Battery state estimation systems and methods using a nonlinear resistance element
Systems and methods are disclosed for estimating a state of a battery system such as a current-limited state of power and/or a voltage-limited state of power using a battery system model incorporating a nonlinear resistance element. Parameters of elements included in a battery cell model associated with a nonlinear resistance of a battery cell may be directly parameterized and used in connection with state estimation methods. By accounting for the nonlinear effect, embodiments of the disclosed systems and methods may increase available battery power utilized in connection with battery system control and/or management decisions over a larger window of operating conditions.
1. A method of estimating a state of a battery system, the method comprising:
measuring a terminal voltage of the battery system;
measuring a current and a temperature through the battery system;
determining parameters of a battery system model based, at least in part, on the measured terminal voltage of the battery system and the measured current through the battery system, the battery system model comprising at least one nonlinear element configured to model a nonlinear voltage to current response of the battery system, wherein determining the parameters of the battery system model comprises determining parameters associated with the at least one nonlinear element based, at least in part, on a piecewise polynomial approximation of the nonlinear voltage to current response of the battery system, wherein the piecewise polynomial approximation of the nonlinear voltage to current response partitions the nonlinear voltage to current response into regions based on the current and the temperature, with voltage being a polynomial function of the current and the temperature in each respective one of the regions;
determining a predicted battery system voltage based, at least in part, on the battery system model;
estimating the state of the battery system based on the predicted battery system voltage; and
implementing a control action in a vehicle associated with the battery system based on the estimated battery system state, wherein the control action comprises at least one of adjusting a maximum allowed acceleration of the vehicle, adjusting initiation of an electric drivetrain system of the vehicle, and adjusting a regenerative braking acceptance setting of the vehicle.
2. The method of claim 1 , wherein the state of the battery system comprises a state of power of the battery system.
3. The method of claim 2 , wherein the state of the battery system comprises a current-limited state of power of the battery system.
4. The method of claim 2 , wherein the state of the battery system comprises a voltage-limited state of power of the battery system.
5. The method of claim 1 , wherein the state of the battery system comprises a state of charge of the battery system.
6. The method of claim 1 , wherein the battery system model comprises an equivalent circuit model and the nonlinear element comprises a nonlinear resistor.
7. The method of claim 6 , wherein the nonlinear element further comprises a linear capacitor disposed in parallel with the nonlinear resistor.
8. The method of claim 1 , wherein the battery system model further comprises an element modeling an open circuit voltage of the battery system and a linear element disposed in series with the nonlinear element.
9. The method of claim 8 , wherein the linear element comprises a plurality of serially coupled parallel resistor capacitor pairs.
10. The method of claim 1 , wherein the battery system model comprises a circuit model including elements configured to model ohmic resistance, charge transfer, and mass transfer processes of the battery system.
11. The method of claim 1 , wherein determining the parameters of the battery system model further comprises determining parameters associated with the at least one nonlinear element based further, at least in part, on a Butler-Volmer model describing the kinetics of charge transfer in the battery system.
12. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform a method of estimating a state of a battery system comprising:
measuring a terminal voltage of the battery system;
measuring a current and a temperature through the battery system;
determining parameters of a battery system model based, at least in part, on the measured terminal voltage of the battery system and the measured current through the battery system, the battery system model comprising at least one nonlinear element configured to model a nonlinear voltage to current response of the battery system, wherein determining the parameters of the battery system model comprises determining parameters associated with the at least one nonlinear element based, at least in part, on a piecewise polynomial approximation of the nonlinear voltage to current response of the battery system, the piecewise polynomial approximation of the nonlinear voltage to current response partitions the nonlinear voltage to current response into regions based on the current and the temperature, with voltage being a polynomial function of the current and the temperature in each respective one of the regions;
determining a predicted battery system voltage based, at least in part, on the battery system model;
estimating the state of the battery system based on the predicted battery system voltage; and
implementing a control action in a vehicle associated with the battery system based on the estimated battery system state, wherein the control action comprises at least one of adjusting a maximum allowed acceleration of the vehicle, adjusting initiation of an electric drivetrain system of the vehicle, and adjusting a regenerative braking acceptance setting of the vehicle.
13. The non-transitory computer-readable medium of claim 12 , wherein determining the parameters of the battery system model further comprises determining parameters associated with the at least one nonlinear element based further, at least in part, on a Butler-Volmer model describing the kinetics of charge transfer in the battery system.