Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
  • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
  • G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
  • G01R19/2506—Arrangements for conditioning or analysing measured signals, e.g. for indicating peak values ; Details concerning sampling, digitizing or waveform capturing
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
  • G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
  • G01R19/2513—Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
  • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
  • G01R23/15—Indicating that frequency of pulses is either above or below a predetermined value or within or outside a predetermined range of values, by making use of non-linear or digital elements (indicating that pulse width is above or below a certain limit)

Definitions

• the present invention relates to a method for very accurately determining the fundamental frequency of a periodic signal including harmonic components.
• the invention also relates to a software product for implementing the method, as well as an electrical energy meter comprising such a software product.
• a field of application particularly contemplated in the invention is that of electric meters used in private homes or in industry to account for the electrical energy delivered by a distribution network of electrical energy and actually used by a customer. user.
• the known electrical networks use a sinusoidal alternating current, single-phase or three-phase, at a determined fundamental frequency, equal to 50 Hz for European networks, and 60 Hz for US networks. Nevertheless, the signals that pass through an electricity distribution network undergo disturbances, some of which, of a continuous nature, and known as harmonic pollution, can be very troublesome.
• the electrical signals of the network are thus not pure sinusoidal signals at the fundamental frequency, but periodic signals comprising not only the fundamental frequency, but also harmonics, that is to say multiples of the fundamental frequency, generated by electronic or electrical equipment (domestic appliances: televisions, computers, printers, microwave ovens, discharge lamps ..., industrial loads: variable speed drives, arc furnaces, welding machines, etc.) connected to the network.
• some electric meters are equipped with software means for performing a harmonic analysis, typically by discrete Fourier transform, network signals in current and voltage received on each of their phases, and to deduce a value called distortion rate or THD (Anglo-Saxon initials set for Total Harmony Distortion), representing the ratio of the rms value of the harmonics to that of the fundamental alternating quantity (current or voltage).
• THD Anglo-Saxon initials set for Total Harmony Distortion
• the present invention aims to provide a method for determining much more accurately the fundamental frequency of a periodic signal having a harmonic content.
• the subject of the invention is a method for determining the fundamental frequency of a periodic signal including harmonic components, characterized in that it comprises the following successive steps:
• a second step of rough estimation of the fundamental frequency in which a first estimated value of the fundamental frequency is calculated from said samples of the signal, the first value being expressed in a selected frequency unit so that the entire portion of the first estimated value has not more than three digits;
• a third step of estimating, to the nearest tenth, in said unit, the fundamental frequency in which a second value estimated at tenth, in said unit, the fundamental frequency is determined from said first value the third step of: o finding, out of a first set of possible frequency values corresponding to variations, by constant step of 0.1 of the first estimated value, a first frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier coefficients of rank 1, is maximum, and o to match the second estimated value to the nearest tenth, in said unit, at said first frequency value.
• the method according to the invention offers the possibility of refining the result and determining the fundamental frequency to the nearest tenth, in the unit under consideration.
• the step of finding the first frequency value of the third estimation step to the nearest tenth, in said unit will advantageously comprise the following successive substeps:
• the method according to the invention advantageously comprises a fourth step of estimating to the nearest hundredth, in said unit, the fundamental frequency in which a third value estimated to the nearest hundredth, in said unit, the fundamental frequency is determined from said second value estimated to the nearest tenth, in said unit, the fourth step consisting of: o searching, among a second set of possible frequency values corresponding to variations, by constant pitch of 0.01, of the second value estimated to the nearest tenth, in said unit, a second frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier Fourier coefficients of rank 1, is maximum, and o match the third value estimated to the nearest hundredth, in said unit, to said second frequency value.
• the step of searching for the second frequency value of the fourth estimation step to the nearest hundredth, in said unit will advantageously comprise substeps similar to those implemented for the third estimation step, again in order to optimize the number of calculations needed.
