and discharge control device  120  described.  FIG.  6    is a first diagram explaining a method for dividing output among the battery system  110  constituted by m battery modules  111  performed by the charge and discharge control device  120  according to the embodiment. In  FIG.  6   , branch numbers such as “1” and “m” of the battery modules  111 - 1  to  111 - m  will be referred to as module numbers, and it is assumed that the module number at the center is “n”. The same applies to  FIG.  7    explained below. Herein, assume that the charge and discharge control device  120 , with respect to the battery module  111 - n  with the central module number among the m battery modules  111 , divides output in accordance with capacity ratios among the battery modules  111 - 1  to  111 -( n −1) the numbers of which are before the battery module  111 - n , and divides output in accordance with resistance ratios among, the battery modules  111 -( n +1) to  111 - m  the numbers of which are after the battery module  111 - n . The charge and discharge control device  120  actually needs to determine the method for dividing output depending on the remaining capacities Q, the resistances R, and the like of the individual battery modules  111 , and a method of the determination will be described later. 
     An output of the entire battery system  110  is represented by P. The charge and discharge control device  120  first divides output among the central battery module  111 - n  and the battery modules  111 - 1  to  111 -( n −1). The output P n  to be divided among the battery modules  111 - 1  to  111 - n  is expressed as in formula (9). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               9 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   Pn 
                   = 
                   
                     
                       
                         n 
                         m 
                       
                       ⨯ 
                       P 
                     
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The charge and discharge control device  120  divides the output P n  expressed by formula (9) among the battery modules  111 - 1  to  111 - n . When the remaining capacities Q of the respective battery modules  111  are represented by Q 1 , . . . , Q n , . . . , Q m , an output P kQ  of the battery modules  111 - k  is expressed by formula (10). The output P kQ  is a result of dividing, by the charge and discharge control device  120 , output among the battery modules  111  in accordance with the ratios of the remaining capacities Q, that is, capacity ratios 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               10 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     kQ 
                   
                   = 
                   
                     
                       
                         
                           Q 
                           k 
                         
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             n 
                           
                           
                             Q 
                             k 
                           
                         
                       
                       ⨯ 
                       
                         n 
                         m 
                       
                       ⨯ 
                       P 
                     
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Subsequently, the charge and discharge control device  120  divides output among the battery modules  111 -( n +1) to  111 - m . When it is assumed that output is divided among the battery modules  111 -( n +1) to  111 - m  in accordance with resistance ratios, the charge and discharge control device  120  divides current among the battery modules  111 . The output of the battery modules  111 -( n +1) to  111 - m  is expressed as P−ΣP kQ  that is obtained by subtracting the output ΣP kQ  of the battery modules  111 - 1  to  111 - n  from the output P. Thus, a value obtained by dividing the output P−ΣP kQ  of the battery modules  111 -( n +1) to  111 - m  by the voltage V is each of currents I n+1  to I m  flowing through the battery modules  111 -( n +1) to  111 - m , respectively. The currents I n+1  to I m  can be expressed as in formula (11). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               11 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     
                       n 
                       + 
                       
                         1 
                         ~ 
                         m 
                       
                     
                   
                   = 
                   
                     
                       
                         P 
                         - 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             n 
                           
                           
                             P 
                             kQ 
                           
                         
                       
                       V 
                     
                     ⁢ 
                        
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Thus, the current I k  flowing through the k-th battery module k out of the battery modules  111 -( n +1) to  111 - m  can be expressed as in formula (12). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               12 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     k 
                   
                   = 
                   
                     
                       
                         1 
                         
                           R 
                           k 
                         
                       
                       ⨯ 
                       
                         1 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               
                                 n 
                                 + 
                                 1 
                               
                             
                             m 
                           
                           
                             1 
                             
                               R 
                               k 
                             
                           
                         
                       
                       ⨯ 
                       
                         I 
                         
                           n 
                           + 
                           
                             1 
                             ~ 
                             m 
                           
                         
                       
                     
                     ⁢ 
                        
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The charge and discharge control device  120  divides the current I k  among the battery modules  111  as in formula (12), and calculates an output P kR  to be divided among the battery modules  111  by obtaining a product of the current I k  and a voltage V k  of each battery module  111  as in formula (13). 
       [Formula 13] 
         P   kR   =I   k ×V k ( W )   (13)
 
     The charge and discharge control device  120  determines the output P n  of the battery module  111 - n , which is a reference module, in accordance with a resistance ratio, but the output P n  is not limited thereto. The charge and discharge control device  120  may determine the output P n  of the battery module  111 - n  from an output obtained by subtracting the output of the battery modules  111 - 1  to  111 -( n −1) and the output of the battery modules  111 -( n +1) to  111 - n  from the output P of the entire battery system  110 . 
     In the example of  FIG.  6   , the charge and discharge control device  120  performs division of output on a group of battery modules among which output is divided in accordance with capacity ratios and the battery module  111 - n  with the central module number collectively, and on a group of battery modules among which output is divided in accordance with resistance ratios collectively. However, the division method is not limited thereto. The charge and discharge control device  120  may determine an output of the battery module  111 - n  with the central module number and outputs of the respective battery modules  111 , among which output is to be divided in accordance with capacity ratios or resistance ratios, on a one-to-one basis. 
       FIG.  7    is a second diagram explaining a method for dividing output among the battery system  110  constituted by m battery modules  111  performed by the charge and discharge control device  120  according to the embodiment. In the example of  FIG.  7   , the charge and discharge control device  120  calculates each output to be assigned from a sum of an output required of the battery module  111 - n  with the central module number and an output required for the target one of the battery modules  111 . Specifically, when the charge and discharge control device  120  performs division in accordance with capacity ratios, because the output required of the battery system  110  is P, the output first assigned to the battery module  111 - n  and the battery module  111 - 1  that is the target battery module, among, m battery modules  111  becomes P/m+P/m=2P/m. The charge and discharge control device  120  assigns an output. P 1  to the battery module  111 - 1  in accordance with the capacity ratio on the basis of the obtained output as expressed by formula (14). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               14 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     1 
                   
