Techniques for controlling charging and/or discharging of batteries using a tanks-in-series model

1. A battery management system, comprising:

a connector for electrically coupling a battery to the battery management system;

at least one sensor configured to detect a battery state;

a programmable chip configured to control at least one of charging and discharging of the battery; and

a controller device configured to:

receive at least one battery state from the at least one sensor;

provide the at least one battery state as input to a tanks-in-series model that represents the battery; and

provide at least one output of the tanks-in-series model to the programmable chip for controlling at least one of charging and discharging of the battery.

2. The battery management system of claim 1 , wherein the tanks-in-series model includes:

a tank model that represents an anode of the battery;

a tank model that represents a separator of the battery; and

a tank model that represents a cathode of the battery.

3. The battery management system of claim 2 , wherein each tank model includes a volume-averaged representation of a P2D model of a corresponding domain.

4. The battery management system of claim 3 , wherein the tanks-in-series model is derived by:

integrating a pseudo 2-dimensional (P2D) model representation over a volume of each domain; and

approximating interfacial fluxes between the domains, wherein a corresponding gradient is expressed as an average value minus an interfacial value of a dependent variable over a length scale.

5. The battery management system of claim 4 , wherein the derivation of the tanks-in-series model further includes determining the interfacial values in a manner that preserves mass and charge conservation between each tank model.

6. The battery management system of claim 4 , wherein integrating the P2D model representation over the volume of each domain results in a set of volume-averaged quantities with temporal evolution of each averaged variable expressed as an overall balance comprising approximated internal source terms and interfacial fluxes.

7. The battery management system of claim 1 , wherein the at least one battery state includes at least one of a terminal voltage of the battery and a surface temperature of the battery.

8. The battery management system of claim 1 , wherein the output includes at least one of a state of charge and a state of health of the battery.

9. A method of managing at least one of charging and discharging of a battery, the method comprising:

receiving, by a controller device, at least one battery state of the battery from at least one sensor;

providing, by the controller device, the at least one battery state as input to a tanks-in-series model that represents the battery; and

controlling, by the controller device, at least one of charging or discharging of the battery by using at least one output of the tanks-in-series model to determine at least one of a current or a voltage for use in the at least one of charging or discharging of the battery;

wherein the tanks-in-series model includes:

a tank model that represents an anode of the battery;

a tank model that represents a separator of the battery; and

a tank model that represents a cathode of the battery.

10. The method of claim 9 , wherein

the tank model that represents the anode of the battery includes a volume-averaged representation of a concentration of lithium ions and potential in an electrolyte of the anode;

the tank model that represents the separator of the battery includes a volume-averaged representation of a concentration of lithium ions and potential in an electrolyte of the separator; and

the tank model that represents the cathode of the battery includes a volume-averaged representation of a concentration of lithium ions and potential in an electrolyte of the cathode.

11. The method of claim 10 , wherein each tank model includes a volume-averaged representation of a pseudo 2-dimensional (p2D) model of a corresponding domain.

12. The method of claim 11 , wherein the tanks-in-series model is derived by:

integrating a p2D model representation over a volume of each domain; and

approximating interfacial fluxes between the domains, wherein a corresponding gradient is expressed as an average value minus an interfacial value of a dependent variable over a length scale.

13. The method of claim 12 , wherein the derivation of the tanks-in-series model further includes determining the interfacial values in a manner that preserves mass and charge conservation between each tank model.

14. The method of claim 12 , wherein integrating the p2D model representation over the volume of each domain results in a set of volume-averaged quantities with temporal evolution of each averaged variable expressed as an overall balance comprising approximated internal source terms and interfacial fluxes.

15. The method of claim 9 , wherein the at least one battery state includes at least one of a terminal voltage of the battery and a surface temperature of the battery.

16. The method of claim 9 , wherein the output includes at least one of a state of charge and a state of health of the battery.

17. A computer-implemented method of deriving a model for controlling at least one of charging and discharging a battery, the method comprising:

integrating, by a computing device, pseudo 2-dimensional (p2D) model representations over volumes of a cathode domain of the battery, an anode domain of the battery, and a separator domain of the battery;

approximating, by the computing device, interfacial fluxes between the domains, wherein a corresponding gradient is expressed as an average value minus an interfacial value of a dependent variable over a length scale to create a tanks-in-series representation of the battery; and

providing, by the computing device, the tanks-in-series representation of the battery as the model for controlling at least one of charging and discharging of the battery.

18. The computer-implemented method of claim 17 , wherein creating the tanks-in-series representation of the battery includes determining, by the computing device, the interfacial values in a manner that preserves mass and charge conservation between each domain of the battery.

19. The computer-implemented method of claim 17 , wherein integrating the p2D model representations over the volumes of the domains results in a set of volume-averaged quantities with temporal evolution of each averaged variable expressed as an overall balance comprising approximated internal source terms and interfacial fluxes.

20. The computer-implemented method of claim 17 , wherein the model accepts at least one of a terminal voltage of the battery and a surface temperature of the battery as input, and wherein the model outputs at least one of a state of charge of the battery and a health of the battery.