Battery Residual Capacity Estimation Using Polynomial Reciprocal Functions
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Solution Overview
Problem
Existing methods for estimating battery residual capacity based on stable open circuit voltage face challenges such as insufficient accuracy, high calculation complexity, and numerical instability due to the use of complex exponential functions, which hinder precise prediction and practical implementation in devices with limited capacity, like vehicle controllers.
Innovation Solution
The method approximates the time-dependent variation of open circuit voltage using a polynomial reciprocal function of n-th degree, determining coefficients through least squares or Kalman filter operations, and estimates residual capacity from the calculated stable open circuit voltage, reducing calculation load and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If complex exponential functions are used to model battery voltage variation, then measurement precision of stable open circuit voltage is improved, but device complexity and calculation load increase
Solution Approach 1:
The patent transforms the complex exponential function parameters into simpler polynomial coefficients. By changing the mathematical representation from exponential decay parameters to polynomial coefficients, the calculation becomes computationally simpler while maintaining the ability to model voltage relaxation behavior accurately.
Solution Approach 2:
The patent replaces complex computational models with simpler polynomial approximations that can be easily calculated. This substitution uses computationally 'cheap' polynomial operations instead of expensive exponential function calculations, making the system suitable for devices with limited processing capacity.
2Measurement precision
If complex exponential functions are used to model battery voltage variation, then measurement precision of stable open circuit voltage is improved, but numerical stability deteriorates
Solution Approach 1:
The patent changes the mathematical formulation from exponential functions to polynomial functions. This parameter transformation eliminates numerical instability issues associated with exponential calculations while preserving the essential voltage relaxation characteristics through polynomial approximation.
3Measurement precision
If higher degree polynomial reciprocal functions are used, then measurement precision of stable open circuit voltage is improved, but device complexity increases
Solution Approach 1:
The patent uses a polynomial reciprocal function of degree n≥2, which provides sufficient accuracy for predicting stable open circuit voltage without over-complicating the model. This partial action approach achieves the necessary precision level without implementing excessively complex higher-degree polynomials that would increase computational burden unnecessarily.
Data Source
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AI summary
In the method for estimating battery residual capacity of the present invention, the voltage measurement values are obtained (step S2). And once it is finished, using the initial values of the coefficients set at the step S3 as starting, the optimization is progressed with renewing each value of the coefficients on the following iterating calculations (step S4). Once the optimum value of each coefficient in the approximation is determined at the step S4, the stable open circuit voltage is calculated by the optimized reciprocal function using thereof at the step S5. And then based thereon, the battery residual capacity is calculated by the predetermined conversion method (step S6).