Abstract:
If a particular selection condition is satisfied, a non-load voltage calculation unit ( 105 ) calculates a no-load voltage Vsep as a voltage piece when the current in approximate straight line obtained by statistical processing using the method of least squares for a plurality of sets of data containing current data I(n) and voltage data V(n) is zero. If a particular current condition or voltage condition is continuously satisfied for a predetermined time, an open-circuit voltage calculation unit ( 106 ) calculates a secondary cell terminal voltage as an open-circuit voltage Voc and a voltage-at-zero-current storing unit ( 108 ) stores voltage-at-zero-current Vzo calculated by a voltage-at-zero-current calculation unit ( 107 ). By using a predetermined voltage change amount adjustment constant ΔVbc/adjustment coefficient Kb, an electromotive force change constant Keq, and a polarization voltage generation constant Kpol, an estimated charge/discharge electric amount calculation unit ( 118 A) calculates an estimated charge/discharge electricity amount ΔQe as a function of the change amount ΔVzo of a voltage-at-zero-current Vzo. It is possible to estimate charge/discharge electricity amount without being affected by the current measurement error.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a technique for estimating the state of charge (SOC) of a rechargeable battery such as a nickel-metal hydride battery (Ni-MH) mounted on a pure electric vehicle (PEV), a hybrid electric vehicle (HEV), and the like as a power source for a motor or a drive source for various loads. 
     BACKGROUND OF THE INVENTION 
     An HEV conventionally executes state of charge (SOC) control on a rechargeable battery to maximize fuel consumption efficiency of the vehicle by detecting voltage, current, temperature, and the like of the rechargeable battery and performing calculations to estimate the SOC of the rechargeable battery. For accurate execution of the SOC control, the SOC of the rechargeable battery during charging/discharging needs to be estimated correctly. 
     In one conventional method for estimating the SOC, a battery voltage V and a charge-discharge current I are measured over a predetermined period, an integrated value ∫I of the current is calculated, and a battery polarization voltage Vc(t−1), which was previously estimated, is updated to Vc(t) based on functions of the temperature T, the battery voltage V, and the integrated current value ∫I to obtain a correction voltage V′ (=V−Vc(t)). A plurality of data sets for the correction voltage V′ and current I are obtained and stored. A linear regression line (voltage V′-current I regression line) is obtained through regression analysis using the data sets. A V intercept of the V′-I regression line is estimated as an electromotive force E, and the SOC is estimated from functions of the previously estimated SOC, the electromotive force E, the temperature T, and the current integration value ∫I (refer, for example, to patent document 1). 
     Patent Document 1: Japanese Laid-Open Patent Publication No. 2001-223033 
     SUMMARY OF THE INVENTION 
     However, the above conventional SOC estimation method has the following problems. 
     To estimate the SOC, the method first measures a charging/discharging current flowing through the rechargeable battery with a current sensor. The current sensor needs to measure a large current when used, for example, in an HEV. When a high-precision current sensor is used, the cost will increase. Thus, there is no other way but to use an inexpensive current sensor having a relatively low precision. A current value detected with such a current sensor includes a measurement error. The current error appears as an estimation error of the SOC. In particular, when the charging/discharging rate is smaller than the current error (when, for example, the charging/discharging rate is 1 A and the current error is ±2 A), the estimated SOC starts to behave in an unpredictable manner as time elapses. 
     Further, like in the above prior art example, when the SOC estimation method takes into consideration the influence of the polarization voltage and updates the previously estimated polarization voltage Vc(t−1) of the battery to Vc(t) as a function of the integrated current value measured with the current sensor, the polarization voltage calculated in the past includes a current error, which leads to an estimation error of the polarization voltage. The estimation error accumulates as time elapses, and increases the error between the true value and the estimated value of the SOC. 
     Accordingly, it is an object of the present invention to provide a method and an apparatus for estimating a charging/discharging electricity amount and a polarization voltage without being influenced by a current measurement error, and thereby provide a method and an apparatus for estimating an SOC with a high precision even when a current value includes a measurement error. 
     To achieve the above object, a first aspect of a method for estimating a charging/discharging electricity amount of a rechargeable battery according to the present invention includes the steps of measuring a data set of current flowing through the rechargeable battery and terminal voltage of the rechargeable battery corresponding to the current, and obtaining a plurality of the data sets; calculating a no-load voltage (Vsep) that is a voltage intercept of an approximate line at a zero-current state obtained through statistical processing, such as regression analysis using a least-square method or the like, using the plurality of data sets when a specific selection condition (e.g., the value of the current in the charging direction and the discharging direction is within a predetermined range (e.g., ±50 A), there is at least a predetermined number of the plurality of the data sets in the charging direction and the discharging direction (e.g., ten pieces of data in each direction being included in 60 samples), and the charging/discharging electricity amount during which the plurality of the data sets are being obtained is within a predetermined range (e.g., 0.3 Ah)) is satisfied; calculating an open-circuit voltage (Voc) from the terminal voltage of the rechargeable battery when a specific current condition (e.g., an absolute value of the current is less than 10 A) or voltage condition (e.g., a change amount of the voltage is less than 1 V) is satisfied continuously for a certain period of time (e.g., for 10 seconds); calculating a zero-current state voltage (Vzo) from the no-load voltage or the open-circuit voltage; storing the zero-current state voltage; calculating a zero-current state voltage change amount (ΔVzo) during a period from when the zero-current state voltage is stored to when a zero-current state voltage is calculated subsequently; and calculating an estimated charging/discharging electricity amount (ΔQe) of the rechargeable battery based on the zero-current state voltage change amount. 
     The first aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes the steps of presetting a voltage change amount adjustment constant (ΔVbc) and a voltage change amount adjustment coefficient (Kb), which are determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); presetting an electromotive force change constant (Keq) that is a change amount of an electromotive force for a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery; and presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage for a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount (ΔVzo) using the expression of ΔQe=Kb*(ΔVzo+ΔVbc)/(Keq+Kpol). 
     A second aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention the steps of calculating a polarization voltage (Vpol) of the rechargeable battery based on the estimated charging/discharging electricity amount; storing the calculated polarization voltage; calculating a storage time (th) of the polarization voltage; and calculating a time-dependent voltage change amount (ΔVbp(th)) based on the stored polarization voltage and the storage time. The step of calculating the estimated charging/discharging electricity amount includes calculating an estimated charging/discharging electricity amount based on the time-dependent voltage change amount in addition to the zero-current state voltage change amount. 
     In this case, the step of calculating the time-dependent voltage change amount includes calculating a time-dependent voltage change amount by multiplying the stored polarization voltage by a polarization attenuation ratio that is a function of the storage time. 
     The second aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes the steps of presetting a voltage change amount adjustment coefficient (Kb), which is determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); presetting an electromotive force change constant (Keq) that is a change amount of an electromotive force with respect to a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery; and presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage with respect to a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo and the time-dependent voltage change amount ΔVbp(th) using the expression of
 
Δ Qe=Kb *(Δ Vzo+ΔVbp ( th ))/( Keq+Kpol ).
 
