Patent Publication Number: US-10790556-B2

Title: Battery system

Description:
This nonprovisional application is based on Japanese Patent Application No. 2018-004919 filed on Jan. 16, 2018 with the Japan Patent Office, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     Field 
     The present disclosure relates to battery systems, and more particularly to a battery system including a battery pack configured to include a plurality of secondary batteries connected in parallel. 
     Description of the Background Art 
     Japanese Patent Laying-Open No. 2006-138750 discloses a battery monitoring apparatus for monitoring the state of a secondary battery block (battery pack). The secondary battery block is formed of a plurality of parallel cell blocks connected in series. Each of the plurality of parallel cell blocks is formed of a plurality of cells (secondary batteries) connected in parallel. 
     In this battery monitoring apparatus, an amount of voltage change in each parallel cell block before and after energization is calculated, and an amount of current change in the secondary battery block before and after energization is calculated. Then, internal resistance of each parallel cell block is calculated from the amount of voltage change and the amount of current change calculated, to determine an abnormality of the cells based on the calculated internal resistance. 
     SUMMARY 
     In the battery monitoring apparatus described above, although an abnormality of the cells can be determined, no consideration is given to current variation caused by temperature variation that occurs between the cells of a parallel cell block. When temperature variation occurs between cells of a parallel cell block, resistance variation between the cells increases, resulting in increased current variation between the cells. As a result, even if battery protection control is performed based on a total current or an average current flowing in the parallel cell block, for example, it may not be possible to protect a cell in which a relatively large current flows in the parallel cell block. 
     An object of the present disclosure is to provide a battery system capable of implementing appropriate battery protection control in consideration of current variation caused by temperature variation between a plurality of secondary batteries connected in parallel. 
     A battery system according to one aspect of the present disclosure includes: a battery pack formed of a plurality of secondary batteries connected in parallel; a cooling device configured to supply a cooling medium to the battery pack; and a controller configured to estimate current variation between the plurality of secondary batteries caused by temperature variation between the plurality of secondary batteries. The plurality of secondary batteries include a first battery and a second battery. The controller is configured to calculate a first temperature index having correlation with a temperature of the first battery, using an amount of heat generated by the first battery, the first battery having a relatively low temperature of the plurality of secondary batteries, and a cooled amount of the first battery by the cooling device. The controller is configured to set a temperature additional value using information related to a heat generating state of the battery pack. The controller is configured to calculate a second temperature index having correlation with a temperature of the second battery, using an amount of heat generated by the second battery, the second battery having a temperature calculated by adding the temperature additional value to the temperature of the first battery, and a cooled amount of the second battery by the cooling device. The controller is configured to calculate an evaluation value indicating a degree of the temperature variation by subtracting the first temperature index from the second temperature index. The controller is configured to estimate a degree of the current variation using the calculated evaluation value and a temperature of the battery pack. 
     Accordingly, the second temperature index is calculated using the set temperature additional value, thereby allowing the evaluation value to be calculated with a high degree of accuracy. As a result, the current variation between the plurality of secondary batteries connected in parallel caused by the temperature variation between the plurality of secondary batteries can be estimated with a high degree of accuracy. Thus, appropriate battery protection control can be implemented on the plurality of secondary batteries. 
     In one embodiment, the information related to a heat generating state of the battery pack is information about a current in the battery pack. The controller is configured to set the temperature additional value to a higher value, when a root-mean-square value of the current is higher, than a value which is set when the root-mean-square value is lower. 
     Accordingly, the temperature additional value can be set appropriately in accordance with the heat generating state of the battery pack based on the root-mean-square value of the current. 
     In one embodiment, the first battery has the lowest temperature of the plurality of secondary batteries. The second battery has the highest temperature of the plurality of secondary batteries. The battery system further includes a detection device configured to detect the temperature of the first battery. The controller is configured to acquire the temperature of the first battery using the detection device, and to calculate the temperature of the second battery by adding the temperature additional value to the temperature of the first battery. 
