Detecting method for detecting internal state of a rechargeable battery, detecting device for practicing said detecting method, and instrument provided with said detecting device

• US 6,563,318 B2
• Filed: 05/23/2001
• Issued: 05/13/2003
• Est. Priority Date: 05/23/2000
• Status: Expired due to Fees

• Current Assignee: Canon Kabushiki Kaisha (Canon Inc.)
• Original Assignee: Canon Kabushiki Kaisha (Canon Inc.)
• Inventors: Degura, Yasusaburo, Kawakami, Soichiro
• Primary Examiner(s): Tso, Edward H.
• Application Number:
  US09/862,307
• Publication Number:
  US 20020109506A1
• Time in Patent Office: 720 Days
• Field of Search: 324/426, 324/427, 324/428, 324/430, 324/431, 324/432, 324/433, 320/132, 320/134, 320/136, 320/149, 320/DIG.19, 320/DIG.21
• US Class Current: 324/426
• CPC Class Codes: G01R 31/389 Measuring internal impedance, internal conductance or related variables
• CPC Class Codes: G01R 31/392 Determining battery ageing or deterioration, e.g. state of health
• CPC Class Codes: G01R 31/52 Testing for short-circuits, leakage current or ground faults

Abstract

A detecting method for detecting an internal state of an inspective rechargeable battery (B_a), said internal state including a deterioration state, an electricity storable capacity, a remaining capacity, and an internal resistance of said inspective rechargeable battery (B_a), comprising: (1) a step in which basic data (BD) of characteristics of a normal non-deteriorated rechargeable battery (B_n) as a reference rechargeable battery for said inspective rechargeable battery (B_a) are provided; and (2) a step in which for said inspective rechargeable battery (B_a), a voltage value or/and a current value thereof are measured, and the measured result is compared with said basic data (BD) obtained in said step (1) to judge whether or not said inspective rechargeable battery (B_a) is of a deterioration mode and to detect the internal state thereof.

Claims

1. A detecting method for detecting an internal state of an inspective rechargeable battery (B_a), said internal state including a deterioration state, an electricity storable capacity, a remaining capacity, and an internal resistance of said inspective rechargeable battery (B_a),

said detecting method comprising:

(1) a step in which basic data (BD) of characteristics of a normal non-deteriorated rechargeable battery (B_n) as a reference rechargeable battery for said inspective rechargeable battery (B_a) are provided; and

(2) a step in which for said inspective rechargeable battery (B_a), a voltage value or/and a current value thereof are measured, and the measured result is compared with said basic data (BD) obtained in said step (1) to judge;

(i) the inspective rechargeable battery (B_a) is short-circuited,

(ii) the internal resistance of the inspective rechargeable battery (B_a) is increased,

(iii) the electricity storable capacity of the inspective rechargeable battery (B_a) is decreased,

(iv) the electricity storable capacity of the rechargeable battery (B_a) is decreased and the internal resistance thereof is increased, or

(v) the inspective rechargeable battery (B_a) is normal.

3. The detecting method according to claim 1, wherein said basic data (BD) comprises averaged basic data obtained by providing a plurality of normal non-deteriorated rechargeable batteries (B_n) and subjecting said plurality of normal non-deteriorated rechargeable batteries (B_n) to charging and discharging under various temperature conditions and at various rates of charge or discharge where the battery voltages, and the remaining capacities or the discharged electricity quantities of the normal non-deteriorated rechargeable batteries (B_n) are measured and averaging the measured battery voltages and the measured remaining capacities or the measured discharged electricity quantities of the normal non-deteriorated rechargeable batteries (B_n).

4. The detecting method according to claim 1, wherein said basic data (BD) are basic data previously obtained by way of computer simulation.

5. The detecting method according to claim 3, wherein said basic data are obtained by way of computer simulation on the basis of said averaged basic data (BD).

6. The detecting method according to claim 1, wherein the inspective rechargeable battery (B_a) is judged of whether or nor it is short-circuited, then the inspective rechargeable battery (B_a) is judged of whether or not the electricity storable capacity of the battery is decreased or whether or not the internal resistance of the battery is increased.

7. The detecting method according to claim 1, wherein:

(1) the inspective rechargeable battery (B_a) is judged to be short-circuited when the battery falls in any of the following cases (i) to (iv);

(i) a case where when the inspective rechargeable battery (B_a) is paused without subjecting to charging or discharging, the battery has a decrease with the passage of time in the open-circuit voltage,

(ii) a case where upon charging, an increase in the battery voltage or open-circuit voltage of the inspective rechargeable battery (B_a) is smaller than that of the normal rechargeable battery (B_n) which is corresponding to the inspective rechargeable battery (B_a),

(iii) a case where in comparison with the normal rechargeable battery (B_n), the open-circuit voltage of the inspective rechargeable battery (B_a) is smaller than that of the normal rechargeable battery (B_n) and a decrease in the battery voltage of the inspective rechargeable battery (B_a) upon discharging is greater than that of the normal rechargeable battery (B_n), and

(iv) a case where the internal resistance of the inspective rechargeable battery (B_a) is smaller than that of the normal rechargeable battery (B_n);

(2) when the inspective rechargeable battery (B_a) is judged to be not short-circuited in the judgment (1) but it falls in any of the following cases (i) to (iii), the inspective rechargeable battery (B_a) is judged that the internal resistance is increased;

(i) a case where the open-circuit voltage of the inspective rechargeable battery (B_a) is substantially the same as that of the normal rechargeable battery (B_n) but an increase in the battery voltage of the former upon charging is greater than that of the latter,

(ii) a case where the open-circuit voltage of the inspective rechargeable battery (B_a) is substantially the same as that of the normal rechargeable battery (B_n) but a decrease in the battery voltage of the former upon discharging is greater than that of the latter, and

(iii) a case where the internal resistance of the inspective rechargeable battery (B_a) is greater than that of the normal rechargeable battery (B_n);

(3) when the inspective rechargeable battery (B_a) is judged to be not short-circuited in the judgment (1) but it falls in any of the following cases (i) and (ii), the inspective rechargeable battery (B_a) is judged that the electricity storable capacity is decreased;

(i) a case where an increase in the battery voltage of the inspective rechargeable battery (B_a) upon charging and an increase in the open-circuit voltage thereof after the charging are greater than those of the normal rechargeable battery (B_n), and

(ii) a case where a decrease in the battery voltage of the inspective rechargeable battery (B_a) upon discharging and a decrease in the open-circuit voltage thereof after the discharging are smaller than those in a case where the inspective rechargeable battery (B_a) is short-circuited but they are greater than those of the normal rechargeable battery (B_n); and

(4) when the inspective rechargeable battery (B_a) does not fall in any of the cases mentioned in the above judgments (1) to (3), it is judged to be normal.

8. The detecting method according to claim 1, wherein said basic data (BD) include one or more of data or function formulas selected from those mentioned in the following (1) to (5):

(1) for a non-deteriorated normal rechargeable battery, basic data of a relationship Voc(Q) or Q(Voc) of the open-circuit voltage (Voc) to the remaining capacity (Q) which are obtained by way of measurement or function formulas obtained on the basis of said data;

(2) for said non-deteriorated normal rechargeable battery when it is in a full-charged state, basic data of relationships between battery voltages (Vd) measured when the rechargeable battery is subjected to discharging at various battery temperatures (T) and at various discharging currents (Id), open-circuit voltages (Voc) measured when the discharging is temporarily suspended, said discharging currents (Id) and said battery temperatures (T) or a function formula Vd(Voc, Id, T) obtained on the basis of said data; and

basic data or a function formula of a battery voltage-related function formula Vd(Q, Id, T) or Q(Vd, Id, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) to the remaining capacity which are described in the above (1);

(3) internal resistance-related basic data computed from a relation expression Vd=Voc−

Id×

Rd or Rd=(Voc−

Vd)/Id when the internal resistance of the normal rechargeable battery is made to be Rd in the above (2), or a function formula Rd(Voc, Id, T) or Rd(Vd, Id, T) obtained on the basis of said data, in addition, basic data or a function formula of an internal resistance-related function formula Rd(Q, Id, T) or Q(Rd, Id, T) obtained with reference to aforesaid data and aforesaid function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above (1);

(4) for the above non-deteriorated normal rechargeable battery when the remaining capacity thereof is zero, data of relationships between battery voltages (Vc) measured when the rechargeable battery is subjected to charging at various battery temperatures (T) and at various charging currents (Ic), open-circuit voltages (Voc) measured when the charging is temporarily suspended, said discharging currents (Ic) and said battery temperatures (T) or a function formula Vc(Voc, Ic, T) obtained on the basis of said data, in addition, data or a function formula of a battery voltage-related function formula Vc(Q, Ic, T) or Q(Vc, Ic, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above (1);

(5) internal resistance-related data computed from a relation expression Vc=Voc+Ic×

Rc or Rc=(Vc−

Voc)/Ic when the internal resistance of the normal rechargeable battery is made to be Rc in the above (4), or a function formula Rc(Voc, Ic, T) obtained on the basis of said data, in addition, data or a function formula of an internal resistance-related function formula Rc(Q, Ic, T) or Q(Rc, Ic, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above (1).

