Capacity estimation method, degradation estimation method and degradation estimation apparatus for lithium-ion cells, and lithium-ion batteries

• US 6,586,940 B2
• Filed: 03/12/2001
• Issued: 07/01/2003
• Est. Priority Date: 03/13/2000
• Status: Expired due to Fees

• Current Assignee: Nippon Telegraph and Telephone Corporation
• Original Assignee: Nippon Telegraph and Telephone Corporation
• Inventors: Hirai, Toshiro, Asakura, Kaoru
• Primary Examiner(s): Sherry, Michael
• Assistant Examiner(s): TIBBITS, PIA FLORENCE
• Application Number:
  US09/804,503
• Publication Number:
  US 20010022518A1
• Time in Patent Office: 841 Days
• Field of Search: 324/426, 324/427, 320/132, 320/134
• US Class Current: 324/426
• CPC Class Codes: G01R 31/3842 combining voltage and current measurements
• CPC Class Codes: G01R 31/392 Determining battery ageing or deterioration, e.g. state of health
• CPC Class Codes: G01R 31/396 Acquisition or processing of data for testing or for monitoring individual cells or groups of cells within a battery
• CPC Class Codes: H01M 10/48 Accumulators combined with arrangements for measuring, testing or indicating the condition of cells, e.g. the level or density of the electrolyte constructional details of current conducting connections for detecting conditions inside cells or batteries, e.g. details of voltage sensing terminals, H01M50/569
• CPC Class Codes: H02M 3/07 using capacitors charged and discharged alternately by semiconductor devices with control electrode , e.g. charge pumps
• CPC Class Codes: Y02E 60/10 Energy storage using batteries

Abstract

A capacity estimation method for a Li-ion cell is provided. In the method, according to a first aspect, an elapsed time from the time when charge voltage in constant current charge reaches a predetermined voltage to the time when charge condition is changed to a constant voltage mode is used for calculating an estimated capacity of said Li-ion cell. According to a second aspect, a charge current after a lapse of a predetermined time from the time when charge condition is changed to a constant voltage mode is used. According to a third aspect an elapsed time from the time when charge condition is changed to a constant voltage mode to the time when charge current becomes α (0<α<1) times is used.

Claims

1. A method for providing a capacity estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode; and

calculating an estimated capacity Ce of said Li-ion cell by using a function of said elapsed time t.

2. The method of claim 1, further comprising the steps of:

obtaining said elapsed time t for a charge current of said constant current charge mode having a value in a range from Co/(30 hours) to Co/(1 hour);

wherein Co is a nominal capacity of said Li-ion cell, and the step of calculating includes determining said estimated capacity Ce by using an equation Ce/Co=A×

t^B, A and B being positive constants, and B being an exponent of said elapsed time t.

3. The method of claim 2, further comprising the steps of:

repeating a charge and discharge cycle at least two times by using another Li-ion cell, which is used to provide a capacity estimation target and which is the same kind of Li-ion cell as said Li-ion cell, wherein said charge and discharge cycle includes a charge period from 3 hours to 10 days, a discharge period, and a rest period between said charge period and said discharge period, the rest period having a value of at least 0;

obtaining a discharge capacity Cn, and an elapsed time tn, which is a third time from when another charge voltage from another constant current charge reaches the predetermined voltage Vs to a fourth time when another charge condition is changed from the constant current charge mode to the constant voltage charge mode in each cycle; and

determining values of said constants A and B from said elapsed time tn and said discharge capacity Cn.

4. A method for providing a degradation estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode;

calculating an estimated capacity Ce of said Li-ion cell by using a function of said elapsed time t; and

determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

5. The method of claim 4, wherein the step of calculating includes determining said estimated capacity Ce by using an equation Ce/Co=A×

t^B, A and B being positive constants.

6. A degradation estimation apparatus for a Li-ion cell, comprising:

means for obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode; and

a circuit to calculate an estimated capacity Ce of said Li-ion cell by using a function of said elapsed time t; and

means for outputting a signal indicating that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

7. The degradation estimation apparatus of claim 6, wherein said estimated capacity Ce is calculated by using an equation Ce/Co=A×

t^B, and A and B are positive constants.

