Abstract:
A system for determining an operating limit of at least one battery according to some embodiments of the present invention comprises a voltage module that measures a voltage V across at least one battery during first and second periods. A current sensor that measures current I supplied by the at least one battery during the first and second periods. A limit module estimates a sum of a polarization voltage V P  and an open circuit voltage V 0  of the at least one battery at the second period based on the voltage V and current I of the at least one battery at the first period and an ohmic resistance R 0  of the at least one battery.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is related to U.S. patent application Ser. No. 10/989,159, filed Nov. 15, 2004, which is hereby incorporated by reference. 
   FIELD OF THE INVENTION 
   The present invention relates to batteries and battery systems, and more particularly to a maximum and minimum power limit calculator for batteries and battery systems. 
   BACKGROUND OF THE INVENTION 
   Battery systems may be used to provide power in a wide variety applications. Exemplary transportation applications include hybrid electric vehicles (HEV), electric vehicles (EV), Heavy Duty Vehicles (HDV) and Vehicles with 42-volt electrical systems. Exemplary stationary applications include backup power for telecommunications systems, uninterruptible power supplies (UPS), and distributed power generation applications. Examples of the types of batteries that are used include nickel metal hydride (NiMH) batteries, lead-acid batteries and other types of batteries. A battery system may include a plurality of battery subpacks that are connected in series and/or in parallel. The battery subpacks may include a plurality of batteries that are connected in parallel and/or in series. 
   The maximum and/or minimum power that can be delivered by batteries, battery subpacks and/or battery systems varies over time as a function of a temperature of the batteries, battery state of charge (SOC) and/or battery age. For example in transportation applications such as HEVs or EVs, it is important for the powertrain control system to know the maximum and/or minimum power limit of the battery system. The powertrain control system typically receives an input request for power from an accelerator pedal. The powertrain control system interprets the request for power relative to the maximum power limit of the battery system (when the battery system is powering the wheels). The minimum power limits may be relevant during recharging and/or regenerative braking. Exceeding the maximum and/or minimum power limits may damage the batteries and/or the battery system and/or reduce the operational life of the batteries and/or the battery system. 
   In addition, the demands of an application should not be suddenly clamped as the battery system reaches its maximum and/or minimum power limit. To provide smooth operation, the battery system should be able to predict the maximum and/or minimum power limits and communicate the power limits to the application. 
   SUMMARY OF THE INVENTION 
   A system for determining an operating limit of at least one battery according to some embodiments of the present invention comprises a voltage module that measures a voltage across at least one battery during first and second periods. A current sensor that measures current supplied by the at least one battery during the first and second periods. A limit module estimates a sum of a polarization voltage and an open circuit voltage of the at least one battery at the second period based on the voltage and current of the at least one battery at the first period and an ohmic resistance of the at least one battery. 
   In some implementations, the limit module calculates at least one of a maximum current limit and/or a minimum current limit for the at least one battery at the second period based on the sum, at least one of a maximum voltage limit and/or a minimum voltage limit, respectively, and the ohmic resistance of the at least one battery. The first period occurs before the second period. The limit module calculates at least one of a maximum power limit and a minimum power limit of the at least one battery based on the at least one of the maximum current limit and/or the minimum current limit, respectively, and the at least one of the maximum voltage limit and/or the minimum voltage limit, respectively. 
   In other implementations, a battery system comprises the system of claim  1  and further comprises the at least one battery. A battery subpack includes N−1 additional batteries connected in series with the at least one battery. M−1 additional battery subpacks connected in parallel with the battery subpack. 
   Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein: 