9. The detecting method according to claim 1, wherein when the inspective rechargeable battery (B_a) is in a paused state, a change with the passage of time in open-circuit voltage (Voc) thereof is measured;

the inspective rechargeable battery (B_a) is judged to be short-circuited when a decrease rate (−

dVoc/dt) of the Voc is greater than a prescribed value v₀, that is, −

dVoc/dt>

v₀>

0, and the inspective rechargeable battery (B_a) is judged to be not short-circuited when said increase rate of the Voc is 0≦

−

dVoc/dt≦

v₀.

10. The detecting method according to claim 8, wherein when the inspective rechargeable battery (B_a) is in a paused state without subjecting to charging or discharging, with reference to the data or relation expression of the relation Q(Voc), a remaining capacity of said rechargeable battery is computed.

11. The detecting method according to claim 8, wherein when the inspective rechargeable battery (B_a) is in a paused state without subjecting to charging or discharging, said rechargeable battery is judged of whether the battery is normal or deteriorated by measuring a change with the passage of time in the open-circuit voltage (Voc), discharging an electricity quantity q₁ of a current value I₁×

a time t₁ from the measured open-circuit voltage, and measuring a battery voltage (V) of said battery duration until said discharging is terminated and an open-circuit voltage (Voc) of said battery after the termination of the discharging.

12. The detecting method according to claim 11, wherein judgment of the inspective rechargeable battery (B_a) is performed as will be described below:

(1) when a decrease rate (−

dVoc/dt) of the open-circuit voltage (Voc) is greater than a prescribed value v₀, that is, −

dVoc/dt>

v₀>

0, the inspective rechargeable battery (B_a) is judged to be short-circuited;

(2) when the inspective rechargeable battery (B_a) does not correspond to the above (1), with reference to the basic data mentioned in (1) of claim 8, a remaining capacity Q₀=Q(Voc₀) when the open-circuit voltage of the normal rechargeable battery (B_n)is Voc₀ is estimated and an open-circuit voltage Voc=Voc(Q₀−

q₁) of the normal rechargeable battery is estimated when an electricity quantity q₁ is discharged from Q₀, and when a difference between the open-circuit voltage Voc(Q₀−

q₁) of the normal rechargeable battery (B_n) and the measured open-circuit voltage Voc₁ of the inspective rechargeable battery (B_a) is f₀≦

[Voc(Q₀−

q₁)−

Voc₁]≦

f₁(f₀<

0<

f₁) which is an allowable variation range of the characteristics of the normal rechargeable battery (B_n) as a product, the inspective rechargeable battery (B_a) is judged to be free of a decrease in the electricity storable capacity; and

by assuming that transient characteristics of the battery voltage of the inspective rechargeable battery at an initial stage when discharging for the inspective rechargeable battery is initiated can be expressed by an equation V=V₁+(Voc₀−

V₁)×

e<sup>−

t/τ</sup>

(with V being a battery voltage, t being a discharging time, V₁ being a battery voltage of the battery when the discharging time is extrapolated to infinity, and τ

being a time constant decided by an internal resistance or the like of the battery), in accordance with the battery voltage V to a measured discharging time and in accordance with said equation, a time constant τ

when the discharging is initiated at a discharging current I₁ from the open-circuit voltage Voc₀ and a battery voltage V₁ are computed where when the internal resistance of the inspective rechargeable battery is made to be R₁, there is obtained an equation V₁=Voc₀−

I₁×

R₁ or R₁=(Voc₀−

V₁)/I₁;

in accordance with this equation, an internal resistance R₁ of the B_a inspective rechargeable battery (B_a)is estimated, and this internal resistance R₁ of the inspective rechargeable battery (B_a) is compared with the internal resistance Rd(Voc₀, I₁, T)[or Rd(Q₀, I₁, T)] of the normal rechargeable battery (B_n) which is obtained from the function formula Rd(Voc, Id, T) or Rd(Q0, Id, T) mentioned in (3) of claim 8, where judgment is performed as will be described below,

(i) when the internal resistance R₁ of the inspective rechargeable battery (B_a) is substantially the internal resistance Rd(Voc₀, I1, T) or Rd(Q₀, I₁, T) of the normal rechargeable battery (B_n), in other words, when the internal resistance R₁ of the inspective rechargeable battery (B_a)falls in an allowable variation range of r₁≦

[R₁−

Rd(Q₀, I₁, T)]≦

r₂(r₁<

0<

r₂) for the normal rechargeable battery (B_n) as a product, the inspective rechargeable battery (B_a)is judged that it is normal, and

(ii) when the internal resistance R₁ of the inspective rechargeable battery (B_a) falls in a variation range of [R₁−

Rd(Q₀, I₁, T)]>

r₂(0<

r₂), the inspective rechargeable battery (B_a) is judged that the internal resistance is increased; and

(3) when the inspective rechargeable battery (B_a) does not correspond to the above (1) and a difference between the open-circuit voltage Voc(Q₀−

q₁) of the normal rechargeable battery (B_n) and the measured open-circuit voltage Voc₁ of the inspective rechargeable battery (B_a) is in a range of [Voc(Q₀−

q₁)−

Voc₁]>

f₁(0<

f₁), the inspective rechargeable battery (B_a) is judged that the electricity storable capacity is decreased.

13. The detecting method according to claim 12, wherein in the judgment (2)-(ii) of claim 12, when the inspective rechargeable battery (B_a) is judged that the internal resistance is increased, for the inspective rechargeable battery, an electricity quantity q₂ of a current value I₂×

a time t₂ is discharged from the open-circuit voltage Voc₁, where a battery voltage duration until the discharging operation is terminated and an open-circuit voltage Voc₂ after the termination of the discharging operation are measured, then by assuming that transient characteristics of the battery voltage of the inspective rechargeable battery (B_a) at a initial stage of the commencement of the discharging operation can be expressed by an equation V=V₂+(Voc₁−

V₂)×

e<sup>−

t/τ</sup>

(with V being a battery voltage, t being a discharging time, V₂ being a battery voltage of the battery when the discharging time t is extrapolated to infinity, and τ

being a time constant), in accordance with the battery voltage V to a measured discharging time and in accordance with said equation, a time constant τ

when the discharging operation is initiated at a discharging current I₂ from the open-circuit voltage Voc₁ and a battery voltage V₂ are computed, then an internal resistance R₂ of the inspective rechargeable battery at this time is computed from an equation V₂=Voc₁−

I₂×

R₂ or R₂=(Voc₁−

V₂)/I₂, successively by assuming that the internal resistance of the inspective rechargeable battery (B_a) is increased from the internal resistance Rd(Q, Id, T) of the normal rechargeable battery (B_n) to a×

Rd(Q, Id, T)+b (where each of a and b is a constant) and in accordance with an equation R₁−

[a×

Rd(Q₀, I₁, T)+b]=0 (where each of a and b is a constant) and an equation R₂−

[a×

Rd(Q₀−

q₁, I₂, T)+b]=0 (where each of a and b is a constant) or an equation R₂−

[a×

Rd(Q₁, I₂, T)+b]=0 (where each of a and b is a constant) using Q₁=Q₀−

q₁=Q(Voc₁), the constant a and the constant b are computed to estimate a value of the increased internal resistance Rd′

=a×

Rd(Q, Id, T)+b.

14. The detecting method according to claim 12, wherein in the judgment (3) of claim 12, when the inspective rechargeable battery (B_a) is judged that the electricity storable capacity is decreased, by assuming that the electricity storable capacity C′

of the inspective rechargeable battery is D times the electricity storable capacity C of the normal rechargeable battery (where D is a constant and is 0<

D<

1) and making the remaining capacity Q₀′

of the inspective rechargeable battery to be Q₀′

=Q₀×

D (where Q₀ is a remaining capacity of the normal rechargeable battery (B_n), and D is a constant and is 0<

D<

1) and with reference to the remaining capacity Q₀ of the normal rechargeable battery which is corresponding to the open-circuit voltage Voc₀ of the inspective rechargeable battery, the remaining capacity Q₀′

=Q₀×

D of the inspective rechargeable battery, the remaining capacity Q₁ of the normal rechargeable battery which is corresponding to the open-circuit voltage Voc₁ of the inspective rechargeable battery, and the remaining capacity Q₁′

=Q₀′

−

q₁=Q₁×

D of the inspective rechargeable battery and also with reference to function formulas Voc(Q)=Voc(Q₀′

/D)=Voc₀ and Voc(Q₁)=Voc(Q₁′

/D)=Voc(Q₀′

/D−

q₁/D)=Voc₁ which are obtained on the basis of the basic data mentioned in (1) of claim 8, a value of the constant D and a value of the remaining capacity Q₁′

=Q₀′

−

q₁=Q₁×

D are estimated, where judgment of the inspective rechargeable battery is performed as will be described below,

(i) when a difference between the internal resistance R₁ computed in the (2) of claim 12 and an internal resistance Rd(Q₀′

/D, I₁, T) estimated from the above basic data falls in a range of r₁≦

[R₁−

Rd(Q₀′

/D, I₁, T)]≦

r₂(r₁<

0<

r₂), the inspective rechargeable battery is judged that the internal resistance is not increased but the electricity storable capacity is decreased, and

