System and method for determining both an estimated battery state vector and an estimated battery parameter vector

• US 20070236182A1
• Filed: 03/02/2006
• Published: 10/11/2007
• Est. Priority Date: 03/02/2006
• Status: Active Grant

• Current Assignee: LG Energy Solution Limited (LG Corporation)
• Original Assignee: LG Chem Limited (LG Corporation)
• Inventors: Plett, Gregory
• Granted Patent: US 7,521,895 B2
• Time in Patent Office: Days
• US Class Current: 320/132
• CPC Class Codes: G01R 31/367 Software therefor, e.g. for battery testing using modelling or look-up tables

Abstract

A system and a method for determining an estimated battery state vector and an estimated battery parameter vector are provided. The method includes determining an estimated battery parameter vector indicative of a parameter of the battery at the first predetermined time based on a plurality of predicted battery parameter vectors, a first plurality of predicted battery output vectors, and a battery output vector. The method further includes determining the estimated battery state vector indicative of a state of the battery at the first predetermined time based on a plurality of predicted battery state vectors, a second plurality of predicted battery output vectors, and the battery output vector.

Claims

1. A method for determining an estimated battery state vector and an estimated battery parameter vector, the estimated battery state vector being indicative of a state of a battery at a first predetermined time, the estimated battery parameter vector being indicative of a parameter of the battery at the first predetermined time, the method comprising:

determining a plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise associated with a sensor measuring a battery output variable, an uncertainty of the state of the battery, an uncertainty of the battery input noise, and an uncertainty of the sensor noise at a second predetermined time prior to the first predetermined time;

determining a plurality of predicted battery state vectors that are indicative of the state of the battery and an uncertainty of the state of the battery at the first predetermined time based on the plurality of estimated augmented battery state vectors;

determining a plurality of predicted battery parameter vectors that are indicative of the parameter of the battery and an uncertainty of the parameter of the battery at the first predetermined time;

determining a first plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and an uncertainty of the output variable at the first predetermined time based on the plurality of predicted battery parameter vectors;

determining a second plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and the uncertainty of the output variable at the first predetermined time based on the plurality of estimated augmented battery state vectors and the plurality of predicted battery state vectors;

determining a battery output vector having at least one measured value of a battery output variable obtained at the first predetermined time;

determining an estimated battery parameter vector indicative of the parameter of the battery at the first predetermined time based on the plurality of predicted battery parameter vectors, the first plurality of predicted battery output vectors, and the battery output vector; and

determining an estimated battery state vector indicative of the state of the battery at the first predetermined time based on the plurality of predicted battery state vectors, the second plurality of predicted battery output vectors, and the battery output vector.

2. The method of claim 1, wherein determining the plurality of estimated augmented battery state vectors comprises:

retrieving an estimated battery state vector indicative of the state of the battery at the second predetermined time from a memory;

determining a first estimated augmented battery state vector indicative of the state of the battery, the battery input noise, and the sensor noise at the second predetermined time, based on the estimated battery state vector, an expected battery input noise vector, and an expected sensor noise vector;

retrieving an estimated battery state vector covariance matrix indicative of the uncertainty of the state of the battery at the second predetermined time from the memory;

determining a first estimated augmented battery state vector covariance matrix indicative based on the estimated battery state vector covariance matrix, a covariance matrix indicative of the uncertainty of the battery input noise and a covariance matrix indicative of the uncertainty of the sensor noise; and

calculating the plurality of estimated augmented battery state vectors based on the first estimated augmented battery state vector and the first estimated augmented battery state vector covariance matrix.

3. The method of claim 2, wherein calculating the plurality of estimated augmented battery state vectors comprises:

setting one member of the plurality of estimated augmented battery state vectors equal to the first estimated augmented battery state vector;

setting a first additional set of L members of the plurality of estimated augmented battery state vectors equal to the first estimated augmented battery state vector added to a constant value multiplied by respective columns extracted from a matrix square-root of the first estimated augmented battery state vector covariance matrix, where L is the length of the first estimated augmented battery state vector; and

setting a second additional set of L members of the plurality of estimated augmented battery state vectors equal to the constant value multiplied by respective columns extracted from the matrix square-root of the first estimated augmented battery state vector covariance matrix subtracted from the first estimated augmented battery state vector.