       FIG. 1  is a functional block diagram of an exemplary battery system including battery subpacks with batteries, battery control modules and a master control module; 
       FIG. 2  is a functional block diagram of an exemplary battery control module; 
       FIG. 3  is an electrical schematic of an equivalent circuit for an exemplary battery; 
       FIG. 4  is an exemplary flowchart illustrating steps for generating a maximum power limit for the battery system of  FIG. 1  when V max  is known; 
       FIG. 5  is an exemplary flowchart illustrating steps for generating a minimum power limit for the battery system of  FIG. 1  when V min  is known; 
       FIG. 6  is an exemplary flowchart illustrating steps for generating a maximum power limit for the battery system of  FIG. 1  when I max  is known; and 
       FIG. 7  is an exemplary flowchart illustrating steps for generating a minimum power limit for the battery system of  FIG. 1  when I min  is known. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. For purposes of clarity, the same reference numbers will be used in the drawings to identify the same elements. As used herein, the term module refers to an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. 
   Referring now to  FIG. 1 , an exemplary embodiment of a battery system  10  is shown to include M battery subpacks  12 - 1 ,  12 - 2 , . . . , and  12 -M (collectively battery subpacks  12 ). The battery subpacks  12 - 1 ,  12 - 2 , . . . , and  12 -M include N series connected batteries  20 - 11 ,  20 - 12 , . . . , and  20 -NM (collectively batteries  20 ). Battery control modules  30 - 1 ,  30 - 2 , . . . and  30 -M (collectively battery control modules  30 ) are associated with each of the battery subpacks  12 - 1 ,  12 - 2 , . . . and  12 -M, respectively. In some embodiments, M is equal to 2 or 3, although additional or fewer subpacks may be used. In some embodiments, N is equal to 12-24, although additional and/or fewer batteries may be used. 
   The battery control modules  30  sense voltage across and current provided by the battery subpacks  12 . Alternatively, the battery control modules  30  may monitor one or more individual batteries  20  in the battery subpacks  12  and appropriate scaling and/or adjustment is performed. The battery control modules  30  communicate with a master control module  40  using wireless and/or wired connections. The master control module  40  receives the power limits from the battery control modules  30  and generates a collective power limit. The battery control module  30  may be integrated with the master control module  40  in some embodiments. 
   Referring now to  FIG. 2 , some of the elements of the battery control modules  30  are shown. The battery control modules  30  include a voltage and/or current measuring module  60  that measures voltage across the battery subpack  12  and/or across one or more individual batteries  20  in the battery subpack  12 . The battery control modules  30  further include a battery state of charge (SOC) module  68  that periodically calculates the SOC of the batteries  20  in the battery subpacks  12 . A power limit module  72  calculates a maximum current limit I lim , voltage limit V lim , and/or power limit P lim  for the battery subpack  12  and/or one or more batteries  20  in the battery subpack  12 , as will be described further below. The limits may be maximum and/or minimum limits. A contactor control module  74  controls one or more contactors (not shown) that are associated with the control and/or connection of the batteries  20  in the battery subpacks  12 . A clock circuit  76  generates one or more clock signals for one or more modules within the battery control module  30 . 
   Referring now to  FIG. 3 , an equivalent circuit for the battery  20  is show where R 0  represents ohmic resistance of the battery, V P  represents the polarization voltage, V 0  represents the open circuit voltage, I represents battery current and V represents battery voltage. V and I are measured values. R p  varies with temperature, duration of applied current and SOC. V 0  and R 0  vary primarily with SOC. V P  is equal to measured current I times R p . 
   Using the equivalent circuit and Kirchoffs voltage rules for the battery  20 , V=V 0 +V P +IR 0 . By manipulating this equation, an equation for the open circuit voltage V 0  and polarization voltage V P  is V 0 +V P =V−IR 0 . The values of V and I are measured by the system and R 0  is estimated. Alternately, the system may perform a continuous calculation of R 0 . In particular, 
             R   0     =       (       V   i     -     V     i   -   1         )       (       I   i     -     I     i   -   1         )             
when performed on reversal of current.
 
