Battery Model Using Taylor Series for Dynamic Parameter Estimation
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Solution Overview
Problem
Existing battery models struggle to accurately predict performance for longer periods and higher current amplitudes, leading to reduced precision and increased resource consumption, especially during sporty driving styles.
Innovation Solution
A computer-implemented method using a mathematical battery model based on an equivalent circuit with RC elements, where model parameters are approximated using a Taylor series expansion around an operating point, allowing for improved estimation of operating parameters such as state of charge and electrical resistance, enabling precise predictions for longer periods and higher currents.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If model parameters are assumed to be constant in the neighborhood of an operating point, then processing is simpler and faster, but prediction precision deteriorates for longer periods and higher current amplitudes
Solution Approach 1:
The patent applies parameter changes by transitioning from constant parameter assumptions to time-varying parameter models. Specifically, it uses Taylor series expansions to represent parameters (such as resistance and capacitance values) as functions of time and operating conditions, allowing the model to adapt to changing battery states while maintaining analytical solvability through structured mathematical formulations.
Solution Approach 2:
The patent implements dynamics by making the model parameters dynamic rather than static. The equivalent circuit model parameters (resistances, capacitances, time constants) are expressed as time-dependent functions using Taylor series expansions, enabling the model to capture transient behaviors and dynamic responses of the battery under varying load conditions and extended prediction horizons.
2Measurement precision
If a more complex model is used to improve prediction accuracy for longer periods and higher currents, then precision improves, but device complexity and resource consumption increase
Solution Approach 1:
The patent manages model complexity through parameter changes by using Taylor series expansions with truncated terms. This approach allows the model to capture dynamic behavior without requiring full numerical simulation complexity. The structured mathematical form maintains analytical solvability while incorporating time-varying effects, balancing accuracy and computational tractability.
Solution Approach 2:
The patent extracts only the essential dynamic characteristics needed for accurate prediction by using Taylor series expansions that capture the dominant time-varying behavior. Rather than modeling all possible complexities, it extracts and represents only the critical dynamic effects (through first or second-order terms) that significantly impact prediction accuracy for extended periods and high current conditions.
3Ease of manufacture
If constant parameters are used in the battery model, then the model remains simple and analytically solvable, but it cannot accurately predict performance for longer prediction periods and higher current amplitudes
Solution Approach 1:
The patent resolves this contradiction by changing parameters from constant to time-varying functions while maintaining analytical solvability. The Taylor series expansion provides a structured way to represent parameter variation that preserves the mathematical tractability of the equivalent circuit model, allowing closed-form or semi-closed-form solutions to be derived even with time-dependent parameters.
Solution Approach 2:
The patent introduces dynamics into the previously static model by expressing parameters as functions of time and operating conditions. This dynamic representation enables the model to accurately predict battery performance under varying loads and extended time periods while retaining the simplicity and analytical solvability characteristics of the equivalent circuit approach through structured mathematical formulations.
Data Source
AI summary
A method for determining at least one estimated operating parameter of a battery including receiving at least one measured operating parameter of the battery and determining the at least one estimated operating parameter from the at least one measured operating parameter using a mathematical battery model based on an equivalent circuit of the battery having at least one RC element. The battery model defines a relationship between the battery voltage applied to the battery and a battery current flowing through the battery in dependence of model parameters including at least one time constant and/or at least one electrical resistance with respect to the equivalent circuit. The battery model takes into account an n-th power of a Taylor series expansion of the at least one time constant and/or the at least one electrical resistance around an operating point of the battery.