Method of Detecting System Function by Measuring Frequency Response

Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. The time profile of this signal has a duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time record by rectifying relative to the sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency

Method of Detecting System Function by Measuring Frequency Response

Methods of rapidly measuring an impedance spectrum of an energy storage device in-situ over a limited number of logarithmically distributed frequencies are described. An energy storage device is excited with a known input signal, and aresponse is measured to ascertain the impedance spectrum. An excitation signal is a limited time duration sum-of-sines consisting of a select number offrequencies. In one embodiment, magnitude and phase of each frequency ofinterest within the sum-of-sines is identified when the selected frequencies and sample rate are logarithmic integer steps greater than two. This technique requires a measurement with a duration of one period of the lowest frequency. In another embodiment, where selected frequencies are distributed in octave steps, the impedance spectrum can be determined using a captured time record that is reduced to a half-period of the lowest frequency

Method of Estimating Pulse Response Using an Impedance Spectrum

Electrochemical Impedance Spectrum data are used to predict pulse performace of an energy storage device. The impedance spectrum may be obtained in-situ. A simulation waveform includes a pulse wave with a period greater than or equal to the lowest frequency used in the impedance measurement. Fourier series coefficients of the pulse train can be obtained. The number of harmonic constituents in the Fourier series are selected so as to appropriately resolve the response, but the maximum frequency should be less than or equal to the highest frequency used in the impedance measurement. Using a current pulse as an example, the Fourier coefficients of the pulse are multiplied by the impedance spectrum at corresponding frequencies to obtain Fourier coefficients of the voltage response to the desired pulse. The Fourier coefficients of the response are then summed as reassembled to obtain the overall time domain estimate of the voltage using series analysis