                   = 
                   
                     
                       
                         
                           Q 
                           1 
                         
                         
                           
                             Q 
                             1 
                           
                           + 
                           
                             Q 
                             n 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           P 
                         
                         m 
                       
                     
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In the charge and discharge control device  120 , the output of the battery module  111 - n  and the battery module  111 - 2 , to which an output is to be assigned next, is (P−P 1 )/(m−1)+(P−P 1 )/(m−1)=2(P−P 1 )/(m−1) obtained by addition of (P−P 1 )/(m−1). (P−P 1 )/(m−1) is obtained by dividing, among m−1 battery modules  111 , a result of subtracting the output P 1  assigned to the battery module  111 - 1  from the output P. The charge and discharge control device  120  assigns an output P 2  to the battery module  111 - 2  is accordance with the capacity ratio on the basis of the obtained output as expressed by formula (15). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               15 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     2 
                   
                   = 
                   
                     
                       
                         
                           Q 
                           2 
                         
                         
                           
                             Q 
                             2 
                           
                           + 
                           
                             Q 
                             n 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               P 
                               - 
                               
                                 P 
                                 1 
                               
                             
                             ) 
                           
                         
                         
                           m 
                           - 
                           1 
                         
                       
                     
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In a similar manner, the charge and discharge control device  120  assigns an output P n−1  to a battery module  111 -( n −1) in accordance with a capacity ratio as expressed by formula (16). In formula (16), a part with Σ on the right side is expressed as in formula (17). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               16 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       n 
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           Q 
                           
                             n 
                             - 
                             1 
                           
                         
                         
                           
                             Q 
                             
                               n 
                               - 
                               1 
                             
                           
                           + 
                           
                             Q 
                             n 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               P 
                               - 
                               
                                 
                                   ∑ 
                                   
                                     k 
                                     = 
                                     1 
                                   
                                   
                                     n 
                                     - 
                                     2 
                                   
                                 
                                 
                                   P 
                                   k 
                                 
                               
                             
                             ) 
                           
                         
                         
                           m 
                           - 
                           
                             ( 
                             
                               n 
                               - 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               17 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       
                         n 
                         - 
                         2 
                       
                     
                     
                       P 
                       k 
                     
                   
                   = 
                   
                     
                       P 
                       1 
                     
                     + 
                     
                       
                         P 
                         2 
                       
                       ⁢ 
                           
                       … 
                     
                     + 
                     
                       P 
                       
                         n 
                         - 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Next, a method of dividing output according to resistance ratios on a one-to-one basis performed by the charge and discharge control device  120  will be described. In the case where the battery modules  111  of the battery system  110  are connected in parallel, the charge and discharge control device  120  divides current. The charge and discharge control device  120  can calculate currents I n  to I m  assigned to battery modules  111 - n  to  111 - m , respectively, among the m battery modules  111  of the battery system  110  such that a power obtained by subtracting the outputs of the battery modules  111 - 1  to  111 -( n −1) from the output P of the entire battery system  110  is divided by the voltage V of the battery modules  111 - n  to  111 - m  as expressed by formula (18). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               18 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     
                       n 
                       ~ 
                       m 
                     
                   
                   = 
                   
                     
                       
                         P 
                         - 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             
                               n 
                               - 
                               1 
                             
                           
                           
                             P 
                             k 
                           
                         
                       
                       V 
                     
                     ⁢ 
                        
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     The charge and discharge control device  120  can divide current among the battery module  111 - n , the battery module  111 -( n +1), and the battery module  111 - k  as expressed by formula (19), formula (20), and formula (21), respectively, in a manner similar to formulas (14) to (16) of division in accordance with capacity ratios. 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               19 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     n 
                   
                   = 
                   
                     
                       
                         
                           R 
                           n 
                         
                         
                           
                             R 
                             n 
                           
                           + 
                           
                             R 
                             m 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           
                             I 
                             
                               n 
                               ~ 
                               m 
                             
                           
                         
                         
                           m 
                           - 
                           
                             ( 
                             
                               n 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                        
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               20 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     
                       n 
                       + 
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           
                             n 
                             + 
                             1 
                           
                         
                         
                           
                             R 
                             
                               n 
                               + 
                               1 
                             
                           
                           + 
                           
                             R 
                             m 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 I 
                                 
                                   n 
                                   ~ 
                                   m 
                                 
                               
                               - 
                               
                                 I 
                                 n 
                               
                             
                             ) 
                           
                         
                         
                           
                             ( 
                             
                               m 
                               - 
                               1 
                             
                             ) 
                           
                           - 
                           
                             ( 
                             
                               n 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                        
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               21 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     k 
                   
                   = 
                   
                     
                       
                         
                           R 
                           k 
                         
                         
                           
                             R 
                             k 
                           
                           + 
                           
                             R 
                             m 
                           
                         
                       
                       ⨯ 
                       
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 I 
                                 
                                   n 
                                   ~ 
                                   m 
                                 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     n 
                                   
                                   
                                     k 
                                     - 
                                     1 
                                   
                                 
                                 
                                   I 
                                   
                                     j 
                                       
                                   
                                 
                               
                             
                             ) 
                           
                         
                         
                           
                             ( 
                             
                               m 
                               - 
                               k 
                               + 
                               n 
                             
                             ) 
                           