     A third aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention the steps of calculating a polarization voltage of the rechargeable battery based on the estimated charging/discharging electricity amount, calculating an electromotive force (Veq) of the rechargeable battery based on the stored zero-current state voltage and the polarization voltage; storing the calculated electromotive force; calculating a measured charging/discharging electricity amount (ΔQm) during a period in which the electromotive force is being stored from current flowing through the rechargeable battery; calculating an electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ) based on the stored electromotive force and the measured charging/discharging electricity amount; and calculating an electromotive force change amount (ΔVeq) that is a difference between the electromotive force for calculating the estimated charging/discharging electricity amount and the stored electromotive force. The step of calculating the estimated charging/discharging electricity amount includes calculating an estimated charging/discharging electricity amount based on the electromotive force change amount in addition to the zero-current state voltage change amount. 
     In this case, the step of calculating the electromotive force for calculating the estimated charging/discharging electricity amount includes calculating, as the electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ), an electromotive force corresponding to a state of charge obtained by subtracting or adding the measured charging/discharging electricity amount (ΔQm) from or to a state of charge corresponding to the stored electromotive force by referring to an electromotive force characteristic with respect to a state of charge of the rechargeable battery that is prepared beforehand and is parameterized by a temperature. 
     The third aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes the steps of presetting for the zero-current state voltage change amount (ΔVzo) a voltage change amount adjustment constant (ΔVbc) and a voltage change amount adjustment coefficient (kb) that are determined depending on a physical property and a charging/discharging state of the rechargeable battery, and presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage for a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo, the electromotive force change amount, and the measured charging/discharging electricity amount using the expression of ΔQe=Kb*(ΔVzo+ΔVbc)/(ΔVeq/ΔQm+Kpol). 
     A fourth aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention the steps of calculating a polarization voltage (Vpol) of the rechargeable battery based on the estimated charging/discharging electricity amount; storing the calculated polarization voltage; calculating a storage time (th) of the polarization voltage; calculating a time-dependent voltage change amount (ΔVbp(th)) based on the stored polarization voltage and the storage time; calculating an electromotive force (Veq) of the rechargeable battery based on the stored zero-current state voltage and the stored polarization voltage; storing the calculated electromotive force; calculating a measured charging/discharging electricity amount (ΔQm) during a period in which the electromotive force is being stored from current flowing through the rechargeable battery; calculating an electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ) based on the stored electromotive force and the measured charging/discharging electricity amount; and calculating an electromotive force change amount (ΔVeq) that is a difference between the electromotive force for calculating the estimated charging/discharging electricity amount and the stored electromotive force. The step of calculating the estimated charging/discharging electricity amount includes calculating an estimated charging/discharging electricity amount based on the time-dependent voltage change amount and the electromotive force change amount in addition to the zero-current state voltage change amount. 
     In this case, the step of calculating the time-dependent voltage change amount includes calculating a time-dependent voltage change amount by multiplying the stored polarization voltage by a polarization attenuation ratio that is a function of the storage time. 
     Further, the step of calculating the electromotive force for calculating the estimated charging/discharging electricity amount includes calculating, as the electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ), an electromotive force corresponding to a state of charge obtained by subtracting or adding the measured charging/discharging electricity amount (ΔQm) from or to a state of charge corresponding to the stored electromotive force by referring to an electromotive force characteristic with respect to a state of charge of the rechargeable battery that is preset and is parameterized by a temperature. 
     A fourth aspect of the rechargeable battery charging/discharging electricity amount estimation method according to the present invention further includes the steps of presetting an adjustment coefficient (Kb), which is determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); and presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage for a charging/discharging electricity amount in a usage area of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo, the time-dependent voltage change amount ΔVbp(th), the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the expression of ΔQe=Kb*(ΔVzo+ΔVbp(th))/(ΔVeq/ΔQm+Kpol). 
     To achieve the above object, a first aspect of an apparatus for estimating a charging/discharging electricity amount of a rechargeable battery according to the present invention includes a current measurement unit for measuring current flowing through the rechargeable battery as current data (I(n)); a voltage measurement unit for measuring terminal voltage of the rechargeable battery as voltage data (V(n)); a no-load voltage calculation unit for obtaining a plurality of data sets, each including current data from the current measurement unit and voltage data from the voltage measurement unit corresponding to the current data, and for calculating a no-load voltage (Vsep) that is a voltage intercept of an approximate line at a zero-current state obtained through statistical processing, such as regression analysis using a least-square method or the like, using the plurality of data sets when a specific selection condition (e.g., the value of the current in the charging direction and the discharging direction is within a predetermined range (e.g., ±50 A), there is at least a predetermined number of the plurality of the data sets in the charging direction and the discharging direction (e.g., ten pieces of data in each direction being included in 60 samples), and the charging/discharging electricity amount during which the plurality of the data sets are being obtained is within a predetermined range (e.g., 0.3 Ah)) is satisfied; an open-circuit voltage calculation unit for calculating an open-circuit voltage (Voc) from the terminal voltage of the rechargeable battery when a specific current condition (e.g., an absolute value of the current is less than 10 A) or voltage condition (e.g., a change amount of the voltage is less than 1 V) is satisfied continuously for a predetermined period of time (e.g., for 10 seconds); a zero-current state voltage calculation unit for calculating a zero-current state voltage (Vzo) from the no-load voltage or the open-circuit voltage; a zero-current state voltage storage unit for storing the zero-current state voltage; a zero-current state voltage change amount calculation unit for calculating a zero-current state voltage change amount (ΔVzo) during a period from when the zero-current state voltage is stored to when a zero-current state voltage is calculated subsequently; and an estimated charging/discharging electricity amount calculation unit for calculating an estimated charging/discharging electricity amount (ΔQe) of the rechargeable battery based on the zero-current state voltage change amount. 
     The first aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention further includes a voltage change amount adjustment constant-adjustment coefficient setting unit for presetting a voltage change amount adjustment constant (ΔVbc) and a voltage change amount adjustment coefficient (Kb), which are determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); an electromotive force change constant setting unit for presetting an electromotive force change constant (Keq) that is a change amount of an electromotive force with respect to a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery; and a polarization voltage generation constant setting unit for presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage with respect to a change amount of a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo using the expression of ΔQe=Kb*(ΔVzo+ΔVbc)/(Keq+Kpol). 
     A second aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention a polarization voltage calculation unit for calculating a polarization voltage (Vpol) of the rechargeable battery based on the estimated charging/discharging electricity amount; a polarization voltage storage unit for storing the polarization voltage calculated by the polarization voltage calculation unit; and a time-dependent voltage change amount calculation unit for calculating a time-dependent voltage change amount (ΔVbp(th)) based on the polarization voltage stored in the polarization voltage storage unit and a storage time of the polarization voltage. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount based on the time-dependent voltage change amount in addition to the zero-current state voltage change amount. 
     In this case, the time-dependent voltage change amount calculation unit calculates the time-dependent voltage change amount by multiplying the polarization voltage stored in the polarization voltage storage unit by a polarization attenuation ratio that is a function of the storage time. 
     The second aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention further includes a voltage change amount adjustment coefficient setting unit for presetting a voltage change amount adjustment coefficient (Kb), which is determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); an electromotive force change constant setting unit for presetting an electromotive force change constant (Keq) that is a change amount of an electromotive force with respect to a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery; and a polarization voltage generation constant setting unit for presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage with respect to a change amount of a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo and the time-dependent voltage change amount ΔVbp(th) using the expression of ΔQe=Kb*(ΔVzo+ΔVbp(th))/(Keq+Kpol). 