4. The method of claim 1, wherein determining the plurality of estimated augmented battery state vectors comprises:

retrieving an estimated battery state vector indicative of the state of the battery at the second predetermined time from a memory;

determining a first estimated augmented battery state vector indicative of the state of the battery, the battery input noise, and the sensor noise at the second predetermined time based on the estimated battery state vector, an expected battery input noise vector, and an expected sensor noise vector;

retrieving an estimated battery state vector square-root covariance matrix indicative of the uncertainty of the state of the battery at the second predetermined time from the memory;

determining a first estimated augmented battery state vector square-root covariance matrix indicative of the uncertainty of the state of the battery, the battery input noise, and the sensor noise, based on the estimated battery state vector square-root covariance matrix, a covariance matrix indicative of the uncertainty of the battery input noise and a covariance matrix indicative of the uncertainty of the sensor noise; and

calculating the plurality of estimated augmented battery state vectors based on the first estimated augmented battery state vector and the first estimated augmented battery state vector square-root covariance matrix.

5. The method of claim 4, wherein calculating the plurality of estimated augmented battery state vectors comprises:

setting one member of the plurality of estimated augmented battery state vectors equal to the first estimated augmented battery state vector;

setting a first additional set of L members of the plurality of estimated augmented battery state vectors equal to the first estimated augmented battery state vector added to a constant value multiplied by respective columns extracted from the estimated augmented battery state vector square-root covariance matrix, where L is the length of the estimated augmented battery state vector; and

setting a second additional set of L members of the plurality of estimated augmented battery state vectors equal to the constant value multiplied by respective columns extracted from the first estimated augmented battery state vector square-root covariance matrix subtracted from the first estimated augmented battery state vector.

6. The method of claim 1, wherein determining the plurality of predicted battery state vectors comprises:

extracting values indicative of the state of the battery and of the uncertainty of the state of the battery at the second predetermined time from the plurality of estimated augmented battery state vectors, to obtain a first plurality of estimated battery state vectors;

extracting values indicative of the battery input noise and an uncertainty of the battery input noise at the second predetermined time from the first plurality of estimated augmented battery state vectors, to obtain a plurality of estimated battery input noise vectors;

generating a battery input vector having at least one measured value of a battery input variable at the second predetermined time; and

determining the plurality of predicted battery state vectors based on the first plurality of estimated battery state vectors, the first plurality of predicted battery input noise vectors, and the battery input vector.

7. The method of claim 1, wherein determining the plurality of predicted battery parameter vectors comprises:

retrieving from a memory an estimated battery parameter vector indicative of the parameter of the battery at the second predetermined time;

retrieving an estimated battery parameter vector covariance matrix indicative of an uncertainty of the parameter of the battery at the second predetermined time from the memory;

determining an estimated battery parameter noise covariance matrix indicative of an uncertainty of a parameter noise at the second predetermined time; and

calculating the plurality of predicted battery parameter vectors based on the estimated battery parameter vector, the estimated battery parameter vector covariance matrix, and the estimated battery parameter noise covariance matrix.

8. The method of claim 7, wherein calculating the plurality of predicted battery parameter vectors comprises:

setting one member of the plurality of predicted battery parameter vectors equal to the estimated battery parameter vector;

determining a predicted battery parameter vector covariance matrix indicative of an uncertainty of the parameter of the battery at the first predetermined time based on the estimated battery parameter vector covariance matrix and the estimated battery parameter noise covariance matrix;

setting a first additional set of L members of the plurality of predicted battery parameter vectors equal to the first estimated battery parameter vector added to a constant value multiplied by respective columns extracted from a matrix square-root of the first predicted battery parameter vector covariance matrix, where L is the length of the first estimated battery parameter vector; and

setting a second additional set of L members of the plurality of predicted battery parameter vectors equal to the constant value multiplied by respective columns extracted from a matrix square-root of the first predicted battery parameter vector covariance matrix subtracted from the first estimated battery parameter vector.

9. The method of claim 1, wherein determining the plurality of predicted battery parameter vectors comprises:

retrieving an estimated battery parameter vector indicative of the parameter of the battery at the second predetermined time from a memory;

retrieving an estimated battery parameter vector square-root covariance matrix indicative of an uncertainty of the parameter of the battery at the second predetermined time from the memory;

determining an estimated battery parameter noise square-root covariance matrix indicative of an uncertainty of a parameter noise at the second predetermined time; and

calculating the plurality of predicted battery parameter vectors based on the estimated battery parameter vector, the estimated battery parameter vector square-root covariance matrix, and the estimated battery parameter noise square-root covariance matrix.

