Technique for estimation of internal battery temperature

1 . A method for estimating an internal temperature of a battery, the method comprising:

injecting a plurality of periodic signals into the battery, wherein each of the periodic signals have a different frequency of a plurality of frequencies;

obtaining multiple terminal impedance measurements for the battery in response to the plurality of periodic signals, wherein each of the terminal impedance measurements is obtained at a respective different one of the plurality of frequencies;

determining model parameters for a multivariable polynomial regression model for estimating the internal temperature of the battery;

inputting the multiple terminal impedance measurement into the multivariable polynomial regression model as a plurality of inputs; and

applying the multivariable polynomial regression model to the multiple terminal impedance measurements to estimate the internal temperature of the battery as an output of the multivariable polynomial regression model.

2 . The method of claim 1 , wherein the plurality of frequencies are selected to compensate for effects of at least one of battery state of charge (SOC) or battery state of health (SOH) dependencies of the model.

3 . The method of claim 1 , wherein the determining the model parameters comprises:

obtaining training data from a set of training batteries; and

applying a linear least squares fit to the training data.

4 . The method of claim 3 , wherein the training data comprises alternating current (AC) data and temperature data for the set of training batteries.

5 . The method of claim 1 further comprising calibrating the model parameters using at least one initial set of impedance measurements for the battery.

6 . The method of claim 5 , wherein the calibrating the model parameters further includes:

identifying a nearest neighbor dataset in a library of training datasets using the at least one initial set of impedance measurements; and

perturbing the model parameters to fit model parameters of the identified nearest neighbor dataset;

wherein the at least one set of initial impedance measurements is taken at a beginning of a life of the battery.

7 . The method of claim 1 further comprising augmenting an equation comprising the multivariable polynomial regression model using at least one of an additional input and a monomial term.

8 . The method of claim 7 , wherein the additional input includes at least one of a battery terminal voltage or a charge capacity of the battery.

9 . The method of claim 7 wherein the additional term includes at least one of an input to compensate for battery state of charge (SOC), a function of another measurement of the battery, or a memory term.

10 . A method for estimating an internal temperature of a battery from terminal impedance measurements of the battery, the method comprising:

obtaining multiple terminal impedance measurements for the battery at a plurality of frequencies based on a plurality of periodic signals injected into the battery, wherein each of the periodic signals have a different frequency of the plurality of frequencies;

deriving model parameters for a multivariable polynomial regression model, the deriving comprising:

obtaining training data from a set of training batteries similar to the battery; and

applying a linear least squares fit to the training data; and

combining the multiple terminal impedance measurements using the multivariable polynomial regression model to produce an estimate of the internal temperature of the battery as an output of the multivariable polynomial regression model;

wherein the plurality of frequencies span a range of frequencies selected to reduce dependence of the estimate of the internal temperature of the battery on a state of health (SOH) of the battery and a state of charge (SOC) of the battery.

11 . The method of claim 10 further comprising augmenting an equation comprising the multivariable polynomial regression model to include an input to compensate for battery state of charge (SOC).

12 . The method of claim 10 further comprising augmenting an equation comprising the multivariable polynomial regression model by adding a function of another measurement of the battery to the equation.

13 . The method of claim 10 further comprising augmenting an equation comprising the multivariable polynomial regression model to include a memory term.

14 . The method of claim 10 further comprising calibrating the model parameters using at least one initial set of impedance measurements for the battery, wherein the calibrating the model parameters further includes:

identifying a nearest neighbor dataset in a library of training datasets comprising the training data using the at least one initial set of impedance measurements; and

perturbing the model parameters to fit model parameters of the identified nearest neighbor dataset.

15 . The method of claim 10 further comprising augmenting an equation comprising the multivariable polynomial regression model using at least one of an additional input and a monomial term.

16 . The method of claim 10 further comprising augmenting an equation comprising the multivariable polynomial regression model by adding a higher-order cross-term to the equation.

17 . A system for estimating an internal temperature of a battery from a plurality of terminal impedance measurements obtained for the battery, wherein the plurality of terminal impedance measurements are taken at a plurality of frequencies, the system comprising:

at least one hardware processor; and

at least one memory storing instructions that cause the at least one hardware processor to perform operations comprising:

providing a multivariable polynomial regression model comprising a number of model parameters, the multivariable polynomial regression model configured to combine the plurality of terminal impedance measurements to generate an estimate the internal temperature of the battery;

wherein the plurality of frequencies span a range of frequencies selected to reduce dependence of the estimate of the internal temperature of the battery on a state of health (SOH) of the battery and a state of charge (SOC) of the battery;

obtaining the plurality of terminal impedance measurements for the battery based on a plurality of periodic signals injected into the battery, wherein each of the periodic signals have a different frequency of the plurality of frequencies;

inputting the plurality of terminal impedance measurement into the multivariable polynomial regression model as a plurality of inputs; and

applying the multivariable polynomial regression model to the plurality of terminal impedance measurements to estimate the internal temperature of the battery as an output of the multivariable polynomial regression model.

18 . The system of claim 17 , wherein the battery comprises a rechargeable battery.

19 . The system of claim 17 , wherein model parameters of the multivariable polynomial regression model are determined by obtaining training data from a set of training batteries and applying a linear least squares fit to the training data.

20 . The system of claim 17 , wherein the model parameters are calibrated using at least one initial set of impedance measurements for the battery, wherein the calibrating the model parameters further includes:

identifying a nearest neighbor dataset in a library of training datasets using the at least one initial set of impedance measurements; and

perturbing the model parameters to fit model parameters of the identified nearest neighbor dataset.