     A third aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention a polarization voltage calculation unit for calculating a polarization voltage of the rechargeable battery based on the estimated charging/discharging electricity amount; a first electromotive force calculation unit for calculating an electromotive force (Veq) of the rechargeable battery based on the zero-current state voltage stored in the zero-current state voltage storage unit and the polarization voltage calculated by the polarization voltage calculation unit; an electromotive force storage unit for storing the electromotive force calculated by the first electromotive force calculation unit; a measured charging/discharging electricity amount calculation unit for calculating a measured charging/discharging electricity amount (ΔQm) during a period in which the electromotive force is being stored in the electromotive force storage unit from current flowing through the rechargeable battery; a second electromotive force calculation unit for calculating an electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ) based on the electromotive force stored in the electromotive force storage unit and the measured charging/discharging electricity amount; and an electromotive force change amount calculation unit for calculating an electromotive force change amount (ΔVeq) that is a difference between the electromotive force for calculating the estimated charging/discharging electricity amount and the electromotive force stored in the electromotive force storage unit. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount based on the electromotive force change amount in addition to the zero-current state voltage change amount. 
     In this case, the second electromotive force calculation unit calculates, as the electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ), an electromotive force corresponding to a state of charge obtained by subtracting or adding the measured charging/discharging electricity amount (ΔQm) from or to a state of charge corresponding to the electromotive force stored in the electromotive force storage unit by referring to an electromotive force characteristic with respect to a state of charge of the rechargeable battery that is prepared beforehand and is parameterized by a temperature. 
     The third aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention further includes a voltage change amount adjustment constant-adjustment coefficient setting unit for presetting a voltage change amount adjustment constant (ΔVbc) and a voltage change amount adjustment coefficient (Kb), which are determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); and a polarization voltage generation constant setting unit for presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage with respect to a charging/discharging electricity amount in a usage region of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo, the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the expression of ΔQe=Kb*(ΔVzo+ΔVbc)/(ΔVeq/ΔQm+Kpol). 
     A fourth aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention further includes in the first aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention a polarization voltage calculation unit for calculating a polarization voltage (Vpol) of the rechargeable battery based on the estimated charging/discharging electricity amount; a polarization voltage storage unit for storing the polarization voltage calculated by the polarization voltage calculation unit; a time-dependent voltage change amount calculation unit for calculating a time-dependent voltage change amount (ΔVbp(th)) based on the polarization voltage stored in the polarization voltage storage unit and a storage time; a first electromotive force calculation unit for calculating an electromotive force (Veq) of the rechargeable battery based on the zero-current state voltage stored in the zero-current state voltage storage unit and the polarization voltage stored in the polarization voltage storage unit; an electromotive force storage unit for storing the electromotive force calculated by the first electromotive force calculation unit; a measured charging/discharging electricity amount calculation unit for calculating a measured charging/discharging electricity amount (ΔQm) during a period in which the electromotive force is being stored in the electromotive force storage unit from current flowing through the rechargeable battery; a second electromotive force calculation unit for calculating an electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ) based on the electromotive force stored in the electromotive force storage unit and the measured charging/discharging electricity amount; and an electromotive force change amount calculation unit for calculating an electromotive force change amount (ΔVeq) that is a difference between the electromotive force for calculating the estimated charging/discharging electricity amount and the electromotive force stored in the electromotive force storage unit. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount based on the time-dependent voltage change amount and the electromotive force change amount in addition to the zero-current state voltage change amount. 
     In this case, the time-dependent voltage change amount calculation unit calculates the time-dependent voltage change amount by multiplying the polarization voltage stored in the polarization voltage storage unit by a polarization attenuation ratio that is a function of the storage time. 
     Further, the second electromotive force calculation unit calculates, as the electromotive force for calculating the estimated charging/discharging electricity amount (Veq 2 ), an electromotive force corresponding to a state of charge obtained by subtracting or adding the measured charging/discharging electricity amount (ΔQm) from or to a state of charge corresponding to the electromotive force stored in the electromotive force storage unit by referring to an electromotive force characteristic with respect to a state of charge of the rechargeable battery that is prepared beforehand and is parameterized by a temperature. 
     The fourth aspect of the rechargeable battery charging/discharging electricity amount estimation apparatus according to the present invention further includes a voltage change amount adjustment coefficient setting unit for presetting an adjustment coefficient (Kb), which is determined depending on a physical property and a charging/discharging state of the rechargeable battery, for the zero-current state voltage change amount (ΔVzo); and a polarization voltage generation constant setting unit for presetting a polarization voltage generation constant (Kpol) that is a change amount of a polarization voltage with respect to a charging/discharging electricity amount in a usage area of a state of charge and that is determined depending on the physical property and the charging/discharging state of the rechargeable battery. The estimated charging/discharging electricity amount calculation unit calculates the estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo, the time-dependent voltage change amount ΔVbp(th), the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the expression of ΔQe=Kb*(ΔVzo+ΔVbp(th))/(ΔVeq/ΔQm+Kpol). 
     To achieve the above object, a method for estimating a polarization voltage of a rechargeable battery according to the present invention includes calculating an estimated charging/discharging electricity amount using any one of the first to fourth aspects of the method for estimating a charging/discharging electricity amount of a rechargeable battery; and re-calculating a polarization voltage of the rechargeable battery based on the estimated charging/discharging electricity amount. 
     To achieve the above object, a method for estimating a state of charge of a rechargeable battery according to the present invention includes calculating an estimated charging/discharging electricity amount using any one of the first to fourth aspects of the method for estimating a charging/discharging electricity amount of a rechargeable battery; and calculating a state of charge of the rechargeable battery based on the estimated charging/discharging electricity amount. 
     To achieve the above object, an apparatus for estimating a polarization voltage of a rechargeable battery according to the present invention includes a polarization voltage re-calculation unit for re-calculating a polarization voltage of the rechargeable battery based on an estimated charging/discharging electricity amount calculated by any one of the first to fourth aspects of the apparatus for estimating a charging/discharging electricity amount of a rechargeable battery. 
     To achieve the above object, an apparatus for estimating a state of charge of a rechargeable battery according to the present invention includes a state-of-charge calculation unit for calculating a state of charge of the rechargeable battery based on an estimated charging/discharging electricity amount calculated by any one of the first to fourth aspects of the apparatus for estimating a charging/discharging electricity amount of a rechargeable battery. 
     According to the present invention, an estimated charging/discharging electricity amount including substantially no current measurement error is calculated based on a measured voltage involving little influence from current measurement error (a zero-current state voltage calculated from a no-load voltage or an open-circuit voltage), and a polarization voltage and an SOC that are not influenced by a current measurement error are calculated using the estimated charging/discharging electricity amount. This improves the precision of SOC estimation, and enables a battery to undergo SOC management that executes protection control and prolongs the life of the battery. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram showing an example structure for a battery pack system according to a first embodiment of the present invention; 
         FIG. 2  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a charging/discharging electricity amount estimation method for a rechargeable battery according to the first embodiment; 
         FIG. 3  is a block diagram showing an example structure of a battery pack system according to a second embodiment of the present invention; 
         FIG. 4  is a graph showing a polarization voltage attenuation ratio γ that is a function of a storage time th of a polarization voltage used to calculate a time-dependent voltage change amount ΔVbp(th); 
         FIG. 5  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a charging/discharging electricity amount estimation method for a rechargeable battery according to the second embodiment; 
         FIG. 6  is a block diagram showing an example structure of a battery pack system according to a third embodiment of the present invention; 
         FIG. 7  is a graph showing electromotive force Veq-state-of-charge SOC characteristics used to calculate an electromotive force change amount ΔVeq from a stored electromotive force (first electromotive force Veq 1 ) and an electromotive force for calculating the estimated charging/discharging electricity amount (second electromotive force Veq 2 ) obtained from a measured charging/discharging electricity amount ΔQm; 
         FIG. 8  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a charging/discharging electricity amount estimation method for a rechargeable battery according to the third embodiment; 
         FIG. 9  is a block diagram showing an example structure of a battery pack system according to a fourth embodiment of the present invention; 
         FIG. 10  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a charging/discharging electricity amount estimation method for a rechargeable battery according to the fourth embodiment; and 
         FIG. 11  is a graph showing time changes of an estimated charging/discharging electricity amount ΔQe calculated based on the flowchart of  FIG. 10  and time changes of a true charging/discharging electricity amount ΔQt calculated based on an integrated current value measured using a high-precision current sensor. 
     
