Method and device for determining the remaining run time of a battery

1. Method for determining the remaining run time (Δt i ) of a battery that is supplying power to an appliance, comprising the steps of:

during operation of the appliance measuring the voltage (U i ) supplied by the battery at different points in time (t i ) in order to obtain time-voltage-pairs (t i , U i ), and

calculating the remaining run time (Δt i ) of the battery, wherein the calculation is based on the measured time-voltage-pairs (t i , U i ) and on a relationship between the measured voltage (U i ), the corresponding point in time (t i ) and the total run time

(T i ) of the battery which can be derived from a time dependent formulation of the Nernst equation for this relationship.

2. Method according to claim 1 , wherein the calculation of the remaining run time (Δt i ) of the battery is carried out when the measured voltage (U i ) drops below a predetermined voltage threshold value (U tr ).

3. Method according to claim 1 , wherein the remaining run time (Δt i ) at a specific point in time t i reads Δt i =T 1 −t i .

4. Method according to claim 1 , wherein the time dependent formulation of the Nernst equation reads:

U

i

=

C

1

+

C

2

⁢

T

·

log

⁡

(

T

1

-

t

i

T

2

+

t

i

)

with—U i being the measured voltage supplied by the battery at the point in time t i ,

C 1 being a constant relating to the standard cell potential of the battery,

C 2 being a constant that depends on the type of battery,

T being the temperature,

T 1 being the total run time of the battery, and

T 2 being a parameter depending on the initial state of the battery.

5. Method according to claim 1 , wherein the relationship for the measured time-voltage-pairs (t i , U i ) reads

x

i

=

T

1

-

t

i

T

2

⁢

⁢

with

⁢

⁢

x

i

=

10

(

U

i

-

C

1

C

2

⁢

T

)

U i being the measured voltage supplied by the battery at the point in time t i ,

C 1 being a constant relating to the standard cell potential of the battery,

C 2 being a constant that depends on the type of battery,

T being the temperature,

T 1 being the total run time of the battery, and

T 2 being a parameter depending on the initial state of the battery.

6. Method according to claim 1 , wherein the total run time (T 1 ) of the battery ( 4 ) is determined by linear regression of the time-voltage-pairs (t i , U i ).

7. Method according to claim 6 , wherein the linear regression is performed by minimizing the function

f

⁡

(

A

,

B

)

=

∑

i

=

1

n

⁢

⁢

(

x

i

-

(

At

i

+

B

)

)

2

,

where

⁢

⁢

A

=

-

1

T

2

,

B

=

T

1

T

2

and n is the number of time-voltage-pairs (t i , U i ) used for the linear regression.

8. Method according to claim 1 , wherein the measured time-voltage-pairs (t i , U i ) are subjected to a smoothing method prior to performing the calculation.

9. Method according to claim 1 , wherein a gliding window is applied to the measured time-voltage-pairs (t i , U i ) and the time-voltage-pair (t i , U i ) with maximum voltage value (max(U i )) is selected from each window to perform the calculation.

10. Method according to claim 1 , wherein an output signal is generated if the remaining run time (Δt i ) is found to be below a predetermined time threshold value (Δt tr ).

11. A device for determining the remaining run time (Δt i ) of a battery that is supplying power to an appliance, comprising:

a measuring device adapted to measure the voltage (U i ) supplied by the battery at different points in time (t i ) during operation of the appliance in order to obtain time-voltage-pairs (t i , U i ), and

a computing device programmed to calculate the remaining run time (Δt i ) of the battery on the basis of the measured time-voltage-pairs (t i , U i ) and of a relationship between the measured voltage (U i ), the corresponding point in time (t i ) and the total run time (T 1 ) of the battery which can be derived from a time dependent formulation of the Nernst equation for this relationship.

12. A device according to claim 11 , further comprising a comparator ( 14 ) configured to compare the measured voltage (U i ) with a predetermined voltage threshold value (U tr ) and to initiate the calculation of the remaining run time (Δt i ) by the computing device ( 10 ) if the measured voltage (U i ) drops below the predefined voltage threshold value (U tr ).

13. A device according to claim 11 , wherein the device is configured to carry out

a method for determining the remaining run time (Δt) of a battery that is supplying power to an appliance, the comprising the steps of:

during operation of the appliance measuring the voltage (Ui) supplied by the battery at different points in time (ti) in order to obtain time-voltage-pairs (ti, Ui), and

calculating the remaining run time (Δt,) of the battery, wherein the calculation is based on the measured time-voltage-pairs (ti, Ui) and on a relationship between the measured voltage (Ui), the corresponding point in time (ti) and the total run time (T) of the battery which can be derived from a time dependent formulation of the Nernst equation for this relationship.

14. A non-transitory machine-readable storage medium comprising a machine-readable program code, adapted to be executed by a device for determining the remaining run time (Δt i ) of a battery that is supplying power to an appliance, and making the device carry out the method according to claim 1 when the device is executing the program code.