     Accordingly, the evaluation value indicating the degree of the temperature variation can be calculated appropriately. 
     The foregoing and other objects, features, aspects and advantages of the present disclosure will become more apparent from the following detailed description of the present disclosure when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  schematically shows a configuration of a vehicle having mounted thereon a battery system according to an embodiment of the present disclosure. 
         FIG. 2  shows an example of a detailed configuration of a battery pack shown in  FIG. 1 . 
         FIG. 3  shows an example of temperature variations in the highest temperature cell and the lowest temperature cell of a plurality of cells connected in parallel. 
         FIG. 4  shows an example of relation between temperature and resistance of a cell. 
         FIG. 5  is a flowchart illustrating a procedure for estimating current variation between cells. 
         FIG. 6  is a map for determining a coefficient f used in an equation (1) and an equation (4). 
         FIG. 7  shows dependence of resistance of a cell on temperature. 
         FIG. 8  shows dependence of resistance of a cell on remaining capacity. 
         FIG. 9  shows a plurality of cells connected in parallel. 
         FIG. 10  is a map of maximum current correction gain G. 
         FIG. 11  shows relation between temperature and resistance of a cell. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An embodiment of the present disclosure will be described hereinafter in detail with reference to the drawings. It should be noted that the same or corresponding parts are designated by the same symbols in the drawings and will not be described repeatedly. 
       FIG. 1  schematically shows a configuration of a vehicle  1  having mounted thereon a battery system according to the embodiment of the present disclosure. In the following description, vehicle  1  is described as a hybrid vehicle as an example. 
     Referring to  FIG. 1 , vehicle  1  includes a battery system  2 , a PCU (Power Control Unit)  30 , MGs (Motor Generators)  41 ,  42 , an engine  50 , a power split device  60 , a drive shaft  70 , and a driving wheel  80 . 
     Battery system  2  includes a battery pack  10 , a monitoring unit  20 , a cooling device  24 , and an ECU (Electronic Control Unit)  100 . Cooling device  24  is a device for supplying a cooling medium (cooling air in the present embodiment) to battery pack  10 , and includes a duct  25 , a fan  26 , and a temperature sensor  27 . The cooling medium may be coolant. 
     Engine  50  is an internal combustion engine such as a gasoline engine or a diesel engine, which converts combustion energy generated by combustion of an air-fuel mixture into kinetic energy of a movable member such as a piston or a rotor, to thereby output motive power. Power split device  60  includes, for example, a planetary gear mechanism having three rotation shafts of a sun gear, a carrier and a ring gear. Power split device  60  transmits motive power output from engine  50  to MG  41  and driving wheel  80 . 
     MGs  41 ,  42  are each an AC rotating electrical machine, such as a three-phase AC synchronous motor having a permanent magnet embedded in a rotor. MG  41  is mainly used as a power generator driven by engine  50  through power split device  60 . Electric power generated by MG  41  is supplied to at least one of MG  42  and battery pack  10  through PCU  30 . 
     MG  42  mainly operates as a motor, and drives driving wheel  80  by receiving at least one of electric power from battery pack  10  and electric power generated by MG  41 . Driving power from MG  42  is transmitted to drive shaft  70 , and to driving wheel  80 . During braking or suppression of acceleration on a downslope by vehicle  1 , on the other hand, MG  42  operates as a power generator and regenerates electric power. Electric power generated by MG  42  is supplied to battery pack  10  through PCU  30 . 
     Battery pack  10  is configured to include a plurality of cells connected in parallel (the detailed configuration of which will be described later). Each cell is a secondary battery such as a lithium ion secondary battery or a nickel-metal hydride secondary battery. Battery pack  10  stores electric power for driving MGs  41 ,  42 . That is, battery pack  10  can supply electric power to MG  41  or MG  42  through PCU  30 . Battery pack  10  can also be charged by receiving generated electric power through PCU  30  during power generation of MGs  41 ,  42 . 
     Monitoring unit  20  includes a voltage detection device  21 , a current detection device  22 , and a temperature detection device  23 . Voltage detection device  21  detects a voltage (hereinafter also referred to as “cell voltage”) VBi of the plurality of cells connected in parallel in battery pack  10 . Current detection device  22  detects a charge/discharge current IB in battery pack  10 . Temperature detection device  23  detects temperatures TB 1  to TBj of battery pack  10  using thermistors ( 1 ) to (j) provided at a plurality of locations in battery pack  10  and the like. 
     Duct  25  is a passage through which to supply the cooling air to battery pack  10 . Duct  25  is provided with fan  26 . Although fan  26  is provided on duct  25  at the air inlet side in this embodiment, fan  26  may be provided on duct  25  at the air outlet side. Fan  26  operates based on a control signal from ECU  100 , for example. Temperature sensor  27  detects a temperature TC of the cooling air supplied to battery pack  10  through duct  25 . 