                           - 
                           
                             ( 
                             
                               n 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                         
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     The charge and discharge control device  120  can assign the output P kR  to the battery module  111 - k  by obtaining a product of the current I k  of the battery module  111 - k  assigned as expressed by the formula (21) and the voltage V k  of the battery module  111 - k , for example. 
     Next, a method for dividing output on the basis of the comparison result of parameters performed by the output control unit  127  of the charge and discharge control device  120  will be described. The output control unit  127  first selects a battery module  111  to be a reference among the battery modules  111 . While the output control unit  127  may determine the battery module  111  to be a reference in any manner from the battery system  110 , the output control unit  127  selects a battery module  111  having a SOC the value of which is the closest to the average SOC among the battery modules  111  included in the battery system  110  as the battery module  111 - n  to be the reference herein. Hereinafter, a method of assigning an output by the output control unit  127  will be specifically described assuming that a battery module  111  for which the output control unit  127  determines an output is the battery module  111 - 1 . 
     The output control unit  127  compares the remaining capacity Q n , the charge state SOC n , and the resistance R n  of the battery module  111 - n  with the remaining capacity Q 1 , the charge state SOC 1 , and the resistance R 1  of the battery module  111 - 1  to determine the larger or smaller of ones of the respective parameters. The number of comparison patterns is 2{circumflex over ( )}3=8. The output control unit  127  performs similar comparison between the battery module  111 - n  and the other battery modules  111 , and determines assignment of an output to each of the battery modules  111 . Hereinafter, for simplicity of explanation, it is assumed that the battery system  110  is constituted by two battery modules, which are the battery module  111 - 1  and the battery module  111 - n , and a method of assigning an output based on the magnitudes of the respective parameters performed by the output control unit  127  will be described. As methods for dividing required output for efficiently using the battery system  110 , a method of division in accordance with capacity ratios and a method of division to reduce Joule heat can be considered. 
     The method of division in accordance with capacity ratios is a method of dividing the required output P in accordance with the ratios of the remaining capacities Q. For example, when an output to be assigned to the battery module  111 - 1  is represented by P 1  and the output to be assigned to the battery module  111 - n  is represented by P n , the relation of formula (22) is satisfied. The output control unit  127  determines the output P 1  as expressed by formula (23), and determines the output P n  as expressed by formula (24). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               22 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   P 
                   = 
                   
                     
                       P 
                       1 
                     
                     + 
                     
                       
                         P 
                         n 
                       
                       ⁢ 
                           
                       
                         ( 
                         W 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               23 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     1 
                   
                   = 
                   
                     
                       
                         Q 
                         1 
                       
                       
                         
                           Q 
                           1 
                         
                         + 
                         
                           Q 
                           n 
                         
                       
                     
                     ⁢ 
                     P 
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               24 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     n 
                   
                   = 
                   
                     
                       
                         Q 
                         n 
                       
                       
                         
                           Q 
                           1 
                         
                         + 
                         
                           Q 
                           n 
                         
                       
                     
                     ⁢ 
                     P 
                     ⁢ 
                         
                     
                       ( 
                       W 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     In the method of division to reduce Joule heat as well, the output P 1  of the battery module  111 - 1  and the output P n  of the battery module  111 - n  satisfy the aforementioned relation of formula (22). In addition, when controlled currents of the battery modules  111 - 1  and  111 - n  are represented by I 1b  and I nb , respectively, the joule heat of the battery system  110  can be expressed by formula (25). 
       [Formula 25] 
         P=I   1b   2   R   1   +I   nb   2   R   n ( W )   (25)
 
     With the configuration in which the battery modules  111  are connected in series or in parallel with the DC-DC converters  114  therebetween, the battery system  110  can control the currents on the battery module  111  side of a DC-DC converter  114  relatively freely by controlling the switching elements SW 11  to SW 14  of the bridge circuit  306  on the device  130  side thereof. Note that the total current I of the battery system  110  is a sum of currents to be assigned to the battery modules  111  when the battery modules  111  are connected in parallel with each other. When the battery modules  111  are connected in series, the total current I is the same on the device  130  side of the DC-DC converter  114 , and is assumed to be divided among the battery modules  111  in a manner similar to the case of parallel connection. Thus, the relation of formula (26) is satisfied. 
       [Formula 26] 
         I=I   1b   +I   nb ( A )   (26)
 
     To reduce Joule heat, the output control unit  127  determines a current I 1b  to be assigned to the battery module  111 - 1  as in formula (27), and determines a current I nb  to be assigned to the battery module  111 - n  as in formula (28). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               27 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     
                       1 
                       ⁢ 
                       b 
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           n 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             n 
                           
                         
                       
                       ⨯ 
                       I 
                     
                     ⁢ 
                         
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               28 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     nb 
                   
                   = 
                   
                     
                       
                         
                           R 
                           1 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             n 
                           
                         
                       
                       ⨯ 
                       I 
                     
                     ⁢ 
                         
                     
                       ( 
                       A 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     The output control unit  127  can calculate the output P 1  of the battery module  111 - 1  by obtaining a product of the voltage V 1b  and the current I 1b  of the battery module  111 - 1  as expressed by formula (29), and calculate the output P n  of the battery module  111 - n  by obtaining a product of the voltage V nb  and the current I nb  of the battery module  111 - n  as expressed by formula (30). 
       [Formula 29] 
         P   1 =V 1b   ×I   1b ( W )   (29)
 
       [Formula 30] 
         P   n =V nb   ×I   nb ( W )   (30)
 
     Next, methods of dividing output performed by the output control unit  127  of the charge and discharge control device  120  in the aforementioned eight patterns of comparison of parameters will be described. Note that, in the description below, the output control unit  127  of the charge and discharge control device  120  is assumed to divide a required output of 100 [W] among two battery modules  111 . 
     A case of pattern 1: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≥R n  will be described.  FIG.  8    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 1: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≥R n .  FIG.  8    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is smaller than the charge state SCC 1  of the battery module  111 - 1 , that is, SOC 1 ≥SOC n , and Q 1 ≥Q n  and R 1 ≥R n . Note that, in  FIG.  8   , for simplicity of description, the battery module  111 - 1  is described as module  1 , and the battery module  111 - n  is described as module n. The same applies in the figure of each pattern mentioned below. In addition,  FIG.  9    is a graph illustrating an example of a discharge curve of the battery module  111 - 1  when the output control unit  127  of the charge and discharge control device  120  according to the embodiment divides output in pattern 1.  FIG.  10    is a graph illustrating an example of a discharge curve of the battery module  111 - n  when the output control unit  127  of the charge and discharge control device  120  according to the embodiment divides output in pattern 1. 
     When division in accordance with capacity ratios is performed in the condition of pattern 1, the output control unit  127  calculates the output P 1q  of the battery module  111 - 1  as in formula (31), and calculates the output of the battery module  111 - n  as in formula (32). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               31 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       1 
                       ⁢ 
                       q 
                     
