Method of Detecting System Function by Measuring Frequency Response

• US 20100274510A1
• Filed: 05/03/2010
• Published: 10/28/2010
• Est. Priority Date: 12/21/2004
• Status: Active Grant

• Current Assignee: Battelle Energy Alliance LLC (Battelle Memorial Institute)
• Original Assignee: Montana Tech of the University of Montana (University of Montana System)
• Inventors: Morrison, John L., Morrison, William H., Christophersen, Jon P.
• Granted Patent: US 8,352,204 B2
• Time in Patent Office: Days
• US Class Current: 702/75
• CPC Class Codes: G01R 31/2837 Characterising or performance testing, e.g. of frequency response transient response G01R27/28

Abstract

Methods of rapidly measuring the 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 the response is measured to ascertain the impedance spectrum. The excitation signal is a limited time duration sum-of-sines consisting of a select number of frequencies. In one embodiment, magnitude and phase of each of frequency of interest 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 the 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.

Claims

1. A method for detecting system function of an energy storage device under test by measuring frequency response, the method comprising the steps of:

(a) generating a vector of frequencies, by a method comprising the steps of (1) selecting a lowest frequency, (2) selecting an integer step factor, (3) multiplying the lowest frequency by the integer step factor to obtain a second frequency, (4) multiplying the second frequency by the integer step factor to obtain a next frequency, and (5) repeating step (4) until each frequency in the vector of frequencies is generated;

(b) generating a vector of amplitudes and phases;

(c) assembling a wideband excitation signal using the vector of frequencies and the vector of amplitudes and phases;

(d) conditioning the excitation signal to be compatible with the energy storage device under test;

(e) exciting the energy storage device under test with the conditioned excitation signal for one period of the lowest frequency;

(f) capturing a response time record with a data acquisition system; and

(g) processing the response time record to obtain the frequency response.

2. The method of claim 1, wherein said integer step factor is greater than 2.

3. The method of claim 1, wherein said excitation signal is a sum of sines excitation signal.

4. The method of claim 3, wherein said response time record is captured at a sampling rate that is step factor harmonic to said sum of sines excitation signal and is at least said step factor squared times a highest frequency in said sum of sines excitation signal.

5. The method of claim 1, wherein said response time record is processed by rectifying said response time record relative to various forms.

6. The method of claim 5, wherein the response time record is rectified with r forms, where r is said integer step factor, and N is the number of samples over the period (i.e., n=n₁, n₂, . . . , N), the first form of the rectification is:

7. The method of claim 6, wherein each of said r forms are summed up to obtain r different sums including m₁ . . . m_r.

8. The method of claim 7, wherein said summation terms (m₁ . . . m_r) are normalized to said response time record

S₁=Qm₁,S₂=Qm₂S_r=Qm_r

Where m₁ . . . m_r are summation terms of said rectified signal

Q is the number of periods in said response time record for a frequency being detected

S₁, S₂, . . . , S_r are corrected summation terms.

9. The method of claim 8, wherein said rectified signal is used to calculate magnitude and phase of said response time record with

10. The method of claim 9, wherein said magnitude and phase of said response time record are calculated at each frequency interesting said vector of frequencies to generate an impedance spectrum of said frequency response.

22. The method of claim 10, further comprising the step of:

(h) repeating steps (a)-(g), except wherein in steps (a)(7) said lowest and said third frequency are removed from the vector of frequencies, and in step (e) the energy storage device under test is excited for one-quarter period of said lowest frequency; and

combining said frequency response from step (g) and the frequency response from step (h) to obtain a frequency response with a duration of three-quarters of a period of said lowest frequency.

11. A method for detecting system function of an energy storage device under test by measuring frequency response, the method comprising the steps of:

(a) generating a vector of frequencies, by a method comprising the steps of (1) selecting a lowest frequency, (2) selecting an integer step factor, (3) multiplying the lowest frequency by the integer step factor to obtain a second frequency, (4) multiplying the second frequency by the integer step factor to obtain a third frequency, (5) multiplying the third frequency by the integer step factor to obtain a next frequency, (6) repeating step (5) until each frequency in the vector of frequencies is generated, and (7) removing the second frequency from the vector of frequencies;

(b) generating a vector of amplitudes and phases;

(c) assembling a wideband excitation signal using the vector of frequencies and the vector of amplitudes and phases;

(d) conditioning the excitation signal to be compatible with the energy storage device under test;

(e) exciting the energy storage device under test with the conditioned excitation signal for one-half period of the lowest frequency;

(f) capturing a response time record with a data acquisition system; and

(g) processing the response time record to obtain the frequency response.

12. The method of claim 11, wherein said integer step factor is a factor of two (i.e., r=2, 4, 8, 16, etc.).

13. The method of claim 11, wherein said excitation signal is a sum of sines excitation signal.

14. The method of claim 13, wherein said response time record is captured at a sampling rate that is octave harmonic to said sum of sines excitation signal and is at least four times a highest frequency in the sum of sines excitation signal.

15. The method of claim 11, wherein the captured response time record is inverted and concatenated to said captured response time record.

16. The method of claim 11, wherein response time record is processed by rectifying the response time record relative to sine and cosine.

17. The method of claim 16, wherein said response time record is rectified using a method selected from the group consisting of non-zero crossing, with N as the number of samples over the period the sine wave form of the rectification is:

18. The method of claim 17, wherein said rectified signal is used to calculate magnitude and phase of said response time record with

19. The method of claim 18, wherein said calculated magnitude and phase of said lowest frequency are used to generate a half-period time record that is subtracted from said response time record.

20. The method of claim 17, wherein said summation terms (m₁ . . . m_r) are normalized to said response time record.

S₁=Qm₁,S₂=Qm₂, . . . S_r=Qm,

Where m₁ . . . m_r are summation terms of the rectified signal

Q is the number of periods in the time record for the frequency being detected

S₁, S₂, . . . S_r are the corrected summation terms.

21. The method of claim 20, wherein the magnitude and phase response are calculated at each frequency in said vector of frequencies to generate an impedance spectrum of said frequency response.