     PCU  30  performs bidirectional power conversion between battery pack  10  and MG  41 , or bidirectional power conversion between battery pack  10  and MG  42 , based on a control signal from ECU  100 . PCU  30  is configured to control the states of MGs  41 ,  42  independently of each other, and can bring MG  41  into a regenerating (power generating) state, while bringing MG  42  into a power running state, for example. PCU  30  is configured to include, for example, two inverters provided to correspond to MGs  41 ,  42 , respectively, and a converter capable of boosting a DC voltage supplied to each inverter to a voltage equal to or higher than an output voltage from battery pack  10 . 
     ECU  100  is configured to include a CPU (Central Processing Unit)  102 , a memory (a ROM (Read Only Memory) and a RAM (Random Access Memory))  105 , and an input/output port (not shown) through which to input/output various signals. ECU  100  controls charge/discharge of battery pack  10  by controlling engine  50  and PCU  30  based on a signal received from each sensor or each detection device, and a program and a map stored in memory  105 . 
       FIG. 2  shows an example of a detailed configuration of battery pack  10  shown in  FIG. 1 . Referring to  FIG. 2 , in this battery pack  10 , a plurality of cells are connected in parallel to form a block (or a module), and a plurality of the blocks are connected in series to form battery pack  10 . Specifically, battery pack  10  includes blocks  10 - 1  to  10 -M connected in series, and each of blocks  10 - 1  to  10 -M includes N cells connected in parallel. 
     Voltage detection device  21  includes voltage sensors  21 - 1  to  21 -M. Voltage sensors  21 - 1  to  21 -M detect voltages of blocks  10 - 1  to  10 -M, respectively. That is, voltage sensor  21 - 1  detects a voltage VB 1  of the N cells forming block  10 - 1 . Similarly, voltage sensors  21 - 2  to  21 -M detect voltages VB 2  to VBM of the N cells forming blocks  10 - 2  to  10 -M, respectively. Current detection device  22  detects a current IB flowing in each of blocks  10 - 1  to  10 -M. That is, current detection device  22  detects a total current flowing in the N cells of each block. 
     In battery pack  10  configured to include the plurality of cells connected in parallel in this manner, temperature variation occurs between the plurality of cells connected in parallel (hereinafter referred to simply as “between the cells”). For example, there is variation in initial resistance (product variation) between the cells. Since a relatively large current flows in a cell having a relatively low resistance, the cell of lower initial resistance may have a relatively high temperature. The temperature variation also occurs depending on the arrangement of a cell (such as whether the cell is in the vicinity of the center or in the vicinity of an end within a case), or the cooling structure (such as the configuration of the cooling air passage) within the case. 
       FIG. 3  shows an example of temperature variations in the highest temperature cell and the lowest temperature cell of the plurality of cells connected in parallel. The highest temperature cell indicates a cell having the highest temperature of the plurality of cells connected in parallel. The lowest temperature cell indicates a cell having the lowest temperature of the plurality of cells connected in parallel. Referring to  FIG. 3 , lines L 1  and L 2  indicate temperature variation in the lowest temperature cell and temperature variation in the highest temperature cell, respectively, and a line L 3  indicates variation in a temperature difference ΔT between the highest temperature cell and the lowest temperature cell. When current IB starts to flow in battery pack  10  at time to, both cells start to increase in temperature. The temperature increases differently for each cell depending on the factors noted, causing temperature difference ΔT (temperature variation) to occur between both cells. 
     Since a cell having a higher temperature has a lower resistance than a cell having a lower temperature, increased temperature variation between the cells results in increased resistance variation between the cells. Since a relatively large current flows in a cell having a relatively low resistance, increased resistance variation between the cells results in increased current variation between the cells. 
       FIG. 4  shows an example of relation between temperature and resistance of a cell. Referring to  FIG. 4 , the horizontal axis indicates temperature Tce of a cell, and the vertical axis indicates resistance Rce of a cell. Temperature Tce and resistance Rce of a cell have such relation that resistance Rce decreases as temperature Tce increases, and the magnitude of resistance variation relative to temperature variation increases (the slope of a curve increases) as the temperature decreases. 
     A point P 1  indicates relation between temperature and resistance of the lowest temperature cell of the plurality of cells connected in parallel, and a point P 2  indicates relation between temperature and resistance of the highest temperature cell of the plurality of cells connected in parallel. Temperature difference ΔT (temperature variation) between the highest temperature cell and the lowest temperature cell causes a resistance difference ΔR (resistance variation) to occur between both cells. This resistance difference ΔR (resistance variation) in turn causes a current difference (current variation) to occur between the highest temperature cell and the lowest temperature cell. 
