Method and system for determining phasor components of a periodic waveform

1. A method of determining phasor components of a periodic waveform, wherein the method is performed by a phasor determination system having processing circuitry and comprises:

a) sampling the periodic waveform at a sampling frequency,

b) determining a frequency spectrum of the sampled periodic waveform by means of a frequency transform utilizing a Gaussian window, wherein a ratio n p defined by a duration (T 0 ) of the sampling of the periodic waveform divided by a width (t w ) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T 0 /2)/t w )^2), where t is time, t w is the width of the Gaussian window, and T 0 is the duration of the sampling of the periodic waveform,

c) selecting a region of the frequency spectrum containing a frequency peak (P) defined by a group of consecutive frequency bins (H 0 -H 6 ) each being defined by a frequency value and a magnitude value, and

d) determining the phasor components of the periodic waveform based on the group of consecutive frequency bins (H 0 -H 6 ).

2. The method according to claim 1 , wherein step d) involves estimating an amplitude of the frequency peak and a frequency of the frequency peak by adapting amplitude and frequency of a Gaussian function that is based on a Fourier transform of the Gaussian window to fit the group of consecutive frequency bins.

3. The method according to claim 2 , including obtaining a respective phase, provided by the frequency transform, of each of at least two of the frequency bins (H 0 -H 6 ), and interpolating between the obtained phases to determine a frequency peak phase, which is the phase of the frequency peak.

4. The method according to claim 2 , wherein the width (t w ) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform.

5. The method according to claim 2 , wherein the group of frequency bins (H 0 -H 6 ) contains at least five frequency bins.

6. The method according to claim 1 , including obtaining a respective phase, provided by the frequency transform, of each of at least two of the frequency bins (H 0 -H 6 ), and interpolating between the obtained phases to determine a frequency peak phase, which is the phase of the frequency peak.

7. The method according to claim 1 , wherein the width (t w ) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform.

8. The method according to claim 1 , wherein the group of frequency bins (H 0 -H 6 ) contains at least five frequency bins.

9. The method according to claim 1 , wherein the frequency transform is a discrete Fourier transform.

10. The method according to claim 1 , wherein the periodic waveform is a measurement of one of voltage and current.

11. The method according to claim 1 , further comprising applying the determined phasor components in impedance measurements.

12. A phasor determination system configured to determine phasors of a periodic waveform, including:

processing circuitry configured to:

sample the periodic waveform at a sampling frequency,

determine a frequency spectrum of the sampled periodic waveform by means of a frequency transform utilizing a Gaussian window, wherein a ratio n p defined by a duration (T 0 ) of the sampling of the periodic waveform divided by a width (t w ) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T 0 /2)/t w )^2), where t is time, t w is the width of the Gaussian window, and T 0 is the duration of the sampling of the periodic waveform,

select a region of the frequency spectrum containing a frequency peak (P) defined by a group of consecutive frequency bins (H 0 -H 6 ) each being defined by a frequency value and a magnitude value, and

determine phasor components of the periodic waveform based on the group of consecutive frequency bins (H 0 -H 6 ).

13. The phasor determination system according to claim 12 , wherein the processing circuitry is configured to determine the phasor components by estimating an amplitude of the frequency peak and a frequency of the frequency peak by adapting amplitude and frequency of a Gaussian function that is based on a Fourier transform of the Gaussian window to fit the group of consecutive frequency bins.

14. The phasor determination system according to claim 13 , wherein the processing circuitry is configured to obtain a respective phase, provided by the frequency transform, of each of at least two of the frequency bins (H 0 -H 6 ), and interpolate between the obtained phases to determine a frequency peak phase.

15. The phasor determination system according to claim 13 , wherein the width (t w ) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform.

16. The phasor determination system according to claim 12 , wherein the processing circuitry is configured to obtain a respective phase, provided by the frequency transform, of each of at least two of the frequency bins (H 0 -H 6 ), and interpolating between the obtained phases to determine a frequency peak phase.

17. The phasor determination system according to claim 12 , wherein the width (t w ) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform.

18. The phasor determination system according to claim 12 , wherein the periodic waveform is a measurement of one of current and voltage.

19. A non-transitory computer-readable medium storing a computer program for determining phasors of a periodic waveform, the computer program including computer code, which when executed on a processing unit of a phasor determination system causes the phasor determination system to:

sample the periodic waveform at a sampling frequency,

determine a frequency spectrum of the sampled periodic waveform by means of a frequency transform utilizing a Gaussian window, wherein a ratio n p defined by a duration (T 0 ) of the sampling of the periodic waveform divided by a width (t w ) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T 0 /2)/t w )^2), where t is time, t w is the width of the Gaussian window, and T 0 is the duration of the sampling of the periodic waveform,

select a region of the frequency spectrum containing a frequency peak (P) defined by a group of consecutive frequency bins (H 0 -H 6 ) each being defined by a frequency value and a magnitude value, and

determine phasor components of the periodic waveform based on the group of consecutive frequency bins (H 0 -H 6 ).