(ii) when said difference falls in a range of [R₁−

Rd(Q₀′

/D, I₁, T)]>

r₂(0<

r₂), the inspective rechargeable battery is judged that the internal resistance is increased and the electricity storable capacity is decreased;

then, for the inspective rechargeable battery, an electricity quantity q₁ of a current value I₁×

a time t₁ is discharged from the open-circuit voltage Voc₀, followed by discharging an electricity quantity q₂ of a current value I₂×

a time t₂, where a battery voltage of the inspective rechargeable battery duration until the discharging operation is terminated and an open-circuit voltage Voc₂ after the termination of the discharging operation are measured, and by assuming that transient characteristics of the battery voltage of the inspective rechargeable battery at a initial stage of the commencement of the discharging operation can be expressed by an equation V=V₂+(Voc₁−

V₂)×

e<sup>−

t/τ</sup>

(with V being a battery voltage, t being a discharging time, V₂ being a battery voltage of the battery when the discharging time t is extrapolated to infinity, and τ

being a time constant), in accordance with the battery voltage V to a measured discharging time and in accordance with said equation, a time constant τ

when the discharging operation is initiated at a discharging current I₂ from the open-circuit voltage Voc₁ and a battery voltage V₂are computed, then an internal resistance R₂ of the inspective rechargeable battery at this time is computed from an equation V₂=Voc₁−

I₂×

R₂ or R₂=(Voc₁−

V₂)/I₂, successively by assuming that the internal resistance of the inspective rechargeable battery is increased from the internal resistance Rd(Q, Id, T) of the normal rechargeable battery to a×

Rd(Q, Id, T)+b (where each of a and b is a constant) and in accordance with an equation R₁−

[a×

Rd(Q₀, I₁, T)+b]=0 (where each of a and b is a constant) and an equation R₂−

[a×

Rd(Q₁, I₂, T)+b]=R₂−

[a×

Rd(Q₀−

q₁/D, I₂, T)+b=0 (where each of a and b is a constant) [where Q₀=Q₀′

/D, Q₁=Q₀−

q₁/D=Q₁′

/D, and Q₀′ and

Q₁′

are a remaining capacity when the open-circuit voltage is Voc₀ and a remaining capacity when the open-circuit voltage is Voc₁ respectively], the constant a and the constant b are computed to estimate a value of the increased internal resistance Rd′

=a×

Rd(Q′

/D, Id, T)+b (where Q′

is a true remaining capacity when the electricity storable capacity is decreased) of the inspective rechargeable battery, whereby a deteriorated state and a remaining capacity of the inspective rechargeable are capable of being detected.

15. The detecting method according to claim 8 or 10, wherein for the inspective rechargeable battery which is in a paused state without subjecting to charging or discharging, after an open-circuit voltage Voc thereof is measured, charging for said rechargeable battery is started at a charging voltage Ic₁ where a battery voltage Vc of the battery is measured, followed by charging an electricity quantity q₁ of a time t₁×

a charge-and-discharge efficiency Eff where the charging operation is terminated when the battery voltage of the battery becomes Vc₁, where a change with the passage of time in the open-circuit voltage Voc of the battery is measured and a stable open-circuit voltage of the battery is made to be Voc₁.

16. The detecting method according to claim 8, wherein for the inspective rechargeable battery which is in a paused state without subjecting to charging or discharging, after an open-circuit voltage Voc thereof is measured, charging for said rechargeable battery is started at a charging voltage Ic₁ where a battery voltage Vc of the battery is measured, followed by charging an electricity quantity q₁ of a time t₁×

a charge-and-discharge efficiency Eff where the charging operation is terminated when the battery voltage of the battery becomes Vc₁, where an open-circuit voltage Voc₁ of the battery after an elapse of a prescribed period of time is measured.

17. The detecting method according to claim 15 or 16, wherein:

(1) when the inspective rechargeable battery falls in any of the following cases (i) to (iii), the inspective battery is judged to be short-circuited;

(i) a case where with reference to the basic data mentioned in (1) of claim 8, a remaining capacity Q₀ of the normal rechargeable battery when the open-circuit voltage of the normal rechargeable battery is Voc₀ is estimated, and when a difference between an open-circuit voltage Voc(Q₀+q₁) of the normal rechargeable battery which is estimated with reference to the basic data mentioned in (1) of claim 8 and the open-circuit voltage Voc₁ of the inspective rechargeable battery falls in a range of [Voc(Q₀+q₁)−

Voc₁]>

g₁(g₁>

0),

(ii) a case where a difference between a battery voltage Vc(Q₀+q₁, Ic₁, T) of the normal rechargeable battery which is estimated with reference to the basic data mentioned in (4) of claim 8 and the battery voltage Vc₁ of the inspective rechargeable battery falls in a range of [Vc(Q₀+q₁, Ic₁, T)−

Vc₁]>

j₁(j₁>

0), and

(iii) a case where a difference between an internal resistance Rc(Voc₀, Ic, T) of the normal rechargeable battery which is estimated with reference to the basic data mentioned in (5) of claim 8 and an internal resistance Rc₁ of the inspective rechargeable battery which is obtained in accordance with the equation Rc₁=(Vc₁−

Voc₁)/Ic₁ falls in a range of [Rc₁−

Rc(Voc₁, Ic₁, T)]<

z₁(z₁<

0);

(2) when the difference between the open-circuit voltage Voc(Q₀+q₁) of the normal rechargeable battery and the open-circuit voltage Voc₁ of the inspective rechargeable in the above (1)-(i) falls in a range of g₀≦

[Voc(Q₀+q₁)−

Voc₁]≦

g₁(g₀<

0<

g₁), the inspective rechargeable battery is judged that the electricity storable capacity is not decreased, then by assuming that transient characteristics of the battery voltage (Vc) of the inspective rechargeable battery at an initial stage when the charging operation for the battery is commenced can be expressed by the equation

18. The detecting method according to claim 17, wherein in the judgment (2)-(ii) of claim 17, when the inspective rechargeable battery is judged that the internal resistance is increased, for the inspective rechargeable battery which is in a paused state, charging is performed at least two times, that is, an electricity quantity q1 of a current value Ic₁×

a time t₁ is charged from the battery voltage Voc₀, followed by charging an electricity quantity q2 of a current value Ic₂×

a time t₂ where a battery voltage Vc of the inspective rechargeable battery duration until the charging operation is terminated and an open-circuit voltage Voc₂ of the inspective rechargeable battery after the termination of the charging operation are measured, then by assuming that transient characteristics of the battery voltage of the inspective rechargeable battery at a initial stage of the commencement of the charging operation can be expressed by an equation Vc=V₂−

(V₂−

Voc₁)×

e<sup>−

t/τ</sup>

(with Vc being a battery voltage, t being a discharging time, V₂ being a battery voltage of the battery when the discharging time t is extrapolated to infinity, and τ

being a time constant) and in accordance with the battery voltage V to a measured discharging time and in accordance with said equation, a time constant τ

when the charging operation is initiated at a discharging current Ic₂ from the open-circuit voltage Voc₁ and a battery voltage V₂ are computed, then an internal resistance Rc₂ of the inspective rechargeable battery at this time is computed from an equation V₂=Voc₁+Ic₂×

Rc₂ or Rc₂=(V₂−

Voc₁)/Ic₂, successively by assuming that the internal resistance of the inspective rechargeable battery is increased from the internal resistance Rc(Q, Ic, T) of the normal rechargeable battery to a×

Rc(Q, Ic, T)+b (where each of a and b is a constant) and in accordance with an equation Rc₁−

[a×

Rc(Q₀, Ic₁, T)+b]=0 (where each of a and b is a constant) and an equation Rc₂−

[a×

Rc(Q₀+q₁, Ic₂, T)+b]=0 (where each of a and b is a constant) or an equation Rc₂−

[a×

Rc(Q₁, Ic₂, T)+b]=0 (where each of a and b is a constant) using Q₁=Q(Voc₁), the constant a and the constant b are computed to estimate a value of the increased internal resistance Rc′

=a×

Rc(Q, Ic, T)+b, whereby a deteriorated state and a remaining capacity of the inspective rechargeable battery are capable of being detected.

19. The detecting method according to claim 17, wherein in the judgment (2)-(iii) of claim 17, when the inspective rechargeable battery is judged that the electricity storable capacity is decreased, by assuming that the electricity storable capacity C′

of the inspective rechargeable battery is D times the electricity storable capacity C of the normal rechargeable battery (where D is a constant and is 0<

D<

1) and making the remaining capacity Q₀′

of the inspective rechargeable battery to be Q₀′

=Q₀×

D (where Q₀ is a remaining capacity of the normal rechargeable battery, and D is a constant and is 0<

D<

1) and with reference to the remaining capacity Q₀ of the normal rechargeable battery which is corresponding to the open-circuit voltage Voc₀ of the inspective rechargeable battery, the remaining capacity Q₀′

=Q₀×

D of the inspective rechargeable battery, the remaining capacity Q₁ of the normal rechargeable battery which corresponds to the open-circuit voltage Voc₁ of the inspective rechargeable battery, and the remaining capacity Q₁′

=Q₀′

+q₁=Q₁×

D of the inspective rechargeable battery and also with reference to function formulas Voc(Q₀)=Voc(Q₀′

/D)=Voc₀ and Voc(Q₁)=Voc(Q₁′

/D)=Voc(Q₀′

/D+q₁/D)=Voc₁ which are obtained on the basis of the basic data mentioned in (1) of claim 8, a value of the constant D and a value of the remaining capacity Q₁′

=Q₀′

+q₁=Q₁×

D are estimated, where judgment of the inspective rechargeable battery is performed as will be described below,

