Method of Estimating Pulse Response Using an Impedance Spectrum
First Claim
1. A method of assessing the condition of an energy storage device by estimating a response to an excitation pulse, the method comprising the steps of:
- a. measuring an impedance spectrum, the impedance spectrum comprising of at least a lowest frequency and at least a highest frequency;
b. configuring a simulated pulse, the simulated pulse comprising at least a low frequency;
c. decomposing the simulated pulse by Fourier analysis to obtain Fourier series coefficients, the Fourier series coefficients comprising at least a maximum frequency;
d. combining the Fourier series coefficients of the simulated pulse with the measured impedance spectrum to obtain an estimate response at each Fourier coefficient;
e. assembling the estimated response at each Fourier coefficients into an overall time response of the energy storage device; and
f. subtracting the assembled overall time response from a bias voltage of the energy storage device to estimate the response to the excitation pulse.
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Abstract
Electrochemical Impedance Spectrum (EIS) data are used directly to predict the pulse performance of an energy storage device. The impedance spectrum of the EIS is obtained in-situ using pre-existing techniques. A simulation waveform is configured such that the period of the pulse is greater than or equal to the lowest frequency of the impedance measurement. If the pulse is assumed to be periodic for analysis purposes, the complex Fourier series coefficients can be obtained. The number of harmonic constituents are selected so as to appropriately resolve the response, but the maximum frequency should be less than or equal to the highest frequency of the impedance measurement. In some cases, the measured frequencies of the impedance spectrum do not match the corresponding harmonic components of the simulated pulse wave. This is resolved by estimating the impedance measurements at the desired frequencies using linear interpolation, cubic spline fits, or other comparable methods. Using a current pulse as an example, the Fourier coefficients of the pulse are multiplied by the impedance spectrum at the corresponding frequency to obtain the Fourier coefficients of the voltage response to the desired pulse. The Fourier coefficients of the response are then summed reassemble to obtain the overall time domain estimate of the voltage using the Fourier series analysis. Thus, the response of an energy storage device to an anticipated or desired pulse can be estimated using low-level, charge neutral impedance measurements combined with Fourier series analysis.
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Citations
10 Claims
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1. A method of assessing the condition of an energy storage device by estimating a response to an excitation pulse, the method comprising the steps of:
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a. measuring an impedance spectrum, the impedance spectrum comprising of at least a lowest frequency and at least a highest frequency; b. configuring a simulated pulse, the simulated pulse comprising at least a low frequency; c. decomposing the simulated pulse by Fourier analysis to obtain Fourier series coefficients, the Fourier series coefficients comprising at least a maximum frequency; d. combining the Fourier series coefficients of the simulated pulse with the measured impedance spectrum to obtain an estimate response at each Fourier coefficient; e. assembling the estimated response at each Fourier coefficients into an overall time response of the energy storage device; and f. subtracting the assembled overall time response from a bias voltage of the energy storage device to estimate the response to the excitation pulse. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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Specification