8. A Li-ion battery having a charge and discharge control arrangement, comprising:

a memory to store numerical data used to calculate an estimated capacity Ce of Li-ion cells in said Li-ion battery;

means for obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when charge condition is changed from a constant current charge mode to a constant voltage charge mode; and

a circuit for calculating said estimated capacity Ce of said Li-ion cells by using said elapsed time t and said numerical data.

9. The Li-ion battery of claim 8, wherein said estimated capacity Ce is calculated by using an equation Ce/Co=A×

t^B, and A and B are positive constants.

10. The Li-ion battery of claim 9, further comprising:

means for outputting a warning indicating that said Li-ion battery is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

11. The Li-ion battery of claim 10, wherein said warning includes at least one of a warning by displaying characters, a warning by displaying an image, a warning by a beep, and a warning by a voice.

12. A method for providing a capacity estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when the charge voltage reaches a charge limit voltage Vc, a charge current being no greater than Co/(20 hours), wherein Co is a nominal capacity of said Li-ion cell; and

calculating an estimated specific capacity Ce/Co of said Li-ion cell by using an equation Ce/Co=At+B, wherein Ce is an estimated capacity of said Li-ion cell, and A and B are positive constants.

13. The method of claim 12, further comprising the steps of:

repeating a charge and discharge cycle at least three times by using another Li-ion cell, which is the same kind of Li-ion cell as a Li-ion cell and which is a target of capacity estimation, wherein said charge and discharge cycle includes a charge period from 3 days to 10 days by said constant current and constant voltage process, a discharge period, a rest period between said charge period and said discharge period, wherein the rest period is at least 0, and wherein the charge current in said charge period is no greater than Co/(20 hours), discharge current in said discharge period is a value in a range from Co/(5 hours) to Co/(0.5 hour) and a predetermined discharge cut-off voltage Vd is used in said discharge period;

obtaining a discharge capacity Cn and an elapsed time tn, which is another time difference from a third time when another charge voltage in the constant current charge reaches a predetermined voltage Vs to a fourth time when another charge voltage reaches a charge limit voltage Vc, in each cycle; and

determining values of said constants A and B from said elapsed time tn and said discharge capacity Cn.

14. The method of claim 13, wherein said estimated capacity Ce is calculated by using an equation Ce/Co=At+B, and A and B are positive constants.

15. A capacity estimation apparatus for a Li-ion cell, comprising:

means for obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge voltage reaches a predetermined voltage Vs in a constant current charge mode to a second time when the charge voltage reaches a charge limit voltage Vc; and

a first circuit to calculate an estimated specific capacity Ce/Co of said Li-ion cell by using an equation Ce/Co=At+B, wherein Ce is an estimated capacity of said Li-ion cell, Co is a nominal capacity of said Li-ion cell, and A and B are positive constants;

a second circuit to estimate a degradation state of said Li-ion cell based on said estimated specific capacity Ce/Co, and providing an estimated degredation state; and

means for at least one of displaying the estimated degradation state and generating an alarm to warn of the estimated degradation state.

16. A Li-ion battery having a charge and discharge control arrangement, comprising:

a memory to store numerical data used for calculating an estimated specific capacity Ce/Co of Li-ion cells in said Li-ion battery, wherein Ce is an estimated capacity of said Li-ion cells and Co is a nominal capacity of said Li-ion cells;

means for obtaining an elapsed time t, which is a time difference from a first time when a charge voltage from a constant current charge reaches a predetermined voltage Vs in a constant current charge mode to a second time when the charge voltage reaches a charge limit voltage Vc, said Li-ion cell being charged by a constant current and a constant voltage process; and

a circuit to calculate said estimated specific capacity Ce/Co of said Li-ion cell by using an equation Ce/Co=At+B and said numerical data, wherein A and B are positive constants;

means for outputting said estimated specific capacity Ce/Co.

17. A method for providing a capacity estimation of a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, a charge current after a lapse of a predetermined time from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode; and

calculating an estimated capacity of said Li-ion cell by using said charge current.

18. A method for providing a capacity estimation of a Li-ion cell, comprising the step of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of a factor α and

a charge current Ic in said constant current charge mode, wherein the factor α

is between 0 and 1; and

calculating an estimated capacity of said Li-ion cell by using said elapsed time t.

