# Method of estimating pulse response using an impedance spectrum

## Abstract

Electrochemical Impedance Spectrum data are used to predict pulse performance 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 and reassembled to obtain the overall time domain estimate of the voltage using the Fourier series analysis.

- Inventors:

- Issue Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1160237

- Patent Number(s):
- 8,868,363

- Application Number:
- 12/813,750

- Assignee:
- Battelle Energy Alliance, LLC (Idaho Falls, ID)

- DOE Contract Number:
- AC07-05ID14517

- Resource Type:
- Patent

- Resource Relation:
- Patent File Date: 2010 Jun 11

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 25 ENERGY STORAGE

### Citation Formats

```
Morrison, John L, Morrison, William H, Christophersen, Jon P, and Motloch, Chester G.
```*Method of estimating pulse response using an impedance spectrum*. United States: N. p., 2014.
Web.

```
Morrison, John L, Morrison, William H, Christophersen, Jon P, & Motloch, Chester G.
```*Method of estimating pulse response using an impedance spectrum*. United States.

```
Morrison, John L, Morrison, William H, Christophersen, Jon P, and Motloch, Chester G. Tue .
"Method of estimating pulse response using an impedance spectrum". United States. https://www.osti.gov/servlets/purl/1160237.
```

```
@article{osti_1160237,
```

title = {Method of estimating pulse response using an impedance spectrum},

author = {Morrison, John L and Morrison, William H and Christophersen, Jon P and Motloch, Chester G},

abstractNote = {Electrochemical Impedance Spectrum data are used to predict pulse performance 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 and reassembled to obtain the overall time domain estimate of the voltage using the Fourier series analysis.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2014},

month = {10}

}

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