10. The method of claim 9, wherein calculating the plurality of predicted battery parameter vectors comprises:

setting one member of the plurality of predicted battery parameter vectors equal to the estimated battery parameter vector;

determining a predicted battery parameter vector square-root covariance matrix indicative of an uncertainty of the parameter of the battery at the first predetermined time based on the estimated battery parameter vector square-root covariance matrix and the estimated battery parameter noise covariance matrix;

setting a first additional set of L members of the plurality of predicted battery parameter vectors equal to the first estimated battery parameter vector added to a constant value multiplied by respective columns extracted from the first predicted battery parameter vector square-root covariance matrix, where L is the length of the first estimated battery parameter vector; and

setting a second additional set of L members of the plurality of predicted battery parameter vectors equal to the constant value multiplied by respective columns extracted from the first predicted battery parameter vector square-root covariance matrix subtracted from the first estimated battery parameter vector.

11. The method of claim 1, wherein determining the first plurality of predicted battery output vectors comprises:

retrieving an estimated battery state vector indicative of the state of the battery at the second predetermined time from a memory;

generating a battery mean sensor noise vector indicative of the average sensor noise at the first predetermined time and a battery mean input noise vector indicative of the average battery input noise at the second predetermined time;

generating a first battery input vector having at least one measured value of a battery input variable at the first predetermined time;

generating a second battery input vector having at least one measured value of a battery input variable at the second predetermined time; and

determining the first plurality of predicted battery output vectors based on the plurality of predicted battery parameter vectors, the first battery input vector, the second battery input vector, the battery mean sensor noise vector, the battery mean input noise vector, and the estimated battery state vector.

12. The method of claim 1, wherein determining the second plurality of predicted battery output vectors comprises:

extracting values indicative of the sensor noise and of the uncertainty of the sensor noise at the second predetermined time from the plurality of estimated augmented battery state vectors, to obtain a plurality of estimated sensor noise vectors;

generating the first battery input vector having at least one measured value of a battery input variable at the first predetermined time; and

determining the second plurality of predicted battery output vectors based on the plurality of predicted battery state vectors, the first battery input vector, the plurality of estimated sensor noise vectors.

13. The method of claim 1, wherein determining the estimated battery parameter vector comprises:

determining a first predicted battery output vector indicative of at least one output variable of the battery at the first predetermined time based on the first plurality of predicted battery output vectors;

determining a predicted battery parameter vector indicative of the parameter of the battery at the first predetermined time based on an estimated battery parameter vector indicative of the parameter of the battery at the second predetermined time;

determining a parameter gain matrix based on the predicted battery parameter vector, the first predicted battery output vector, the plurality of predicted battery parameter vectors, and the plurality of predicted battery output vectors; and

calculating the estimated battery parameter vector based on the battery output vector, the first predicted battery output vector, the predicted battery parameter vector, and the parameter gain matrix.

14. The method of claim 13, wherein determining the first predicted battery output vector comprises calculating a weighted average of the plurality of predicted battery output vectors.

15. The method of claim 13, wherein determining the parameter gain matrix comprises:

determining a predicted battery output vector covariance matrix based on the first predicted battery output vector and the plurality of predicted battery output vectors;

determining a predicted cross-covariance matrix between a battery output vector and a battery parameter vector based on the first predicted battery output vector, the plurality of predicted battery output vectors, the predicted battery parameter vector, and the plurality of predicted battery parameter vectors; and

calculating the parameter gain matrix based on the predicted cross-covariance matrix and the predicted battery output vector covariance matrix.

16. The method of claim 15, wherein determining the predicted battery output vector covariance matrix comprises:

determining a predicted battery output vector square-root covariance matrix based on the first predicted battery output vector and the plurality of predicted battery output vectors; and

calculating the predicted battery output vector covariance matrix based on the predicted battery output vector square-root covariance matrix and the predicted battery output vector square-root covariance matrix.

17. The method of claim 13, wherein calculating the estimated battery parameter vector comprises:

determining an innovation vector based on the battery output vector and the first predicted battery output vector;

determining an update vector based on the parameter gain matrix and the innovation vector; and

calculating the estimated battery parameter vector based on the predicted battery parameter vector and the update vector.

18. The method of claim 13, further comprising determining an estimated battery parameter vector covariance matrix at the first predetermined time based on the first predicted battery parameter vector, the first plurality of predicted battery parameter vectors, the parameter gain matrix, and the first predicted battery output vector covariance matrix.