19. A method for providing a capacity estimation of a Li-ion cell, comprising the steps of:

repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

obtaining, when said Li-ion cell is charged by the constant current and the constant voltage process, an elapsed time t_α

, which is a time difference from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of a factor α and

another charge current Ic0 in said constant current charge mode, wherein the factor α

is between 0 and 1;

obtaining an estimated specific capacity Ce/Co by using a first equation Ce/Co=−

At_α

+B when said elapsed time t_α

increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is an estimated capacity, Co is a nominal capacity and A and B are positive constants;

obtaining said estimated specific capacity Ce/Co by using a second equation Ce/Co=+At_α

+B′

when said elapsed time t_α

decreases as the number of repetitions of said charge and discharge cycle increases, wherein B′

is a positive constant; and

obtaining said estimated capacity Ce by using said estimated specific capacity Ce/Co and said nominal capacity Co.

20. The method of claim 19, wherein α

is ½

.

21. The method of claim 19, comprising the steps of:

repeating a charge and discharge cycle at least one of 5 and 6 times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell, which is the same kind of Li-ion cell as another Li-ion cell which is a target of capacity estimation is charged by said constant current and constant voltage process, and a discharge period, in which said Li-ion cell is discharged until a voltage of said Li-ion cell reaches a discharge cut-off voltage Vd, wherein the charge period per one cycle is from one of 3 hours and 3 days to 10 days, a discharge current is from 0.2 CmA to 2.0 CmA, in which 1 CmA is a value obtained by dividing Co by one hour, and ambient temperature is one of from 0 to 45 Celsius degrees and from 15 to 30 Celsius degrees;

obtaining said elapsed time t_α

and capacity C of said Li-ion cell C by integrating said discharge current with respect to time in each charge and discharge cycle;

calculating a specific capacity C/Co in each of said charge and discharge cycle;

recording t_α

and the specific capacity C/Co obtained in an nth cycle, where n is a positive integer, as a function of n to provide t_α

(n) and Cr(n);

determining said constants A, B and B′

so that said first equation and said second equation approximately represent a correlation between t_α

(n) and Cr(n), when assuming that t_α

=t_α

(n) and Ce/Co=Cr(n); and

estimating a capacity of said another Li-ion cell, which is a target of capacity estimation, by using determined values of said constants A, B and B′

in said first equation and said second equation.

22. A method for providing a capacity estimation for a Li-ion cell, comprising the steps of:

repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

obtaining a charge current I_tm after a lapse of a predetermined time tm from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode, wherein a first condition 0<

tm≦

0.8Co/Ic0 is satisfied, Co is a nominal capacity of said Li-ion cell and Ic0 is a charge current in said constant current charge mode;

obtaining a first estimated specific capacity Ce/Co by using a first equation Ce/Co=−

MI_tm+N′

, when said charge current I_tm increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is a specific capacity of said Li-ion cell and M and N′

are positive constants;

obtaining a second estimated specific capacity Ce/Co by using a second equation Ce/Co=+MI_tm+N′

, when said charge current I_tm decreases as the number of repetitions of said charge and discharge cycle increases, wherein N′

is a positive constant; and

obtaining said estimated capacity Ce by using said first and second estimated specific capacity Ce/Co and said nominal capacity Co.

23. The method of claim 22, wherein said predetermined time tm is from 1 minute to 15 minutes.

24. The method of claim 22, further comprising the steps of:

repeating a charge and discharge cycle at least 5 times, wherein said charge and discharge cycle includes a charge period, in which another Li-ion cell, which is the same kind of Li-ion cell as said Li-ion cell and is a target of capacity estimation, is charged by said constant current and constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged until a voltage of said charged Li-ion cell reaches a discharge cut-off voltage Vd, wherein a charge period per one cycle is from 3 hours to 10 days, a discharge current is from 0.2 CmA to 2.0 CmA, wherein 1 CmA is a value obtained by dividing Co by one hour, ambient temperature is from 0 to 45 degrees Celsius or from 15 to 30 degrees Celsius;