• An accuracy to the nearest one thousandth in said unit can be further advantageously obtained by providing a fifth step of estimating to the nearest thousandth, in said unit, the fundamental frequency in which a fourth value estimated to within a thousandth, in said unit, of the fundamental frequency is determined from said third value estimated to the nearest hundredth, in said unit, the fifth step consisting in:
• the present invention also relates to a software product intended to be implemented by a microprocessor or a microcontroller, and carrying out the steps of the method according to the invention.
• a particular application of the invention concerns the determination of the fundamental frequency of the phase voltage and the phase and neutral currents of an electrical energy distribution network comprising at least one phase and one neutral.
• another object of the invention is an electrical energy meter receiving a voltage between at least one phase and a neutral as well as phase and neutral currents of an electrical energy distribution network, characterized in that it comprises means for analog-to-digital conversion of the voltage and phase currents, a microcontroller and software means implementing the method according to the invention for determining the fundamental frequency of the voltage and currents. live and neutral
• FIG. 1 illustrates in the form of a block diagram the different steps of the method according to the invention for determining the fundamental frequency to the nearest thousandth, in the unit under consideration;
• FIG. 2 illustrates simulation results
• FIG. 3 illustrates in the form of a different block diagram in the steps preferably implemented for determining the fundamental frequency to the nearest tenth, in the unit under consideration;
• FIG. 4 illustrates in the form of a different block diagram, in steps preferentially implemented for determining the fundamental frequency to the nearest hundredth, in the unit under consideration;
• FIG. 5 illustrates in the form of a block diagram various sub-steps preferentially implemented for the determination of the fundamental frequency to the nearest thousandth, in the unit under consideration;
• FIG. 6 illustrates an example of samples of a harmonic content signal whose fundamental frequency is to be determined with great precision
• FIG. 7 schematically illustrates an electric energy meter implementing the method according to the invention.
• the present invention is based on the known principle that one can obtain a discrete spectral representation of any sampled signal, periodic or not, from a discrete Fourier transform. So, the signal can be decomposed as a sum of pure signals (sine and cosine) weighted by coefficients called Fourier coefficients.
• i is the reference of a current sample
• the amplitude ⁇ ( 0 ) of the signal at the fundamental frequency F 0 can be expressed as a function of the discrete Fourier coefficients of rank 1 calculated for this frequency according to the relation:
• the process according to the invention consists, as will now be detailed with reference to FIG. 1, of making a first rough estimate of the fundamental frequency of the signal, expressed in a frequency unit chosen so that the integer part of the first estimated value comprises at most three digits, then search successively for a more precise estimate, typically to the nearest tenth, in the unit under consideration, then to the nearest hundredth, in the unit under consideration, then to the nearest thousandth, in the unit under consideration, looking for each time the frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier coefficients of rank 1 according to the relations (2) and (3) above, is maximum.
• - s (t) represents the periodic signal having a harmonic content, whose fundamental frequency is to be determined
• - F is an estimate of the fundamental frequency to the nearest thousandth, in the considered unit.
• a first step 100 of the method according to the invention consists of sampling and weighting the signal s (t) at a predefined sampling frequency F e so as to deliver a determined number N d samples of the signal.
• the purpose of weighting is to limit the signal in time.
• a Hanning weighting window is preferably used which makes it possible to obtain the desired limitation with little influence on the signal.
• a second step 200 of rough estimation of the fundamental frequency is then performed, in which a first estimated value F of the fundamental frequency is calculated from said samples of the signal.
• the detection of zero crossings ("zero crossing" in English terminology) is preferably used for this second step.
• a test is performed on two successive samples of signal to determine if they are of opposite sign. Zero crossings on rising edge and falling edge are counted over the one second horizon.
• a linear interpolation is preferably performed on the last detection of a zero crossing.
• the first estimated value F of the fundamental frequency is delivered. This value is however not very precise (maximum precision to one tenth of the considered unit).
• the first value F is expressed in a chosen frequency unit so that the integer part of this first value comprises at most three digits.
• the unit considered in the following process is Hertz.
• the unit considered in the continuation will be KiloHertz.