     In this manner, temperature variation between the cells results in increased current variation between the cells. As a result, even if battery protection control is performed using a total current (IB) and an average current (IB/N) flowing in the plurality of cells connected in parallel (block) without processing the currents, it may not be possible to protect a cell in which a relatively large current flows. 
     In battery system  2  according to this embodiment, current variation between the cells caused by temperature variation between the cells is estimated. 
     With regard to the temperature variation, it is practically difficult to measure the temperature variation by actually detecting the temperature for each cell. In this embodiment, therefore, the temperature of the highest temperature cell and the temperature of the lowest temperature cell are determined as described below. 
     Specifically, ECU  100  acquires a plurality of detection results using thermistors provided at a plurality of locations in battery pack  10 . ECU  100  determines a temperature (TBmin) of the lowest temperature cell using a detection result showing the lowest temperature from the plurality of detection results acquired. ECU  100  determines a temperature, calculated by adding a temperature additional value to the determined temperature of the lowest temperature cell, as the temperature of the highest temperature cell. In this embodiment, the temperature additional value indicates a maximum value of the temperature variation between the cells in battery pack  10 . 
     Here, assuming that the temperature additional value is a fixed value, for example, the temperature variation between the cells in battery pack  10  increases as an amount of heat generated in battery pack  10  increases, causing the temperature additional value to deviate from an appropriate value. As a result, the accuracy of estimation of the temperature of the highest temperature cell may be reduced. 
     In this embodiment, therefore, ECU  100  sets the temperature additional value using information related to a heat generating state of battery pack  10 . In this embodiment, the information related to a heat generating state of battery pack  10  is a current. ECU  100  sets the temperature additional value to a higher value, when a root-mean-square value of the current is higher, than a value which is set when the root-mean-square value is lower. Accordingly, the temperature additional value can be set appropriately. 
     ECU  100  calculates, for each of the highest temperature cell and the lowest temperature cell, a temperature index (Ftmax, Ftmin) having correlation with the cell temperature in consideration of heat generation and cooling of the cell. ECU  100  sets an evaluation function (ΔF) indicating the degree of the temperature variation between the cells by subtracting the temperature index (Ftmin) of the lowest temperature cell from the temperature index (Ftmax) of the highest temperature cell. 
     Since the magnitude of resistance variation relative to temperature variation increases as the temperature decreases, resistance difference ΔR (resistance variation) and the resultant current difference (current variation) between the cells may increase as the temperature decreases. In battery system  2  according to this embodiment, therefore, the degree of the current variation between the cells (maximum current correction gain) is estimated using, together with the evaluation function (ΔF), the temperature of battery pack  10  (as will be described later, the lowest temperature (TBmin) of temperatures TB 1  to TBj detected by temperature detection device  23  is used in this embodiment). 
     Referring now to  FIG. 5 , a process of estimating the current variation between the cells is described.  FIG. 5  is a flowchart illustrating a procedure for estimating the current variation between the cells. The process shown in this flowchart is repeated by ECU  100  shown in  FIG. 1  in a prescribed operation cycle dt for each block forming battery pack  10 . 
     In step (step is hereinafter referred to as S)  100 , ECU  100  acquires lowest temperature TBmin in battery pack  10  and temperature TC of the cooling air. ECU  100  acquires lowest temperature TBmin from the plurality of temperatures TB 1  to TBj detected using temperature detection device  23 . ECU  100  acquires temperature TC of the cooling air using temperature sensor  27 . 
     In S 102 , ECU  100  acquires an airflow volume of fan  26 . For example, ECU  100  may acquire the airflow volume of fan  26  based on a control command value to fan  26 , or may acquire the airflow volume of fan  26  based on power or a voltage supplied to fan  26 , or may acquire the airflow volume of fan  26  using a rotation speed sensor provided on fan  26 . 
     In S 104 , ECU  100  calculates a cooling coefficient h. ECU  100  sets cooling coefficient h using the airflow volume of fan  26 , and a map (or an equation or the like) showing relation between the airflow volume and cooling coefficient h. The map showing relation between the airflow volume and cooling coefficient h is adapted by experiment and the like. The airflow volume and cooling coefficient h have such relation that cooling coefficient h increases in value as the airflow volume increases. 
     In S 106 , ECU  100  calculates a resistance value Rtmin of the lowest temperature cell of the plurality of cells connected in parallel. ECU  100  calculates Rtmin by the following equation (1), for example:
 