obtaining said charge current I_tm and capacity C of said another Li-ion cell by integrating said discharge current with respect to time in each charge and discharge cycle;

calculating a specific capacity C/Co in each charge and discharge cycle;

recording the charge current I_tm and the specific capacity C/Co obtained in an nth cycle, where n is a positive integer, as a first function I_tm(n) and a second function Cr(n);

determining said constants M and N′

so that said first equation and said second equation approximately represent a correlation between the first function I_tm(n) and the second function Cr(n) when assuming that I_tm=I_tm(n) and Ce/Co=Cr(n); and

estimating another capacity of said another Li-ion cell which is a target of capacity estimation, by calculating said first equation and said second equation using the said constants M and N′

.

25. A method for providing a degradation estimation of a Li-ion cell, comprising the steps of:

repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage method, an elapsed time t_α

, which is a time difference from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

a charge current Ic0 in said constant current charge mode, wherein α

is between 0 and 1;

obtaining a first estimated specific capacity Ce/Co by using a first equation Ce/Co=−

At_α

+B, when said elapsed time t_α

increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is an estimated capacity, Co is a nominal capacity and A and B are positive constants;

obtaining a second estimated specific capacity Ce/Co by using a second equation Ce/Co=+At_α

+B′

, when said elapsed time t_α

decreases as a number of repetitions of said charge and discharge cycle increases, wherein A and B′

are positive constants; and

obtaining said estimated capacity Ce by using said first and second estimated specific capacity Ce/Co and said nominal capacity Co; and

determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity.

26. A method for providing a degradation estimation of a Li-ion cell, comprising the steps of:

repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

obtaining a charge current I_tm after a lapse of a predetermined time tm from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode, wherein 0<

tm≦

0.8Co/Ic0 is satisfied, Co is a nominal capacity of said Li-ion cell and Ic0 is a charge current in said constant current charge mode;

obtaining a first estimated specific capacity Ce/Co by using a first equation Ce/Co=−

MI_tm+N′

, when said charge current I_tm increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is an estimated capacity of said Li-ion cell and M and N′

are positive constants;

obtaining a second estimated specific capacity Ce/Co by using a second equation Ce/Co=+MI_tm+N′

, when said charge current I_tm decreases as the number of repetitions of said charge and discharge cycle increases, wherein N′

is a positive constant; and

obtaining said estimated capacity Ce by using said first and second estimated specific capacity Ce/Co and said nominal capacity Co;

determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity.

27. A degradation estimation apparatus for a Li-ion cell, comprising:

a cell control arrangement comprising;

means for repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

means for obtaining, when said Li-ion cell is charged by the constant current and constant voltage process, an elapsed time t_α

from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

a charge current Ic0 in said constant current charge mode, wherein α

is between 0 and 1;

a memory to store said elapsed time t_α

as a function t_α

(n) of n in an nth cycle for each charge and discharge cycle;

a logic circuit including;

means for obtaining a first estimated specific capacity Ce/Co by using a first equation Ce/Co=−

At_α

+B, when said elapsed time t_α

increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is an estimated capacity, Co is a nominal capacity and A and B are positive constants;

means for obtaining a second estimated specific capacity Ce/Co by using a second equation Ce/Co=+At_α

+B′

, when said elapsed time t_α

decreases as the number of repetitions of said charge and discharge cycle increases, wherein B′

is a positive constant; and

means for obtaining said estimated capacity Ce by using said first and second estimated specific capacity Ce/Co and said nominal capacity Co; and

means for determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity.

28. A degradation estimation apparatus for a Li-ion cell, comprising:

a cell control arrangement comprising;

means for repeating a charge and discharge cycle a plurality of times, wherein said charge and discharge cycle includes a charge period, in which said Li-ion cell is charged by a constant current and a constant voltage process to provide a charged Li-ion cell, and a discharge period, in which said charged Li-ion cell is discharged;

means for obtaining a charge current I_tm after a lapse of a predetermined time tm from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode, wherein a condition of 0<

tm≦

0.8Co/Ic0 is satisfied, Co is a nominal capacity of said Li-ion cell and Ic0 is a charge current in said constant current charge mode;

a memory to store said charge current I_tm as a function I_tm(n) of n in an nth cycle for each charge and discharge cycle;

a logic circuit including;

means for obtaining a first estimated specific capacity Ce/Co by using a first equation Ce/Co=−

