Battery EMF Curve Determination Using Differentiable Curve Fitting
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Solution Overview
Problem
Existing battery management systems face inefficiencies in determining electromotive force (EMF) curves, leading to inaccurate state of charge (SoC) and state of health (SoH) estimations, particularly due to the complexity of battery dynamics and the need for detailed mathematical models that are often unfeasible with current methods like polynomials and genetic algorithms.
Innovation Solution
A computer-implemented method using a curve fitting model with differentiable terms, including constant, linear, exponential, and periodic components, specifically tailored for battery EMF curves, which captures the dynamics of batteries through a fitting function that can include damped and non-damped trigonometric terms and Fourier series, allowing for accurate EMF curve determination and derivative calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If equivalent circuit models with look-up tables are used for EMF curves, then hardware requirements are reduced, but accuracy and efficiency of battery state estimation deteriorates
Solution Approach 1:
The patent transforms the EMF curve from a discrete look-up table into a continuous mathematical function representation. By changing the parameter storage format from tabular data to analytical equations, the system achieves higher accuracy in battery state estimation while maintaining computational efficiency through direct mathematical evaluation rather than iterative table lookup.
Solution Approach 2:
The patent replaces the mechanical/table-based data storage and retrieval system with a mathematical function-based system. Instead of storing EMF values in discrete tables and interpolating between them, the invention uses continuous mathematical functions to directly compute EMF values, eliminating the need for complex table management hardware while improving precision.
2Productivity
If genetic algorithms or polynomials are used to fit EMF curves, then mathematical modeling is simplified, but computational efficiency and feasibility in real-time applications deteriorates
Solution Approach 1:
The patent performs the curve fitting process in advance during system initialization or offline processing, pre-determining the optimal mathematical function parameters. This preliminary action eliminates the need for complex real-time fitting computations, significantly improving computational efficiency while the fitting complexity is confined to the offline phase.
Solution Approach 2:
The patent creates a simplified mathematical copy of the complex battery EMF characteristics through fitted functions. By capturing the essential behavior patterns in closed-form mathematical expressions, the system reproduces accurate EMF curves without requiring the complex iterative optimization processes needed during the fitting phase, thus achieving real-time applicability.
3Measurement precision
If detailed mathematical models are used to capture battery dynamics, then accuracy of EMF curve determination is improved, but feasibility of implementation deteriorates
Solution Approach 1:
The patent extracts the essential characteristics of battery EMF behavior from complex measurement data and represents them through simplified mathematical functions. By separating the core functional relationships from the noise and complexity in raw data, the invention achieves accurate EMF curve determination while maintaining implementation feasibility through clean, direct mathematical models.
Solution Approach 2:
The patent captures the dynamic behavior of battery EMF across different states of charge through time-varying mathematical functions. By using functions that can adapt to changing battery conditions (such as temperature and charge rate effects), the system maintains high accuracy in EMF determination while keeping the models implementable through standard mathematical operations rather than complex adaptive systems.
Data Source
AI summary
Provided herein is a method and system for determining an electromotive force curve of a battery for use in battery control applications. Measured data is received identifying an electromotive force for a plurality of state of charge values of the battery. A fitting processing is performed by using a curve fitting model for determining an electromotive force curve based on the measured data, the electromotive force curve indicating a continuous relationship between the electromotive force and a state of charge of the battery. The curve fitting model includes a fitting function consisting of only differentiable terms.