(i) when a difference between the internal resistance Rc₁ computed in the (2) of claim 17 and an internal resistance Rc(Q_0′

/D,Ic₁, T) estimated from the above basic data falls in a range of z₁≦

[Rc₁−

Rc(Q₀′

/D, Ic₁, T)]≦

z₂(z₁<

0<

z₂), the inspective rechargeable battery is judged that the internal resistance is not increased but the electricity storable capacity is decreased, and

(ii) when said difference falls in a range of [Rc₁−

Rc(Q₀′

/D, Ic₁, T)]>

z₂(0<

z₂), the inspective rechargeable battery is judged that the internal resistance is increased and the electricity storable capacity is decreased;

then, for the inspective rechargeable battery, an electricity quantity q₂ of a current value Ic₂×

a time t₂ is charged from the open-circuit voltage Voc₁, where a battery voltage of the inspective rechargeable battery duration until the charging operation is terminated and an open-circuit voltage Voc₂ after the termination of the charging operation are measured, and by assuming that transient characteristics of the battery voltage of the inspective rechargeable battery at a initial stage of the commencement of the charging operation can be expressed by an equation Vc=V₂−

(V₂−

Voc₁)×

e<sup>−

t/τ</sup>

(with Vc being a battery voltage, t being a charging time, V₂ being a battery voltage of the battery when the charging time t is extrapolated to infinity, and τ

being a time constant), in accordance with the battery voltage Vc to a measured charging time t and in accordance with said equation, a time constant τ

when the charging operation is initiated at a charging current Ic₂ from the open-circuit voltage Voc₁ and a battery voltage V₂ are computed, then an internal resistance Rc₂ of the inspective rechargeable battery at this time is computed from an equation V₂=Voc₁+Ic₂×

Rc₂ or Rc₂=(V₂−

Voc₁)/Ic₂, successively by assuming that the internal resistance of the inspective rechargeable battery is increased from the internal resistance Rc(Q₀′

/D, Ic, T) of the normal rechargeable battery to a×

Rc(Q₀′

/D, Ic, T)+b (where each of a and b is a constant) and in accordance with an equation Rc₁−

[a×

Rc(Q₀′

/D, Ic₁, T)+b]=0 (where each of a and b is a constant) and an equation Rc₂−

[a×

Rc(Q₀′

/D+q₁/D, Ic₂, T)+b]=0 or an equation Rc₂−

[a×

Rd(Q₁′

/D, Ic₂, T)+b]=0 (where each of a and b is a constant) using Q₁=Q₁′

/D=Q(Voc₁), the constant a and the constant b are computed to estimate a value of the increased internal resistance Rc′

=a×

Rc(Q′

/D, Ic, T)+b (where Q′

is a true remaining capacity when the electricity storable capacity is decreased) of the inspective rechargeable battery, whereby a deteriorated state and a remaining capacity of the inspective rechargeable are capable of being detected.

20. The detecting method according to claim 1, wherein the inspective rechargeable battery is subjected to charging and the charging operation is terminated at a battery voltage Vc_E, where a change with the passage of time in the open-circuit voltage Voc of the battery is detected.

21. The detecting method according to claim 1, wherein the inspective rechargeable battery is subjected to charging and the charging operation is terminated at a battery voltage Vc_E, where an open-circuit voltage Voc_E of the battery after an elapse of a prescribed period of time is detected.

22. The detecting method according to claim 20, wherein a time t since the termination of the charging operation and an open-circuit voltage Voc of the inspective rechargeable battery at that time are measured, by making an open-circuit voltage of the inspective rechargeable battery when the open-circuit voltage Voc becomes to be a steady state to be Voc_E and assuming that the open-circuit voltage Voc can be expressed by an equation Voc=Voc_E+(Vc_E−

Voc_E)×

e<sup>−

t/τ</sup>

(with Voc being an open-circuit voltage, t being a time, Voc_E being an open-circuit voltage when the time t is extrapolated to infinity, and τ

being a time constant), in accordance with this equation and from the Voc values measured at a plurality of time points, a time constant τ

is computed and a value of the Voc_E is estimated.

23. The detecting method according to claim 20 or 21, wherein the inspective rechargeable battery is judged to be short-circuited when the inspective rechargeable battery falls in any of the following cases (i) and (ii);

(i) a case where a change with the passage of time in the open-circuit voltage Voc of the inspective rechargeable battery, namely, a decrease rate (−

dVoc/dt) of the open-circuit voltage is greater than that (v_e) of the corresponding normal rechargeable battery, that is, −

dVoc_E/dt>

v_e>

0, and

(ii) a case where the charge termination voltage Vc_E of the inspective rechargeable battery is smaller than that (m₀) of the corresponding normal rechargeable battery, that is, Vc_E<

m₀(0<

m₀).

24. The detecting method according to claim 1, wherein the inspective rechargeable battery is charged by a constant current-constant voltage charging method wherein the inspective rechargeable battery is charged at a prescribed constant current value until the battery voltage reaches a prescribed upper limit battery voltage Vc_L and following this constant current discharging operation, the inspective rechargeable battery whose battery voltage is Vc_L is charged at a constant voltage Vc_L and after an elapse of a prescribed period of time, the charging operation is terminated, where the inspective rechargeable battery is judged with respect to internal state while comparing with a normal rechargeable battery corresponding to the inspective rechargeable battery as will be described below:

(1) when the inspective rechargeable battery falls in any of the following cases (i) to (iii), the inspective rechargeable battery is judged to be short-circuited;

(i) a case where a change (−

dVoc_E/dt) with the passage of time in the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging in the constant current-constant voltage charging operation is greater than that (v_e) of the corresponding normal rechargeable battery, that is, −

dVoc_E/dt>

v_e>

0,

(ii) a case where the battery voltage (Vc_E) of the inspective rechargeable battery when the entire charging operation is terminated is smaller than that (m₀) of the corresponding normal rechargeable battery, that is, Vc_E<

m₀(0<

m₀), and

(iii) a case where an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery upon the constant current charging operation is smaller than that (S₀) of the corresponding normal rechargeable battery, that is, dVc/dt<

S₀(0<

s₀);

(2) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery upon the constant current charging is greater than that (s₁) the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging in the constant current-constant voltage charging operation is smaller than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_E<

Voc_n, the inspective rechargeable battery is judged that the internal resistance is increased;

(3) when a period of time consumed to reach the upper limit voltage (Vc_L) from the prescribed battery voltage in the constant current charging operation for the inspective rechargeable batter is shorter than that for the corresponding normal rechargeable battery or an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery in the constant current charging is greater than that (s₁) of the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging in the constant current-constant voltage charging operation is greater than that (Voc_n) of the corresponding normal rechargeable battery, that is, Voc_E≧

Voc_n>

0, the inspective rechargeable battery is judged that the electricity storable capacity is decreased;

(4) when a period of time consumed to reach the upper limit voltage (Vc_L) from the prescribed battery voltage in the constant current charging for the inspective rechargeable batter is substantially the same as that for the corresponding normal rechargeable battery or an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery in the constant current charging operation is substantially the same as that (s₁) of the corresponding normal rechargeable battery, that is, s₀≦

dVc/dt≦

s₁(0<

s₀<

s₁), and the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging in the constant current-constant voltage charging operation is substantially the same as or greater than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_n≦

Voc_E, the inspective rechargeable battery is judged to be normal;

whereby the internal state of the inspective rechargeable battery is capable of being detected.

25. The detecting method according claim 1, wherein when constant current charging for the inspective rechargeable battery is terminated by detecting a battery voltage thereof, a change with the passage of time in the battery voltage, a battery temperature of the battery or a change with the passage of time in the battery temperature,

(1) when the inspective rechargeable battery falls in any of the following cases (i) to (iii), the inspective rechargeable battery is judged to be short-circuited:

(i) a case where a change (−

dVoc_E/dt) with the passage of time in the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging is greater than that (v_e) of a normal rechargeable battery corresponding to the inspective rechargeable battery and having been subjected to the constant current charging in the same manner as the inspective rechargeable battery, that is, −

dVoc_E/dt>

v_e>

0,

(ii) a case where an increase rate (dT/dt) of the battery temperature (T) of the inspective rechargeable battery upon the constant current charging operation is greater than that (u₀) of the corresponding normal rechargeable battery, that is, dT/dt>

u₀>

0, and

(iii) a case where an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery upon the constant current charging operation is smaller than that (s₀) of the corresponding normal rechargeable battery, that is, 0<

dVc/dt<

s₀;

(2) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery upon the constant current charging operation is greater than that (s₁) of the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after the termination of the constant current charging operation is smaller than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_E<

Voc_n, the inspective rechargeable battery is judged that the internal resistance is increased;

(3) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery during the constant current charging operation is greater than that (s₁) of the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after the termination of the constant current charging operation is greater than (Voc_n) of the corresponding normal rechargeable battery, that is, Voc_E>

Voc_n(0<

Voc_n), the inspective rechargeable battery is judged that the electricity storable capacity is decreased;

(4) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery during the constant current charging operation is substantially the same as that (s₁) of the corresponding normal rechargeable battery, that is, s₀≦

dVc/dt≦

s₁(0<

s₀<

s₁), and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after the termination of the constant current charging operation is substantially the same as or greater than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_n≦

Voc_E, the inspective rechargeable battery is judged to be normal;

whereby the internal state of the inspective rechargeable battery is capable of being detected.