MI_tm+N′

, when said charge current I_tm increases or remains unchanged as a number of repetitions of said charge and discharge cycle increases, wherein Ce is an estimated capacity of said Li-ion cell and M and N′

are positive constants;

means for obtaining a second estimated specific capacity Ce/Co by using a second equation Ce/Co=+MI_tm+N′

, when said charge current I_tm decreases as the number of repetitions of said charge and discharge cycle increases, wherein N′

is a positive constant; and

means for obtaining said estimated capacity Ce by using said first and second estimated specific capacity Ce/Co and said nominal capacity Co;

means for determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity.

29. A Li-ion battery comprising:

a measuring part, when a charge and discharge cycle is repeated a plurality of times, obtaining an elapsed time t_α

from a first time when charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

a charge current Ic0 in said constant current charge mode, wherein said charge and discharge cycle includes a charge period in which said Li-ion cell is charged by a constant current and constant voltage process and a discharge period in which said charged Li-ion cell is discharged;

a memory storing said elapsed time t_α

as a function t_α

(n) of n in the nth cycle for each cycle;

a logic circuit comprising;

means for obtaining an estimated specific capacity Ce/Co by using a first equation Ce/Co=−

At_α

+B when said elapsed time t_α

increases or remains unchanged as the number of repetition of said cycle increases, wherein Ce is a specific capacity, Co is a nominal capacity and A and B are positive constants;

means for obtaining said estimated specific capacity Ce/Co by using a second equation Ce/Co=+At_α

+B′

when said elapsed time t_α

decreases as the number of repetition of said cycle increases, wherein B′

is a positive constant; and

means for obtaining said estimated capacity Ce by using said estimated specific capacity Ce/Co and said nominal capacity Co; and

means for judging that said Li-ion cell is degraded when said estimated capacity Ce becomes smaller than a predetermined limit capacity.

30. A Li-ion battery comprising:

a measuring arrangement, when a charge and discharge cycle is repeated a plurality of times, obtaining a charge current I_tm after a lapse of a predetermined time tm from the time when charge condition is changed from a constant current charge mode to a constant voltage charge mode, wherein 0<

tm≦

0.8Co/Ic0 is satisfied, Co is a nominal capacity of said Li-ion cell and Ic is charge current in said constant current charge mode, wherein said charge and discharge cycle includes a charge period in which said Li-ion cell is charged by a constant current and constant voltage method and a discharge period in which said charged Li-ion cell is discharged;

a memory to store said charge current I_tm as a function I_tm(n) of n in the nth cycle for each cycle;

a logic circuit comprising;

means for obtaining an estimated specific capacity Ce/Co by using a first equation Ce/Co=−

MI_tm+N′

when said charge current I_tm increases or remains unchanged as the number of repetition of said cycle increases, wherein Ce is a specific capacity of said Li-ion cell and M and N′

are positive constants;

means for obtaining said estimated specific capacity Ce/Co by using a second equation Ce/Co=+MI_tm+N′

when said charge current I_tm decreases as the number of repetition of said cycle increases, wherein N′

is a positive constant; and

means for obtaining said estimated capacity Ce by using said estimated specific capacity Ce/Co and said nominal capacity Co;

means for judging that said Li-ion cell is degraded when said estimated capacity Ce becomes smaller than a predetermined limit capacity.

31. A method for providing a capacity estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, a charge current It after a lapse of a time t, which is from 30 seconds to 30 minutes, from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode; and

calculating an estimated capacity Ce of said Li-ion cell by using said charge current It and a first equation Ce/Co+−

a×

It+b, wherein Co is a nominal capacity of said Li-ion cell, and a and b are positive constants.

32. The method of claim 31, wherein said constants a and b are calculated by a second equation a=d×

t^e and a third equation b=f×

t^h, wherein each of d, e, f, and h are constants greater than zero.

