System, method, and article of manufacture for determining an estimated battery state vector

• US 20070103120A1
• Filed: 11/10/2005
• Published: 05/10/2007
• Est. Priority Date: 11/10/2005
• Status: Active Grant

• Current Assignee: LG Energy Solution Limited (LG Corporation)
• Original Assignee: LG Chem Limited (LG Corporation)
• Inventors: Plett, Gregory
• Granted Patent: US 7,446,504 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
• CPC Class Codes: Y02E 60/10 Energy storage using batteries

Abstract

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

Claims

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

determining a first plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise, 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 second 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 first plurality of estimated augmented battery state vectors;

determining a third 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 first plurality of estimated augmented battery state vectors and the second plurality of predicted battery state vectors;

determining a first battery output vector having at least one measured value of a battery output variable; and

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

2. The method of claim 1, wherein determining the first 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 an 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 an uncertainty of the battery input noise and a covariance matrix indicative of an uncertainty of the sensor noise; and

determining the first 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 determining the first plurality of estimated augmented battery state vectors comprises:

setting one member of the first 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 first 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 first 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 first 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 an 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 an 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 an uncertainty of the battery input noise and a covariance matrix indicative of an uncertainty of the sensor noise; and

determining the first 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 determining the first plurality of estimated augmented battery state vectors comprises:

setting one member of the first 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 first 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 first 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 second plurality of predicted battery state vectors comprises:

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

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

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

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

extracting values indicative of the sensor noise and of an uncertainty of the sensor noise at the second predetermined time from the first plurality of estimated augmented battery state vectors, to obtain a fourth 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 third plurality of predicted battery output vectors based on the second plurality of predicted battery state vectors, the first battery input vector, the fourth plurality of estimated sensor noise vectors.

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

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

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 third plurality of predicted output vectors;

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

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

9. The method of claim 8, wherein determining the first predicted battery state vector comprises calculating a weighted average of the second plurality of predicted battery state vectors.

10. The method of claim 8, wherein determining the first predicted battery output vector comprises calculating a weighted average of the third plurality of predicted battery output vectors.

11. The method of claim 8, wherein determining the gain matrix comprises:

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

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

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

12. The method of claim 11, wherein determining the first predicted battery output vector covariance matrix comprises:

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

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

13. The method of claim 8, wherein calculating the first estimated battery state vector comprises:

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

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

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

14. The method of claim 8, further comprising determining an estimated battery state vector covariance matrix at the first predetermined time based on the first predicted battery state vector, the second plurality of predicted battery state vectors, the gain matrix, and the first predicted battery output vector covariance matrix.

15. The method of claim 8, further comprising determining an estimated battery state vector square-root covariance matrix at the first predetermined time based on the first predicted battery state vector, the second plurality of predicted battery state vectors, the gain matrix, and a predicted battery output vector square-root covariance matrix.

16. A system for determining an estimated battery state vector indicative of a state of a battery at a 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 first plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise, 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 second 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 first plurality of estimated augmented battery state vectors, the computer further configured to determine a third plurality of predicted battery output vectors that are indicative of an at least one output variable of the battery and an uncertainty of the output variable at the first predetermined time based on the first plurality of estimated augmented battery state vectors and the second plurality of predicted battery state vectors, the computer further configured to determine a first battery output vector based on the first signal, the computer further configured to determine a first estimated battery state vector indicative of the state of the battery at the first predetermined time based on the second plurality of predicted battery state vectors, the third plurality of predicted battery output vectors, and the first battery output vector.

17. The system of claim 16, wherein the computer is further configured to retrieve an estimated battery state vector indicative of the state of the battery at the second predetermined time from a memory, the computer further configured to determine 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, the computer further configured to retrieve an estimated battery state vector covariance matrix indicative of an uncertainty of the state of the battery at the second predetermined time from the memory, the computer further configured to determine a first estimated augmented battery state vector covariance matrix indicative of an uncertainty of the state of the battery, the battery input noise, and the sensor noise, based on the estimated battery state vector covariance matrix, a covariance matrix indicative of an uncertainty of the battery input noise and a covariance matrix indicative of an uncertainty of the sensor noise, the computer further configured to determine the first 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.

18. The system of claim 16, wherein the computer is further configured to determine a first predicted battery state vector indicative of the state of the battery at the first predetermined time based on the second plurality of predicted battery state vectors, the computer further configured to determine a first predicted battery output vector indicative of at least one output variable of the battery at the first predetermined time based on the third plurality of predicted output vectors, the computer further configured to determine a gain matrix based on the first predicted battery state vector, the first predicted battery output vector, the second plurality of predicted battery state vectors, and the third plurality of predicted battery output vectors, the computer further configured to calculate the first estimated battery state vector based on the first predicted battery state vector, the first predicted battery output vector, the gain matrix, and the first battery output vector.

19. An article of manufacture, comprising:

a computer storage medium having a computer program encoded therein for determining an estimated battery state vector indicative of a state of a battery at a first predetermined time, the computer storage medium comprising;

code for determining a first plurality of estimated augmented battery state vectors that are indicative of a state of the battery, a battery input noise, a sensor noise, 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;

code for determining a second 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 first plurality of estimated augmented battery state vectors;

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

code for determining a first battery output vector having at least one measured value of a battery output variable; and

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

20. The article of manufacture of claim 19, wherein the code for determining the first estimated battery state vector comprises:

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

code for 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 third plurality of predicted output vectors;

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

code for calculating the first estimated battery state vector based on the first predicted battery state vector, the first predicted battery output vector, the gain matrix, and the first battery output vector.