Battery Cell Impedance Model with Dynamic Oustaloup Exponent
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Solution Overview
Problem
Existing battery cell impedance models fail to accurately account for the non-linear dependence of the low-frequency component on operating points, particularly cell current and temperature, leading to inaccuracies in modeling diffusion effects.
Innovation Solution
A method using the Oustaloup recursive approximation to model the cell impedance, adjusting the exponent η based on cell current, temperature, and charging state, by minimizing the difference between measured and modeled clamping voltage through iterative configuration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a fixed exponent η is used in the Oustaloup approximation for low-frequency impedance modeling, then the model structure remains simple, but the accuracy deteriorates because it cannot capture the non-linear dependence on operating points
Solution Approach 1:
The patent applies the dynamics principle by making the exponent η a dynamic parameter that varies with operating conditions (current, temperature, charging state) rather than a fixed value. This allows the impedance model to adapt to changing battery conditions, capturing the non-linear behavior of diffusion effects while maintaining a relatively simple Oustaloup approximation structure.
Solution Approach 2:
The patent implements parameter changes by allowing the exponent η to change based on operating point conditions. Specifically, η is determined as a function of current, temperature, and charging state, enabling the model to accurately represent varying diffusion dynamics without requiring a completely different model structure for each condition.
2Measurement precision
If the exponent η is configured to depend on operating points (current, temperature, charging state), then the modeling accuracy improves, but the complexity of determining and updating the model increases
Solution Approach 1:
The patent applies preliminary action by pre-determining the functional relationship between the exponent η and operating conditions (current, temperature, charging state). This functional dependency is established beforehand, allowing the model to automatically adapt to varying conditions without requiring complex real-time calculations or extensive measurements during operation.
3Measurement precision
If iterative configuration with measurement series is performed to minimize voltage differences, then the model accuracy improves, but the time and computational resources required increase
Solution Approach 1:
The patent implements feedback by using an iterative optimization process that minimizes the difference between measured terminal voltage and modeled terminal voltage. The model parameters (particularly the exponent η) are adjusted based on this voltage difference feedback, allowing the model to converge to accurate predictions while systematically reducing errors across the measurement data.
Data Source
AI summary
A computer-implemented method for providing a cell impedance model for a battery cell by providing the cell impedance model with a low frequency component of as an Oustaloup approximation of a substantially linear low frequency component of a Nyquist relationship, measuring (S1) the battery cell at different operating points and at different frequencies to obtain measurement series with a terminal voltage, wherein the operating points are determined at least by the cell current and/or charging state; and configuring (S2) and providing (S3) the cell impedance model with the measurement series by minimizing a difference between the measured and modeled terminal voltage, wherein the exponent value is configured using an exponent function depending on the respective operating point.