    
    
     DESCRIPTION OF REFERENCE NUMBERS 
     
         
         
           
               1 A,  1 B,  1 C,  1 D Battery Pack System 
               100  Battery Pack 
               101 A,  101 B,  101 C,  101 D, Battery ECU (Charging/Discharging Electricity amount Estimation Apparatus, Polarization Voltage Estimation Apparatus, SOC Estimation Apparatus) 
               102  Voltage Measurement Unit 
               103  Current Measurement Unit 
               104  Temperature Measurement Unit 
               105  No-load Voltage Calculation Unit 
               106  Open-Circuit Voltage Calculation Unit 
               107  Zero-Current State Voltage Calculation Unit 
               108  Zero-Current State Voltage Storage Unit 
               109  Zero-current State Voltage Change Amount Calculation Unit 
               110  Polarization Voltage Calculation Unit 
               1101  Lookup table (LUT) 
               111  Polarization Voltage Storage Unit 
               1111  Timer 
               112  Time-Dependent Voltage Change Amount Calculation Unit 
               113  First Electromotive Force Calculation Unit 
               114  Electromotive Force Storage Unit 
               115  Measured Charging/Discharging Electricity amount Calculation Unit 
               116  Second Electromotive Force Calculation Unit 
               1161  Lookup Table (LUT) 
               117  Electromotive Force Change Amount Calculation Unit 
               118 A,  118 B,  118 C,  118 D Estimated Charging/Discharging Electricity amount Calculation Unit 
               119  SOC Calculation Unit 
               120  Polarization Voltage Re-calculation Unit 
               1201  Lookup Table (LUT) 
               121  Voltage Change Amount Adjustment Constant (ΔVbc)-Adjustment Coefficient (Kb) Setting Unit 
               1211  Lookup Table (LUT) 
               122  Electromotive Force Change Constant (Keq) Setting Unit 
               1221  Lookup Table (LUT) 
               123  Polarization Voltage Generation Constant (Kpol) Setting Unit 
               1231  Lookup Table (LUT) 
               124  Voltage Change Amount Adjustment Coefficient (Kb) Setting Unit 
           
         
       
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will now be described with reference to the drawings. 
     First Embodiment 
       FIG. 1  is a block diagram showing an example structure for a battery pack system according to a first embodiment of the present invention. In  FIG. 1 , a battery pack system  1 A includes a battery pack  100  and a battery ECU  101 A including an SOC estimation apparatus of the present invention which is part of a microcomputer system. 
     The battery pack  100 , mounted for example on an HEV, is formed by a plurality of battery blocks that are electrically connected in series. Each battery block is formed by a plurality of cells or battery modules, e.g., nickel-metal hydride batteries, which are electrically connected in series in order to obtain a predetermined output to a motor. 
     The battery ECU  101 A includes a voltage measurement unit  102  for measuring a terminal voltage for each battery block in the battery pack  100  detected by a voltage sensor (not shown) in predetermined sampling cycles as voltage data V(n), a current measurement unit  103  for measuring a charging/discharging current of the battery pack  100  detected by a current sensor (not shown) in predetermined sampling cycles as current data I(n) (the sign of which indicates either the charging direction or the discharging direction), and a temperature measurement unit  104  for measuring the temperature of each battery block in the battery pack  100  detected by a temperature sensor (not shown) as temperature data T(n). 
     The voltage data V(n) from the voltage measurement unit  102  and the current data I(n) from the current measurement unit  103  are input as a data set into a no-load voltage calculation unit  105 . The no-load voltage calculation unit  105  determines that the data set of voltage data V(n) and current data I(n) is an effective data set when a specific selection condition is satisfied, that is, the value of the current data I(n) in the charging direction (−) and the discharging direction (+) is within a predetermined range (e.g., ±50 A), there is at least a predetermined number of current data I(n) in the charging direction and the discharging direction (e.g., ten pieces of data in each direction being included in 60 samples), and the charging/discharging electricity amount during which the data set is being obtained is within a predetermined range (e.g., 0.3 Ah). 
     Next, the no-load voltage calculation unit  105  obtains a linear voltage-current line (approximate line) from the effective data sets by performing statistical processing such as regression analysis using a least-square method or the like to calculate a no-load voltage Vsep, which is a voltage value (voltage intercept) in a zero-current state. 
     The voltage data V(n) and the current data I(n) are also input into an open-circuit voltage calculation unit  106 . When a specific current condition (e.g., an absolute value of the current data I(n) is less than 10 A) or a specific voltage condition (e.g., a change amount of the voltage data V(n) is less than 1 V) is satisfied continuously for a certain period of time (e.g., for 10 seconds), the open-circuit voltage calculation unit  106  adds a value obtained by multiplying a component resistance Rcom by an average value Iave of the current data I(n) to an average value Vave of the voltage data V(n) of each battery block to correct a voltage drop caused by a component resistor and calculate an open-circuit voltage Voc
 
