EP2598898A1

EP2598898A1 - Determination of the fundamental frequency of a periodic signal including harmonic components

Info

Publication number: EP2598898A1
Application number: EP11743292.2A
Authority: EP
Inventors: Gwladys Chanedeau; Jean-Paul Gaubert; Laurent Rambault
Original assignee: Itron France SAS
Current assignee: Itron France SAS
Priority date: 2010-07-30
Filing date: 2011-07-05
Publication date: 2013-06-05
Also published as: FR2963433B1; AU2011284588B2; WO2012013883A1; FR2963433A1; AU2011284588A1; BR112013002288A2

Abstract

The invention relates to a method for determining the fundamental frequency of a periodic signal including harmonic components, comprising: calculating, during a first rough estimation (200) of the fundamental frequency and from samples of the signal, a first estimated value of the fundamental frequency, said value being expressed in a frequency unit that is selected such that the entire portion of the first estimated value comprises at most three digits; and then using a step (300) of estimating the fundamental frequency to the nearest tenth, in said unit, in order to determine, from said first value, a second estimated value, in said unit, of the fundamental frequency to the nearest tenth, by searching, from among a first set of possible frequency values corresponding to variations, at a constant spacing of 0.1, in the estimated first value, for a first frequency value for which the corresponding signal amplitude, calculated from the discrete Fourier coefficients of rank 1, is at a maximum. Similar additional steps (400; 500) can then be used to obtain an estimate of the fundamental frequency to the nearest hundredth, in said unit, and then to the nearest thousandth, in said unit, respectively.

Description

DETERMINATION OF THE FUNDAMENTAL FREQUENCY OF A PERIODIC SIGNAL INCLUDING HARMONIC COMPONENTS

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, although not limiting, 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.

Today, 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.

In order to be able to determine the presence of harmonic polluters, 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).

Today, it would be desirable to go further in the analysis so as to discriminate between polluting equipment and polluted equipment. This can only be done by accurately determining the amplitudes, and especially the phases at all harmonic frequencies. In order to determine the harmonic frequencies present in a signal, the fundamental frequency of the signal must be very precisely determined beforehand.

To date, some counters can estimate the fundamental frequency from a detection of zero crossings of the signal. This technique guarantees maximum precision to the nearest tenth of Hertz. This is nevertheless insufficient to determine the amplitudes, and especially the phases of the harmonics with the necessary precision.

The present invention aims to provide a method for determining much more accurately the fundamental frequency of a periodic signal having a harmonic content.

To do this, 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 first step of sampling and weighting said signal at a predefined sampling frequency to deliver a determined number N of samples of the signal;

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.

Thus, in the case where the rough estimate only makes it possible to obtain a decimal value of fundamental frequency with at most one digit after the decimal point, 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.

In a preferred implementation, 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:

1) initializing the current value of the fundamental frequency to the first estimated value and a possible frequency value of said first set to said first estimated value incremented by 0.1;

2) calculating a first amplitude of the signal at the current value and a second amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

3) Comparison of the first amplitude and the second amplitude calculated;

4) If the second amplitude is greater than the first amplitude, 4i) replacing the current value by the possible frequency value, then incrementing the possible frequency value of said first set of 0.1;

4ii) calculating a third amplitude of the signal at the current value and a fourth amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

4iii) reiterating the substeps 4i) to 4ii) as long as the fourth amplitude is greater than the calculated third amplitude;

5) Otherwise,

5i) replacement of the possible frequency value by the current value decremented by 0.1;

5ii) calculating a third amplitude of the signal at the current value and a fourth amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

5iii) as long as the fourth amplitude is greater than the calculated third amplitude, replacing the current value by the possible frequency value, decrementing the possible frequency value of said first set of 0.1 and reiterating substep 5ii) ;

6) Match the first desired frequency value to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

This optimizes the number of calculations required.