19. The method of claim 13, further comprising determining an estimated battery parameter vector square-root covariance matrix at the first predetermined time based on the first predicted battery parameter vector, the first plurality of predicted battery parameter vectors, the parameter gain matrix, and a predicted battery output vector square-root covariance matrix.

20. The method of claim 1, wherein determining the estimated battery state vector comprises:

determining a predicted battery state vector indicative of the state of the battery at the first predetermined time based on the plurality of predicted battery state vectors;

determining a second predicted battery output vector indicative of at least one output variable of the battery at the first predetermined time based on the plurality of predicted output vectors;

determining a state gain matrix based on the predicted battery state vector, the second predicted battery output vector, the plurality of predicted battery state vectors, and the second plurality of predicted battery output vectors; and

calculating the estimated battery state vector based on the predicted battery state vector, the second predicted battery output vector, the state gain matrix, and the battery output vector.

21. The method of claim 20, wherein determining the predicted battery state vector comprises calculating a weighted average of the plurality of predicted battery state vectors.

22. The method of claim 20, wherein determining the second predicted battery output vector comprises calculating a weighted average of the second plurality of predicted battery output vectors.

23. The method of claim 20, wherein determining the state gain matrix comprises:

determining a predicted battery output vector covariance matrix based on the second predicted battery output vector and the second plurality of predicted battery output vectors;

determining a predicted cross-covariance matrix between a battery output vector and a battery state vector based on the second predicted battery output vector, the second plurality of predicted battery output vectors, the predicted battery state vector, and the plurality of predicted battery state vectors; and

calculating the state gain matrix based on the predicted cross-covariance matrix and the predicted battery output vector covariance matrix.

24. The method of claim 23, wherein determining the predicted battery output vector covariance matrix comprises:

determining a predicted battery output vector square-root covariance matrix based on the second predicted battery output vector and the second plurality of predicted battery output vectors; and

calculating the predicted battery output vector covariance matrix based on the predicted battery output vector square-root covariance matrix and the predicted battery output vector square-root covariance matrix.

25. The method of claim 20, wherein calculating the estimated battery state vector comprises:

determining an innovation vector based on the second battery output vector and the second predicted battery output vector;

determining an update vector based on the state gain matrix and the innovation vector; and

calculating the estimated battery state vector based on the predicted battery state vector and the update vector.

26. The method of claim 20, further comprising determining an estimated battery state vector covariance matrix at the first predetermined time based on the predicted battery state vector, the plurality of predicted battery state vectors, the state gain matrix, and the predicted battery output vector covariance matrix.

27. The method of claim 20, further comprising determining an estimated battery state vector square-root covariance matrix at the first predetermined time based on the predicted battery state vector, the plurality of predicted battery state vectors, the state gain matrix, and a predicted battery output vector square-root covariance matrix.

28. A system for determining an estimated battery state vector and an estimated battery parameter vector, the estimated battery state vector being indicative of a state of a battery at a first predetermined time, the estimated battery parameter vector being indicative of a parameter of the battery at the first predetermined time, the system comprising:

a sensor configured to generate a first signal indicative of an output variable of the battery; and

a computer operably coupled to the sensor, the computer configured to determine a plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise associated with a sensor measuring a battery output variable, an uncertainty of the state of the battery, an uncertainty of the battery input noise, and an uncertainty of the sensor noise at a second predetermined time prior to the first predetermined time, the computer further configured to determine a plurality of predicted battery state vectors that are indicative of the state of the battery and an uncertainty of the state of the battery at the first predetermined time based on the plurality of estimated augmented battery state vectors, the computer further configured to determine a plurality of predicted battery parameter vectors that are indicative of the parameter of the battery and an uncertainty of the parameter of the battery at the first predetermined time, the computer further configured to determine a first plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and an uncertainty of the output variable at the first predetermined time based on the plurality of predicted battery parameter vectors, the computer further configured to determine a second plurality of predicted battery output vectors that are indicative of at least one output variable of the battery and the uncertainty of the output variable at the first predetermined time based on the plurality of estimated augmented battery state vectors and the plurality of predicted battery state vectors, the computer further configured to determine a battery output vector based on the first signal, the computer further configured to determine an estimated battery parameter vector indicative of the parameter of the battery at the first predetermined time based on the plurality of predicted battery parameter vectors, the first plurality of predicted battery output vectors, and the battery output vector, the computer further configured to determine an estimated battery state vector indicative of the state of the battery at the first predetermined time based on the plurality of predicted battery state vectors, the second plurality of predicted battery output vectors, and the battery output vector.