                   
                   = 
                   
                     
                       
                         
                           Q 
                           1 
                         
                         
                           
                             Q 
                             1 
                           
                           + 
                           
                             Q 
                             n 
                           
                         
                       
                       ⁢ 
                       P 
                     
                     = 
                     
                       
                         
                           80 
                           
                             80 
                             + 
                             25 
                           
                         
                         ⨯ 
                         100 
                       
                       = 
                       
                         76.19 
                         W 
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               32 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     nq 
                   
                   = 
                   
                     
                       
                         
                           Q 
                           n 
                         
                         
                           
                             Q 
                             1 
                           
                           + 
                           
                             Q 
                             n 
                           
                         
                       
                       ⁢ 
                       P 
                     
                     = 
                     
                       
                         
                           25 
                           
                             80 
                             + 
                             25 
                           
                         
                         ⨯ 
                         100 
                       
                       = 
                       
                         23.81 
                            
                         W 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     The hour of use of the battery module  111 - 1  when the output P 1q  is as expressed by formula (31) is expressed by formula (33), and the hour of use of the battery module  111 - n  when the output P nq  is as expressed by formula (32) is expressed by formula (34). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               33 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
                       Hour 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       use 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       battery 
                       ⁢ 
                           
                       module 
                       ⁢ 
                           
                       111 
                     
                     - 
                     1 
                   
                   = 
                   
                     
                       80 
                       76.19 
                     
                     = 
                     
                       1.05 
                       
                         ( 
                         h 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               34 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
                       Hour 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       use 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       battery 
                       ⁢ 
                           
                       module 
                       ⁢ 
                           
                       111 
                     
                     - 
                     n 
                   
                   = 
                   
                     
                       25 
                       23.81 
                     
                     = 
                     
                       1.05 
                       
                         ( 
                         h 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     In the case of performing division to reduce Joule heat in the condition of pattern 1, when the voltages of the battery modules  111 - 1  and  111 - n  are each assumed to be 20 V, the current flowing through the battery modules  111 - 1  and  111 - n  is 100 [W]÷20 [V]=5 [A]. Accordingly, the output control unit  127  calculates the current I 1b  of the battery module  111 - 1  as in formula (35), and calculates the current I nb  of the battery module  111 - n  as in formula (36). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               35 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     
                       1 
                       ⁢ 
                       b 
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           n 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             n 
                           
                         
                       
                       ⨯ 
                       I 
                     
                     = 
                     
                       
                         
                           5 
                           
                             10 
                             + 
                             5 
                           
                         
                         ⨯ 
                         I 
                       
                       = 
                       
                         1.67 
                             
                         
                           ( 
                           A 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               36 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     nb 
                   
                   = 
                   
                     
                       
                         
                           R 
                           1 
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             n 
                           
                         
                       
                       ⨯ 
                       I 
                     
                     = 
                     
                       
                         
                           10 
                           
                             10 
                             + 
                             5 
                           
                         
                         ⨯ 
                         I 
                       
                       = 
                       
                         3.33 
                             
                         
                           ( 
                           A 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     The output control unit  127  calculates the output of the battery module  111 - 1  as in formula (37) using the current I 1b  calculated according to formula (35), and calculates the output P nj  of the battery module  111 - n  as in formula (38) using the current I nb  calculated according to formula (36). 
       [Formula 37] 
         P   1j =V 1b   ×I   1b =20×1.67=33.33( W )   (37)
 
       [Formula 38] 
         P   nj V nb   ×I   nb =20×3.33=66.67( W )   (38)
 
     The hour of use of the battery module  111 - 1  when the output P 1j  is as expressed by formula (37) is expressed by formula (39), and the hour of use of the battery module  111 - n  when the output P nj  is as expressed by formula (38) is expressed by formula (40). 
     
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               39 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
                       Hour 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       use 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       battery 
                       ⁢ 
                           
                       module 
                       ⁢ 
                           
                       111 
                     
                     - 
                     1 
                   
                   = 
                   
                     
                       80 
                       33.33 
                     
                     = 
                     
                       2.4 
                       
                         ( 
                         h 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
       
         
           
             [ 
             
               Formula 
               ⁢ 
                   
               40 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
                       Hour 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       use 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       battery 
                       ⁢ 
                           
