Method for estimating state of charge for lithium-ion batteries

1. A method for estimating a state of charge (SoC) a lithium-ion (Li+) battery at a time instant, comprising steps of:

measuring a charge current, a discharge current, an open circuit voltage (OCV), and an output voltage during an off-line operation of the Li+ battery;

constructing a battery model of the Li+ battery, wherein the battery model is constructed based on a single particle operation of the Li+ battery, where the battery model describes a relationship between the SoC, the charge current, the discharge current;

determining, using a nonlinear optimization, a function expressing a relationship between the SoC and the OCV of the Li+ battery, wherein the relationship is based on off-line measurements of the measuring the charge current, the discharge current, and the OCV; and

estimating the SoC and parameters of the battery model concurrently, wherein the SoC and the parameters are estimated based on the battery model, the function, and on-line measurements of the charge current, the discharge current, and the OCV, wherein the steps are performed in a processor connected to the Li+ battery.

2. The method of claim 1 , wherein an average concentration of Li+ ions in electrodes of the Li+ battery represents a state of the SoC; and the constructing further comprises:

determining dynamics of the average concentration of the Li+ ions as a state equation, based on the battery model.

3. The method of claim 2 , wherein the dynamics of the average concentration is

{dot over ( x )}( t )=− au ( t )

where {dot over (x)}(t) is the average concentration or the SoC, a is a charge and discharge coefficient, U (t) is the charge and discharge current.

4. The method of claim 1 , wherein the determining further comprising

defining the output voltage as a first function of the SoC, and a second function of the charge and discharge current;

parameterizing the first function using a first set of parameters;

selecting a cost function as a measure of an error between the measured OCV and a predicted OCV, which is computed by the first function using the measured SoC; and

minimizing the cost function to determine values of the first set of parameters.

5. The method of claim 4 , wherein the minimizing solves a nonlinear optimization problem.

6. The method of claim 2 , wherein the estimating further comprises:

augmenting the state equation by including dynamics of parameters to produce augmented dynamics, wherein the dynamics of the parameters is represented by {dot over (ξ)}(t)=0, wherein {dot over (ξ)} represent unknown parameters of the battery model, and t represents time;

predicting a priori, the SoC, and the parameters;

determining a covariance of an error of off-line measurements of the measuring based on the predicted SoC and the parameters;

estimating, a posteriori, the SoC, and the parameters;

calculating a covariance of an error of estimation of the estimating, based on the estimated SoC, and the parameters; and

repeating the predicting, the determining, the estimating, and the calculating.

7. The method of claim 1 , wherein the estimating further comprises:

transforming the battery model in a standard form; and

determining a nonlinear adaptive estimator to produce the estimated SoC and parameters based on a transformed system.

8. The method of claim 7 , wherein the nonlinear adaptive estimator includes an auxiliary filter based on the transformed battery model, the measured discharge current, and the charge current and its time derivatives, and the output voltage, to produce auxiliary signals, a parameter estimator, based on the measured and estimated terminal output voltages, and the auxiliary signals, to produce the estimated parameters of the battery model, and a state estimator, based on the measured discharge and charge current, the measured terminal output voltages, the transformed battery model, the auxiliary signals, and the estimated parameters, to produce the estimated SoC.

9. The method of claim 7 , wherein the transforming is a state transformation.

10. The method of claim 8 , wherein the state estimator and the parameter estimator are described by differential equations, respectively.

11. The method of claim 1 , wherein the estimating is performed on-line.

12. The method of claim 1 , wherein the estimating is performed in nonlinear and adaptive forms.

13. The method of claim 1 , wherein the estimating is performed using an extended Kalman filter.

14. A method for estimating a state of charge (SoC) a lithium-ion (Li+) battery at a time instant, comprising steps of:

measuring a charge current, a discharge current, an open circuit voltage (OCV), and an output voltage during an off-line operation of the Li+ battery;

constructing a battery model of the Li+ battery, wherein the battery model is constructed based on a single particle operation of the Li+ battery, where the battery model describes a relationship between, the charge current, the discharge current, and the OCV of the Li+ battery;

partitioning parameters of the battery model into k sets, where each set of the parameters is identified by measuring different sets of data off-line; and

determining each set of the parameters and the SoC sequentially by performing the measuring sequentially, wherein the steps are performed in a processor.

15. The method of claim 14 , wherein the determining comprises

determining k−1 sets of the parameters by their corresponding off-line measurements; and

determining the k th set of the parameters and the SoC jointly by the k th on-line measurement.