Patent Publication Number: US-2016231389-A1

Title: Deterioration function calculation device, deterioration rate estimation device, deterioration rate estimation system, deterioration function calculation method, deterioration rate estimation method, and program

Description:
TECHNICAL FIELD 
     The present invention relates to a deterioration function calculation device, a deterioration function calculating method, and a program which calculate a deterioration function related to a deterioration rate of a secondary battery and a deterioration rate estimation device, a deterioration rate estimation system, a deterioration rate estimating method, and a program which estimate deterioration of a secondary battery. 
     Priority is claimed on Japanese Patent Application No. 2013-219352, filed Oct. 22, 2013, the content of which is incorporated herein by reference. 
     BACKGROUND ART 
     In operating secondary batteries, it is necessary to diagnose deterioration thereof and estimate the remaining life thereof. Deterioration curves indicating relationships of running times and deterioration rates of secondary batteries when the secondary batteries are operated in general aspects are illustrated in catalogues of the secondary batteries in some cases. When such deterioration curves can be referred to, the deterioration curves can be compared with cycle rates in operating current secondary batteries to estimate the life of the secondary batteries. However, since aspects illustrated in catalogues and actual usage aspects generally differ, there are differences between relationships of actual running times to deterioration rates and the deterioration curves illustrated in the catalogues. 
     A technique of estimating a deterioration state and the remaining life of a secondary battery by providing upper threshold values in operating a current/temperature/state-of-charge (SOC) of the secondary battery and using the number of times relevant values exceed the upper threshold values in the operating as a parameter is disclosed in Patent Literature 1. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1 
     Japanese Unexamined Patent Application, First Publication No. 2010-139260 
     SUMMARY OF INVENTION 
     Problems to be Solved by the Invention 
     The technique disclosed in Patent Literature 1 estimates the life of the secondary battery using a formula of estimating deteriorated states generated based on shapes and items of different formulae. For this reason, the technique disclosed in Patent Literature 1 can generate a deterioration estimating formula based on history information when the secondary battery was operated in the same load pattern in the past and accurately estimate deterioration of the secondary battery operated in the same load pattern when the deterioration is estimated. However, the technique disclosed in Patent Literature 1 may not be capable of accurately estimating deterioration of the secondary battery operated in an unknown load pattern when the deterioration is estimated. 
     An object of the present invention is to provide a deterioration function calculation device, a deterioration rate estimation device, a deterioration rate estimation system, a deterioration function calculating method, a deterioration rate estimating method, and a program for the purpose of accurately estimating a deterioration rate even when a secondary battery is operated in an unknown operation aspect. 
     Means for Solving the Problem 
     According to a first aspect of the present invention, a deterioration function calculation device includes a storage unit, an equivalent coefficient calculation unit, an equivalent running time calculation unit, and a deterioration function calculation unit. The storage unit associates and stores running times of a secondary battery in previous operations of the secondary battery with deterioration rates of the secondary battery in the running times for each operation. The equivalent coefficient calculation unit calculates equivalent coefficients used for normalizing the running times based on values related to the previous operations in the secondary battery for each operation. The equivalent running time calculation unit calculates equivalent running times that are the normalized running times based on the running times and the equivalent coefficients related to the operations relevant to the running times with respect to the running times associated and stored with the operations and the deterioration rates by the storage The deterioration function calculation unit calculates a deterioration function indicating relationships of the equivalent running times and the deterioration rates based on the equivalent running times and the deterioration rates associated with the running times used for calculating the equivalent running times and stored by the storage unit. 
     According to a second aspect of the present invention, in the first aspect, the deterioration function calculation device is an equivalent coefficient calculation unit generating the equivalent coefficients such that degrees of scattering between the deterioration rates stored by the storage unit, and the equivalent running times calculated based on the running times associated with the deterioration rates and the deterioration rates acquired from the deterioration function become smaller. 
     According to a third aspect of the present invention, in the first or second aspect, the deterioration function calculation device is an equivalent running time calculation unit dividing the running times into partial running times for each operation state, multiplying the partial running times by the equivalent coefficients according to operation states, calculating a sum thereof, and calculating the equivalent running times. 
