Method and apparatus for modeling diffusion in an electrochemical system

1. An energy management controller for a vehicle comprising:

a processor configured to:

estimate an initial diffusion voltage,

calculate a diffusion voltage using an equation based on a diffusion circuit model and the estimated initial diffusion voltage, and

determine a battery condition parameter using the diffusion voltage, wherein to estimate the initial diffusion voltage, the processor is further configured to:

determine a first voltage as a difference between a key-off voltage measured when the vehicle is turned off and a key-on voltage measured when the vehicle is turned on,

select a starting diffusion voltage based on a predetermined curve of diffusion voltage versus time,

determine a determined diffusion voltage based on the first diffusion voltage and an elapsed time between when the vehicle is turned off and when the vehicle is turned on, and

estimate the initial diffusion voltage as the determined diffusion voltage if the difference between the starting diffusion voltage and the determined diffusion voltage matches, within a predetermined amount, the first voltage; and

a memory coupled to the processor, the memory configured to store the battery condition parameter.

2. The controller of claim 1 wherein the diffusion circuit model comprises a diffusion capacitor coupled to a variable resistance.

3. The controller of claim 2 wherein the variable resistance varies based on a charge on the diffusion capacitor.

4. The controller of claim 3 wherein the equation based on the diffusion circuit model includes a time constant that varies based on the charge on the diffusion capacitor.

5. The controller of claim 4 wherein the time constant and the charge on the diffusion capacitor are related with a decreasing exponential relationship.

6. The controller of claim 1 wherein the battery condition parameter is a state of charge of a corresponding battery.

7. The controller of claim 1 , wherein the processor is further configured to relate the diffusion voltage to an overall voltage of an associated battery.

8. The controller of claim 7 , wherein the processor is further configured to estimate a state of charge based on the overall voltage.

9. An apparatus for determining a diffusion voltage in an electrochemical cell, comprising:

means for estimating an initial diffusion voltage;

means for calculating a diffusion voltage using an equation based on a diffusion circuit model and the estimated initial diffusion voltage; and

means for determining a battery condition parameter using the diffusion voltage, wherein the means for estimating the initial diffusion voltage comprises:

means for determining a first voltage as a difference between a key-off voltage measured when a vehicle is turned off and a key-on voltage measured when the vehicle is turned on,

means for selecting a staffing diffusion voltage based on a predetermined curve of diffusion voltage versus time,

means for determining a determined diffusion voltage based on the first diffusion voltage and an elapsed time between when the vehicle is turned off and when the vehicle is turned on, and

means for estimating the initial diffusion voltage as the determined diffusion voltage if the difference between the starting diffusion voltage and the determined diffusion voltage matches, within a predetermined amount, the first voltage; and

a memory coupled to the processor, the memory configured to store the battery condition parameter.

10. The apparatus of claim 9 wherein the diffusion circuit model comprises a diffusion capacitor coupled to a variable resistance.

11. The apparatus of claim 10 wherein the variable resistance varies based on a charge on the diffusion capacitor.

12. The apparatus of claim 11 wherein the equation based on the diffusion circuit model includes a time constant that varies based on the charge on the diffusion capacitor.

13. The apparatus of claim 12 wherein the time constant and the charge on the diffusion capacitor are related with a decreasing exponential relationship.

14. The apparatus of claim 9 , further comprising:

means for relating the diffusion voltage to an overall voltage of an associated battery; and

means for estimating a state of charge based on the overall voltage.

15. A method for determining a diffusion voltage in an electrochemical cell, comprising the steps of:

estimating, by a processor, an initial diffusion voltage;

calculating, by the processor, a diffusion voltage using an equation based on a diffusion circuit model and the estimated initial diffusion voltage; and

determining, by the processor, a battery condition parameter using the diffusion voltage, wherein the step of estimating the initial diffusion voltage comprises the steps of:

determining a first voltage as a difference between a key-off voltage measured when a vehicle is turned off and a key-on voltage measured when the vehicle is turned on,

selecting a starting diffusion voltage based on a predetermined curve of diffusion voltage versus time,

determining a determined diffusion voltage based on the first diffusion voltage and an elapsed time between when the vehicle is turned off and when the vehicle is turned on, and

estimating the initial diffusion voltage as the determined diffusion voltage if the difference between the starting diffusion voltage and the determined diffusion voltage matches, within a predetermined amount, the first voltage.

16. The method of claim 15 wherein the diffusion circuit model comprises a diffusion capacitor coupled to a variable resistance.

17. The method of claim 16 wherein the variable resistance varies based on a charge on the diffusion capacitor.

18. The method of claim 17 wherein the equation based on the diffusion circuit model includes a time constant that varies based on the charge on the diffusion capacitor.

19. The method of claim 18 wherein the time constant and the charge on the diffusion capacitor are related with a decreasing exponential relationship.

20. The method of claim 15 , further comprising the steps of:

relating the diffusion voltage to an overall voltage of an associated battery; and

estimating a state of charge based on the overall voltage.