Battery state-of-charge observer

• US 8,922,217 B2
• Filed: 05/08/2012
• Issued: 12/30/2014
• Est. Priority Date: 05/08/2012
• Status: Expired due to Fees

• Current Assignee: GM Global Technology Operations LLC (General Motors Company)
• Original Assignee: GM Global Technology Operations LLC (General Motors Company)
• Inventors: Mao, Xiaofeng, Tang, Xidong
• Primary Examiner(s): WILLIAMS, ARUN C
• Application Number:
  US13/466,394
• Publication Number:
  US 20130300190A1
• Time in Patent Office: 966 Days
• Field of Search: 324/431
• US Class Current: 324/431
• CPC Class Codes: G01R 31/3648 comprising digital calculation means, e.g. for performing an algorithm
• CPC Class Codes: G01R 31/367 Software therefor, e.g. for battery testing using modelling or look-up tables
• CPC Class Codes: G01R 31/3842 combining voltage and current measurements
• CPC Class Codes: G01R 31/389 Measuring internal impedance, internal conductance or related variables

Abstract

A robust battery state-of-charge observer determines a state-of-charge as function of an open circuit voltage by taking into account battery parameter uncertainties, which are due to battery age, variation, and operating conditions, (e.g. temperature and SOC level). Each of the time-varying battery parameter values are bounded. By utilizing the parameter variation bounds in the design process and constantly minimizing the estimation error covariance matrix, the robust observer achieves enhanced robustness to the variations of battery age, variation, and operating conditions such as temperature and SOC level.

Claims

1. A method of determining a state-of-charge for a battery while connected to a plurality of loads, the method comprising the steps of:

measuring a terminal voltage of the battery at a plurality of time steps;

measuring a terminal current draw of the battery coinciding with the measured terminal voltage at the plurality of time steps;

measuring a temperature of the battery coinciding with the measured terminal voltage at the plurality of time steps;

generating a state vector of a battery system model as a function of battery parameters, the measured voltage, the measured current, and the measured temperature for each time step, the battery parameters including internal battery resistance and capacitance;

generating an estimated state vector as a function of nominal battery system matrices and battery parameter uncertainties for each time step;

generating a stator vector for an augmented system as a function of the state vector of the battery system model and the estimated state vector for each time step;

generating a covariance for the state vector of the augmented system for each time step;

determining an upper bound of the covariance by recursively minimizing the upper bound of the covariance for each time step;

determining an open circuit voltage based on an updated state vector utilizing the minimized upper bound;

determining the state of charge of the battery as a function of the open circuit voltage; and

regulating the battery in response to the state of charge.

2. The method of claim 1 wherein the battery system model utilizes a two-RC pair equivalent circuit model, wherein the circuit model is represented by the formula:

V=V_oc+IR+V_dl+V_df

where V_oc is the open circuit voltage, V_dl is a double layer voltage, V_df is a diffuse voltage, I is a terminal battery current, and R is an ohmic resistance.

3. The method of claim 2 wherein the battery system model is transformed into discrete counterparts.

4. The method of claim 3 wherein the transformed battery system model is represented by the following matrices:

5. The method of claim 4 wherein the parameters of the battery system model are bounded and are represented by the following formula:

6. The method of claim 5 wherein the variations are norm bounded, and wherein the variations are represented as norm bound matrices as follows:

7. The method of claim 6 wherein generating the state vector of the battery system model is represented by the following formula:

x(k)=└

V_dl(k)V_df(k)V_oc(k)┘

.

8. The method of claim 7 wherein generating the estimated state vector for the battery system model is represented by the following formula:

{circumflex over (x)}_(k+1|k)=φ

_k{circumflex over (x)}<sub>(k|k−

1)</sub>+B_kI_k+K_k(V_k−

C_k{circumflex over (x)}<sub>(k|k−

1)</sub>−

D_kI_k)

where {circumflex over (x)}<sub>(k|k−

1)</sub> is an estimated state vector at step k based on all the information up to step k−

1, I_k is a measured current at time step k, V_k is a measured voltage at time step k, and observer gains φ

_k and K_k are unknown matrices determined online at each time step.