     According to a fourth aspect of the present invention, a deterioration rate estimation device includes an input unit, an equivalent coefficient calculation unit, an equivalent running time calculation unit, and a deterioration rate estimation unit. The input unit receives inputs of running times of a secondary battery and values related to operations of the secondary battery. The equivalent coefficient calculation unit calculates equivalent coefficients used fur normalizing the running times based on the values related to the operations received as the inputs. The equivalent running time calculation unit calculates equivalent running times that are the normalized running times based on the running times received as the inputs and the equivalent coefficients. The deterioration rate estimation unit estimates the deterioration rates of the secondary battery based on a deterioration function indicating relationships of the equivalent running times and the deterioration rates of the secondary battery, and the calculated equivalent running times. 
     According to a fifth aspect of the present invention, In the fourth aspect, the deterioration rate estimation device is the deterioration rate estimation unit estimating the deterioration rates of the secondary battery based on a deterioration function calculated by the deterioration function calculation unit of the deterioration function calculation device according to any one of the first and third aspects and the calculated equivalent running times. 
     According to a sixth aspect of the present invention, a deterioration function calculating method of calculates a deterioration function used for estimating deterioration rates of a secondary battery. The deterioration function calculating method includes a step of calculating, by a deterioration function calculation device, equivalent coefficients used for normalizing running times of the secondary battery based on values related to previous operations of the secondary battery for each operation. The deterioration function calculating method includes a step of calculating, by the deterioration function calculation device, equivalent running times that are the normalized running times bases on the running times and the equivalent coefficients related to the operations relevant to the running times with respect to the running times associated and stored with the operations and the deterioration rates in a storage unit. The storage unit associates and stores the running times of the secondary battery in the previous operations of the secondary battery with the deterioration rates of the secondary battery in the running times for each operation. The deterioration function calculating method includes a step of calculating, by the deterioration function calculation device, a deterioration function indicating relationship between the equivalent running times and the deterioration rates based on the equivalent running times and the deterioration rates associated with the running times used for calculating the equivalent running times and stored by the storage unit. 
     A seventh aspect of the present invention is a deterioration rate estimating method of a secondary battery. The deterioration rate estimating method includes a step of receiving, by a deterioration rate estimation device, inputs of running times of the secondary battery and values related to operations of the secondary battery. The deterioration rate estimating method includes a step of calculating, by the deterioration rate estimation device, equivalent coefficients used for normalizing the running times based on the values related to the operations received as the inputs. The deterioration rate estimating method includes a step of calculating, by the deterioration rate estimation device, equivalent running times that are the normalized running times based on the running times received as the inputs and the equivalent coefficients. The deterioration rate estimating method includes a step of estimating, by the deterioration rate estimation device, the deterioration rates of the secondary battery based on a deterioration function indicating relationships of the equivalent running times and the deterioration rates of the secondary battery, and the calculated equivalent running times. 
     An eighth aspect of the present invention is a program causing a computer to function as a storage unit, an equivalent coefficient calculation unit, an equivalent running time calculation unit, and a deterioration function calculation unit. The storage unit associates and stores running times of a secondary battery in previous operations of the secondary battery with deterioration rates of the secondary battery in the running times for each operation. The equivalent coefficient calculation unit calculates equivalent coefficients used for normalizing the running times based on values related to the previous operations in the secondary battery for each operation. The equivalent running time calculation unit calculates equivalent running times that are the normalized running times based on the running times and the equivalent coefficients related to the operations relevant to the running times with respect to the running times associated and stored with the operations and the deterioration rates by the storage unit. The deterioration function calculation unit calculates deterioration function indicating a relationship between the equivalent running times and the deterioration rates based on the equivalent running times and the deterioration rates associated with the running times used for calculating the equivalent running times and stored by the storage unit. 
     A ninth aspect of the present invention is a program causing a computer to function as an input unit, an equivalent coefficient calculation unit, an equivalent running time calculation unit, and a deterioration rate estimation unit. The input unit receives inputs of the running times of the secondary battery and values related to the operations of the secondary battery The equivalent coefficient calculation unit calculates equivalent coefficients used for normalizing the running times based on the values related to the operations received as the inputs. The equivalent running time calculation unit calculates equiv it running times that are the normalized running times based on the running times received as the inputs and the equivalent coefficients. The deterioration rate estimation unit estimates the deterioration rates of the secondary battery based on a deterioration function indicating relationships of the equivalent running times and the deterioration rates of the secondary battery, and the calculated equivalent running times. 