                       module 
                       ⁢ 
                           
                       111 
                     
                     - 
                     n 
                   
                   = 
                   
                     
                       25 
                       66.67 
                     
                     = 
                     
                       0.375 
                       
                         ( 
                         h 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     When the out control unit  127  has performed division of output by the method to reduce Joule heat, because the battery module  111 - n  ends operation, that is, is completely discharged in 0.375 h, Joule heat can be reduced but power remains in the battery module  111 - 1 , and the efficiency of the battery system  110  is therefore lowered. Thus, when the comparison result corresponds to pattern 1, it is preferable that the output control unit  127  divide the required output in accordance with capacity ratios. 
     A case of pattern 2: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≤R n  will be described.  FIG.  11    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment an the case of pattern 2: SOC 1 ≥SOC n , Q 1 ≥Q n , and R 1 ≤R n .  FIG.  11    illustrates parameters in a case where the charge state SOC n  of the battery module  111 - n  is smaller than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≥SOC n , and Q 1 ≥Q n  and R 1 ≤R n . In pattern 2, the discharge curve of the battery module  111 - 1  is similar to that in  FIG.  9   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  10   . 
     When division in accordance with capacity ratios is performed in the condition of pattern 2, the output control unit  127  calculates the output of 76.19 [W] and the hour of use of 1.05 [h] of the battery module  111 - 1  and calculates the output of 23.81 [W] and the hour of use of 1.05 [h] of the battery module  111 - n  according to calculation methods similar to those described above. In addition, when division to reduce Joule heat is performed in the condition of pattern 2, the output control unit  127  calculates the output of 66.67 [W] and the hour of use of 1.2 [h] of the battery module  111 - 1  and calculates the output of 33.33 [W] and the hour of use of 0.75 [h] of the battery module  111 - n  according to calculation methods similar to those described above. When the output control unit  127  performs division of output to reduce Joule heat, because the battery module  111 - n  ends operation, that is, is completely discharged first, power remains in the battery module  111 - 1 , and the efficiency of the battery system  110  is therefore lowered. Thus, in the case where the comparison result corresponds to pattern 2, it is preferable that the output control unit  127  divide the required output in accordance with capacity ratios. 
     In the condition of R1≤Rn, however, the hour of use of the battery module  111 - 1  under division to reduce Joule heat may be longer than that of the battery module  111 - n  depending on the resistance ratio. For example, when the resistance R 1  of the battery module  111 - 1  is 2Ω and the resistance R n  of the battery module  111 - n  is 10Ω, the output and the hour of use of the battery module  111 - 1  are 83.33 [W] and 0.96 [h], respectively, and the output and the hour of use of the battery module  111 - n  are 16.67 [W] and 1.5 [h], respectively. In this case, when the battery system  110  is discharged at the outputs divided under control to reduce Joule heat by the output control unit  127 , the battery module  111 - 1  is discharged faster, and the magnitude relation of the SOCs of the battery modules is reversed. Thus, the output control unit  127  may perform the division to reduce Joule heat until the magnitude relation of the SOCs is reversed, and switch the control after the relation of the SOCs is reversed. A method for switching the control will be described later. 
     A case of pattern 3: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≥R n  will be described.  FIG.  12    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 3: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≥R n .  FIG.  12    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is smaller than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≥SOC n , and Q 1 ≤Q n  and R 1 ≥R n . In pattern 3, the discharge curve of the battery module  111 - 1  is similar to that in  FIG.  9   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  10   . 
     In the case of division in accordance with capacity ratios in the condition of pattern 3, the output control unit  127  calculates the output of 44.44 [W] and the hour of use of 0.9 [h] of the battery module  111 - 1  and calculates the output of 55.56 [W] and the hour of use of 0.9 [h] of the battery module  111 - n  according to calculation methods similar to those described above. In addition, when division to reduce Joule heat is performed in the condition of pattern 3, the output control unit  127  calculates the output of 33.33 [W] and the hour of use of 1.2 [h] of the battery module  111 - 1  and calculates the output of 66.67 [W] and the hour of use of 0.75 [h] of the battery module  111 - n  according to calculation methods similar to those described above. When the output control unit  127  performs division of output to reduce Joule heat, because the battery module  111 - n  ends operation, that is, is completely discharged first, power remains in the battery module  111 - 1 , and the efficiency of the battery system  110  is therefore lowered. Thus, when the comparison result corresponds to pattern 3, it is preferable that the output control unit  127  divide the required output in accordance with capacity ratios. 
     A case of pattern 4: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≤R n  will be described.  FIG.  13    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 4: SOC 1 ≥SOC n , Q 1 ≤Q n , and R 1 ≤R n .  FIG.  13    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is smaller than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≥SOC n , and Q 1 ≤Q n  and R 1 ≤R n . In pattern 4, the discharge curve of the battery module  111 - 1  similar to that in  FIG.  9   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  10   . 
     When division in accordance with capacity ratios is performed in the condition of pattern 4, the output control unit  127  calculates the output of 44.44 [W] and the hour of use of 0.9 [h] of the battery module  111 - 1  and calculates the output of 55.56 [W] and the hour of use of 0.9 [h] of the battery module  111 - n  according to calculation methods similar to those described above. In addition, in the case of division to reduce Joule heat in the condition of pattern 4, the output control unit  127  calculates the output of 66.67 [W] and the hour of use of 0.6 [h] of the battery module  111 - 1  and calculates the output of 33.33 [W] and the hour of use of 1.5 [h] of the battery module  111 - n  according to calculation methods similar to those described above. When the comparison result corresponds to pattern 4, because the hour of use of the battery module  111 - 1  becomes shorter and the difference of the battery module  111 - 1  in the SOC from the battery module  111 - n  can be made smaller, the output control unit  127  performs division of output to reduce Joule heat. Note that the magnitude relation of the SOCs of the battery modules changes through use. A method of control when the magnitude relation of the SOCs changes will be described later. 