   In one embodiment, the maximum voltage V max  of the system is known and V max =V 0 +V P +I max R 0 . Substitution of the calculation for V 0 +V P  from a prior sampling interval into the equation for V max  yields V max =(V−IR o )+I max R o . In this case, we are assuming that V 0 +V P  for the current sampling interval is approximately equal to V 0 +V P  of the prior sampling interval (in other words, V 0 +V P ≅V t=i−1 −I t=i−1 R 0 ). This approximation is valid if the sampling interval is sufficiently small since the battery and ambient conditions are very similar. For example in some implementations, a sampling interval 10 ms&lt;T&lt;500 ms may be used, although other sampling intervals may be used. In one embodiment, T=100 ms. If the sampling interval is determined to be excessive in duration then R o  would be increased as a constant or as a temperature dependent variable. 
   Solving for I max  yields the following: 
             I   max     =           V   max     -     V     t   =     i   -   1         +       I     t   =     i   -   1         ⁢     R   0           R   0       .           
Therefore, since P max =V max I max ,
 
   
     
       
         
           
             P 
             max 
           
           = 
           
             
               
                 V 
                 max 
               
               ⁡ 
               
                 ( 
                 
                   
                     
                       V 
                       max 
                     
                     - 
                     
                       V 
                       
                         t 
                         = 
                         
                           i 
                           - 
                           1 
                         
                       
                     
                     + 
                     
                       
                         I 
                         
                           t 
                           = 
                           
                             i 
                             - 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         R 
                         0 
                       
                     
                   
                   
                     R 
                     0 
                   
                 
                 ) 
               
             
             . 
           
         
       
     
   
   Referring now to  FIG. 4 , a method  100  for calculating P max  is shown. In step  102 , i is set equal to 0. In step  106 , a timer is reset. In step  108 , i is incremented. In step  110 , current I and voltage V of one or more batteries  20  and/or the battery subpack  12  are measured. In step  114 , I is multiplied by R 0  and stored as the i th  sample. In step  118 , V is stored as the i th  sample. In step  122 , control determines whether the timer is up. If step  122  is false, control returns to step  106 . If step  122  is true, control continues with step  124  and determines whether i=1. If step  124  is true, control returns to step  106 . If step  124  is false, control continues with step  128  and calculates I max . Control continues with step  130  and calculates P max  and then returns to step  106 . 
   Additional processing may be performed depending upon the configuration. For example, if V and I are sensed for each battery and there are N batteries are in series, then the P max  and other calculations can be scaled. Other calculations will occur if the N batteries are connected in another fashion. The P max  calculation and other calculations can also be made at other intervals, on demand, when an event occurs, randomly, and/or using any other criteria. 
   Systems that specify V max  also typically specify V min , which yields the following relationships using a similar approach: 
             I   min     =           V   min     -     V     t   =     i   -   1         +       I     t   =     i   -   1         ⁢     R   0           R   0       .           
Therefore, since P min =V min I min ,
 
   
     
       
         
           
             P 
             min 
           
           = 
           
             
               
                 V 
                 min 
               
               ⁡ 
               
                 ( 
                 
                   
                     
                       V 
                       min 
                     
                     - 
                     
                       V 
                       
                         t 
                         = 
                         
                           i 
                           - 
                           1 
                         
                       
                     
                     + 
                     
                       
                         I 
                         
                           t 
                           = 
                           
                             i 
                             - 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         R 
                         0 
                       
                     
                   
                   
                     R 
                     0 
                   
                 
                 ) 
               
             
             . 
           
         
       
     
   
   Referring now to  FIG. 5 , a method  140  for calculating V min  is shown. If step  124  is false, control continues with step  144  and calculates I min  and with step  146  and calculates P min . As can be appreciated, steps  144  and  146  can be added to the method  100  in  FIG. 4  so that I max  and P max  and/or I min  and P min  can be calculated. 
   Alternately for systems having a known I lim  and using a similar approach,
 
 V   max   =I   max   R   0   +V   t=i−1   −I   t=i−1   R   0 .
 
Therefore, since P max =V max I max ,
 
 P   max   =I   max ( I   max   R   0   +V   t=i−1   −I   t=i−1   R   0 ).
 
   Referring now to  FIG. 6 , a method  150  for calculating I max  is shown. If step  124  is false, control continues with step  154  and calculates I max  and with step  156  and calculates P max . 
   Systems that specify I max  also typically specify I min , which yields the following relationships using a similar approach:
 
 V   min   =I   min   R   0   +V   t=i−1   −I   t=i−1   R   0 .
 
Therefore, since P min =V min I min ,
 
 P   min   =I   min ( I   min   R   0   +V   t=i−1   −I   t=i−1   R   0 ).
 
   Referring now to  FIG. 7 , a method  160  for calculating I min  is shown. If step  124  is false, control continues with step  164  and calculates I min  and with step  166  and calculates P min . As can be appreciated, steps  164  and  166  can be added to the method  150  in  FIG. 6  so that I max  and P max  and/or I min  and P min  can be calculated. 
   Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.