 Rt min( t )= Riv max× f ( TB min( t ),  RAHR min( t ))   (1)
 
     Rivmax in the equation (1) represents the highest value of variation in initial resistance (product variation) present between the cells. Rivmax is determined in advance by experiment and the like. F is a coefficient indicating a reduction in resistance from the initial resistance value (Rivmax or Rivmin which will be described later), and is a function (map) having the temperature and remaining capacity (RAHR) of the cell as factors. 
     In the equation (1), “t” represents an operational value in the current operation cycle. TBmin is the lowest temperature of temperatures TB 1  to TBj detected by temperature detection device  23 . RAHRmin represents the lowest RAHR of RAHRs in each block. 
     In S 108 , ECU  100  calculates a root-mean-square value IBa of the current. ECU  100  calculates the root-mean-square value of the current using, as shown in the following equation (2), for example, the current value of the current detected by current detection device  22 , and a predetermined number of detection results detected in an immediately preceding predetermined period. ECU  100  may calculate the current value by adding a value, obtained by multiplying the difference between the previous value and the current root-mean-square value by a prescribed constant (smoothing constant) k, to the previous value, as shown in the following equation (3), for example, instead of the equation (2):
 
 IBa ( t )=√{square root over ( IB ( t ) 2   +IB ( t− 1) 2   + . . . +IB ( t−n ) 2 )}  (2)
 
 IBa ( t )= IBa ( t− 1)+ k ×(√{square root over ( IB ( t ) 2   +IB ( t− 1) 2   + . . . +IB ( t−n ) 2 )}−IBa( t− 1))   (3)
 
     In S 110 , ECU  100  sets an offset temperature TBoffset 1 . Offset temperature TBoffset 1  is an offset temperature for calculating the temperature of the highest temperature cell using the temperature of the lowest temperature cell, and indicates temperature variation between the plurality of cells connected in parallel. ECU  100  sets offset temperature TBoffset 1  using, for example, the current value of the root-mean-square value, and a map (or an equation or the like) showing relation between the root-mean-square value and offset temperature TBoffset 1 . The map showing relation between the root-mean-square value and offset temperature TBoffset 1  is adapted by experiment and the like. The root-mean-square value and offset temperature TBoffset 1  have such relation that, for example, the amount of heat generated in the battery pack increases as the root-mean-square value increases, causing the temperature variation to increase, and thus causing offset temperature TBoffset 1  to increase in value. 
     In S 112 , ECU  100  calculates a resistance value Rtmax of the highest temperature cell of the plurality of cells connected in parallel. ECU  100  calculates Rtmax by the following equation (4), for example:
 
 Rt max( t )= Riv min× f ( TB min( t )+ TB offset1,  RAHR min( t )+ RAHR offset)   (4)
 