     In addition, a tenth aspect is a deterioration rate estimation system including a storage unit, a first equivalent coefficient calculation unit, a first equivalent running time calculation unit, a deterioration function calculation unit, an input unit, a second equivalent coefficient calculation unit, a second equivalent running time calculation unit, and a deterioration rate estimation unit. The storage unit associates and stores running times of a secondary battery in previous operations of the secondary battery with deterioration rates of the secondary battery in the running times for each operation. The first equivalent coefficient calculation unit calculates equivalent coefficients used for normalizing the running times based on values related to the previous operations in the secondary battery for each operation. The first equivalent running time calculation unit calculates equivalent running times that are the nomalized running times based on the running times and the equivalent coefficients calculated by the first equivalent coefficient calculation unit with respect to the running times associated and stored with the operations and the deterioration rates by the storage unit. The deterioration function calculation unit configured to calculate a deterioration function indicating relationships of the equivalent running times and the deterioration rates based on the equivalent running times calculated by the first equivalent running time calculation unit and the deterioration rates associated and stored with the running times used for calculating the equivalent running times by the storage unit. The second equivalent coefficient calculation unit calculates equivalent coefficients used for normalizing the running times based on the values related to the operations received as the inputs. The second equivalent running time calculation unit calculates equivalent running times that are the normalized running times based on the running times received as the inputs and the equivalent coefficients calculated by the second equivalent coefficient calculation unit. The deterioration rate estimation unit estimates the deterioration rates of the secondary battery based on the deterioration function calculated by the deterioration function calculation unit and the equivalent running times calculated by the second equivalent running time calculation unit. 
     Effects of the Invention 
     According to at least one of the above-mentioned aspects, the deterioration function calculation device can calculate the deterioration function for the purpose of accurately estimating the deterioration rate even when the secondary battery is operated in an unknown operation aspect. According to at least one of the above-mentioned aspects, the deterioration rate estimation device can accurately estimate the deterioration rate even when the secondary battery is operated in an unknown operation aspect. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic block diagram showing a constitution of a deterioration rate estimation system according to a first embodiment. 
         FIG. 2  is a flowchart showing a method of calculating a deterioration function according to the first embodiment. 
         FIG. 3  is a flowchart showing a method of estimating a deterioration rate according to the first embodiment. 
         FIG. 4A  is a view showing an example of the method of calculating the deterioration function according to the first embodiment. 
         FIG. 4B  is a view showing an example of the method of calculating the deterioration function according to the first embodiment. 
         FIG. 5  is a schematic block diagram showing a constitution of a deterioration rate estimation system according to a second embodiment. 
         FIG. 6  is a flowchart showing a method of calculating deterioration function according to the second embodiment. 
         FIG. 7  is a flowchart showing a method of estimating a deterioration rate according to the second embodiment. 
         FIG. 8  is a schematic block diagram showing a constitution of a computer according to at least one embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     Hereinafter, embodiments will be described in detail reference to the drawings. 
       FIG. 1  is a schematic block diagram showing a constitution of a deterioration rate estimation system  100  according to a first embodiment. 
     The deterioration rate estimation system  100  estimates a deterioration rate of a secondary battery. The deterioration rate estimation system  100  includes a deterioration function calculation device  110  and a deterioration rate estimation device  120 . 
     The deterioration function calculation device  110  calculates a deterioration function used for estimating the deterioration rate of the secondary battery. A deterioration ion curve is an aspect of the deterioration function. The deterioration function can be expressed as a graph to acquire the deterioration curve. The deterioration function calculation device  110  includes a storage unit  111 , a first equivalent coefficient calculation unit  112 , a first equivalent running time calculation unit  113 , a deterioration function calculation unit  114 , and a deterioration function evaluation unit  115 . 
     The storage unit  111  associates and stores running times of the secondary battery in previous operations of the secondary battery and values related to the operations of the secondary battery when the running times have passed and deterioration rates of the secondary battery when the running times have passed for each operation. In the embodiment, the storage unit  111  stores a plurality of types of values such as a charging rate, a temperature, a current, and a voltage as the values related to the operations of the secondary battery. 