(Voc= V ave+ R com* I ave)
 
     The no-load voltage Vsep from the no-load voltage calculation unit  105  and the open-circuit voltage Voc from the open-circuit voltage calculation unit  106  are input into a zero-current state voltage calculation unit  107 . The zero-current state voltage calculation unit  107  determines that the calculation accuracy is sufficiently high and selects the no-load voltage Vsep when the above selection condition is satisfied. The zero-current state voltage calculation unit  107  also determines that the calculation accuracy is sufficiently high and selects the open-circuit voltage Voc when the selection condition is not satisfied but the above current condition or voltage condition is satisfied continuously for a certain period of time and outputs the selected voltage as a zero-current state voltage Vzo. When none of the conditions is satisfied, the zero-current state voltage Vzo is not calculated. This structure ensures a sufficiently high calculation accuracy of the zero-current state voltage Vzo. 
     The zero-current state voltage Vzo from the zero-current state voltage calculation unit  107  is input into a zero-current state voltage storage unit  108 , where it is stored as a voltage Vzoh. 
     A zero-current state voltage Vzo calculated subsequently by the zero-current state voltage calculation unit  107  and the zero-current state voltage Vzoh stored in the zero-current state voltage storage unit  108  are input into a zero-current state voltage change amount calculation unit  109 , where an amount of change by which the zero-current state voltage Vzo changes from the stored zero-current state voltage Vzoh (zero-current state voltage change amount) ΔVzo is calculated. Here, the voltage change amount is not calculated as an amount of voltage change occurring in a predetermined time. The zero-current state voltage that is calculated is stored, and an amount of voltage change occurring between the stored zero-current state voltage and the subsequently calculated zero-current state voltage is calculated. This reduces failures in the calculation of the voltage change amount when the no-load voltage Vsep and the open-circuit voltage Voc cannot be obtained. 
     A voltage change amount adjustment constant (ΔVbc)-adjustment coefficient (Kb) setting unit  121  presets a voltage change amount adjustment constant ΔVbc and a voltage change amount adjustment coefficient Kb by referring to a lookup table (LUT)  1211  prestoring values of the voltage change amount adjustment constant ΔVbc and the voltage change amount adjustment coefficient Kb parameterized by a temperature in a manner that the values depend on polarization characteristics determined by the physical properties of the rechargeable battery or voltage attenuation characteristics determined by the charging/discharging (usage) state of the rechargeable battery. For example, the LUT  1211  stores 0.01 V as a value of the voltage change amount adjustment constant ΔVbc corresponding to a temperature of 25° C. The adjustment coefficient Kb is a coefficient that is appropriately set in accordance with an actual system. 
     An electromotive force change constant (Keq) setting unit  122  presets an electromotive force change constant Keq based on temperature data T(n) measured by the temperature measurement unit  104  by referring to a lookup table (LUT)  1211 . More specifically, the electromotive force change constant setting unit  122  refers to the inclination of the characteristic curve of values of the electromotive force change constant Keq with respect to values of the charging (or discharging) current amount in an SOC usage region (e.g., in an SOC range of 20 to 80%) prestored in the LUT  1221  and parameterized by a temperature in a manner that the values depend on the physical properties or charging/discharging (usage) state of the rechargeable battery. For example, the LUT  1211  stores 0.1 V/Ah as a value of the electromotive force change constant Keq corresponding to a temperature of 25° C. 
     A polarization voltage generation constant (Kpol) setting unit  123  presets a polarization voltage generation constant Kpol based on temperature data T(n) measured by the temperature measurement unit  104  by referring to a lookup table (LUT)  1231 . More specifically, the polarization voltage generation constant setting unit  123  refers to the inclination of the characteristic curve of values of the polarization voltage generation constant Kpol with respect to values of the charging (or discharging) current amount prestored in the LUT  1231  and parameterized by a temperature in a manner that the values depend on the physical properties or charging/discharging (usage) state of the rechargeable battery. For example, the LUT  1231  stores 0.1 V/Ah as a value of the polarization voltage generation constant Kpol corresponding to a temperature of 25° C. and an SOC of 60%. 
     The zero-current state voltage change amount ΔVzo from the zero-current state voltage change amount calculation unit  109 , the voltage change amount adjustment constant ΔVbc and the voltage change amount adjustment coefficient Kb from the voltage change amount adjustment constant-adjustment coefficient setting unit  121 , the electromotive force change constant Keq from the electromotive force change constant setting unit  122 , the polarization voltage generation constant Kpol from the polarization voltage generation constant setting unit  123  are input into an estimated charging/discharging electricity amount calculation unit  118 A. The estimated charging/discharging electricity amount calculation unit  118 A calculates an estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo using the following expression.
 
Δ Qe=Kb *(Δ Vzo+ΔVbc )/( Keq+Kpol )
 
     Here, the zero-current state voltage Vzo obtained from the no-load voltage Vsep or the open-circuit voltage Voc is not used but the zero-current state voltage change amount ΔVzo is used to calculate the estimated charging/discharging electricity amount ΔQe during a predetermined period from when the voltage Vzo is calculated once to when the voltage Vzo is calculated subsequently. The reason for using the zero-current state voltage change amount ΔVzo instead of the zero-current state voltage Vzo is as follows. The no-load voltage Vsep or the open-circuit voltage Voc is modeled as being formed by elements including an electromotive force element and a polarization voltage element. The electromotive force element and the polarization voltage element change in a manner dependent on the charging/discharging electricity amount. Thus, the estimated charging/discharging electricity amount ΔQe can be calculated from the zero-current state voltage change amount ΔVzo. Further, the reason why the voltage change amount adjustment constant ΔVbc is added to the zero-current state voltage change amount ΔVzo in the expression for calculating the estimated charging/discharging electricity amount ΔQe is that a polarization generated during a predetermined period attenuates and the addition corrects the attenuation amount of polarization. 
     The estimated charging/discharging electricity amount ΔQe is input into a polarization voltage re-calculation unit  120 . The polarization voltage re-calculation unit  120  re-calculates the polarization voltage Vpe based on temperature data T(n) measured by the temperature measurement unit  104  by referring to a lookup table (LUT)  1201 . More specifically, the polarization voltage re-calculation unit  120  refers to the characteristic curve or expression of values of the polarization voltage Vpe with respect to values of the estimated charging/discharging electricity amount ΔQe prestored in the LUT  1201  and parameterized by a temperature. 
     Further, the estimated charging/discharging electricity amount ΔQe is input into an SOC calculation unit  119 , where the SOC of each battery block in the battery pack  100  is calculated using the polarization voltage Vpe etc. based on the estimated charging/discharging electricity amount ΔQe. 
     In the present embodiment, the charging/discharging electricity amount is not calculated by integrating the measured current as in the prior art example, but the charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage that involves little influence of a current measurement error. This improves the calculation accuracy of the polarization voltage and the SOC. 
     The processing procedures for estimating the SOC and the polarization voltage in the battery pack system with the above-described structure of the present embodiment will now be described with reference to  FIG. 2 . 
       FIG. 2  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a rechargeable battery charging/discharging electricity amount estimation method according to the first embodiment. In  FIG. 2 , voltage data V(n) and current data I(n) are first measured as a data set (step S 201 ). Next, determination is performed as to whether the data set of voltage data V(n) and current data I(n) measured in step S 201  satisfies the specific selection condition described above to examine whether the data set is an effective data set (step S 202 ). When the data set satisfies the specific selection condition in the determination of step S 202  (Yes), the processing proceeds to step S 203 , where a plurality of effective data sets are obtained (e.g., ten data sets in each of the charging/discharging directions are obtained from 60 samples), a linear approximate line (V-I line) is obtained from the effective data sets through statistical processing such as regression analysis using a least-square method or the like, and the V-intercept of the approximate line is calculated as the no-load voltage Vsep. Next, the zero-current state voltage Vzo is calculated from the calculated no-load voltage Vsep (step S 206 ), and is stored as the voltage Vzoh (Vzoh←Vzo: step S 207 ). 
     When the data set does not satisfy the specific selection condition in the determination of step S 202  (No), the processing proceeds to step S 204  to determine whether the data set satisfies the specific current condition or voltage condition described above continuously for a certain period of time. When the data set satisfies the specific current condition (e.g., when the absolute value of the current data I(n) is less than 10 A continuously for 10 seconds) (Yes) or satisfies the voltage condition (e.g., when the change amount of the voltage data V(n) is less than 1 V continuously for 10 seconds) in the determination of step S 204  (Yes), the processing proceeds to step S 205 , where the value obtained by multiplying the average value Iave of the current data I(n) by the component resistance Rcom is added to the average value Vave of the voltage data V(n) of each battery block during that time to correct the voltage drop caused by the component resistor and calculate the open-circuit voltage Voc (Voc=Vave+Rcom*Iave). Next, the zero-current state voltage Vzo is calculated from the calculated open-circuit voltage Voc (step S 206 ) and stored as the voltage Vzoh (Vzoh←Vzo: step S 207 ). 
     When the data set does not satisfy the specific current condition and the voltage condition in the determination of step S 204  (No), this routine is ended and the processing is terminated. 
     The change amount (zero-current state current change amount) ΔVzo by which the voltage Vzo calculated in step S 206  in the subsequent interrupt processing changes from the zero-current state voltage Vzoh stored in step S 207  is calculated (step S 208 ). 
     Next, the voltage change amount adjustment constant ΔVbc and the voltage change amount adjustment coefficient Kb, the electromotive force change constant Keq, and the polarization voltage generation constant Kpol are preset (steps S 209 , S 210  and S 211 ), and the estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo using the expression ΔQe=Kb*(ΔVzo+ΔVbc)/(Keq+Kpol) (step S 212 ). 
     Further, because the polarization voltage is a value dependent on the history of charging/discharging operations of the battery, the polarization voltage is re-calculated from the estimated charging/discharging electricity amount ΔQe (step S 214 ). 
     Further, the SOC is calculated using the polarization voltage Vpe etc. based on the estimated charging/discharging electricity amount ΔQe calculated in this manner (step S 213 ). 
     As described above, the state-of-charge SOC and the polarization voltage Vpe of each battery block in the battery pack  100  are estimated. 
     Although the linear function expression of the zero-current state voltage change amount ΔVzo is used to calculate the estimated charging/discharging electricity amount ΔQe in the present embodiment, an N degree function expression (N is a natural number) or an exponential function expression may be used instead. 
     Second Embodiment 
       FIG. 3  is a block diagram showing an example structure of a battery pack system  1 B according to a second embodiment of the present invention. In  FIG. 3 , the components having the same structure and functions as the components of the first embodiment illustrated in  FIG. 1  will be given the same reference numbers as those components and will not be described. 
     A battery ECU  1 B of the present embodiment calculates an estimated charging/discharging electricity amount ΔQe not only by using a zero-current state voltage change amount ΔVzo as in the first embodiment but also by obtaining a time-dependent voltage change amount ΔVbp(th) from a stored polarization voltage Vph and a storage time th and using the time-dependent voltage change amount ΔVbp(th) instead of using a voltage change amount adjustment coefficient ΔVbc. 
     In  FIG. 3 , an estimated charging/discharging electricity amount ΔQe from an estimated charging/discharging electricity amount calculation unit  118 B is input into a polarization voltage calculation unit  110 . The polarization voltage calculation unit  110  calculates a polarization voltage Vpol based on temperature data T(n) measured by a temperature measurement unit  104  by referring to a lookup table (LUT)  1101 . More specifically, the polarization voltage calculation unit  110  refers to the characteristic curve or expression of values of the polarization voltage Vpol with respect to values of the estimated charging/discharging electricity amount ΔQe prestored in the LUT  1101  and parameterized by a temperature. 
     The polarization voltage Vpol from the polarization voltage calculation unit  110  is input into a polarization voltage storage unit  111  and is stored as a voltage Vph, and its storage time th is counted by a timer  1111 . The polarization voltage Vph stored in the polarization voltage storage unit  111  and the storage time th counted by the timer  1111  are input into a time-dependent voltage change amount calculation unit  112 , where the stored polarization voltage Vph is multiplied by a polarization voltage attenuation ratio γ(th) that is a function of the storage time th shown in  FIG. 4  to calculate a time-dependent voltage change amount ΔVbp(th). 
     A zero-current state voltage change amount ΔVzo from a zero-current state voltage change amount calculation unit  109 , the time-dependent voltage change amount ΔVbp(th) from the time-dependent voltage change amount calculation unit  112 , a voltage change amount adjustment coefficient Kb from a voltage change amount adjustment coefficient setting unit  124 , an electromotive force change coefficient Keq from an electromotive force change coefficient setting unit  122 , and a polarization voltage generation constant Kpol from a polarization voltage generation constant setting unit  123  are input into an estimated charging/discharging electricity amount calculation unit  118 B. The estimated charging/discharging electricity amount calculation unit  118 B calculates an estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo and the time-dependent voltage change amount ΔVbp(th) using the following expression.
 
Δ Qe=Kb *(Δ Vzo+ΔVbp ( th ))/( Keq+Kpol )
 
     The remaining structure and functions are the same as in the first embodiment. 
     In the present embodiment, the time-dependent voltage change amount ΔVbp(th) is used instead of the voltage change amount adjustment coefficient ΔVbc. This improves the calculation accuracy of the estimated charging/discharging electricity amount ΔQe as compared with the first embodiment. 
       FIG. 5  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a rechargeable battery charging/discharging electricity amount estimation method according to the second embodiment. In  FIG. 5 , the steps that are the same as the steps of the first embodiment illustrated in  FIG. 2  will be given the same reference numbers as those steps and will not be described. 
     The voltage change amount adjustment coefficient Kb, the electromotive force change constant Keq, and the polarization voltage generation constant Kpol are preset (steps S 501 , S 210 , and S 211 ), and the estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo and the time-dependent voltage change amount ΔVbp(th) using the time-dependent voltage change amount ΔVbp(th) that has been previously calculated in a loop, which will be described later, and stored. The calculation uses the expression ΔQe=Kb*(ΔVzo+ΔVbp(th))/(Keq+Kpol) (step S 502 ). 
     Next, the polarization voltage Vpol is calculated based on the estimated charging/discharging electricity amount ΔQe calculated previously in step S 502  (step S 503 ). The calculated polarization voltage Vpol is stored as the voltage Vph, and its storage time th is calculated (step S 505 ). Next, the stored polarization voltage Vph is multiplied by the polarization voltage attenuation ratio γ(th) that is a function of the storage time th to calculate the time-dependent voltage change amount ΔVbp(th) (step S 506 ). The time-dependent voltage change amount ΔVbp(th) calculated in this manner is used to subsequently calculate the estimated charging/discharging electricity amount ΔQe in step S 502 . 
     The remaining part of the processing procedures is the same as in the first embodiment. 
     Third Embodiment 
       FIG. 6  is a block diagram showing an example structure of a battery pack system  1 C according to a third embodiment of the present invention. In  FIG. 6 , the components having the same structure and functions as the components of the first and second embodiments illustrated in  FIGS. 1 and 3  will be given the same reference numbers as those components and will not be described. 
     A battery ECU  1 C of the present embodiment calculates an estimated charging/discharging electricity amount ΔQe not only by using a zero-current state voltage change amount ΔVzo as in the first embodiment but also by calculating an electromotive force Veq 1  from a zero-current state voltage Vzo and a polarization voltage Vpol, obtaining an electromotive force change amount ΔVeq from a stored electromotive force Veq 1 , and using a value obtained by dividing an electromotive force change coefficient ΔVeq by a measured charging/discharging electricity amount ΔQm obtained from current data I(n) instead of using an electromotive force change coefficient Keq. 
     In  FIG. 6 , a polarization voltage Vpol from a polarization voltage calculation unit  110  and a zero-current state voltage Vzoh stored in a zero-current state voltage storage unit  108  are input into a first electromotive force calculation unit  113 . Here, the polarization voltage Vpol is subtracted from the stored zero-current state voltage Vzoh to calculate a first electromotive force Veq 1 . The first electromotive force Veq 1  is stored in an electromotive force storage unit  114 . 
     Further, current data I(n) from a current measurement unit  103  is input into a measured charging/discharging electricity amount calculation unit  115 , where the current data I(n) is integrated to calculate a measured charging/discharging electricity amount ΔQm. The measured charging/discharging electricity amount ΔQm from the measured charging/discharging electricity amount calculation unit  115  and an electromotive force Veq 1  stored in the electromotive force storage unit  114  are input into a second electromotive force calculation unit  116 . 
     The second electromotive force calculation unit  116  calculates a second electromotive force Veq 2 , which is an electromotive force for calculating an estimated charging/discharging electricity amount, based on temperature data T(n) measured by a temperature measurement unit  104  by referring to a lookup table (LUT)  1161 . More specifically, the second electromotive force calculation unit  116  refers to the characteristic curve or expression of values of the electromotive force Veq with respect to values of the SOC prestored in the LUT  1161  and parameterized by a temperature. The second electromotive force Veq 2  is calculated by calculating an electromotive force corresponding to an SOC obtained by adding or subtracting the measured charging/discharging electricity amount ΔQm to or from the SOC corresponding to the stored first electromotive force Veq 1  as shown in the graph in  FIG. 7 . 
     The first electromotive force Veq 1  stored in the electromotive force storage unit  114  and the second electromotive force Veq 2  from the second electromotive force calculation unit  116  are input into an electromotive force change amount calculation unit  117 , where a difference between the first electromotive force Veq 1  and the second electromotive force Veq 2  is calculated as an electromotive force change amount ΔVeq as shown in the graph in  FIG. 7 . 
     A zero-current state voltage change amount ΔVzo from a zero-current state voltage change amount calculation unit  109 , a voltage change amount adjustment constant ΔVbc and a voltage change amount adjustment coefficient Kb from a voltage change amount adjustment constant-adjustment coefficient setting unit  121 , a polarization voltage generation constant Kpol from a polarization voltage generation constant setting unit  123 , an electromotive force change amount ΔVeq from an electromotive force change amount calculation unit  117 , and a measured charging/discharging electricity amount ΔQm from a measured charging/discharging electricity amount calculation unit  115  are input into an estimated charging/discharging electricity amount calculation unit  118 C. The estimated charging/discharging electricity amount calculation unit  118 C calculates the estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo, the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the following expression.
 