     Rivmin in the equation (4) represents the lowest value of variation in initial resistance (product variation) present between the cells. Since the highest temperature cell has a higher cell temperature and a lower resistance than the lowest temperature cell, Rivmin is used for the calculation of resistance Rtmax of the highest temperature cell, and Rivmax is used for the calculation of resistance Rtmin of the lowest temperature cell. Rivmin is determined in advance by experiment and the like. 
     As described above, f is a coefficient indicating a reduction in resistance from the initial resistance value (Rivmin or Rivmax), and is a function (map) having the temperature and the remaining capacity (RAHR) of the cell as factors. In the equation (4), the temperature of the highest temperature cell, that is, a value obtained by adding offset temperature TBoffset 1  to the temperature (TBmin) of the lowest temperature cell is used as a factor of the temperature of the cell. An offset amount RAHRoffset is a prescribed value for calculating RAHRmax indicating the highest RAHR of RAHRs in each block using RAHRmin. 
     Here,  FIG. 6  is a map for determining coefficient f used in the equation (1) and the equation (4). Referring to  FIG. 6 , coefficient f is determined based on the temperature and the remaining capacity (RAHR) of the cell. Basically, coefficient f increases in value as the temperature and RAHR decrease, and coefficient f decreases in value as the temperature and RAHR increase. The specific values in the map are determined in advance by experiment and the like. 
       FIG. 7  shows dependence of resistance of a cell on temperature. Referring to  FIG. 7 , the horizontal axis indicates temperature Tce of a cell, and the vertical axis indicates resistance Rce of a cell. Temperature Tce and resistance Rce have such relation that resistance Rce increases as temperature Tce decreases, and resistance Rce decreases as temperature Tce increases. 
     A point P 3  indicates relation between temperature Tce and resistance Rce of the lowest temperature cell of the plurality of cells connected in parallel. In this embodiment, as shown in the equation (1), resistance Rtmin of the lowest temperature cell is estimated using TBmin showing the lowest temperature in battery pack  10 . 
     A point P 4  indicates relation between temperature Tce and resistance Rce of the highest temperature cell of the plurality of cells connected in parallel. In this embodiment, as shown in the equation (4), Rtmax of the highest temperature cell is estimated using the value, obtained by adding temperature offset amount TBoffset 1  to TBmin showing the lowest temperature in battery pack  10 , as the temperature of the highest temperature cell. 
       FIG. 8  shows dependence of resistance of a cell on remaining capacity. Referring to  FIG. 8 , the horizontal axis indicates the remaining capacity (RAHR (%)) on a block-by-block basis, and the vertical axis indicates resistance Rce of a cell. RAHR and resistance Rce have such relation that resistance Rce increases as RAHR decreases. 
     A point P 5  indicates relation between resistance Rce and RAHR of the lowest temperature cell of the plurality of cells connected in parallel. As can be understood from the figure, the sensitivity of variation in RAHR relative to variation in resistance is higher in a region where RAHR is lower. In this embodiment, therefore, as shown in the equation (1), resistance Rtmin of the lowest temperature cell is estimated using RAHRmin indicating the lowest RAHR of RAHRs in each block. 
     A point P 6  indicates relation between resistance Rce and RAHR of the highest temperature cell of the plurality of cells connected in parallel. In this embodiment, as shown in the equation (4), resistance Rtmax of the highest temperature cell is estimated using the value, obtained by adding prescribed offset amount RAHRoffset to RAHRmin, as RAHR of the highest temperature cell. 
     In S 114 , ECU  100  calculates temperature index Ftmax (second temperature index) of the highest temperature cell of the plurality of cells connected in parallel by the following equations:
 
 Ft max( t )= Ft max( t− 1)+ Fk ×( Qt max( t )− Ct max( t ))   (5)
 
 Qt max( t )= Qt max( t− 1)+ Qkt max×( Rt max( t )× It max( t ) 2   ×dt−Qt max( t− 1))   (6)
 
 Ct max( t )= Ct max( t− 1)+ Ckt max×( h ( t )×( TB min( t )+ TB offset2− TC ( t ))× dt−Ct max( t− 1))   (7)
 
     In each equation, Qtmax represents an amount of heat generated by the highest temperature cell (heat generation term associated with energization), and Ctmax represents a cooled amount of the highest temperature cell (cooling term by cooling device  24 ). Fk is a prescribed correction coefficient. In an equation (6), Itmax represents a current in the highest temperature cell, and Qktmax is a prescribed constant (smoothing constant). Itmax is calculated by an equation (11) described later. 
     In an equation (7), TBoffset2 is an offset value for causing this cooling term of the highest temperature cell to be calculated as a greater value than a cooling term of the lowest temperature cell which will be described later. TC is the temperature of the cooling air detected by temperature sensor  27  ( FIG. 1 ) as described above. H (t) is the aforementioned cooling coefficient. 
     ECU  100  calculates Rtmax and Itmax, and calculates amount of generated heat Qtmax by the highest temperature cell by the equation (6) using calculated Rtmax and Itmax. Then, ECU  100  calculates, using calculated amount of generated heat Qtmax and cooled amount Ctmax calculated by the equation (7), temperature index Ftmax (second temperature index) of the highest temperature cell by an equation (5). 
     In S 116 , ECU  100  calculates temperature index Ftmin (first temperature index) of the lowest temperature cell of the plurality of cells connected in parallel by the following equations:
 
 Ft min( t )= Ft min( t− 1)+ Fk ×( Qt min( t )− Ct min( t ))   (8)
 
 Qt min( t )= Qt min( t− 1)+ Qkt min×( Rt min( t )× It min( t ) 2   ×dt−Qt min( t− 1))   (9)
 
 Ct min( t )= Ct min( t− 1)+ Ckt min×( h ( t )×( TB min( t )− TC ( t ))× dt−Ct min( t− 1))   (10)
 