In the case where it is desired to further refine the result, 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:

o searching, among a third set of possible frequency values corresponding to variations, in a constant pitch of 0.001 of the third value estimated to the nearest hundredth, in said unit, a third frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier coefficients of rank 1, is maximum, and o match the fourth estimated value to the nearest thousandth, in said unit, said third frequency value.

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. For this purpose, 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

The present invention will be better understood from the following description given with reference to the appended figures, in which:

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.

For a periodic signal at a given fundamental frequency and having a harmonic content, the two discrete Fourier coefficients of rank h can be expressed according to the following relations:

(Relationships (1))

in which :

- a _h (F) and b _h (F) represent the discrete Fourier coefficients of rank h at the frequency F;

- T is the period of the signal, inverse of the frequency F;

- T _e is the sampling period;

- N is the total number of samples considered;

- NT is the total number of periods of the signal on which the samples were taken;

i is the reference of a current sample;

-, 5 (is a sample of the signal.

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:

^ ( ₀ ) = / ai ² ( ₀ ) + ô ₁ ² ( ₀ ) (Relation (2))

With, according to the relations (1) above

i N- \ 2T

" _L (b) = -Σ- ^ S {i) œs (2 F ₀ iT _e )

(Relationships (3)) In a preferred embodiment, 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.

In the following, we will agree the following notations:

- s (t) represents the periodic signal having a harmonic content, whose fundamental frequency is to be determined;

- F i is an estimate of the fundamental frequency at the tenth io ^_i

near, in the considered unit;

- F o is an estimate of the fundamental frequency to the nearest hundredth, in the considered unit;

- F is an estimate of the fundamental frequency to the nearest thousandth, in the considered unit.

According to the simplified block diagram shown in FIG. 1, 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. According to this known method, 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. To refine the result obtained, a linear interpolation is preferably performed on the last detection of a zero crossing. At the end of the second step 200, 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). It is important to note, for the sake of understanding, that 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. Thus, for a fundamental frequency signal of the order of 50 or 60 Hertz, the unit considered in the following process is Hertz. On the other hand, if one is in the presence of signals of the order of 50 000 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:

searching, among 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 coefficients discrete Fourier of rank 1, is maximal, and

- Match the second estimated value to the nearest tenth, in the unit considered at said first frequency value.

The third step 300 thus returns to search, among all the possible values F such that

F = F x + p x O, l

ïo ^-1

p = 0; ± 1; ± 2 ... the value for which we get the relationship

Max relation (4)

For example, if a coarse frequency of 51.3 Hz is found at the end of step 200, the considered unit is Hertz, and 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.

At the end of step 300, 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.

In other cases, 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. Here, a third estimated value F ₉ is determined from the second value F i in:

io ^_i

seeking, among a second set of possible frequency values corresponding to variations, by a constant pitch of 0.01, of the second estimated value _{10 10} -i, a second frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier coefficients of rank 1, is maximal, and

by matching the third estimated value F ₂ to the second frequency value resulting from the search.

The third step 400 thus returns to search, among all the possible values F such that

-2

F F + gx 0.01 q = 0; ± 1; ± 2 ...

the value for which we get the relationship

Max relation (5).

For example, if a frequency estimated at one-tenth of a Hz near

51.3 Hz is found at the end of step 300, 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.

At the end of step 400, a third value F ₉ estimated to the nearest hundredth, in the considered unit, of the fundamental frequency is thus delivered.

If the accuracy obtained is not satisfactory for the intended application, the method can be continued by a fifth step 500 estimate to the nearest thousandth, in the unit considered, of the fundamental frequency. Here again, 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. As a result, a fourth estimated value

F is determined from the third estimated value F ₉ in:

10 ^D 10 ²

searching, among a third set of possible frequency values corresponding to variations, by a constant pitch of 0.001, of the third estimated value _ ₂ , a third frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier coefficients of rank 1, is maximum, and

- matching the fourth estimated value ^ ₁₀ -3 to the third frequency value from the search.

The fourth step 500 thus returns to search, among all the possible values F such that

£ 10 ^J

FF _ ₂ + £ x 0.001

10 ^l

£, 10 ^{~ J}

k = 0; ± 1; ± 2 ...

the value for which we get the relationship

Max relation (6).

For example, if a frequency estimated at one hundredth of a Hz near

51.32 Hz is found at the end of step 400, 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.

At the end of step 500, a fourth value ^ ₁₀ -3 estimated to the nearest thousandth, in the unit in question, of the fundamental frequency is thus delivered.

One might think that the process could continue like this. Nevertheless, the simulations carried out by the Applicant have made it possible to show that the estimation method has a limit, typically to the nearest thousandth, in the unit under consideration. Indeed, the estimation of the fundamental frequency depends on the following different parameters:

the period T of the signal whose frequency is sought fundamental ;

- the variation x on T corresponding to the precision

- the sampling period T _e

- the total number N _T of periods of the signal on which the samples were taken

- the total number N of samples considered, given by the relation

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.

More precisely, 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

Hanning.

We note the relationship:

T _f = N _T x T = N x T _e

with:

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

Thus, if N is equal to 1250, we obtain:

Tf = 1250 x 256 ps = 0.32 s which corresponds to a number N _T of 16 periods of 50 Hz,

and for N equal to 5000, we obtain: => T = 5000 x 256 ps = 1, 28 s, which is a number N _T of 64 periods of 50 Hz,

In the graph of Figure 2, 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.

It appears clearly in FIG. 2 that, to obtain a precision that is finer than 0.1 Hertz, it is necessary to choose a number of samples greater than a certain threshold, denoted NQ I, here corresponding to 150 samples. To obtain an accuracy that is finer than 0.01 Hertz, it is necessary to choose a number of samples greater than a second threshold, itself greater than the first, and denoted No, where here 400 samples correspond. Finally, to obtain a precision even finer than 0.001 Hertz, it is necessary to choose a number of samples greater than a third threshold higher than the other two and noted No, where here corresponds to 600 samples.

It follows in particular from this graph that a precision to the nearest thousandth of a Hertz for a fundamental frequency signal close to 50 Hertz can be obtained by choosing a number of samples N equal to at least 600.

Of course, the minimum number of samples must be recalculated for each fundamental frequency to be estimated and for each expected sampling frequency, depending on the desired accuracy.

In the steps of the method described with reference to FIG. 1, 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.

A preferred implementation of the sub-step of searching within steps 300, 400 and 500 for reducing the number of calculations performed will now be described with reference to FIGS. 3 to 5:

Referring firstly to Figure 3, 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.

For these two values ₀ and ^ ₁₀ -i, we then calculate (sub-step 302) the two amplitudes A (F ₀ ) and A {F γ) obtained from the coefficients of

Discrete Fourier of rank 1, that is, in accordance with the above-mentioned relations (2) and (3)

These two amplitudes are then compared (in step 303).

In the case where the amplitude A {F γ) is greater than the amplitude A (F ₀ ), this means, according to the invention, that the value F i constitutes a

³ io ^_i

best estimate of the fundamental frequency than the value ₀ . So we replace (in step 304) the current value ₀ by the possible frequency value ^ ι, then we search if there exists, in the first set, another even better value by incrementing the possible frequency value F ι of said first set of 0, 1. This can be expressed by the relationships:

10 ¹

F = F + 0.1

10 ^"1 10 ^{" 1}

Then (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 ι) 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. In this case, 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).

If, on the other hand, at the end of the comparison sub-step 303, the amplitude A {F γ) is smaller than the amplitude A (F ₀ ), this means, according to the invention, that the value F ₀ is a better estimate of the fundamental frequency that valeuri ⁷ i. It is useless to go in this case to find the values of the first set greater than ^ ₁₀ -ι ■ So we keep a current value equal to ₀ , but we replace

(In 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:

^F o ⁼ · ^ ο

F = F ₀ - o, \

10 ¹

We then calculate (sub-step 309), for these two new values ₀ and F! , the two amplitudes A (F ₀ ) and A (F ^ _) obtained from the discrete Fourier coefficients of rank 1, and a new comparison is made (in step 310) of the amplitudes obtained.