     A case of pattern 5: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≥R n  will be described.  FIG.  14    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 5: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≥R n .  FIG.  14    illustrates parameters in a case where the charge state SOC n  of the battery module  111 - n  is larger than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≤SOC n , and Q 1 ≥Q n  and R 1 ≥R n .  FIG.  15    is a graph illustrating an example of a discharge curve of the battery module  111 - 1  when the output control unit  127  of the charge and discharge control device  120  according to the embodiment divides output in pattern 5.  FIG.  16    is a graph illustrating an example of a discharge curve of the battery module  111 - n  when the output control unit  127  of the charge and discharge control device  120  according to the embodiment divides output in pattern 5. 
     Because the output of the battery module  111 - n  having the higher SOC becomes larger and the hour of use of the battery module  111 - n  becomes shorter in the division of output to reduce Joule heat than that in the division in accordance with capacity ratios, the output control unit  127  performs the division of output to reduce Joule heat. Note that the magnitude relation of the SOCs of the battery modules changes as a result of use. A method of control when the magnitude relation of the SOCs changes will be described later. 
     A case of pattern 6: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≤R n  will be described.  FIG.  17    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 6: SOC 1 ≤SOC n , Q 1 ≥Q n , and R 1 ≤R n .  FIG.  17    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is larger than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≤SOC n , and Q 1 ≥Q n  and R 1 ≤R n . In pattern 6, the discharge curve of the battery module  111 - 1  is similar to that in  FIG.  15   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  16   . 
     Because the output of the battery module  111 - n  having the higher SOC becomes smaller and the hour of use of the battery module  111 - n  becomes longer in the division of output to reduce Joule heat, the difference between the SOCs will not decrease. Thus, the output control unit  127  performs the division of output in accordance with capacity ratios. 
     A case of pattern 7: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≥R n  will be described.  FIG.  18    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 7: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≥R n .  FIG.  18    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is larger than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≤SOC n , and Q 1 ≤Q n  and R 1 ≥R n . In pattern 7, the discharge curve of the battery module  111 - 1  is similar to that in  FIG.  15   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  16   . 
     In a manner similar to the case of pattern 6, because the output of the battery module  111 - n  having the higher SOC becomes smaller and the hour of use of the battery module  111 - n  becomes longer in the division of output to reduce Joule heat, the difference between the SOCs will not decrease. Thus, the output control unit  127  performs the division of output in accordance with capacity ratios. 
     A case of pattern 8: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≤R n  will be described.  FIG.  19    is a table illustrating an example of division of output performed by the output control unit  127  of the charge and discharge control device  120  according to the embodiment in the case of pattern 8: SOC 1 ≤SOC n , Q 1 ≤Q n , and R 1 ≤R n .  FIG.  19    illustrates parameters when the charge state SOC n  of the battery module  111 - n  is larger than the charge state SOC 1  of the battery module  111 - 1 , that is, SOC 1 ≤SOC n , and Q 1 ≤Q n  and R 1 ≤R n . In pattern 8, the discharge curve of the battery module  111 - 1  is similar to that in  FIG.  15   , and the discharge curve of the battery module  111 - n  is similar to that in  FIG.  16   . 
     In a manner similar to the cases of pattern 6 and pattern 7, because the output of the battery module  111 - n  having the higher SOC becomes smaller and the hour of use of the battery module  111 - n  becomes longer in the division of output to reduce Joule heat, the difference between the SOCs will not decrease. Thus, the output control unit  127  performs the division of output in accordance with capacity ratios. 
     In the examples of pattern 1 to pattern 8 described above, the parameters are determined in any way and the output control unit  127  performs division of output. However, the control method varies depending on the ratios of the resistances R. Thus, the output control unit  127  is preferably used for division in accordance with capacity ratios when the discharge time of a battery module  111  having a high SOC is long, and is preferably used for division to reduce Joule heat when the discharge time of a battery module  111  having a high SOC is short. 
     In addition, although comparison of the parameters is performed at the start of control in the examples of pattern 1 to pattern 8 described above, the output control unit  127  need not keep the same method of division of output until the end of operation on the basis of the comparison result at the start of control because SOCs, remaining capacities Q, resistances R, and the like change with time. In other words, the output control unit  127  may switch the method of division of output at timing of SOC 1 =SOC n , Q 1 =Q n , or R 1 =R n  as charging or discharging progresses. 
       FIG.  20    is a diagram illustrating an example of discharge curves of the individual battery module  111 - 1  and  111 - n  when the output control unit  127  of the charge and discharge control device  120  according to the embodiment performs division of output in pattern 1. In  FIG.  20   , similarly to  FIG.  8    and the like, the battery module  111 - 1  is described as “module 1”, and the battery module  111 - n  is described as “module n” for simple description. The same applies to the figure of each pattern mentioned below. When the comparison result of parameters corresponds to the condition of pattern 1, the output control unit  127  can use both of the battery modules  111 - 1  and  111 - n  completely to the SOC of 0% at the end of operation with outputs obtained by division in accordance with capacity ratios determined at the start of control as illustrated in  FIG.  20   . Thus, when the comparison result of the parameters corresponds to the condition in pattern 1, the output control unit  127  need not change the method for dividing output from the start of the control until the end of operation. 
     Next, in the method of dividing output to reduce Joule heat when the comparison result of the parameters corresponds to the condition in pattern 4, assume a case where the output control unit  127  uses the battery module  111 - 1  with an output of 66.67 W for an hour of use of 0.6 h and the battery module  111 - n  with an output of 33.33 W for an hour of use of 1.5 h. In this case, because the battery system  110  detects end of discharge at the hour of use of 0.6 h of the battery module  111 - 1 , the discharge ends before the battery module  111 - n  is completely discharged. Note that, in the case of pattern 4, while the SOC 1  of the battery module  111 - 1  is higher than the SOC n  of the battery module  111 - n  at the start of control, the SOC n  of the battery module  1111 - n  becomes higher than the SOC 1  of the battery module  111 - 1  through use because the decreasing speed of the SOC 1  of the battery module  111 - 1  is higher. Thus, it is expected that the comparison result of the parameters at the start of control changes to the comparison result in pattern 8. In this case, the output control unit  127  switches the method for division of output from the method of dividing output to reduce Joule heat to the division in accordance with capacity ratios. As described above, because SOCs, remaining capacities Q, and resistances R change with time, the output control unit  127  controls charging and discharging by switching the control on division of output, that is, the method of division of output when the parameter comparison result changes. 
