Arc fault detection

1. A method comprising:

acquiring a first waveform using an arc-fault detection circuit having active filters and signal amplifiers;

determining, using a hardware processor, a first Average Magnitude Different Function (AMDF) of the first waveform acquired using the arc-fault detection circuit;

locating a first minimum peak of the first AMDF; and

determining whether an arc fault is detected as a function of the first minimum peak.

2. The method of claim 1 , further comprising:

deriving a modified waveform by applying a time-delay to the first waveform;

calculating a frequency-response plot of the modified waveform;

calculating a high frequency minima in a high-frequency range of the frequency-response plot, the high-frequency range being outside of a pass-band of the arc-fault detection circuit;

calculating a low-frequency minima in a low-frequency range of the frequency-response plot, the low-frequency range being within the pass-band of the arc-fault detection circuit;

calculating a ratio of the low-frequency minima to the high-frequency minima; and

determining whether the arc fault is detected as a function of the calculated ratio.

3. The method of claim 2 , calculating the frequency-response plot, comprising:

performing a Fast Fourier Transform (FFT) on the modified waveform.

4. The method of claim 3 , further comprising

smoothing the FFT.

5. The method of claim 1 , wherein acquiring the first waveform comprises acquiring the first waveform using an arc-fault detection circuit having active filters and signal amplifiers arranged in a Sallen-Key topology.

6. A method comprising:

acquiring a first waveform using an arc-fault detection circuit having active filters and signal amplifiers;

calculating, using a hardware processor, a frequency-response plot of the waveform acquired using the arc-fault detection circuit;

estimating a noise amplitude in a high-frequency range of the frequency-response plot, the high-frequency range being outside of a pass-band of the arc-fault detection circuit, the noise amplitude being estimated by performing a first curve fit of a high-frequency range;

performing a second curve fit of a low-frequency range to a function to calculate an amplitude in the low-frequency range, the low-frequency range being within the pass-band of the arc-fault detection circuit, the function being 1/f β -dependent, where:

0<β<2; and

determining whether an arc fault is detected based on a ratio of the noise amplitude in the high-frequency range and the amplitude in the low-frequency range.

7. The method of claim 6 , estimating the noise comprising:

generating a logarithm of the frequency-response plot;

performing a first linear curve fit on the high-frequency range of the logarithm of the frequency-response plot, the first linear curve fit producing a first value at a first selected frequency.

8. The method of claim 7 , performing the second curve fit comprising:

performing a second linear curve fit on the low-frequency range of the logarithm of the frequency-response plot, the second linear curve fit producing a slope and a second value at a second selected frequency.

9. The method of claim 8 , determining whether the arc fault is detected comprising:

calculating a ratio of the second value to the first value.

10. The method of claim 9 , further comprising:

determining whether the calculated ratio exceeds a predetermined threshold; and

indicating that the arc fault is detected in response to the ratio exceeding the predetermined threshold.

11. The method of claim 8 , further comprising:

determining whether the slope is less than zero; and

indicating that the arc fault is detected in response to the slope being less than zero.

12. The method of claim 11 , further comprising:

determining whether a standard deviation (SD) of the second curve fit is less than a predetermined SD-threshold (threshold SD ); and

indicating that the arc fault is detected in response to the SD being less than threshold SD .

13. The method of claim 12 , further comprising:

calculating a ratio of the second value to the first value;

determining whether the calculated ratio exceeds a predetermined ratio threshold (threshold RATIO ); and

indicating that no arc fault is detected in response to the ratio not exceeding threshold RATIO .

14. The method of claim 13 , further comprising:

indicating that the arc fault is detected in response to:

the slope being less than zero;

the SD being less than threshold SD ; and

the ratio exceeding threshold RATIO .

15. The method of claim 7 , calculating the frequency-response plot comprising:

performing a Fast Fourier Transform (FFT) on the waveform.

16. The method of claim 15 , further comprising:

smoothing the FFT.

17. The method of claim 6 , wherein acquiring the first waveform comprises acquiring the first waveform using an arc-fault detection circuit having active filters and signal amplifiers arranged in a Sallen-Key topology.