Determining the state of-charge of batteries via selective sampling of extrapolated open circuit voltage
View Patent ↗A method for estimating the state-of-charge of a battery. The method includes collecting a plurality of voltage measurements during operation of the system containing the battery and determining a time-constant of relaxation and an open-circuit voltage corresponding to the battery based, at least in part, on the voltage measurements. The method further includes estimating the state-of-charge of the battery based, at least in part, on the open-circuit voltage.
1. A method of determining a state-of-charge of a battery within a system powered at least in part by the battery comprising:
collecting a plurality of voltage measurements from the battery during operation of the system;
deriving a time-constant of relaxation and an open-circuit voltage corresponding to the battery from the voltage measurements and a mathematical model of the battery that relates the voltage measurements to the open-circuit voltage and the time-constant of relaxation; and,
estimating the state-of-charge of the battery based, at least in part, on the open-circuit voltage;
wherein the mathematical model comprises a closed mathematical expression that includes the open-circuit voltage and the time-constant of relaxation; and,
wherein the closed mathematical expression is of the form: V(t)=OCV−αe t/τ , wherein V(t) is one of the voltage measurements at a given point in time, OCV is the open-circuit voltage, α is an overpotential, and τ is the time-constant of relaxation.
2. The method of claim 1 , wherein determining the time-constant of relaxation and the open-circuit voltage comprises regressing the time-constant of relaxation and the open-circuit voltage using the closed expression as a regression function.
3. The method of claim 2 , further comprising determining an overpotential value by regressing the overpotential together with the time-constant of relaxation and open-circuit voltage.
4. The method of claim 2 , further comprising determining a regression interval based at least in part on the time-constant of relaxation.
5. The method of claim 4 , wherein the regression interval is used, at least in part, to estimate the uncertainty of the open-circuit voltage.
6. The method of claim 4 , wherein collecting a plurality of voltage measurements comprises collecting the plurality of voltage measurements over a first time interval.
7. The method of claim 6 , wherein the first time interval encompasses and has a duration greater than the regression interval.
8. The method of claim 1 , wherein a plurality of amperage measurements are also collected during operation of the system.
9. The method of claim 1 , wherein a mathematical relationship between the open-circuit voltage and the state-of-charge is used to estimate the uncertainty of the prediction of the state-of-charge from the open-circuit voltage.
10. The method of claim 9 , wherein the mathematical relationship comprises a set of measurements relating the open-circuit voltage and the state-of-charge.
11. A method of operation within a system powered at least in part by a battery, the method comprising:
collecting a plurality of voltage measurements of the battery over a first time interval and during operation of the system, wherein the plurality of voltage measurements are to be used to estimate a state-of-charge of the battery;
adjusting a time-constant value based on the plurality of voltage measurements collected over the first time interval, the time-constant value indicating a rate at which the battery voltage transitions from a voltage under load to an open-circuit voltage; and
adjusting the duration of the first time interval based at least in part on the time-constant value;
wherein adjusting the time-constant value comprises regressing the time-constant value using the function V(t)=OCV−αe t/τ , wherein V(t) is one of the voltage measurements at a given point in time within a regression interval, OCV is the open-circuit voltage, α is an overpotential, and τ is the time-constant value.
12. The method of claim 11 , wherein the first time interval encompasses and has a duration equal or greater than the regression interval.
13. A system powered at least in part by a battery, the system comprising:
voltage measurement circuitry coupled to the battery to generate a plurality of measurements of the battery voltage during operation of the system;
battery management circuitry coupled to the voltage measurement circuitry, the battery management circuitry configured to determine a time-constant of relaxation and an open-circuit voltage for the battery from (i) the plurality of measurements of the battery voltage and (ii) a mathematical model of the battery that relates the battery voltage to the open-circuit voltage and the time-constant of relaxation; and
estimating a state-of-charge of the battery based, at least in part, on the open-circuit voltage;
wherein the mathematical model comprises a closed mathematical expression that includes the open-circuit voltage and the time-constant of relaxation; and,
wherein the closed mathematical expression is of the form: V(t)=OCV−αe t/τ , wherein V(t) is one of the voltage measurements at a given point in time, OCV is the open-circuit voltage, α is an overpotential, and τ is the time-constant of relaxation.
14. The system of claim 13 , wherein the battery management circuitry comprises circuitry to determine the time-constant of relaxation and the open-circuit voltage comprising regressing the time-constant of relaxation and the open-circuit voltage using the closed expression as a regression function.
15. The system of claim 14 , wherein the battery management circuitry further comprises circuitry to determine a regression interval based at least in part on the time-constant of relaxation.
16. The system of claim 15 , wherein the regression interval is used, at least in part, to estimate an uncertainty of the open-circuit voltage.
17. The system of claim 13 , wherein the open-circuit voltage is used to estimate an uncertainty of the estimation of the state-of-charge.
18. The system of claim 17 , wherein the system contains a user interface that presents visual information about the state-of-charge and the uncertainty of the estimation of the state-of-charge, to an operator of the system.
19. The system of claim 13 , wherein the battery is used in an automotive vehicle powered, at least in part, by the battery.
20. The system of claim 13 , wherein the battery is comprised of a plurality of battery cells.