26. The detecting method according to claim 1, wherein when constant current charging for the inspective rechargeable battery is terminated after an elapse of a prescribed period of time since the commencement of the constant current charging or when the battery voltage of the inspective rechargeable battery reaches a prescribed upper limit voltage (Vc_L),

(1) when the inspective rechargeable battery falls in any of the following cases (i) to (iii), the inspective rechargeable battery is judged to be short-circuited:

(i) a case where a change (−

dVoc_E/dt) with the passage of time in the open-circuit voltage (Voc_E) of the inspective rechargeable battery after full-charging is greater than that (v_e) of a normal rechargeable battery corresponding to the inspective rechargeable battery and having been subjected to the constant current charging in the same manner as the inspective rechargeable battery, that is, −

dVoc_E/dt>

v_e>

0,

(ii) a case where a battery voltage (Vc_E) of the inspective rechargeable battery upon the termination of the constant current charging operation is smaller than that (m₀) of the corresponding normal rechargeable battery, that is, Vc_e<

m₀(m₀>

0), and

(iii) a case where an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery upon the constant current charging operation is smaller than that (s₀) of the corresponding normal rechargeable battery, that is, 0<

dVc/dt <

s₀;

(2) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery during the constant current charging operation is greater than that (s₁) of the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after the termination of the constant current charging operation is smaller than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_E≦

Voc_n, the inspective rechargeable battery is judged that the internal resistance is increased;

(3) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery during the constant current charging operation is greater than that (s₁) of the corresponding normal rechargeable battery, that is, dVc/dt>

s₁>

0, and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after the termination of the constant current charging operation is greater than that (Voc_n) of the corresponding normal rechargeable battery, that is, Voc_E>

Voc_n (0<

Voc_n), the inspective rechargeable battery is judged that the electricity storable capacity is decreased;

(4) when an increase rate (dVc/dt) of the battery voltage (Vc) of the inspective rechargeable battery during the constant current charging operation is substantially the same as that (s₁) of the corresponding normal rechargeable battery, that is, s₀≦

dVc/dt≦

s₁(0<

s₀<

s₁), and an open-circuit voltage (Voc_E) of the inspective rechargeable battery after termination of the constant current charging operation is substantially the same as or greater than that (Voc_n) of the corresponding normal rechargeable battery, that is, 0<

Voc_n≦

Voc_E, the inspective rechargeable battery is judged to be normal;

whereby the internal state of the inspective rechargeable battery is capable of being detected.

27. The detecting method according to claim 1, wherein when the inspective rechargeable battery is in a state that it is being subjected to discharging, the inspective rechargeable battery is judged to be in a last stage where a residual electricity quantity capable of being discharged is little or to be short-circuited when the battery voltage is less than a prescribed voltage value from the basic data of a normal rechargeable battery corresponding to the inspective rechargeable battery or when a decrease rate (−

dVd/dt) of the battery voltage (Vd) is greater than a prescribed value (x₁) from said basic data, that is, −

dVd/dt>

x₁(0<

x₁).

28. The detecting method according to claim 1, wherein when the inspective rechargeable battery is in a state that it is being subjected to discharging, a discharging current (Id₀) of the discharging operation and a battery voltage (Vd) of the inspective rechargeable battery are measured, where when the battery voltage (Vd) is greater than a prescribed voltage value the basic data of a normal rechargeable battery corresponding to the inspective rechargeable battery or when a decrease rate (−

dVd/dt) of the battery voltage (Vd) is less than a prescribed value (x₁) from said basic data, that is, 0<

−

dVd/dt x₁, the inspective rechargeable battery is judged to be normal or to be in a deterioration mode other than short-circuit.

29. The detecting method according to claim 28, wherein when the inspective rechargeable battery is in a substantially steady state while being subjected to discharging where a discharging current of the discharging operation is Id₀, a battery temperature of the inspective rechargeable battery is T and a battery voltage of the inspective rechargeable battery is Vd₀ where a remaining capacity of the battery is Q₀ and after an electricity quantity q is discharged, the battery voltage of the inspective rechargeable battery in the steady state becomes to be Vd₁ at a discharging current Id₁, with reference to the basic data mentioned in (1) and (2) of claim 8, a battery voltage Vd₀=Vd(Q₀, Id₀, T) and a remaining capacity Q₀=Q(Vd₀, Id₀, T) of the normal rechargeable battery when the battery voltage is Vd₀ are estimated and a battery voltage Vd(Q₀−

q, Id₁, T) when the remaining capacity becomes (Q₀−

q) from Q₀ and a remaining capacity Q(Vd₁, Id₁, T) of the normal rechargeable battery when the battery current is Id₁ and the battery voltage is Vd₁ are estimated, and the inspective rechargeable battery is subjected as will be described below;

(1)(i) when y₁≦

[Vd₁−

Vd(Q₀−

q, Id₁, T)]≦

y₂(y₁<

0y₂) or (ii) when w₁≦

Q(Vd₁, Id₁, T)−

[Q(Vd₀, Id₀, T)−

q]≦

w₂(w₁<

0<

w₂), the inspective rechargeable battery is judged to be normal;

(2)(i) when [Vd₁−

Vd(Q₀−

q, Id₁, T)]>

y₂(0<

y₂) or (ii) when Q(Vd₁, Id₁, T)−

[Q(Vd₀, Id₀, T)−

q]>

w₂(0<

w₂), the inspective rechargeable battery is judged that the internal resistance is increased; and

(3)(i) when [Vd₁−

Vd(Q₀−

q, Id₁, T)]<

y₁(y₁<

0) or (ii) when Q(Id₁, Vd₁, T)−

[Q(Id₀, Vd₀, T)−

q]<

w₁(w₁<

0), the inspective rechargeable battery is judged that the electricity storable capacity is decreased;

whereby the internal state of the inspective rechargeable battery is capable of being detected.

30. The detecting method according to claim 29, wherein for the inspective rechargeable battery in the substantially steady state where the discharging current is a steady discharging current of I_no and the battery voltage is V_no, when the discharging current is changed n-times (with n being a positive integer of 1, 2, 3, 4, . . . ) such that the discharging current is changed to I_n1 from I_no and an electricity quantity q_n of a current value I_n1×

a time t_n1 is discharged and thereafter, the discharging current is returned to the steady discharging current I_no, battery voltages (V) at a plurality of time points upon changes in the discharging current are measured and by assuming that transient characteristics of the battery voltage (V) when the discharging current is changed can be expressed by an equation V=V_n1+(V_no−

V_n1)×

e<sup>−

t/τ</sup>

(with t being a discharging time, V_n1 being a battery voltage of the battery when the discharging time t is extrapolated to infinity, τ

being a time constant, and n is a positive integer of 1, 2, 3, 4, . . . ), and in accordance with the measured battery voltages V to the time t since the time when the discharging current is changed and in accordance with said equation, the time constant τ

is estimated and a true value of the V_n1 is estimated, whereby the internal state of the rechargeable battery is detected.

31. The detecting method according to claim 30, wherein in a case where the discharging current for the inspective rechargeable battery is changed at least three times such that when the battery voltage in the steady discharging at a discharging current I₁₀ is V₁₀, the discharging current is changed to I₁₁ and an electricity quantity q₁ of a current value I₁₁×

a time t₁₁ from the battery voltage V₁₀ is discharged where the battery voltage is changed to V₂₀ from V₁₀, then, the discharging current I₂₀ of the steady discharging is changed to I₂₁ and an electricity quantity q₂ of a current value I₂₁×

a time t₂₁ is discharged from the battery voltage V₂₀ where the battery voltage is changed to V₃₀ from V₂₀, and the discharging current I₃₀ of the steady discharging is changed to I₃₁ and an electricity quantity q₃ of a current value I₃₁×

a time t₃₁ is discharged from the battery voltage V₃₀ where the battery voltage is changed to V₄₀ from V₃₀, wherein as a result that the discharging current I_n0 of the steady discharging is changed to I_n1 and an electricity quantity q_n of a current value I_n1×

a time t_n1 is discharged, when the inspective rechargeable battery is judged that the internal resistance is increased in (2) of claim 29,

then, by assuming that the internal resistance of the inspective rechargeable battery is changed from the internal resistance Rd(Q, Id, T) of the corresponding normal rechargeable battery to an internal resistance Rd′

(Q, Id, T)=a×

Rd(Q, Id, T)+b (where each of a and b is a constant) and also assuming that transient characteristics of the battery voltage in every change in the discharging current can be expressed by an equation V=V_n1+(V_no−

V_n1)×

e^t/τ

(with t being a discharging time, V_n1 being a battery voltage of the battery when the discharging time t is extrapolated to infinity, τ

being a time constant, and n is a positive integer of 1, 2, 3, 4, . . . ), in accordance with the measured battery voltages V to the time t since the time when the discharging current is changed and in accordance with said equation, the time constant τ

when the discharging current I_n0 is changed to I_n1 is estimated and a true value of the V_n1 is estimated,

further, an open-circuit voltage Voc_n0 of the inspective rechargeable battery having a remaining capacity Q_no when the discharging current is I_no and the battery voltage is expressed to be Voc_n0=V_n0+I_n0×