9. The method of claim 8 wherein the upper bound of the covariance is calculated utilizing first-order partial derivatives of the upper bound with respect to φ

_k and K_k at each time step.

10. The method of claim 9 wherein observer gains φ

_k and K_k are represented by the following expressions;

K_k=(A P<sub>c,k|k−

1</sub>C_k^T+B_kW_c,kD_k^T+Δ

_I,k)(C_kP<sub>c,k|k−

1</sub>C_k^T+D_kW_c,kD_k^T+Δ

_2,k)<sup>−

1</sup>

Φ

_k=A_k+(A_k−

K_kC_k)P<sub>k|k−

1</sub>G_x,k^T(α

_x,k<sup>−

1</sup>I−

G_x,kP<sub>k|k−

1</sub>G_x,k^T)<sup>−

1</sup>G_x,k

where P<sub>c,k|k−

1</sub>, and W_c,k are formulas for determining corrections to the covariance, and T is the measured temperature for a respective time step.

11. The method of claim 10 wherein the state vector of the augmented system is represented by the following expression:

12. The method of claim 11 wherein P_(k+1|k) is the upper bound of the augmented system, and wherein P_(k+1|k) becomes an error covariance matrix of the estimated state vector and is represented by the following formula:

cov{{tilde over (x)}_k+1}≦

P_(k+1|k)

where e_k+1=x_k+1−

{circumflex over (x)}_(k+1|k).

13. The method of claim 1 further comprising the step of outputting the state of charge of the battery to an output device for displaying the state-of-charge to a user of a vehicle.

14. The method of claim 1 wherein the regulatory step comprises outputting the state of charge of the battery to an electronic control unit for regulating the battery terminal voltage.

15. The method of claim 1 wherein the regulating step comprises outputting the state of charge of the battery to an electronic control unit for improving fuel economy of a vehicle.

16. A diagnostic and control system for a vehicle battery comprising:

at least one sensor for monitoring a parameter characteristic of the vehicle battery while supplying a plurality of loads a plurality of time steps; and

an electronic control module coupled to the at least one sensor for receiving parameter characteristic, the electronic control module including a processing unit for determining an open circuit voltage based on a state vector of a battery system model, the state vector being recursively updated as a function of an estimated state vector of the battery system model for each time step, the estimated state vector being generated as a function of the nominal system matrices of the battery system model and battery parameter uncertainties for each time step, the estimated state vector being updated by minimizing an upper bound of a covariance of a state vector for an augmented system of the battery system model at each time step, wherein the augmented system is generated as a function of the state vector of the battery system model and the estimated state vector of the battery system model at each time step;

wherein the control module regulates the vehicle battery in response to a state of charge of the battery as a function of the open circuit voltage.

17. The system of claim 16 wherein the battery system model is transformed into discrete counterparts and is represented by the following expression:

18. The system of claim 17 wherein parameters of the battery system model are bounded and are represented by the following expression:

19. The system of claim 18 wherein the estimated state vector of the battery system model is represented by the following formula:

{circumflex over (x)}_(k+1|k)=φ

_k{circumflex over (x)}<sub>(k|k−

1)</sub>+B_kI_k+K_k(V_k−

C_k{circumflex over (x)}<sub>(k|k−

1)</sub>−

D_kI_k)

where {circumflex over (x)}<sub>(k|k−

1)</sub> is an estimated state vector at step k based on all the information up to step k−

1, I_k is a measured current at time step k, V_k is a measured voltage at time step k, and φ

_k and K_k unknown matrices determined online at time step k.

20. The system of claim 16 further comprising a display device, wherein the state of charge of the battery is displayed to a user.