33. The method of claim 32, further comprising the steps of:

repeating a charge and discharge cycle at least 5 times by using a Li-ion cell, which is a capacity estimation target and a same kind of Li-ion cell as said Li-ion cell, wherein said charge and discharge cycle includes a charge period from 3 hours to one month, in which charging is performed by the constant current and constant voltage process, a discharge period, and a rest period of at least zero between said charge period and said discharge period;

obtaining, in each charge and discharge cycle, charge currents It_ni, after a lapse of times t_ni, which are between 30 seconds and 30 minutes, from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode, wherein n is a number assigned to each cycle and i is a number assigned to each of the times t_ni in each cycle;

obtaining a discharge capacity Cn in each cycle;

determining said constants a and b in said first equation and d, e, f, and h in said first and second equations by using said times t_ni, said charge currents It_ni and said discharge capacity Cn.

34. A method for providing a capacity estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a fist time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

another charge current in said constant current charge mode, where α

is between 0 and 1;

obtaining an estimated capacity Ce of said Li-ion cell by using an equation Ce/Co=At+B and said elapsed time t, wherein Co is a nominal capacity of said Li-ion cell and A and B are positive constants.

35. The method of claim 34, wherein α

is ½

.

36. The method of claim 34, further comprising the steps of:

repeating a charge and discharge cycle at least 5 times by using a Li-ion cell, which is at least one of a capacity estimation target and a same kind of Li-ion cell as said Li-ion cell, wherein said charge and discharge cycle includes a charge period from 3 hours to 10 days, in which a charge is provided by said constant current and constant voltage process and a charge current in said constant current charge mode is from Co/5 hours to Co/0.5 hour, a discharge period, and rest period between said charge period and said discharge period, the rest period being at least 0;

obtaining in each cycle a discharge capacity Cn and an elapsed time tn from a time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to another time when the charge current is a product of α and

another charge current in said constant current charge mode, where α

is between 0 and 1; and

determining values of said constants A and B from said elapsed time tn and said discharge capacity Cn.

37. The method of claim 36, wherein α

is ½

.

38. A method for providing a degradation estimation for a Li-ion cell, comprising the steps of:

obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is the time from when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to another time when a charge current is a product of α and

another charge current in said constant current charge mode, where α

is between 0 and 1;

obtaining an estimated capacity Ce of said Li-ion cell by using an equation Ce/Co=At+B and said elapsed time t, wherein Co is a nominal capacity of said Li-ion cell and A and B are positive constants; and

determining that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

39. The method of claim 38, wherein α

is ½

.

40. A degradation estimation apparatus for a Li-ion cell, comprising:

means for obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

another charge current in said constant current charge mode, where α

is between 0 and 1;

a circuit to obtain an estimated capacity Ce of said Li-ion cell by using said elapsed time t; and

means for outputting a signal indicating that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

41. The capacity estimation apparatus for said Li-ion cell of claim 40, wherein α

is ½

, and said circuit is configured to obtain said estimated capacity Ce by using an equation Ce/Co=At+B and said elapsed time t, wherein Co is a nominal capacity of said Li-ion cell and A and B are positive constants.

42. A Li-ion battery having a charge and discharge control arrangement, comprising:

a memory to store numerical data used for calculating an estimated capacity Ce of Li-ion cells in said Li-ion battery;

means for obtaining, when said Li-ion cell is charged by a constant current and a constant voltage process, an elapsed time t, which is a time difference from a first time when a charge condition is changed from a constant current charge mode to a constant voltage charge mode to a second time when a charge current is a product of α and

another charge current in said constant current charge mode, where α

is between 0 and 1;

a circuit to obtain an estimated capacity Ce of said Li-ion cell by using said elapsed time t.

43. The Li-ion battery of claim 42, wherein α

is ½

, and said circuit is configured to obtain said estimated capacity Ce of said Li-ion cell by using an equation Ce/Co=At+B and said elapsed time t, wherein Co is a nominal capacity of said Li-ion cell and A and B are positive constants.

44. The Li-ion battery of claim 42, further comprising:

means for outputting a warning indicating that said Li-ion cell is degraded when said estimated capacity Ce is smaller than a predetermined limit capacity Cmin.

45. The Li-ion battery of claim 44, wherein said warning is at least one of a warning by an electrical signal, a warning by displaying characters, a warning by displaying an image, a warning by a beep, and a warning by a voice.