Rd′

(Q_n0, I_n0, T)=V_n1+I_n1×

Rd′

(Q_n0, I_n1, T)[where n=1, 2, 3, . . . ],

and when the remaining capacities when battery voltages are V₁₀, V₂₀, and V₃₀ are made to be Q₁₀, Q₂₀, and Q₃₀, the following relationships are established;

32. The detecting method according to claim 30, wherein in a case where the discharging current is changed at least four times from the steady discharging state such that when the battery voltage in the steady discharging at a discharging current I₁₀ is V₁₀, the discharging current is changed to I₁₁ and an electricity quantity q₁ of a current value I₁₁×

a time t₁₁ from the battery voltage V₁₀ is discharged where the battery voltage is changed to V₂₀ from V₁₀, then the discharging current I₂₀ of the steady discharging is changed to I₂₁ and an electricity quantity q₂ of a current value I₂₁×

a time t₂₁ is discharged from the battery voltage V₂₀ where the battery voltage is changed to V₃₀ from V₂₀, successively the discharging current I₃₀ of the steady discharging is changed to I₃₁ and an electricity quantity q₃ of a current value I₃₁×

a time t₃₁ is discharged from the battery voltage V₃₀ where the battery voltage is changed to V₄₀ from V₃₀, finally the discharging current I₄₀ of the steady discharging is changed to I₄₁ and an electricity quantity q₄ of a current value I₄₁×

a time t₄₁ is discharged from the battery voltage V₄₀ where the battery voltage is changed to V₅₀ from V₄₀, wherein as a result that the discharging current I_n0 of the steady discharging is changed to I_n1 and an electricity quantity q_n of a current value I_n1×

a time t_n1 is discharged, when the inspective rechargeable battery is judged that the electricity storable capacity is decreased in (3) of claim 29,

then, the electricity storable capacity of the inspective rechargeable battery is assumed to be decreased from C to C′

=D×

C (where D is a constant of 0<

D<

1), the remaining capacity of the inspective rechargeable battery is assumed to be decreased from the remaining capacity Q of the corresponding normal rechargeable to a remaining capacity Q′

=D×

Q, and the internal resistance of the inspective rechargeable battery is assumed to be increased from the internal resistance Rd(Q, Id, T) of the corresponding normal rechargeable battery to an internal resistance R′

(Q, Id, T)=a×

Rd(Q, Id, T)+b (where each of a and b is a constant),

successively, it is assumed that transient characteristics of the battery voltage in every change in the discharging current can be expressed by an equation V=V_n1+(V_n0−

V_n1)×

e<sup>−

t/τ</sup>

(with t being a discharging time, V_n1 being a battery voltage of the battery when the discharging time t is extrapolated to infinity, τ

being a time constant, and n is a positive integer of 1, 2, 3, 4, . . . ),

in accordance with the measured battery voltages V to the time t since the time when the discharging current is changed and in accordance with said equation, the time constant τ

when the discharging current I_n0 is changed to I_n1 is estimated and a true value of the V_n1 is estimated,

next, an open-circuit voltage Voc_n0 of the inspective rechargeable battery having a remaining capacity Q_n0′

=D×

Q_n0 when the discharging current is I_n0 and the battery voltage is V_n0 is expressed to be Voc_n0=V_n0+I_n0×

Rd′

(Q_n0, I_n0, T)=V_n1+I_n1×

Rd′

(Q_n0, I_n1, T), [where n=1, 2, 3, . . . ],

and when the remaining capacities when battery voltages are V₁₀, V₂₀, V₃₀, and V₄₀ are made to be Q₁₀, Q₂₀, Q₃₀ and Q₄₀, the following relationships are established;

when Q=Q′

/D;

33. The detecting method according to any of claims 30 to 32, wherein a current of Δ

Id is intentionally flown so that the discharging current I_n1 becomes to be I_n1=I_n0+Δ

Id which is greater than the steady discharging current I_n0.

34. The detecting method according to claim 33, wherein the discharging current I_n1 is less than a current value of a rate of 2C.

35. The detecting method according to claim 8, wherein for the inspective rechargeable battery judged to be normal, the internal state thereof is detected as will be described below:

(1) when the inspective rechargeable battery is in a paused state, using data or function formula of the relationship Voc(Q₀)=Voc₀ or Q₀=Q(Voc₀) derived from the open-circuit voltage (Voc₀) of the inspective rechargeable battery and the basic data mentioned in (1) of claim 8, a remaining capacity Q₀ of the inspective rechargeable battery is estimated;

(2) when the inspective rechargeable battery is during it being subjected to charging, a remaining capacity of the inspective rechargeable battery is estimated by any of the following manners (i) to (iii);

(i) by measuring a charging current for the inspective rechargeable battery during the charging operation, a battery temperature and a battery voltage of the inspective rechargeable battery and with reference to the basic data and the function formula Vc(Q, Ic, T) or Q(Vc, Ic, T) mentioned in (4) of claim 8, a remaining capacity of the inspective rechargeable battery is estimated,

(ii) the charging operation is temporarily suspended, where a charging time t and an open-circuit voltage Voc of the inspective rechargeable battery are measured to estimate a remaining capacity of the inspective rechargeable battery at that time, and

(iii) by measuring a charging termination voltage Vc_E of the inspective rechargeable battery and an open-circuit voltage Voc_E of inspective rechargeable battery after the termination of the charging operation and with reference to data or function formulas of a relationship Vc_E(Q_E, Ic, T) [Q_E is a remaining capacity upon the termination of the charging operation] or Q(Vc_E, Ic, T) derived from the basic data or the function formulas mentioned in (4) of claim 8 or data or function formulas of a relationship Voc(Q_E)=Voc_E or Q_E=Q(Voc_E) derived from the basic data or function formulas mentioned in (1) of claim 8, a remaining capacity of the inspective rechargeable battery is estimated;

(3) when the inspective rechargeable battery is during it being subjected to discharging, a remaining capacity of the inspective rechargeable battery is estimated by any of the following manners (i) to (ii);

(i) with reference to the function formula Vd(Q, Id, T) or Q(Vd, Id, T) mentioned in (2) of claim 8, a remaining capacity of the inspective rechargeable battery is estimated, and

(ii) by estimating an internal resistance Rd of the inspective rechargeable battery and with reference to the function formula Q(Rd, Id, T) mentioned in (3) of claim 8, a remaining capacity the inspective rechargeable battery is estimated.

36. The detecting method according to claim 18, wherein for the inspective rechargeable battery judged to be free of short-circuit and of a decrease in the electricity storable but have an increase in the internal resistance, an increased internal resistance Rc′

(Q, Ic, T) upon the charging operation is estimated and with reference to a relation expression Vc=Voc(Q)+Ic×

Rc′

(Q, Ic, T) of a relationship between the battery voltage, the open-circuit voltage Voc(Q), the charging current Ic, and the internal resistance Rc′

(Q, Ic, T) upon the charging operation, the electricity storable capacity C′

of the inspective rechargeable battery upon the termination of the charging operation is estimated from measured values of the charging current, battery voltage and open-circuit voltage upon the termination of the charging operation.

37. The detecting method according to claim 13 or 31, wherein for the inspective rechargeable battery judged to free of short-circuit and of a decrease in the electricity storable but have an increase in the internal resistance, an increased internal resistance Rd′

(Q, Id, T) of the inspective rechargeable battery upon the discharging operation is estimated, and with reference to a relation expression Vd=Voc(Q)−

Id×

Rd′

(Q, Id, T) of said increased internal resistance [in said relation expression, Vd is a battery voltage, Voc(Q) is an open-circuit voltage, Q is a remaining capacity, Id is a discharging current, and Rd′

(Q, Id, T) is said internal resistance] and also reference to a function formula Vd′

=Vd′

(q, Id, T) [where T is a battery temperature], a battery voltage (Vd), a discharging current (Id), and a battery temperature (T) of the inspective rechargeable battery are measured upon the discharging operation, and a remaining capacity (Q) of the inspective rechargeable battery is computed.

38. The detecting method according to claim 19, wherein for the inspective rechargeable battery judged that the electricity storable capacity is decreased, a decrease coefficient D (0<

D<

1) of the decreased electricity storable capacity is estimated, and

(1) when the internal resistance of the inspective rechargeable battery is not decreased, the electricity storable capacity is estimated to be D times the nominal capacity of the corresponding normal rechargeable battery, and

(2) when the internal resistance is increased, with reference to a relation expression Vc=Voc(Q)+Ic×

Rc′

(Q, Ic, T) [where Vc is a battery voltage, Voc is an open-circuit voltage, Q is a remaining capacity, Ic is a charging current, and Rc′

(Q, Id, T) is said increased internal resistance], a remaining capacity (Q) of the inspective rechargeable battery is computed and the value of the computed Q upon termination of full-charging is multiplied by D where the value obtained is estimated as an electricity storable capacity C′

upon the termination of the full-charging.