Δ Qe=Kb *(Δ Vzo+ΔVbc )/(Δ Veq/ΔQm+Kpol )
 
     The remaining structure and functions are the same as in the first embodiment. 
     In the present embodiment, the estimated charging/discharging electricity amount ΔQe is calculated from the electromotive force change amount according to the voltage change amount (ΔVzo+ΔVbc). This improves the calculation accuracy of the estimated charging/discharging electricity amount ΔQe as compared with the first embodiment. 
     The processing procedures for estimating the SOC and the polarization voltage in the battery pack system with the above-described structure of the present embodiment will now be described with reference to  FIG. 8 . 
       FIG. 8  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a rechargeable battery charging/discharging electricity amount estimation method according to the third embodiment. In  FIG. 8 , the steps that are the same as the steps of the first and second embodiments illustrated in  FIGS. 2 and 5  will be given the same reference numbers as those steps and will not be described. 
     The voltage change amount adjustment coefficient ΔVbc, the voltage change amount adjustment coefficient Kb, and the polarization voltage generation constant Kpol are preset (steps S 209  and S 211 ), and the estimated charging/discharging electricity amount ΔQe is calculated as a function of the zero-current state voltage change amount ΔVzo, the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the electromotive force change amount ΔVeq and the measured charging/discharging electricity amount ΔQm that have been previously calculated in a loop, which will be described later, and have been stored. The calculation uses the expression ΔQe=Kb*(ΔVzo+ΔVbc)/(ΔVeq/ΔQm+Kpol) (step S 801 ). 
     Next, the polarization voltage Vpol is calculated based on the estimated charging/discharging electricity amount ΔQe previously calculated in step S 502  (step S 503 ). The polarization voltage Vpol is subtracted from the stored zero-current state voltage Vzoh to calculate the first electromotive force Veq 1  (step S 802 ). Next, the calculated first electromotive force Veq 1  is stored (step S 803 ), and the measured charging/discharging electricity amount ΔQm during when the first electromotive force Veq 1  is being stored is calculated (step S 804 ). The second electromotive force, which is as an electromotive force for calculating an estimated charging/discharging electricity amount, is calculated from the measured charging/discharging electricity amount ΔQm as shown in the graph in  FIG. 7  (step S 805 ), and a difference between the first electromotive force Veq 1  and the second electromotive force Veq 2  is calculated as the electromotive force change amount ΔVeq (step S 806 ). The electromotive force change amount ΔVeq calculated in this manner is used to subsequently calculate the estimated charging/discharging electricity amount ΔQe in step S 801 . 
     The remaining part of the processing procedures is the same as in the first embodiment. 
     Fourth Embodiment 
       FIG. 9  is a block diagram showing an example structure of a battery pack system  1 D according to a fourth embodiment of the present invention. In  FIG. 9 , the components having the same structure and functions as the components of the first, second, and third embodiments illustrated in  FIGS. 1 ,  3 , and  6  will be given the same reference numbers as those components and will not be described. 
     A battery ECU  1 D of the present embodiment calculates an estimated charging/discharging electricity amount ΔQe not only by using a zero-current state voltage change amount ΔVzo as in the first embodiment, but also by calculating a time-dependent voltage change amount ΔVbp(th) from a stored polarization voltage Vph and a stored time th and using the time-dependent voltage change amount ΔVbp(th) instead of using a voltage change amount adjustment constant ΔVbc as in the second embodiment, and further by calculating an electromotive force Veq 1  from a zero-current state voltage Vzo and a polarization voltage Vpo, obtaining an electromotive force change amount ΔVeq from a stored electromotive force Veq 1 , and using a value obtained by dividing an electromotive force change amount ΔVeq by a measured charging/discharging electricity amount ΔQm obtained from current data I(n) instead of using an electromotive force change constant Keq as in the third embodiment. 
     In  FIG. 9 , a zero-current state voltage change amount ΔVzo from a zero-current state voltage change amount calculation unit  109 , a voltage change amount adjustment coefficient Kb from a voltage change amount adjustment coefficient setting unit  124 , a polarization voltage generation constant Kpol from a polarization voltage generation constant setting unit  123 , a time-dependent voltage change amount ΔVbp(th) from a time-dependent voltage change amount calculation unit  112 , an electromotive force change amount ΔVeq from an electromotive force change amount calculation unit  117 , and a measured charging/discharging electricity amount ΔQm from a measured charging/discharging electricity amount calculation unit  115  are input into an estimated charging/discharging electricity amount calculation unit  118 D. The estimated charging/discharging electricity amount calculation unit  118 D calculates an estimated charging/discharging electricity amount ΔQe as a function of the zero-current state voltage change amount ΔVzo, the time-dependent voltage change amount ΔVbp(th), the electromotive force change amount ΔVeq, and the measured charging/discharging electricity amount ΔQm using the following expression.
 
Δ Qe=Kb *(Δ Vzo+ΔVbp ( th ))/(Δ Veq/ΔQm+Kpol )
 
     The remaining structure and functions are the same as in the first, second, and third embodiments. 
     In the present embodiment, the time-dependent voltage change amount ΔVbp(th) is used instead of the voltage change amount adjustment constant ΔVbc, and the estimated charging/discharging electricity amount ΔQe is calculated from the electromotive force change amount according to the voltage change amount (ΔVzo+ΔVbc). This improves the calculation accuracy of the estimated charging/discharging electricity amount ΔQe as compared with the first, second, and third embodiments. 
     The processing procedures for estimating the SOC and the polarization voltage in the battery pack system with the above-described structure of the present embodiment will now be described with reference to  FIG. 10 . 
       FIG. 10  is a flowchart showing the processing procedures for an SOC estimation method and a polarization voltage estimation method including a rechargeable battery charging/discharging electricity amount estimation method according to the fourth embodiment. In  FIG. 10 , the steps that are the same as the steps of the first, second, and third embodiments illustrated in  FIGS. 2 ,  5 , and  8  will be given the same reference numbers as those steps and will not be described. 
     In  FIG. 10 , the processing procedures differ from the first, second, and third embodiments in the processing in step S 1001  for calculating the estimated charging/discharging electricity amount ΔQe. The processing in step S 1001  is described above. 
       FIG. 11  is a graph showing time changes (indicated by a solid line) of the estimated charging/discharging electricity amount ΔQe calculated based on the flowchart of  FIG. 10  in the present embodiment and time changes (indicated by a broken line) of the charging/discharging electricity amount ΔQt (referred to as “true charging/discharging electricity amount” in the present specification) calculated based on an integrated value of current measured by a high-precision current sensor (including no current error). 
     As shown in  FIG. 11 , the present embodiment enables the estimated charging/discharging electricity amount ΔQe to approach the true charging/discharging electricity amount ΔQt. 
     INDUSTRIAL APPLICABILITY 
     As described above, the rechargeable battery charging/discharging current estimation method and apparatus of the present invention calculate the estimated charging/discharging electricity amount including almost no current measurement error from the measured voltage that involves little influence of a current measurement error (no-load voltage or open-circuit voltage) or from the measured charging/discharging electricity amount including a current measurement error. Further, the rechargeable battery polarization voltage estimation method and apparatus and the rechargeable battery SOC estimation method and apparatus of the present invention use the estimated charging/discharging electricity amount including almost no current measurement error to estimate the polarization voltage and the SOC that are not influenced by a current measurement error, so that the methods and apparatuses of the present invention are applicable to electric vehicles that require highly precise SOC estimation, such as a pure electric vehicle (PEV), a hybrid electric vehicle (HEV), and a hybrid electric automobile using a fuel battery and a rechargeable battery.