     Qtmin represents an amount of heat generated by the lowest temperature cell (heat generation term associated with energization), and Ctmin represents a cooled amount of the lowest temperature cell (cooling term by the cooling device). In an equation (9), Itmin represents a current in the lowest temperature cell, and Qktmin is a prescribed constant (smoothing constant). Itmin is calculated by an equation (12) described later. 
     ECU  100  calculates Rtmin and Itmin, and calculates amount of generated heat Qtmin by the lowest temperature cell by the equation (9) using calculated Rtmin and Itmin. Then, ECU  100  calculates, using calculated amount of generated heat Qtmin and cooled amount Ctmin calculated by an equation (10), temperature index Ftmin (first temperature index) of the lowest temperature cell by an equation (8). 
     Rtmax (resistance of the highest temperature cell) in the above equation (6) is calculated by the equation (4). Rtmin (resistance of the lowest temperature cell) in the above equation (9) is calculated by the equation (1). 
     Itmax (current in the highest temperature cell) in the above equation (6) and Itmin (current in the lowest temperature cell) in the above equation (9) are estimated by the following equations assuming that, as shown in  FIG. 9 , each of the plurality of cells connected in parallel is either the highest temperature cell or the lowest temperature cell, and in consideration of a disconnection of one of the cells (a disconnection may cause a current increase in another cell, resulting in increased current variation): 
     
       
         
           
             
               
                 
                   
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                               1 
                             
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                               N 
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                               2 
                             
                           
                         
                       
                     
                     × 
                     
                       
                         I 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       
                         N 
                         - 
                         
                           N 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         - 
                         
                           N 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
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     N is the number of parallel cells in each block ( FIG. 2 ). N1 is the number of highest temperature cells in the N cells connected in parallel, and N2 is the number of disconnected cells. These equations (11) and (12) can be readily derived using Rtmax (resistance of the highest temperature cell) and Rtmin (resistance of the lowest temperature cell) calculated in the above equations (4) and (1), and the model shown in  FIG. 9 . 
     In this embodiment, a condition where the current variation is greatest when battery pack  10  can be used corresponds to N1=1 (the degree of current concentration in the highest temperature cell is highest), and a worst value when battery pack  10  can be used is set to N2 (for example, N2=2 for N=15). 
     Turning back to  FIG. 5 , in S 118 , ECU  100  calculates evaluation function ΔF indicating the degree of the temperature variation between the cells, by subtracting temperature index Ftmin of the lowest temperature cell from temperature index Ftmax of the highest temperature cell, as shown in the following equation (13):
 
Δ F ( t )= Ft max( t )− Ft min( t )   (13)
 