39. The detecting method according to claim 14 or 32, wherein the inspective rechargeable battery is judged that the electricity storable capacity is decreased, and

(1) when the internal resistance of the inspective rechargeable battery is not decreased, a decrease coefficient D (0<

D<

1) of the decreased electricity storable capacity is estimated, and the electricity storable capacity of the inspective rechargeable battery is estimated to be D times the nominal capacity of the corresponding normal rechargeable battery, and

(2) when the internal resistance is increased, the decrease coefficient of the decreased electricity storable capacity and the increased internal resistance upon the discharging operation are estimated as a function formula Rd′

(Q, Id, T), and with reference to a relation expression Vd=Voc(Q)−

Id×

Rd′

(Q, Id, T) [where Vc is a battery voltage, Voc(Q) is an open-circuit voltage, Q is a remaining capacity, Id is a discharging current, and Rc′

(Q, Id, T) is said increased internal resistance]and also reference to a function formula Vd=Vd(Q, Id, T) [where T is a battery temperature], a battery voltage (Vd), a discharging current (Id), and a battery temperature (T) of the inspective rechargeable battery are measured upon the discharging operation to estimate an apparent remaining capacity (Q) of the inspective rechargeable battery, and the apparent remaining capacity (Q) is multiplied by D to obtain a remaining capacity Q′

=D×

Q as a true remaining capacity of the inspective rechargeable battery.

40. The detecting method according to claim 8, wherein for the inspective rechargeable battery is during it being subjected to charging, a remaining capacity Q thereof is computed and a period of time until reaching a remaining capacity upon the termination of the charging operation is computed.

41. The detecting method according to claim 8, wherein for the inspective rechargeable battery is during it being subjected to discharging, after a remaining capacity Q thereof is computed and a remaining capacity Q_min of the inspective rechargeable battery when the battery voltage becomes to be a minimum actuation voltage V_min of an instrument in which the inspective rechargeable battery is used as the power source is computed, an usable capacity (Q−

Q_min) of the inspective rechargeable battery with which the instrument is still able to operate is computed.

42. The detecting method according to claim 41, wherein after the usable capacity (Q−

Q_min) of the inspective rechargeable battery is computed, in accordance with an equation h=(Q−

Q_min)/i (where h is an actuation time of the instrument, and i is an average consumptive current of the instrument) or h=(Vd+V_min)×

(Q−

Q_min)/2p (where p is an average consumptive power), a residual actuation time of the instrument is computed.

43. The detecting method according to claim 11, wherein the discharging current is a rectangular wave pulse current.

44. The detecting method according to claim 15 or 16, wherein the discharging current is a rectangular wave pulse current.

45. The detecting method according to claim 33, wherein the discharging current is a rectangular wave pulse current.

46. The detecting method according to claim 33, wherein the changing discharging current comprises a pausing pulse with no discharging current.

47. The detecting method according to claim 42, wherein the value of the average consumptive current or that of the average consumptive power is a value computed based on an operation pattern and a use frequency of the instrument by a user.

48. The detecting method according to claim 36 or 38, wherein when the performance 100×

C′

/C [%] relating to the electricity storable capacity of the inspective rechargeable battery after having deteriorated becomes to be less than 60%, the inspective rechargeable battery is judged to be over the lifetime.

49. The detecting method according to claim 1, wherein the inspective rechargeable battery is a rechargeable battery in which oxidation-reduction reaction of lithium is used.

50. The detecting method according to claim 1, wherein the inspective rechargeable battery is a rechargeable battery in which a hydrogen storage alloy is used in the anode of the battery.

51. The detecting method according to claim 1, wherein the inspective rechargeable battery is a rechargeable battery in which a nickel hydroxide is used in the cathode.

52. The detecting method according to claim 1, wherein the inspective rechargeable battery is a nickel-cadmium rechargeable battery.

53. The detecting method according to claim 1, wherein the inspective rechargeable battery is a lead-acid rechargeable battery.

54. A detecting device for detecting an internal state of a rechargeable battery in which the detecting method defined in claim 1 is adopted.

55. The detecting device according to claim 54, comprising at least (i) a voltage-detecting means for detecting a voltage between a pair of terminals of an inspective rechargeable battery, (ii) a current-detecting means for detecting a charging or discharging current flown in said inspective rechargeable battery, (iii) a temperature-detecting means for detecting a temperature of said inspective rechargeable battery, and (iv) a memorizing means for memorizing previously acquired basic data of a normal rechargeable battery which is the same kind and the same type of said inspective rechargeable battery or a function formula obtained by digitizing said basic data, wherein from said basic data or said function formula memorized in said memorizing means (iv) and information obtained from said voltage-detecting means (i), said current-detecting means (ii) and said temperature-detecting means (iii), an internal state of said inspective rechargeable battery is detected.

56. The detecting device according to claim 55 which further comprises a current-changing means for intentionally changing a current flown in the inspective rechargeable battery.

57. The detecting device according to claim 56, wherein the current-changing means includes a means for adding a prescribed pulse current to the current flown in the inspective rechargeable battery.

58. The detecting device according to claim 55 which further comprises a current flow change-detecting means for detecting a change in the current flown in inspective rechargeable battery.

59. The detecting device according to claim 55 which further comprises a wave form-processing means for processing a signal wave form outputted from each of the voltage-detecting means (i), the current-detecting means (ii) and the temperature-detecting means (iii).

60. The detecting device according to claim 55 which further comprises a operational means for processing the basic data and the information obtained from each of the voltage-detecting means (i), the current-detecting means (ii) and the temperature-detecting means (iii).

61. The detecting device according to claim 60, wherein the operational means has one or more means selected from the group consisting of (1) a computation means for computing at least either a remaining capacity or an internal resistance of the inspective rechargeable battery, (2) a computation means for computing an usable capacity of the inspective rechargeable battery with which an instrument can be used and at least either an average consumptive current or an average consumptive power which is consumed by said instrument, and (3) a computation means for computing at least either a time required until charging operation for the inspective rechargeable battery is terminated or a remaining capacity of the inspective rechargeable battery after said charging operation is terminated.

62. The detecting device according to claim 55 which further comprises a judging means for judging whether the inspective rechargeable battery is normal or deteriorated and also judging a deterioration mode when the inspective rechargeable battery is deteriorated.

63. The detecting device according to claim 55 which further comprises a means for outputting at least either the information obtained from each of the voltage-detecting means (i), the current-detecting means (ii) and the temperature-detecting means (iii) or information relating to the internal state of the inspective rechargeable battery.

64. The detecting device according to claim 63 which includes an indication means for indicating at least either the information obtained from each of the voltage-detecting means (i), the current-detecting means (ii) and the temperature-detecting means (iii) or the information relating to the internal state of the inspective rechargeable battery.

65. A battery module comprising at least one rechargeable battery and which is provided with a detecting device defined in claim 54.

66. The battery module according to claim 65 which has a communication means to an instrument.

67. An instrument which is provided with a detecting device defined in claim 54.

68. The instrument according to claim 67 which has a communication means.

69. A machine which is provided with a detecting device defined in claim 54.

70. The instrument according to claim 68, wherein said instrument is a cellular phone or a personal digital assistant.

71. The instrument according to claim 67, wherein said instrument is a computer.

72. The machine according to claim 69, wherein said machine comprises a computer.

73. The machine according to claim 69, wherein said machine is a vehicle.

74. The machine according to claim 69, wherein said vehicle is a machine having wheels.

75. The instrument according to claim 67, wherein said instrument is a charger to charge a rechargeable battery.

76. The machine according to claim 69 which has a charger to charge a rechargeable battery.

77. The instrument according to claim 67, wherein said instrument is an instrument for inspecting a rechargeable battery product whether it is good or not good.

78. The machine according to claim 69, wherein said machine is a machine for inspecting a rechargeable battery product whether it is good or not good.

79. A power storage system having a detecting device defined in claim 54.

80. A detecting program for detecting an internal state of a rechargeable battery, the program containing a detecting method defined in claim 1.

81. A memory medium having a detecting program defined in claim 80 therein.

82. The detecting method according to claim 1 or 2, wherein two or more of the judgment items (i) to (v) are used in combination.

84. A detecting program for detecting an internal state of a recharging battery by executing the detecting method of claim 7.

85. A detecting program for detecting an internal state of a recharging battery by executing the detecting method of claim 8.

2. A detecting method for detecting an internal state of an inspective rechargeable battery (B_a), said internal state including a deterioration state, an electricity storable capacity, a remaining capacity and an internal resistance of said inspective rechargeable battery (B_a),

said detecting method comprising:

(1) a step in which basic data (BD) of characteristics of a normal non-deteriorated rechargeable battery (B_n) as a reference rechargeable battery for said inspective rechargeable battery (B_a) are provided; and

(2) a step in which for said inspective rechargeable battery (B_a), a voltage value or/and a current value thereof are measured, and the measured result is compared with said basic data (BD) obtained in said step (1) to judge;

(i) the inspective rechargeable battery (B_a) is short-circuited,

(ii) the internal resistance of the inspective rechargeable battery (B_a) is increased,

(iii) the electricity storable capacity of the inspective rechargeable battery (B_a) is decreased,

(iv) the electricity storable capacity of the rechargeable battery (B_a) is decreased and the internal resistance thereof is increased, or

(v) the inspective rechargeable battery (B_a) is normal,

after this judgment, a remaining capacity of the inspective rechargeable battery (B_a) or a usable capacity thereof with which an instrument can be operated is computed.

83. A detecting program for detecting an internal state of a recharging battery by executing the detecting method of claim 2.