     The first equivalent coefficient calculation unit  112  calculates equivalent coefficients used for normalizing the running times based on the values related to the operations of the secondary battery stored by the storage unit  111 . To be specific, then equivalent coefficients for certain passage times stored by the storage unit  111  are calculated, the first equivalent coefficient calculation unit  112  acquires a plurality of values related to operations until the running times pass after an operation of the secondary battery from the storage unit  111  starts and specifies a usage range of a charging rate, a change rate of the charging rate, operation patterns of a maximum current value, etc. based on the values. The operation patterns are also examples of the values related to the operations of the secondary battery. The first equivalent coefficient calculation unit  112  substitutes the specified operation patterns into a predetermined equivalent coefficient calculating formula and calculates the equivalent coefficient. Note that the equivalent coefficient calculated by the first equivalent coefficient calculation unit  112  is not limited to one. When an equivalent running time calculating formula used for calculating equivalent running times uses a plurality of equivalent coefficients, the first equivalent coefficient calculation unit  112  calculates a plurality of equivalent coefficients. The equivalent coefficient calculating formula is appropriately updated in a process of calculating the deterioration function. A type of the equivalent coefficient calculating formula and initial values of dependent variables are determined in a previous stage of the process of calculating the deterioration function in advance. 
     The first equivalent running time calculation unit  113  calculates equivalent running times that are the normalized running times based on the running times and the equivalent coefficients stored by the storage unit  111 . To be specific, the first equivalent running time calculation unit  113  specifies the operation associated with the running time and substitutes the equivalent coefficient corresponding to the operation and the running time into a predetermined equivalent running time calculating formula to calculate the equivalent running time. The type of the equivalent running time calculating formula is determined in the previous stage of the process of calculating the deterioration function in advance. 
     The deterioration function calculation unit  114  calculates the deterioration function indicating relationships of the equivalent running times and the deterioration rates based on the equivalent running times calculated by the first equivalent running time calculation unit  113  and the deterioration rates. To be specific, the deterioration function calculation unit  114  reads the deterioration rates associated with the running times used for calculating the equivalent running times from the storage unit  111  and generates a plurality of combinations of the equivalent running times and the deterioration rates. The deterioration function calculation unit  114  performs curve fitting based on the combinations to calculate the deterioration function. 
     The deterioration function evaluation unit  115  calculates dispersion of the deterioration function calculated by the deterioration function calculation unit  114  and the deterioration rates and determines that the deterioration function is appropriate when the dispersion is less than a predetermined threshold value. Note that, in the embodiment, a case in which the deterioration function evaluation unit  115  evaluates the deterioration function based on the dispersion of the deterioration rates has been described, but the deterioration function evaluation unit  115  is not limited thereto. In another embodiment, the deterioration function may be evaluated based on degrees of scattering of, for example, a standard deviation, a range, etc. instead of the dispersion. 
     The deterioration rate estimation device  120  estimates the deterioration rates of the secondary battery using the deterioration function calculated by the deterioration function calculation device  110 . The deterioration rate estimation device  120  includes an input unit  121 , a second equivalent coefficient calculation unit  122 , a second equivalent running time calculation unit  123 , and a deterioration rate estimation unit  124 . 
     The input unit  121  receives inputs of load patterns and running times of the secondary battery that is an estimation target of the deterioration rates. The load patterns received by the input unit  121  as the inputs are defined by the values related to the operations used for calculating the equivalent coefficients. 
     The second equivalent coefficient calculation unit  122  calculates the equivalent coefficients from the load patterns received by the input unit  121  based on the equivalent coefficient calculating formula used for calculating the equivalent coefficients by the first equivalent coefficient calculation unit  112 . 
     The second equivalent running time calculation unit  123  substitutes the equivalent coefficients calculated by the second equivalent coefficient calculation unit  122  and the running times received by the input unit  121  as the inputs into the equivalent running time calculating formula to calculate the equivalent running times. 
     The deterioration rate estimation unit  124  estimates the deterioration rates of the secondary battery that is the estimation target from the running times calculated by the second equivalent running time calculation unit  123  based on the deterioration function calculated by the deterioration function calculation device  110 . 
     As described above, the deterioration function calculation device  110  and the deterioration rate estimation device  120  can use equivalent running times obtained by normalizing the running times of the operations due to different load patterns to reduce errors of estimation due to differences of the load patterns. 
     A method of calculating a deterioration function using the deterioration function calculation device  110  according to the first embodiment will be described. 
       FIG. 2  is a flowchart showing the method of calculating the deterioration function according to the first embodiment. 
     Relationships of running times and deterioration rates related to previous operations of a secondary battery with the same performance as the secondary battery that is an estimation target of the deterioration rates are recorded in the storage unit  111  before the deterioration function is calculated. For example, experimental data of secondary batteries of the same type, actual operation data, etc. are recorded in the storage unit  111 . 
     When data is recorded in the storage unit  111 , the first equivalent coefficient calculation unit  112  specifies load patterns related to running times stored by the storage unit  111  for each running time (Step S 1 ). To be specific, the equivalent coefficient calculation unit reads values related to the operations associated with the running times before the funning times and integrates the read values related to the operations to specify the load patterns. 
     The first equivalent coefficient calculation unit  112  substitutes the specified load patterns into the equivalent coefficient calculating formula and calculates the equivalent coefficients (Step S 2 ). Subsequently, the first equivalent running time calculation unit  113  calculates the equivalent running times for the running times stored by the storage unit  111  based on the equivalent coefficients corresponding to the operations related to the running times and the equivalent running time calculating formula (Step S 3 ). 
     Subsequently, the deterioration function calculation unit  114  performs curve fitting based on combinations of the equivalent running times calculated by the first equivalent running time calculation unit  113  and the deterioration rates associated with the running times used for calculating the equivalent running times and calculates the deterioration function (Step S 4 ). The curve fitting can be performed through, for example, a polynomial approximation. 
     The deterioration function evaluation unit  115  calculates dispersion of the deterioration function calculated by the deterioration function calculation unit  114  and the degree of deterioration stored by the storage unit  111  (Step S 5 ). To be specific, the dispersion of the degrees of deterioration stored by the storage unit  111  and the degrees of deterioration obtained by substituting the equivalent running times combined with the degrees of deterioration into the deterioration function is calculated. Note that the dispersion is an example of degrees of scattering. The deterioration function evaluation unit  115  determines whether the dispersion is a predetermined threshold value or more (Step S 6 ). 
     The deterioration function evaluation unit  115  determines that the accuracy of the equivalent coefficient calculating formula and the deterioration function is not sufficient when the calculated dispersion is the predetermined threshold value or more (Step S 6 : YES). The first equivalent coefficient calculation unit  112  updates dependent variables of the equivalent coefficient calculating formula such that the dispersion calculated by the deterioration function evaluation unit  115  becomes smaller (Step S 7 ). Then, the process returns to Step S 2 , and the equivalent coefficient is calculated using the updated equivalent coefficient calculating formula. In other words, the first equivalent coefficient calculation unit  112  generates the equivalent coefficients such that degrees of scattering between the deterioration rates stored by the storage unit  111  and deterioration rates acquired from the equivalent running times calculated based on the running times associated with the deterioration rates and the deterioration function become smaller. Thus, the accuracy of the deterioration function calculated by the deterioration function calculation unit  114  can be secured to a predetermined level or more. 
     On the other hand, the deterioration function evaluation unit  115  determines that the accuracy of the equivalent coefficient calculating formula and the deterioration function is sufficient when the calculated dispersion is less than the threshold value (Step S 6 : NO) and ends the process of calculating the deterioration function. Thus, the deterioration function calculation device  110  can accurately generate the deterioration function indicating relationships of the equivalent running times and the deterioration rates. Therefore, the deterioration function calculation device  110  determines the equivalent coefficient calculating formula which calculates the equivalent coefficients. 
     A method of estimating a deterioration rate using the deterioration rate estimation device  120  according to the first embodiment will be described. 
       FIG. 3  is a flowchart showing the method of estimating the deterioration rate according to the first embodiment. 
     The deterioration rate estimation device  120  estimates the deterioration rates of the secondary battery when the deterioration function is calculated by the deterioration function calculation device  110 . 
     The input unit  121  receives inputs of load patterns and running times of the secondary battery that is the estimation target of the deterioration rates from a manager of the secondary battery, etc. (Step S 8 ). The second equivalent coefficient calculation unit  122  calculates the equivalent coefficients using the equivalent coefficient calculating formula used by the first equivalent coefficient calculation unit  112  based on the load patterns received by the input unit  121  as the inputs (Step S 9 ). In other words, the second equivalent coefficient calculation unit  122  calculates the equivalent coefficient using the equivalent coefficient calculating formula determined to be sufficiently accurate by the deterioration function evaluation unit  115 . 
     The second equivalent running time calculation unit  123  calculates the equivalent running times from the running times received by the input unit  121  as the inputs based on the equivalent coefficients calculated by the second equivalent coefficient calculation unit  122  and a predetermined equivalent running time calculating formula (Step S 10 ). An equivalent running time calculating formula used by the second equivalent running time calculation unit  123  is the same as the equivalent running time calculating formula used by the first equivalent running time calculation unit  113 . 
     The deterioration rate estimation unit  124  estimates the deterioration rates of the secondary battery that is the estimation target from the running times calculated by the second equivalent running time calculation unit  123  based on the deterioration function calculated by the deterioration function calculation device  110  and the equivalent running times calculated by the second equivalent running time calculation unit  123  (Step S 11 ). 
     As described above, according to the present embodiment, the deterioration rate estimation system  100  calculates the deterioration function and estimates the deterioration rates using the equivalent running times obtained by normalizing the running times based on the load patterns related to the operations. Thus, the deterioration rate estimation system  100  can estimate the deterioration rate irrespective of the load patterns related to the operations. In other words, according to the deterioration rate estimation system  100  of the embodiment, even when the secondary battery is operated in an unknown load pattern, the deterioration rate of the secondary battery can be accurately estimated. 
     A calculation of the deterioration function according to the first embodiment 
     will be described using specific examples.  FIGS. 4A and 4B  are views showing examples of a method of calculating a deterioration function according to the first embodiment. 
     As shown in  FIG. 4A , running times and deterioration rates of the secondary battery in previous operations of the secondary battery are associated for each operation in the storage unit  111 . The first equivalent running time calculation unit  113  calculates the equivalent running times from the running times shown in  FIG. 4A . Thus, relationships of the equivalent running times and the deterioration rates can he acquired as shown in  FIG. 4B . Also, the deterioration function calculation unit  114  can perform curve fitting based on the relationships of the equivalent running times and the deterioration rates shown in  FIG. 4B  to acquire the deterioration function (deterioration curves) shown in  FIG. 4B . 
     Second Embodiment 
     When a secondary battery is operated in an actual device, types of values related to operations which can be acquired and sampling periods are likely to be limited compared with when a measurement test is performed in a laboratory. For example, while the sampling periods can be used in units of seconds in the measurement test, the sampling periods may be capable of being used only in units of minutes in the actual device. While a current, a voltage, a temperature, and a charging rate can be acquired as the values related to the operations in the measurement test, only a temperature and a charging rate may be capable of being acquired in the actual device. This is to decrease the amount of data by lengthening the sampling periods or reducing the types of the values related to the operations because the secondary battery is generally operated for a long time, for example, five years or ten years. 
     A deterioration rate estimation system  200  of a second embodiment calculates an appropriate deterioration function and more accurately estimates the deterioration rates even under limited conditions. 
       FIG. 5  is a schematic block diagram showing a constitution of the deterioration rate estimation system  200  according to the second embodiment. 
     In the deterioration rate estimation system  200  of the second embodiment, a deterioration function calculation device  210  includes a cumulative time calculation unit  216  in addition to the constitution of the first embodiment. The deterioration rate estimation system  200  of the second embodiment is different from that of the first embodiment in view of information received by an input unit  221  as inputs and processes of a first equivalent coefficient calculation unit  212 , a first equivalent running time calculation unit  213 , a second equivalent coefficient calculation unit  222 , and a second equivalent running time calculation unit  223 . 
     The cumulative time calculation unit  216  calculates the cumulative time of operations (a partial running time) for each operation condition during running times after operating starts, with respect to the running times that stored by a storage unit  211 . For example, the cumulative time calculation unit  216  calculates the cumulative time that the charging rate of the secondary battery is less than 20%, the cumulative time that the charging rate of the secondary battery is 20% or more and less than 40%, the cumulative that the charging rate of the secondary battery is 40% or more and less than 60%, the cumulative time that the charging rate of the secondary battery is 60% or more and less than 80%, and a cumulative time at which the charging rate of the secondary battery is 80% or more during the running time after the operating starts. Usage ranges of the charging rates of the secondary battery are examples of operation conditions. The cumulative time calculation unit  216  calculates the cumulative times similarly under other operation conditions such as ranges of rates of change of the charging rates and ranges of temperature.  