• a third step 300 estimate to the nearest tenth, in the unit considered, of the fundamental frequency is then performed. During this step 300, a second value estimated to within one-tenth, in the unit under consideration, of the fundamental frequency is determined from the first estimated value F resulting from the first step 200. More precisely, according to the invention, the third step 300 consists of:
• the third step 300 thus returns to search, among all the possible values F such that
• the considered unit is Hertz
• the first set of possible frequency values, in which a search will be made for estimate to one-tenth of a Hertz, of the fundamental frequency shall include not more than nineteen values: 50.1 Hz; 50.2 Hz; 50.3 Hz; 50.4 Hz; 50.5 Hz; 50.6 Hz; 50.7 Hz; 50.8 Hz; 50.9 Hz; 51.0 Hz; 51.1 Hz; 51.2 Hz; 51.3 Hz; 51.4 Hz; 51.5 Hz; 51.6 Hz; 51.7 Hz; 51.8 Hz and 51.9 Hz.
• a second value F i, estimated to the nearest tenth, in the unit in question, of the fundamental frequency is delivered.
• the method of the invention can stop at this level in all cases where a higher accuracy is not sought.
• the method continues with a fourth step 400 of estimate to the nearest hundredth, in the unit considered, of the fundamental frequency.
• This fourth step 400 is similar to the third step 300, except that the initial value of the frequency which one seeks to refine here corresponds to the second estimated value ⁇ 10 -i resulting from the step 300.
• a third estimated value F 9 is determined from the second value F i in:
• the third step 400 thus returns to search, among all the possible values F such that
• the second set of possible frequency values in which an estimate hundredths of Hertz is sought near the fundamental frequency, will include at most the nineteen following values : 51.21 Hz; 51.22 Hz; 51.23 Hz; 51.24 Hz; 51.25 Hz; 51.26 Hz; 51.27 Hz; 51.28 Hz; 51.29 Hz; 51.30 Hz; 51.31 Hz; 51.32 Hz; 51.33 Hz; 51.34 Hz; 51.35 Hz; 51.36 Hz; 51.37 Hz; 51.38 Hz and 51.39 Hz.
• a third value F 9 estimated to the nearest hundredth, in the considered unit, of the fundamental frequency is thus delivered.
• the method can be continued by a fifth step 500 estimate to the nearest thousandth, in the unit considered, of the fundamental frequency.
• the fifth step is very similar to the two steps 300 and 400 described above, except that the initial value of the frequency that one seeks to refine corresponds to the third estimated value F 2 resulting from step 400.
• a fourth estimated value is very similar to the two steps 300 and 400 described above, except that the initial value of the frequency that one seeks to refine corresponds to the third estimated value F 2 resulting from step 400.
• F is determined from the third estimated value F 9 in:
• the fourth step 500 thus returns to search, among all the possible values F such that
• the third set of possible frequency values in which an estimate of one thousandth of Hertz is sought near the fundamental frequency, will comprise at most the nineteen following values : 51.311 Hz; 51.312 Hz; 51.313 Hz; 51.314 Hz; 51.315 Hz; 51.316 Hz; 51.317 Hz; 51.318 Hz; 51.319 Hz; 51.320 Hz; 51.321 Hz; 51.322 Hz; 51.323 Hz; 51.324 Hz; 51.325 Hz; 51.326 Hz; 51.327 Hz; 51.328 Hz and 51.329 Hz.
• a fourth value ⁇ 10 -3 estimated to the nearest thousandth, in the unit in question, of the fundamental frequency is thus delivered.
• Simulations were carried out for a sinusoidal signal of fundamental frequency equal to 50 Hz and for a sampling period T e equal to 256 psec, to measure the influence of the total number N of samples considered on the accuracy of the estimate.
• FIG. 2 represents the variation of the accuracy on the fundamental frequency of the periodic signal (close to 50 Hz) identified at the frequency giving the maximum amplitude of the Discrete Fourier Transform to the fundamental rank, as a function of the number of samples constituting the acquisition window of said sampled signal at a sampling period T e , the weighting window applied being a window of
• Tf the duration in seconds of the acquisition window
• N T the number of periods of the real fundamental period T and N, the number of samples acquired at the sampling period T e
• the ordinate axis is shown on a logarithmic scale from 1 Hz at 10 "9 Hertz, and the axis of abscissa is linear, from 0-6000 samples.