86. A computer program for executing a method for determining an internal state of a battery, wherein the method comprises:

inputting basic data of characteristics of a normal non-deteriorated rechargeable battery as a reference rechargeable battery for a subject rechargeable battery, the basic data of characteristics of the normal non-deteriorated rechargeable battery stored in a memory medium and including at least (i) a battery voltage, (ii) a remaining capacity, and (iii) a discharging capacity, which are aquired by subjecting the normal non-deteriorated rechargeable battery to charging or discharging under various temperature conditions and at various rates of charge or discharge;

inputting at least one of a measured voltage value and a measured current value of the subject rechargeable battery for comparison with the basic data of the normal non-deteriorated rechargeable battery; and

determining, in comparison with the normal non-deteriorated rechargeable battery, at least one of whether (i) the subject rechargeable battery is short-circuited, (ii) the internal resistance of the subject rechargeable battery is increased, (iii) the electricity storable capacity of the subject rechargeable battery is decreased, and (iv) the subject rechargeable bettery is normal.

87. A computer program according to claim 86, wherein the method further comprises computing a remaining charge of the subject rechargeable battery or the a usable capacity of the subject battery in which the subject battery is capable of energizing an instrument.

88. A computer program according to claim 86 or 87, wherein the basic data comprise averaged basic data obtained by providing a plurality of normal non-deteriorated rechargeable batteries and subjecting the plurality of normal non-deteriorated rechargeable batteries to charging and discharging under various temperature conditions and at various rates of charge or discharge where battery voltages and remaining capacities or discharged electricity quantities of the normal rechargeable batteries are measured and averaging the measured battery voltages and the measured remaining capacities or the measured discharged electricity quantities of the normal rechrageable batteries.

89. A computer program according to claim 88, wherein the basic data comprise basic data obtained by computer simulation on the basis of the averaged basic data.

90. A computer program according to claim 86 or 87, wherein the basic data are obtained by computer simulation.

91. A computer program according to claim 86 or 87, wherein said determining step determines, by comparison with the normal non-deteriorated rechargeable battery, if the subject rechargeable battery is not short-circuited, then determines whether or not the electricity storable capacity of the subject rechargeable battery is decreased or whether or not the internal resistance of the subject rechargeable battery is increased.

92. A computer program according to claim 86 or 87, wherein

(1) said determining step determines that the subject rechargeable battery is short-circuit when any of the following conditions (i) to (iv) are satisifed:

(i) without subjecting the subject rechargeable battery to charging or discharging, the battery has a decrease in battery voltage with the passage of time in the open-circuit voltage,

(ii) upon charging, an increase in the battery voltage or open-circuit voltage of the subject rechargeable battery is smaller than that of the normal rechargeable battery,

(iii) the open-circuit voltage of the subject rechargeable battery is smaller than that of the normal rechargeable battery and a descrease in the battery voltage of the subject rechargeable battery upon discharging is greater than that of the normal rechargeable battery, and

(iv) the internal resistance of the subject rechargeable battery is smaller than that of the normal rechargeable battery;

(2) said determining step determines that the subject rechargeable battery is not short-circuited but that the internal resistance of the subject rechargeable battery is increased in comparison to a normal rechargeable battery if the subject rechargeable battery satisfies any of the following conditions (i) to (iii);

(i) the open-circuit voltage of the subject rechargeable battery is substantially the same as that of the normal rechargeable battery but an increase in the battery voltage of the subject rechargeable battery upon charging is greater than that of the normal rechargeable battery,

(ii) the open-circuit voltage of the subject rechargeable battery is substantially the same as that of the normal rechargeable battery but a decrease in the battery voltage of the subject rechargeable battery upon charging is greater than that of the normal rechargeable battery, or

(iii) the internal resistance of the subject rechargeable battery is greater than that of the normal rechargeable battery; and

(3) said determining step determines that the subject rechargeable battery is not short-circuited but that the electricity storable capacity is decreased in comparison to a normal rechargeable battery if the subject rechargeable battery satisfies either of the following conditions (i) and (ii);

an increase in the battery voltage of the subject rechargeable battery upon charging and an increase in the open-circuit voltage thereof after the charging are greater than those of the normal rechargeable battery, or

(ii) a decrease in the battery voltage of the subject rechargeable battery upon charging and a decrease in the open-circuit voltage thereof after the discharging are smaller than those in a case where the subject rechargeable battery is short-circuited but they are greater than those of the normal rechargeable battery; and

(4) said determining step determines that the subject rechargeable battery is normal if the battery does not satisfy any of the above conditions (1) to (3).

93. A computer program according to claim 86 or 87, wherein the basic data include at least one of the following categories of data or function formulas:

(1)

(1) for a non-deteriorated normal rechargeable battery, basic data of a relationship Voc(Q) or Q(Voc) of the open-circuit voltage (Voc) to the remaining capacity (Q) which are obtained by way of measurement or function formulas obtained on the basis of the basic data;

(2) for said non-deteriorated normal rechargeable battery when it is in a full-charged state, basic data of relationships between battery voltages (Vd) measured when the rechargeable battery is subjected to discharging at various battery temperatures (T) and at various discharging currents (Id), open-circuit voltages (Voc) measured when the discharging is temporarily suspended, said discharging currents (Id) and said battery temperatures (T) or a function formula Vd(Voc, Id, T) obtained on the basis of said data; and

basic data or a function formula of a battery voltage-related function formula Vd(Q, Id, T) or Q(Vd, Id, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) to the remaining capacity which are described in the above category (1);

(3) internal resistance-related basic data computed from a relation expression Vd=Voc−

Id×

Rd or Rd=(Voc−

Vd)/Id when the internal resistance of the normal rechargeable battery is made to be Rd in the above (2), or a function formula Rd(Voc, Id, T) or Rd(Vd, Id, T) obtained on the basis of said data, in addition, basic data or a function formula of an internal resistance-related function formula Rd(Q, Id, T) or Q(Rd, Id, T) obtained with reference to aforesaid data and aforesaid function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above cateogry (1);

(4) for the above non-deteriorated normal rechargeable battery when the remaining capacity thereof is zero, data of relationships between battery voltages (Vc) measured when the rechargeable battery is subjected to charging at various battery temperatures (T) and at various charging currents (Ic), open-circuit voltages (Voc) measured when the charging is temporarily suspended, said discharging currents (Ic) and said battery temperatures (T) or a function formula Vc(Voc, Ic, T) obtained on the basis of said data, in addition, data or a function formula of a battery voltage-related function formula Vc(Q, Ic, T) or Q(Vc, Ic, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above category (1);

(5) internal resistance-related data computed from a relation expression Vc=Voc+Ic×

Rc or Rc=(Vc−

Voc)/Ic when the internal resistance of the normal rechargeable battery is made to be Rc in the above (4), or a function formula Rc(Voc, Ic, T) obtained on the basis of said data, in addition, data or a function formula of an internal resistance-related function formula Rc(Q, Ic, T) or Q(Rc, Ic, T) obtained with reference to aforesaid data and aforesaid function formula and also with reference to the data or the function formula of the relationship Voc(Q) of the open-circuit voltage (Voc) which are described in the above category (1).

94. A computer program according to claim 93, wherein, when the subject rechargeable battery does not have a decrease in the electricity storable capacity but has an increase in the internal resistance, the relationship Voc(Q) or Q(Voc) of the open-circuit voltage to the remaining capacity of the normal non-deteriorated rechargeable battery can be applied between the open-circuit voltage and the remaining capacity of the subject rechargeable battery, and

wherein, when the subject rechargeable battery has a decrease in the electricity storable capacity of a value D times that of the normal non-deteriorated rechargeable battery and the remaining capacity of the subject rechargeable battery is Q′

, when the relationship of Q′

to D is made to be Q′

/D=Q, the relationship Voc(Q) or Q(Voc) of the normal non-deteriorated rechargeable battery can be applied between the remaining capacity and the open-circuit voltage of the subject rechargeable battery, where the function formula Voc(Q′

/D) or Q′

/D=Q(Voc) is established.

95. A computer program according to claim 94, wherein, when the subject rechargeable battery is discharged, a change in the discharge current and a change in the battery voltage are measured and an internal state of the subject rechargeable battery is detected as will be described below:

(1) when the electricity storable capacity of the subject rechargeable battery is a value D times that of the normal non-deteriorated rechargeable battery and where the internal resistance of the subject rechargeable battery when the remaining capacity of the subject rechargeable battery Q′

=Q×

D is assumed to be changed to Rd′

(Q, I_d, T) from Rd(Q, T_d, T) of the normal non-deteriorated rechargeable battery, the battery voltage V of the subject rechargeable battery upon the discharging can be expressed as V=Voc(Q)−

I₃×

Rd′

(Q, I_d), T);

(2) in a case where the discharge current is changed n times in an increasing direction during the discharging of the subject rechargeable battery and the discharge current is changed to I_n1 from I_n0 of the stationary discharge current during t time (I_n0<

I_n1), the battery voltage (V) of the transient characteristics of the subject rechargeable battery is expressed by the equation V=V_n1+(V_n0−

V_n1)×

e<sup>−

t/τ</sup>

, (with t being a discharging time, V_n1 being a battery voltage when the discharging time t is extrapolated to infinity, τ

being a time constant, and n being a positive integer of 1, 2, 3, 4, . . . ), and a stationary value V_n1 of the battery voltage (V) when the discharging current is I_n1 is computed from a measured value of the battery voltage (V) and in accordance with aforesaid equation, wherein it is presumed that the remaining capacity is Q′

when the stationary discharge current is I_n0 and the battery voltage if V_n0 and at this time, the battery voltage becomes a stationary value when the discharge current is increased to I_n1, the following equations are established;

96. A computer program according to claim 95, wherein, presuming that: