Electrochemical device power estimator and methods of making and using the same

1. A method comprising:

using any number of sensors to obtain data regarding a terminal voltage of an electrochemical device;

using a controller to determine an equivalent circuit model which operates in a manner approximating the data regarding the terminal voltage comprising an open circuit voltage V OC comprising a constant voltage source V 0 and a voltage V s across a capacitor C S , in series with an overpotential circuit comprising an overpotential voltage V 1 ;

using the controller to determine at least one of the power capabilities of the equivalent circuit model;

using the controller to estimate at least one of the power capabilities of the electrochemical device based upon the determined power capabilities of the equivalent circuit model; and

using the controller to send a signal representative of at least one of the power capabilities of the electrochemical device to a component of a vehicle;

wherein using the controller to estimate at least one of the power capabilities of the electrochemical device based upon the power capabilities of the equivalent circuit model comprises:

imposing a constant input current, I 0 upon the equivalent circuit model;

using the controller to solve for the overpotential voltage, V 1 (t) according to V(t)=V(0)+V S +V 1 (t), where

V

s

=

t

⁢

⁢

I

0

C

s

 and initial conditions V(0), and C s are known,

and to solve for V 1 (t) through a mathematical algorithm;

using the controller to predict an equivalent circuit model power at time, t according to

Power

⁢

⁢

(

t

)

=

I

0

⁢

V

⁡

(

t

)

=

I

0

⁡

(

V

⁡

(

0

)

+

t

⁢

⁢

I

0

C

s

+

V

1

⁡

(

t

)

)

;

 and,

using the controller to correlate the equivalent circuit model power at time, t to the power of the electrochemical device at time t where V 0 (SOC(t))=V 0 (SOC 0 )+k(SOC(t)−SOC(0)) where

k

=

∂

V

0

∂

SOC

 and where SOC is the state of charge of the electrochemical device.

2. A method as set forth in claim 1 wherein the terminal voltage is obtained at a number of temperatures and modeled as a function of temperature within the equivalent circuit model.

3. A method as set forth in claim 1 wherein the value of the voltage V s across the inserted capacitor C S is a function of temperature and modeled as a function of temperature within the equivalent circuit model and where

C

s

=

Q

T

k

where Q T is the total capacity of the electrochemical device,

k

=

∂

V

0

∂

SOC

and SOC is the state of charge of the electrochemical device.

4. A method as set forth in claim 1 wherein the open circuit constant voltage V 0 , voltage V s across the inserted capacitor C S , and overpotential voltage V 1 are regressed in real time.

5. A method as set forth in claim 1 wherein the overpotential circuit model is a linear circuit.

6. A method as set forth in claim 1 wherein the overpotential circuit is a non-linear circuit.

7. A method as set forth in claim 1 wherein the overpotential circuit comprises at least one capacitor.

8. A method as set forth in claim 1 wherein the overpotential circuit comprises at least one resistor.

9. A method as set forth in claim 1 wherein the mathematical algorithm comprises using a numerical integration of the ordinary differential equation of the overpotential circuit voltage to formulate an equation for the time evolution of the overpotential V 1 (t).

10. A method as set forth in claim 1 wherein the mathematical algorithm comprises using a Laplace transform of the overpotential circuit voltage to formulate an equation for the time evolution of the overpotential V 1 (t).

11. A method as set forth in claim 1 wherein the mathematical algorithm comprises using a matrix exponential of the overpotential circuit voltage to formulate an equation for the time evolution of the overpotential V 1 (t).

12. A method as set forth in claim 1 wherein the mathematical algorithm comprises using a close form expression for a FIR circuit model of the overpotential circuit voltage to formulate an equation for the time evolution of the overpotential V 1 (t).

13. A method as set forth in claim 1 wherein the mathematical algorithm comprises using a close form expression for a R+N(R∥C) circuit model of the overpotential circuit voltage to formulate an equation for the time evolution of the overpotential V 1 (t).

14. A method comprising:

using any number of sensors to obtain data regarding a terminal voltage of a electrochemical device;

using the controller to determine an equivalent circuit model which operates in a manner approximating the data regarding the terminal voltage comprising an open circuit voltage V OC comprising a constant voltage source V 0 and a voltage V s across a capacitor C S , in series with an overpotential circuit comprising an overpotential voltage V 1 ;

using the controller to determine at least one of the power capabilities of the equivalent circuit model; and,

using the controller to estimate at least one of the power capabilities of the electrochemical device based upon the determined power capabilities of the equivalent circuit model; and

using the controller to send a signal representative of at least one of the power capabilities of the electrochemical device to a component of a vehicle;

wherein using the controller to estimate at least one of the power capabilities of the electrochemical device based upon the power capabilities of the equivalent circuit model comprises:

imposing an extreme constant input voltage, V upon the equivalent circuit model such that V=(V 0 +V S +V 1 );

using the controller to solve for an equivalent circuit model current at time t by assuming a constant overpotential for the equivalent circuit model through a mathematical algorithm;

using the controller to predict for an equivalent circuit model power at time t via the equation:

Power( t )= VI ( t ); and,

using the controller to correlate the equivalent circuit model power at time, t to the power of the electrochemical device at time t where V 0 (SOC(t))=V 0 (SOC 0 )+k(SOC(t)−SOC(0)) where

k

=

∂

V

0

∂

SOC

and where SOC is the state of charge of the electrochemical device.

15. A method as set forth in claim 14 wherein the mathematical algorithm comprises using a numerical integration of the ordinary differential equation of the overpotential circuit current to formulate an equation for the time evolution of the current overpotential I(t).

16. A method as set forth in claim 14 wherein the mathematical algorithm comprises using a Laplace transform of the overpotential circuit current to formulate an equation for the time evolution of the overpotential current I(t).

17. A method as set forth in claim 14 wherein the mathematical algorithm comprises using a matrix exponential of the overpotential circuit current to formulate an equation for the time evolution of the overpotential I(t).

18. A method as set forth in claim 14 wherein the mathematical algorithm comprises using a close form expression for a FIR circuit model of the overpotential circuit current to formulate an equation for the time evolution of the overpotential I(t).

19. A product comprising: a electrochemical device state estimator constructed and arranged to obtain terminal voltage data of a electrochemical device; determine an equivalent circuit model which operates in a manner approximating the terminal voltage data comprising an open circuit voltage V OC comprising a constant voltage source V 0 and a voltage V s across a capacitor C S , in series with an overpotential circuit comprising an overpotential voltage V 1 ; determining at least one of the power capabilities of the equivalent circuit model; and, estimating at least one of the power capabilities of the electrochemical device based upon the determined power capabilities of the equivalent circuit model wherein estimating at least one of the power capabilities of the electrochemical device based upon the power capabilities of the equivalent circuit model comprises:

imposing a constant input current, I 0 upon the equivalent circuit model;

solving for the overpotential voltage, V 1 (t) according to V(t)=V(0)+V S +V 1 (t), where

V

s

=

tI

0

C

s

 and initial conditions V(0), and C s are known,

and to solve for V 1 (t) through a mathematical algorithm;

predicting an equivalent circuit model power at time, t according to

Power

⁡

(

t

)

=

I

0

⁢

V

⁡

(

t

)

=

I

0

⁡

(

V

⁡

(

0

)

+

tI

0

C

s

+

V

1

⁡

(

t

)

)

;

 and,

correlating the equivalent circuit model power at time, t to the power of the electrochemical device at time t where V 0 (SOC(t))=V 0 (SOC 0 )+k(SOC(t)−SOC(0)) where

k

=

∂

V

0

∂

SOC

 and where SOC is the state of charge of the electrochemical device.