     The first equivalent coefficient calculation unit  212  calculates the equivalent coefficients for each operation condition. The first equivalent coefficient calculation unit  212  may calculate the equivalent coefficients of the operation conditions based on a predetermined numerical formula and may calculate the equivalent coefficients of the operation conditions based on a predetermined probability regardless of the numerical formula. 
     The first equivalent running time calculation unit  213  calculates sums of values obtained by multiplying the cumulative times calculated by the cumulative time calculation unit  216  by the equivalent coefficients calculated by the first equivalent coefficient calculation unit  212  as the equivalent running times for each running time. 
     The input unit  221  receives inputs of the cumulative times for each operation condition until the present time after the operation of the secondary battery that is the estimation target of the deterioration rates starts. 
     The second equivalent, coefficient calculation unit  222  calculates the same equivalent coefficients as the first equivalent coefficient calculation unit  212  for each operation condition. 
     The second equivalent running time calculation unit  223  calculates sums of values obtained by multiplying the cumulative times calculated by a second cumulative time calculation unit  216  by the equivalent coefficients calculated by the second equivalent coefficient calculation unit  222  as the equivalent miming times for each running time. 
     A method of calculating a deterioration function using the deterioration function calculation device  210  according to the second embodiment will be described. 
       FIG. 6  is a flowchart showing the method of calculating the deterioration function according to the second embodiment. 
     The cumulative time calculation unit  216  calculates the cumulative times of the operations for each operation condition during an running time after operating starts with respect to the running times stored by the storage unit  211  (Step S 21 ). The first equivalent coefficient calculation unit  212  calculates the equivalent coefficients for each operation condition (Step S 22 ). 
     Subsequently, the first equivalent running time calculation unit  213  calculates sums of values obtained by multiplying the cumulative times calculated by the cumulative time calculation unit  216  by the equivalent coefficients calculated by the first equivalent coefficient calculation unit  212  as the equivalent running times (Step S 23 ). Subsequently, the deterioration function calculation unit  114  performs curve fitting based on combinations of the equivalent running times calculated by the first equivalent running time calculation unit  213  and the deterioration rates associated with the running times used for calculating the equivalent running times and calculates the deterioration function (Step S 24 ). 
     The deterioration function evaluation unit  115  calculates dispersion of the deterioration function calculated by the deterioration function calculation unit  114  and the degrees of deterioration stored by the storage unit  211  (Step S 25 ). The deterioration function evaluation unit  115  determines whether the dispersion is a predetermined threshold value or more (Step S 26 ).  
     The deterioration function evaluation unit  115  determines that the accuracy of the equivalent coefficients and the deterioration function is not sufficient when the calculated dispersion is the predetermined threshold value or more (Step S 26 : YES). The first equivalent coefficient calculation unit  212  updates the equivalent coefficients such that the dispersion calculated by the deterioration function evaluation unit  115  become smaller (Step S 27 ), and the process returns to Step S 23 . 
     On the other hand, the deterioration function evaluation unit  115  determines that the accuracy of the equivalent coefficient calculating formula and the deterioration function is sufficient when the calculated dispersion is less than the predetermined threshold value (Step S 26 : NO), and the process of calculating the deterioration function ends. Thus, the deterioration function calculation device  210  can accurately generate the deterioration function indicating relationships of the equivalent running times and the deterioration rates. Therefore, the deterioration function calculation device  210  determines the equivalent coefficients. 
     A method of estimating a deterioration rate using the deterioration rate estimation device  220  according to the second embodiment will be described. 
       FIG. 7  is a flowchart showing the method of estimating the deterioration rate according to the second embodiment. 
     The deterioration rate estimation device  220  estimates the deterioration rates of the secondary battery when the deterioration function is calculated by the deterioration function calculation device  210 . 
     The input unit  221  receives inputs of cumulative times for each operation condition of a secondary battery that is the estimation target of the deterioration rates from a user such as a manager of the secondary battery (Step S 28 ). Subsequently, the second equivalent coefficient calculation unit  222  calculates the equivalent coefficients which are finally calculated by the first equivalent coefficient calculation unit  212  as the equivalent coefficients used for estimating the deterioration rates (Step S 29 ). 