     Discharge curves of the battery modules  111 - 1  and  111 - n  when the output control unit  127  does not switch the method of dividing output and when the output control unit  127  switches the method of dividing output will be explained.  FIG.  21    is a diagram illustrating an example of discharge curves when the output control unit  127  of the charge and discharge control device  120  according to the embodiment does not switch the method of dividing output.  FIG.  22    is a diagram illustrating an example of discharge curves when the output control unit  127  of the charge and discharge control device  120  according to the embodiment switches the method of dividing output. 
       FIG.  21    illustrates a case where the output control unit  127  does not switched the method of dividing output from the start of control when the comparison result corresponds to pattern 4. In this case, as described above, because the battery system  110  detects end of discharge at the hour of use of 0.6 h of the battery module  111 - 1 , the discharge ends before the battery module  111 - n  is completely discharged. 
       FIG.  22    illustrates a case where the output control unit  127  has switched the method of dividing output 0.3 hours after the start of control when the comparison result corresponds to pattern 4. The SOC 1  of the battery module  111 - 1  and the SOC n  of the battery module  111 - n  become an equal value of 0.4 at 0.3 hours after the start of control. The output control unit  127  switches the method for dividing output to the division in accordance with capacity ratios so that the output of the battery module  111 - n  with a larger remaining capacity Q increases. As a result, the battery system  110  can completely discharge the battery module  111 - n.    
     As described above, the output control unit  127  compares the charge state of the battery module  111 - n , which is the reference, with the charge state of the other battery module  111 , and selects whether to divide output in accordance with capacity ratios or to divide output to reduce Joule heat. 
     When the charge state of the battery module  111 - n , which is the reference, is lower than the charge state of the other battery module  111 , and an output of the other battery module  111  obtained by the division to reduce Joule heat is larger than an output of the other battery module  111  determined by the division in accordance with capacity ratios, the output control unit  127  divides output to reduce Joule heat and performs control to reduce the Joule heat. When the charge states of the battery modules  111  have changed and the charge state of the battery module  111 - n , which is the reference, has become equal to the charge state of the other battery module  111 , the output control unit  127  switches to control of dividing output in accordance with capacity ratios. When the charge state of the battery module  111 - n , which is the reference, is lower than the charge state of the other battery module  111 , and an output of the other battery module  111  obtained by the division to reduce Joule heat is smaller than an output of the other battery module  111  determined by the division in accordance with capacity ratios, the output control unit  127  divides output in accordance with capacity ratios. 
     Furthermore, when the charge state of the battery module  111 - n , which is the reference, is higher than the charge state of the other battery module  111 , and an output of the battery module  111 - n , which is the reference, obtained by the division to reduce Joule heat is larger than an output of the battery module  111 - n  determined by the division in accordance with capacity ratios, the output control unit  127  divides output to reduce Joule heat and performs control to reduce the Joule heat. When the charge states of the battery modules  111  have changed and the charge state of the battery module  111 - n , which is the reference, has become equal to the charge state of the other battery module  111 , the output control unit  127  switches to control of dividing output in accordance with capacity ratios. When the charge state of the battery module  111 - n , which is the reference, is higher than the charge state of the other battery module  111 , and when an output of the battery module  111 - n , which is the reference, obtained by the division to reduce Joule heat is smaller than an output of the battery module  111 - n  determined by the division in accordance with capacity ratios, the output control unit  127  divides output in accordance with capacity ratios. 
     While the cases where the charge and discharge control device  120  performs discharge has been specifically described in the embodiment, the charge and discharge control device  120  is not limited thereto. The charge and discharge control device  120  can control division among the battery modules  111  during charging by similar control. During charging, the difference between a full-charge capacity and a remaining capacity is a chargeable capacity, and the charge and discharge control device  120  performs comparison by using the relation of the chargeable capacities instead of the remaining capacities. The output control unit  127  of the charge and discharge control device  120  compares the parameters of the battery module  111 - n , which is the reference, and switches between the division of output in accordance with capacity ratios and the division of output to reduce Joule heat as charging or discharging progresses. 
     In addition, while a case where the charge and discharge control device  120  controls the method of dividing output of the battery system  110  including two battery modules  111  has been described, the method of dividing output of a battery system  110  including three or more battery modules  111  can also be controlled by similar control. In addition, while the methods of dividing output during discharging performed by charge and discharge control device  120  are described in the present embodiment, a discharge control device that only performs control of discharge of the battery system  110 , may perform control by similar methods of dividing output during discharging. 
     The operation of the charge and discharge control device  120  will be described with reference to a flowchart,  FIG.  23    is a flowchart illustrating the operation of charge and discharge control performed by the charge and discharge control device  120  according to the embodiment. Upon starting charge and discharge control, the charge and discharge control device  120  obtains information on voltage, current, and capacity of each of the battery modules  111  from the DC-DC converters  114  (step S 1 ). Specifically, as described above, the current obtaining unit  121  obtains information on current, the voltage obtaining unit  123  obtains information on voltage, and the capacity obtaining unit  122  estimates full-charge capacity. The charge and discharge control device  120  estimates the SOC, which is a charge state, the resistance R, and the remaining capacity Q of each of the battery modules  111  by using the information on the voltage, current, and capacity (step S 2 ). Specifically, as described above, the SOC estimating unit  124  estimates the SOC that is a charge state, the resistance estimating unit  125  estimates the resistance R, and the remaining capacity estimating unit  126  estimates the remaining capacity Q. 
     In the charge and discharge control device  120 , the output control unit  127  compares the respective parameters of the individual battery modules  111  estimated in step S 2 , that is specifically, the SOCs that are charge states, the remaining capacities Q, and the resistances R of the battery modules  111  (step S 3 ). The output control unit  127  calculates outputs assigned to the individual battery modules  111  on the basis of the comparison result in step S 3  (step S 4 ), generates output commands and transmits the output commands to the battery modules  111  (step S 5 ). If charging or discharging of the battery system  110  has not been completed (step S 6 : NO), the charge and discharge control device  120  returns the process to step S 1  and repeats the operation described above. If charging or discharging of the battery system  110  has been completed (step S 6 : Yes), the charge and discharge control device  120  terminates the charge and discharge control. 
     Effects produced by the control of division of output in the embodiment will be explained.  FIG.  24    is a first graph illustrating an effect produced by the charge and discharge control device  120  according to the embodiment. Here, assume a case where a first battery module has a remaining capacity Q of 50 Wh and a resistance R of 5Ω, and a second battery module has a remaining capacity Q of 40 Wh and a resistance R of 10Ω. In a comparative example in which a required output is divided into equal powers among the battery modules  111 , a capacity of 30 Wh of the first battery module cannot be used, and the performance of the battery system  110  is limited to that of a battery module  111  with a low SOC, thereby lowering the efficiency. In contrast, in the present control method, entire power of the battery modules  111  can be used, which can improve the efficiency of the battery system  110 . In addition, while an example of battery modules  111  having different characteristics have been described in the embodiment, degraded batteries of the same type can be used, which is expected to lower the cost of the battery system  110 . 
       FIG.  25    is a second graph illustrating an effect produced by the charge and discharge control device  120  according to the embodiment. Here, assume a case where a current of 5 A in total is divided among the first and second battery modules in the condition similar to that in  FIG.  24   . In a comparative example in which a required output is divided into equal powers among the battery modules  111 , a loss of 2.5 2 ×10=62.5 W occurs in the second battery module, and a loss of 2.5 2 ×5=31.3 W occurs in the first battery module. In contrast, in the present control method, because a current of 5 A is divided in accordance with resistance ratios, a loss of 3.33 2 ×5=55.4 W occurs in the first battery modules, and a loss of 1.67 2 ×10=27.9 W occurs in the second battery module. In this manner, the losses of the battery system  110  can be reduced in the present control method as compared with the comparative example. 
     Next, a hardware configuration of the charge and discharge control device  120  will be described. In the charge and discharge control device  120 , all the components from the current obtaining unit  121  to the output control unit  127  are implemented by processing circuitry. The processing circuitry may be constituted by a processor that executes programs stored in a memory and the memory, or may be dedicated hardware. 
       FIG.  26    is a diagram illustrating an example of a case where processing circuitry  200  included in the charge and discharge control device  120  according to the embodiment is constituted by a processor  201  and a memory  202 . When the processing circuitry  200  is constituted by the processor  201  and the memory  202 , the functions of the processing circuitry  200  of the charge and discharge control device  120  are implemented by software, firmware, or a combination of software and firmware. The software or firmware is described in the form of programs and stored in the memory  202 . The processing circuitry  200  implements the functions by reading and executing the programs stored in the memory  202  by the processor  201 . Specifically, the processing circuitry  200  includes the memory  202  for storing programs that results in execution of processes of the charge and discharge control device  120 . In other words, the programs cause a computer to execute the procedures and the methods of the charge and discharge control device  120 . 
     Note that the processor  201  may be a central processing unit (CPU), a processing device, a computing device, a microprocessor, a microcomputer, a digital signal processor (DSP), or the like. In addition, the memory  202  is a nonvolatile or volatile semiconductor memory such as a random access memory (RAM), a read only memory (ROM), a flash memory, an erasable programmable ROM (EPROM), or an electrically EPROM (EEPROM: registered trademark), a magnetic disk, a flexible disk, an optical disk, a compact disc, a mini disc, a digital versatile disc (DVD) or the like, for example. 
       FIG.  27    is a diagram illustrating an example of a case where the processing circuitry  203  included in the charge and discharge control device  120  according to the embodiment is constituted by dedicated hardware. When the processing circuitry  203  is constituted by dedicated hardware, the processing circuitry  203  illustrated in  FIG.  27    is a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or a combination thereof, for example. The functions of the charge and discharge control device  120  may be implemented separately by the processing circuitry  203  function by function, or may be implemented collectively by the processing circuitry  203 . 
     Note that some of the functions of the charge and discharge control device  120  may be implemented by dedicated hardware, and others may be implemented by software or firmware. As described above, the processing circuitry is capable of implementing the above-described functions by dedicated hardware, software, firmware, or a combination thereof. 
     As described above, according to the embodiment, the charge and discharge control device  1120  obtains information on the states of the battery modules  111 - 1  to  111 - m  of the battery system  110  from the battery modules  111 - 1  to  111 - m , estimates parameters indicating the states of the battery modules  111 - 1  to  111 - m , and controls division of output among the battery modules  111 - 1  to  111 - m  so that the differences between the charge states of the battery modules  111 - 1  to  111 - m  become smaller on the basis of the comparison result of comparing the parameters. As a result, the charge and discharge control device  120  can reduce or prevent decrease in the efficiency of the battery system  110  including the battery modules  111 - 1  to  111 - m  having different characteristics from each other. The charge and discharge control device  120  assigns a high output to a battery module  111  having a low resistance R, and can thus charge and discharge the battery system  110  constituted by the battery modules  111  having different characteristics from each other without lowering the efficiency of the battery system  110 . 
     In addition, under the control performed by the charge and discharge control device  120 , the charge and discharge control system  100  can have a configuration in which the battery system  110  includes battery modules  111  with low costs, and a lower cost of the battery system  110  is therefore expected. Furthermore, even when a failure or the like occurs, it is not necessary to replace the entire battery system  110  and it is sufficient that only a battery module  111  is replaced, which can improve the maintenance efficiency of the charge and discharge control system  100 . 
     The configurations presented in the embodiment above are examples, and can be combined with other known technologies or with each other, or can be partly omitted or modified without departing from the gist. 
     REFERENCE SIGNS LIST 
       100  charge and discharge control system;  110  battery system;  111 - 1  to  111 - m  battery module;  112  cell;  113  BMU;  114  DC-DC converter;  115  unit;  120  charge and discharge control device;  121  current obtaining unit;  122  capacity obtaining unit;  123  voltage obtaining unit;  124  SOC estimating unit;  125  resistance estimating unit;  126  remaining capacity estimating unit;  127  output control unit;  128  obtainment unit;  129  estimation unit;  130  device;  301 ,  309  voltmeter;  302 ,  308  ammeter;  303 ,  307  capacitor;  304 ,  306  bridge circuit;  305  transformer;  310  controller; SW 1  to SW 4 , SW 11  to SW 14  switching element.