• each of the steps 300, 400 and 500 comprises a sub-step during which a more precise value is sought from among a first, second and third set of at most nineteen, respectively. possible values of frequency.
• the search for the first frequency value ⁇ 10 -i estimated to the nearest tenth, in the unit considered, of the fundamental frequency comprises a first substep boot 301 in which the current value F 0 of the fundamental frequency is set to the first estimated value F, after step 200, and a frequency value as possible to the first set, denoted in the remainder 10 ⁇ -i is initialized to the first estimated value F incremented by 0, 1.
• sub-step 305 for these two new values 0 and ⁇ 10 -i are computed the two amplitudes A (F 0 ) and A (F ⁇ _) obtained from the discrete Fourier coefficients of rank 1, and proceeds to a new comparison (in step 306) of the amplitudes obtained.
• Sub-steps 304 and 305 are reiterated as long as the amplitude A (F ⁇ ) is greater than the calculated amplitude A (F 0 ).
• the search stops as soon as the result of the comparison (under step 306) is negative.
• the value sought corresponds to the last current value at the end of substeps 304 to 306, for which the comparison was positive, that is to say the value before incrementation. This amounts to decrementing the current value again by 0.1 (in step 307).
• step 308 the possible frequency value 10 10 -i by the current value F 0 decremented by 0.1. This can be expressed by relationships:
• Sub-steps 309 and 310 are reiterated as long as the amplitude A (F ⁇ _i) is greater than the calculated amplitude A (F 0 ).
• the search stops as soon as the result of the comparison (in step 310) is negative.
• the value sought corresponds to the last current value at the end of the sub-steps 311, 309 and 310, for which the comparison was positive, that is to say the value before decrementation. This amounts to incrementing the current value again by 0.1 (in step 312).
• Figures 4 and 5 illustrate a preferred implementation of the step of finding a frequency value, respectively to the nearest hundredth, and to the nearest thousandth, in the unit in question.
• the implementation is similar to that presented with reference to Figure 3, and thus will not be described in detail.
• the steps 401 to 407 on the one hand, and 408 to 412 on the other hand, of FIG. 4 are in all respects identical to the steps 301 to 307, and 308 to 312 described above, except that values ⁇ -i 10 and P as increment / decrement of 0.1 were replaced by values F 2 and no increment / decrement of 0.01.
• the steps 501 to 507 on the one hand, and 508 to 512 on the other hand, of FIG. 5 are in all respects identical to the steps 301 to 307 and 308 to 312 described above, except that values ⁇ -i 10 and no increment / decrement of 0.1 were replaced by Q_ values 3 and no increment / decrement of 0.001.
• the signal s (t) considered is for example a voltage signal of a phase of an electrical distribution network received between a phase and a neutral of a counter 1 shown schematically in FIG. 7. It could also be any phase and neutral current of the electrical power distribution network.
• the counter comprises analogue-digital conversion means 10 and software means 11 making it possible, under the control of a microcontroller 12, to implement the method for determining the fundamental frequency of the signal s (t) to the thousandth of a Hertz near. In this example, 5000 samples at a sampling period of 256 ps are available at the output of the converting means at the end of step 100.
• the coarse estimation step 200 made by the detection method zero crossings, makes it possible to obtain a first estimated value of 51.3 Hz.
• the unit considered here is therefore the Hertz.
• step 303 The comparison of the amplitudes (step 303) giving a negative result here, is continued according to step 308.
• Step 401 Step 402
• step 403 The comparison of the amplitudes (step 403) gives here a positive result, one continues according to step 404:
• steps 404 to 405 are repeated:
• Step 408 Step 409
• step 410 The comparison of the amplitudes (step 410) giving here a positive result, one continues according to the step 411:
• the value of 51.319 Hz is therefore the best estimate to the nearest thousandth of a Hertz that can be obtained.

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• 2010
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• 2011
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