Systems and methods of grounded neutral fault detection by single frequency excitation and leakage spectral analysis

1. A grounded neutral fault detector, comprising:

induction circuits configured to:

generate a leakage signal corresponding to a current imbalance between a line conductor and a neutral conductor for a load; and

a controller configured to:

determine a frequency of a test signal by:

measuring load noise based on a first leakage signal without the test signal being injected, the first leakage signal corresponding to a first current imbalance between the line conductor and the neutral conductor for the load when the test signal is not being injected into the neutral conductor;

analyzing a frequency spectrum of the load noise; and

selecting the frequency of the test signal based on the frequency spectrum of the load noise;

inject the test signal at the selected frequency to the neutral conductor;

measure impedance of a current loop formed by a potential grounded neutral fault based on a second leakage signal corresponding to a second current imbalance with the test signal being injected; and

determine a grounded neutral fault based on the measured impedance.

2. The detector of claim 1 , wherein the controller is further configured to select the frequency of the test signal corresponding to a frequency at which the load noise has the lowest magnitude.

3. The detector of claim 1 , wherein the controller is further configured to:

perform a Fourier transform of the load noise to derive a frequency spectrum of the load noise;

measure magnitudes of the load noise at a plurality of frequencies based on the frequency spectrum of the load noise; and

select the frequency corresponding to a frequency having the lowest magnitude among the plurality of frequencies.

4. The detector of claim 1 , wherein the controller is further configured to:

determine a current response at the selected frequency to the test signal; and

determine the impedance of the current loop as being inversely proportional to a magnitude of the current response.

5. The detector of claim 4 , wherein the controller is further configured to:

between two adjacent samples of a second leakage signal,

multiply an earlier sample of the two adjacent samples with a corresponding point in a reference cosine waveform to derive a cosine product, the reference cosine waveform having the selected frequency;

multiply the earlier sample with a corresponding point in a reference sine waveform to derive a sine product, the reference sine waveform having the selected frequency;

add the cosine product to a first accumulator; and

add the sine product to a second accumulator;

multiply a last sample with the corresponding point in the reference cosine waveform to derive a last cosine product;

multiply the last sample with the corresponding point in the reference sine waveform to derive a last sine product;

add the last cosine product to the first accumulator;

add the last sine product to the second accumulator; and

determine the magnitude of the current response as a square root over a sum of a square of an average of cosine products and a square of an average of sine products.

6. The detector of claim 5 , wherein the reference cosine waveform and the reference sine waveform are prestored at the same location.

7. The detector of claim 5 , wherein a full cycle of the reference cosine waveform and the reference sine waveform are prestored.

8. The detector of claim 1 , wherein the controller is further configured to repeat determining a frequency, injecting the test signal, measuring impedance, and determining the grounded neutral fault.

9. The detector of claim 8 , wherein a sampling rate of the first leakage signal and the second leakage signal remains the same, and a sampling duration of the first leakage signal and the second leakage signal remains the same.

10. The detector of claim 1 , wherein samples of the second leakage signal have an integer number of cycles of the test signal.

11. A method of detecting a grounded neutral fault, comprising:

determining a frequency of a test signal by:

measuring load noise based on a first leakage signal without the test signal being injected, the first leakage signal corresponding to a first current imbalance between a line conductor and a neutral conductor for a load when the test signal is not being injected into the neutral conductor;

analyzing a frequency spectrum of the load noise; and

selecting the frequency of the test signal based on the frequency spectrum of the load noise;

injecting the test signal at the selected frequency to the neutral conductor;

measuring impedance of a current loop formed by a potential grounded neutral fault based on a second leakage signal corresponding to a second current imbalance with the test signal injected; and

determining a grounded neutral fault based on the measured impedance.

12. The method of claim 11 , wherein selecting the frequency further comprises selecting the frequency of the test signal corresponding to a frequency at which the load noise has the lowest magnitude.

13. The method of claim 11 , wherein:

analyzing a frequency spectrum further comprises performing a Fourier transform of the load noise to derive the frequency spectrum of the load noise; and

selecting the frequency further comprises:

measuring magnitudes of the load noise at a plurality of frequencies based on the frequency spectrum of the load noise; and

selecting the frequency corresponding to a frequency having the lowest magnitude among the plurality of frequencies.

14. The method of claim 11 , wherein measuring impedance further comprises:

determining a current response at the selected frequency; and

determining the impedance of the current loop as being inversely proportional to a magnitude of the current response.

15. The method of claim 14 , wherein determining a current response further comprises:

between two adjacent samples of a second leakage signal,

multiplying an earlier sample of the two adjacent samples with a corresponding point in a reference cosine waveform to derive a cosine product, the reference cosine waveform having the selected frequency;

multiplying the earlier sample with a corresponding point in a reference sine waveform to derive a sine product, the reference sine waveform having the selected frequency;

adding the cosine product to a first accumulator; and

adding the sine product to a second accumulator;

multiplying a last sample with the corresponding point in the reference cosine waveform to derive a last cosine product;

multiplying the last sample with the corresponding point in the reference sine waveform to derive a last sine product;

adding the last cosine product to the first accumulator;

adding the last sine product to the second accumulator; and

determining the magnitude of the current response as a square root over a sum of a square of an average of cosine products and a square of an average of sine products.

16. The method of claim 15 , wherein the reference cosine waveform and the reference sine waveform are prestored at the same location.

17. The method of claim 15 , wherein a full cycle of the reference cosine waveform and the reference sine waveform are prestored.

18. The method of claim 11 , further comprising repeating determining a frequency, injecting the test signal, measuring impedance, and determining the grounded neutral fault.

19. The method of claim 18 , wherein a sampling rate of the first leakage signal and the second leakage signal remains the same, and a sampling duration of the first leakage signal and the second leakage signal remains the same.

20. The method of claim 11 , wherein samples of the second leakage signal have an integer number of cycles of the test signal.