     The second equivalent running time calculation unit  223  calculates the equivalent running times from the cumulative times for each operation condition received by the input unit  221  as the inputs based on the equivalent coefficients calculated by the second equivalent coefficient calculation unit  222  and a predetermined equivalent running time calculating formula (Step S 30 ). An equivalent running time calculating formula used by the second equivalent running time calculation unit  223  is the same as the equivalent running time calculating formula used by the first equivalent running time calculation unit  213 . 
     The deterioration rate estimation unit  124  estimates the deterioration rates of the secondary battery that is the estimation target from the running times calculated by the second equivalent running time calculation unit  223  based on the deterioration function calculated by the deterioration function calculation device  210  and the equivalent running times calculated by the second equivalent running time calculation unit  223  (Step S 31 ). 
     As described above, according to the embodiment, the deterioration rate estimation system  200  calculates the cumulative times for a plurality of operation conditions from limited data and calculates equivalent running times from the cumulative times. Thus, the deterioration rate estimation system  200  can appropriately estimate the deterioration rates even When the values related to the operations which can be acquired are limited. Also, the values related to the operations of the secondary battery can be integrated as the cumulative times for the plurality of operation conditions to reduce the amount of data compared with when the values related to the operations such as currents, voltages, charging rates, and temperatures of the times are accumulated even when data is accumulated for a long time such as five years or ten years. 
     Although embodiments have been described in detail above with reference to the drawings, the specific constitutions are not limited to the above-mentioned constitutions and various changes in design, etc. are also possible. 
       FIG. 8  is a schematic block diagram showing a constitution of a computer  900  according to at least one embodiment. 
     The computer  900  includes a CPU  901 , a main storage device  902 , an auxiliary storage device  903 , and an interface  904 . 
     The above-mentioned deterioration rate estimation systems  100  and  200  are installed in the computer  900 . Also, the above-mentioned operations of the processing units are stored in the auxiliary storage device  903  in the form of a program. The CPU  901  reads the program from the auxiliary storage device  903 , develops the program on the main storage device  902 , and executes the above-mentioned processes according to the program. In addition, the CPU  901  secures storage regions corresponding to the above-mentioned storage units  111  and  211  in the main storage device  902  according to the program.  
     Note that the auxiliary storage device  903  is an example of a non-transitory medium in the at least one embodiment. Other examples of the non-transitory media may include a magnetic disk, a magneto-optical disc, a CD-ROM, a DVD-ROM, a semiconductor memory, etc. connected through the interface  904 . Also, when the program is delivered to the computer  900  through communication lines, the computer  900  which receives the delivered program may develop the program on the main storage device  902  and execute the above-mentioned processes. 
     Also, the program may be for the purpose of implementing some of the above-mentioned functions. The program may be so-called differential tiles (differential program) in which the above-mentioned functions are realized in combination with other programs which have already been stored in the auxiliary storage device  903 , 
     Also, the deterioration function calculation device and the deterioration rate estimation device may be installed in separate computers  900 . 
     INDUSTRIAL APPLICABILITY 
     The deterioration function calculation device can calculate a deterioration function for the purpose of accurately estimating the deterioration rates even when the secondary battery is operated in an unknown operation aspect. The deterioration rate estimation device can accurately estimate the deterioration rates even when the secondary battery is operated in an unknown operation aspect. 
     REFERENCE SIGNS LIST 
       100 : deterioration rate estimation system 
       110 : deterioration function calculation device 
       111 : storage unit 
       112 : first equivalent coefficient calculation unit 
       113 : first equivalent running time calculation unit 
       114 : deterioration function calculation unit 
       115 : deterioration function evaluation unit 
       120 : deterioration rate estimation device 
       121 : input unit 
       122 : second equivalent coefficient calculation unit 
       123 : second equivalent running time calculation unit 
       124 : deterioration rate estimation unit 
       200 : deterioration rate estimation system 
       210 : deterioration function calculation device 
       211 : storage unit 
       212 : first equivalent function calculation unit 
       213 : first equivalent running time calculation unit 
       216 : cumulative time calculation unit 
       220 : deterioration rate estimation device 
       221 : input unit 
       222 : second equivalent coefficient calculation unit 
       223 : second equivalent running time calculation unit