     In S 120 , ECU  100  calculates, using calculated evaluation function ΔF and temperature TBmin showing the lowest temperature in battery pack  10 , maximum current correction gain G indicating the degree of the current variation between the cells. 
       FIG. 10  shows a map of maximum current correction gain G. Referring to  FIG. 10 , maximum current correction gain G is determined by evaluation function ΔF indicating the degree of the temperature variation between the cells, and temperature TBmin. This maximum current correction gain G shows that the current variation increases as the value of maximum current correction gain G increases. Generally, maximum current correction gain G increases in value as evaluation function ΔF increases in value (as the temperature variation increases), and as temperature TBmin decreases. 
     Temperature TBmin showing the lowest temperature in battery pack  10  is used because the current variation between the cells may increase as the temperature decreases. 
       FIG. 11  shows relation between temperature and resistance of a cell. Referring to  FIG. 11 , the horizontal axis indicates temperature Tce of a cell, and the vertical axis indicates resistance Rce of a cell. As shown in  FIG. 11 , even with the same temperature difference ΔT between the cells (evaluation function ΔF), resistance difference ΔR (resistance variation) between the cells increases as the cell temperature decreases, which causes the current variation between the cells to increase as well. In this embodiment, therefore, as shown in the map of  FIG. 10 , maximum current correction gain G is calculated in consideration not only of evaluation function ΔF indicating the degree of the temperature variation between the cells, but also of the temperature of battery pack  10 . Moreover, in this embodiment, temperature TBmin showing the lowest temperature in battery pack  10  is used as the most stringent temperature condition. 
     Turning back to  FIG. 5 , in S 122 , ECU  100  calculates a maximum current value Imax by multiplying current IB in battery pack  10  detected by current detection device  22  by maximum current correction gain G. Then, although not particularly depicted, ECU  100  performs various types of limiting control based on this maximum current value Imax, such as limiting current IB so as to prevent maximum current value Imax from exceeding the upper limit, or limiting input/output of battery pack  10  so as to prevent electric power calculated based on maximum current value Imax from exceeding the upper limit. 
     The operation of battery system  2  according to the present embodiment based on the structure and the flowchart as described above is described. 
     In a situation where electric power is supplied from battery pack  10  to MG  42  during travel of vehicle  1 , for example, lowest temperature TBmin in battery pack  10  and cooling air temperature TC are acquired (S 100 ). Then, the fan airflow volume is acquired (S 102 ), and cooling coefficient h is set based on the acquired fan airflow volume (S 104 ). 
     Once cooling coefficient h is determined, resistance value Rtmin of the lowest temperature cell is calculated (S 106 ), root-mean-square value IBa of the current is calculated (S 108 ), and offset temperature TBoffset 1  is calculated in accordance with calculated root-mean-square value IBa (S 110 ). 
     Then, the temperature calculated by adding offset temperature TBoffset 1  to the temperature of the lowest temperature cell is set as the temperature of the highest temperature cell, to calculate resistance value Rtmax of the highest temperature cell (S 112 ). 
     Temperature index Ftmax and temperature index Ftmin are calculated using calculated Rtmax and Rtmin (S 114 , S 116 ), and evaluation function ΔF is calculated (S 118 ). 
     Maximum current correction gain G is calculated based on calculated evaluation function ΔF, temperature TBmin, and the map shown in  FIG. 10 , and calculated maximum current correction gain G and current IB are multiplied together, to calculate maximum current value Itmax (S 122 ). 
     As described above, according to battery system  2  of the present embodiment, evaluation function ΔF indicating the degree of the temperature variation between the cells is calculated, and the degree of the current variation between the cells is estimated using that evaluation function ΔF and temperature TBmin of battery pack  10  (calculation of maximum current correction gain G). Accordingly, appropriate battery protection control can be implemented using maximum current value Imax obtained by multiplying actual current IB by this maximum current correction gain G. In particular, the second temperature index is calculated using an offset temperature offset 1  which is set based on root-mean-square value IBa of the current, thereby allowing evaluation function (evaluation value) ΔF to be calculated with a high degree of accuracy. As a result, the current variation between the plurality of secondary batteries connected in parallel caused by the temperature variation between the plurality of secondary batteries can be estimated with a high degree of accuracy. Accordingly, appropriate battery protection control can be implemented on the plurality of secondary batteries. Therefore, a battery system capable of implementing appropriate battery protection control in consideration of current variation caused by temperature variation between a plurality of secondary batteries connected in parallel can be provided. 
     Moreover, offset temperature offset 1  is set based on the root-mean-square value of the current, thereby allowing offset temperature offset 1  to be set appropriately in accordance with a heat generating state of the battery pack. 
     A modification is described below. 
     Although battery system  2  has been described as being mounted on a hybrid vehicle as an example in the above embodiment, battery system  2  may be mounted on various types of vehicles other than the hybrid vehicle as described above, or on a movable body other than a vehicle. 
     Moreover, although the current variation has been described as being calculated between the lowest temperature cell and the highest temperature cell in the above embodiment, current variation may be calculated between a first cell having a relatively low temperature of the plurality of cells and a second cell having a temperature higher than that of the first cell by a prescribed temperature, for example, to perform appropriate battery protection control in consideration of the calculated current variation. For example, current variation may be calculated between a first cell having the n-th lowest temperature of the plurality of cells and a second cell having the n-th highest temperature of the plurality of cells, to perform appropriate battery protection control in consideration of the calculated current variation. 
     Moreover, although offset temperature offset 1  has been described as being set based on the root-mean-square value of the current in the above embodiment, offset temperature offset 1  is only required to be set using the information related to a heat generating state of the battery pack. For example, offset temperature offset 1  may be set based on the internal resistance of battery pack  10 , or offset temperature offset 1  may be set based on the internal resistance and the voltage of the battery pack. For example, as the internal resistance and the voltage of battery pack  10  increase, the amount of generated heat increases to cause increased temperature variation, and therefore, offset temperature offset 1  may be increased in value. 
     The above modification may be entirely or partially combined as appropriate for implementation. 
     Although the present disclosure has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the scope of the present disclosure being interpreted by the terms of the appended claims.