# US 10,309,995 B2 · Method and system for determining phasor components of a periodic waveform > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,309,995 B2 - Document ID: US10309995B2 - Status: Granted - Kind: B2 - Application number: 15/766,718 - Filed: 2016-10-05 - Published: 2018-11-08 - Granted: 2019-06-04 - Earliest claimed: 2015-10-06 - Assignees: ABB Schweiz AG - Applicants: ABB Schweiz AG - Inventors: Nilanga Abeywickrama; Robert Saers; Tord Bengtsson; Jonas Hedberg - Web page: https://patentgrep.com/patent/US10309995B2 ## CPC - G01R 23/167: with digital filters - G01R 19/2506: {Arrangements for conditioning or analysing measured signals, e.g. for indicating peak values (G01R19/003 takes precedence); Details concerning sampling, digitizing or waveform capturing (displaying waveforms G01R13/00; analog sampling G01R19/0053)} - G01R 19/2513: {Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging} - G06F 17/142: {Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm} - H02H 1/0092: {concerning the data processing means, e.g. expert systems, neural networks} - Y02E 40/70: Smart grids as climate change mitigation technology in the energy generation sector - Y02E 60/00: Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation - Y04S 10/22: Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units - G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - H02H: EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS (indicating or signalling undesired working conditions G01R, e.g. G01R31/00, G08B; locating faults along lines G01R31/08; emergency protective devices H01H) - Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION - Y04S: SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS ## Abstract A method of determining phasor components of a periodic waveform, wherein the method includes: a) sampling the periodic waveform, b) determining a frequency spectrum of the sampled periodic waveform by means of a frequency transform utilizing a Gaussian window function, wherein a ratio np defined by the duration of the sampling of the periodic waveform divided by the width parameter of the Gaussian window function is at least 5, c) selecting a region of the frequency spectrum containing a frequency peak defined by a group of consecutive frequency bins each being defined by a frequency value and a magnitude value, and d) determining phasor components of the periodic waveform based on the group of consecutive frequency bins. ## Claims ### Claim 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 np defined by a duration (T0) of the sampling of the periodic waveform divided by a width (tw) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T0/2)/tw)^2), where t is time, tw is the width of the Gaussian window, and T0 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 (H0-H6) 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 (H0-H6). ### Claim 2 (depends on 1) 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. ### Claim 3 (depends on 2) 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 (H0-H6), and interpolating between the obtained phases to determine a frequency peak phase, which is the phase of the frequency peak. ### Claim 4 (depends on 2) The method according to claim 2, wherein the width (tw) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform. ### Claim 5 (depends on 2) The method according to claim 2, wherein the group of frequency bins (H0-H6) contains at least five frequency bins. ### Claim 6 (depends on 1) 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 (H0-H6), and interpolating between the obtained phases to determine a frequency peak phase, which is the phase of the frequency peak. ### Claim 7 (depends on 1) The method according to claim 1, wherein the width (tw) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform. ### Claim 8 (depends on 1) The method according to claim 1, wherein the group of frequency bins (H0-H6) contains at least five frequency bins. ### Claim 9 (depends on 1) The method according to claim 1, wherein the frequency transform is a discrete Fourier transform. ### Claim 10 (depends on 1) The method according to claim 1, wherein the periodic waveform is a measurement of one of voltage and current. ### Claim 11 (depends on 1) The method according to claim 1, further comprising applying the determined phasor components in impedance measurements. ### Claim 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 np defined by a duration (T0) of the sampling of the periodic waveform divided by a width (tw) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T0/2)/tw)^2), where t is time, tw is the width of the Gaussian window, and T0 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 (H0-H6) 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 (H0-H6). ### Claim 13 (depends on 12) 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. ### Claim 14 (depends on 13) 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 (H0-H6), and interpolate between the obtained phases to determine a frequency peak phase. ### Claim 15 (depends on 13) The phasor determination system according to claim 13, wherein the width (tw) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform. ### Claim 16 (depends on 12) 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 (H0-H6), and interpolating between the obtained phases to determine a frequency peak phase. ### Claim 17 (depends on 12) The phasor determination system according to claim 12, wherein the width (tw) of the Gaussian function forming the Gaussian window is dimensioned to contain at least two periods of the periodic waveform. ### Claim 18 (depends on 12) The phasor determination system according to claim 12, wherein the periodic waveform is a measurement of one of current and voltage. ### Claim 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 np defined by a duration (T0) of the sampling of the periodic waveform divided by a width (tw) of the Gaussian window is at least 5, where the Gaussian window is defined by a Gaussian function e^(−((t−T0/2)/tw)^2), where t is time, tw is the width of the Gaussian window, and T0 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 (H0-H6) 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 (H0-H6).