³ io ^_i

best estimate of the fundamental frequency than the value ₀ . So we replace (under step 311) the current value ₀ by the possible frequency value ^ ι, then we search if there exists, in the first set, another even better value by decrementing again the possible frequency value F ι of said first set of 0.1 - This can be expressed by the relationships:

F ₀ = F.

10 ¹

F = F - 0.1

10 ^"1 10 ^{" 1}

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. In this case, 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.

Indeed, 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. Likewise, 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. An example of application of the method according to the invention, and more specifically the steps according to FIGS. 1, 3, 4 and 5, will now be described with reference to FIGS. 6 and 7. FIG. samples obtained at the end of step 100 (Figure 1) at from a signal from a voltage source.

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.

The table below shows the intermediate results found, according to the steps in Figures 3, 4 and 5:

The comparison of the amplitudes (step 303) giving a negative result here, is continued according to step 308.

The value of 51.3 Hz is therefore the best estimate to the nearest tenth of Hertz that can be obtained. The search for an estimate to the hundredth of Hertz near is then carried out: Step 401 Step 402

F ₀ = 51.30 Hz A (i) = 1477.54 LSB

F = 51.31 Hz A () = 1477.97 LSB

10 ¹

The comparison of the amplitudes (step 403) gives here a positive result, one continues according to step 404:

Comparing the amplitudes (step 406) giving a positive result here, steps 404 to 405 are repeated:

The value of 51.32 Hz is therefore the best estimate to the hundredth of Hertz that can be obtained. The search for an estimate to the nearest thousandth of a Hertz is then carried out:

The comparison of the amplitudes (step 403) giving here a negative result, is continued according to step 408. Step 408 Step 409

F ₀ = 51.320 Hz A ( ₀ ) = 1478.0926 LSB

F, = 51.319 Hz A (

10 ⁵ = 1478.0948 LSB

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.

Thus, thanks to the invention, it is possible to determine a fundamental frequency close to 50 Hz or 60 Hz with a relative accuracy of 20 ppm, or more generally, any fundamental frequency with a precision of one thousandth of a unit.

Claims

A method for determining the fundamental frequency of a periodic signal including harmonic components, characterized in that it comprises the following successive steps:

A first step (100) for sampling and weighting said signal at a predefined sampling frequency to deliver a determined number N of samples of the signal;

A second step (200) 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 part whole of the first estimated value has not more than three digits;

A third step (300) for estimating, to the nearest tenth, in said unit, the fundamental frequency in which a second value, estimated to within one-tenth, in said unit, of the fundamental frequency is determined from said first value; third step (300) consisting in: searching, among 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 the signal, calculated from the discrete Fourier Fourier coefficients of rank 1, is maximum, and o match the second estimated value to the nearest tenth, in said unit, to said first frequency value.

2. Method according to claim 1, characterized in that the step of finding the first frequency value of the third step (300) estimate to the nearest tenth, in said unit, of the fundamental frequency comprises the following successive substeps:

1) initializing (301) the current value of the fundamental frequency to the first estimated value and a possible frequency value of said first set to said first estimated incremented value of 0.1;

2) calculating (302) a first amplitude of the signal at the current value and a second amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

3) comparing (303) the first amplitude and second amplitude calculated;

4) If the second amplitude is greater than the first amplitude,

4i) replacing (304) the current value by the possible frequency value, then incrementing (304) the possible frequency value of said first set of 0.1;

4ii) calculating (305) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

5) Otherwise,

5i) replacing (308) the possible frequency value with the current value decremented by 0.1;

5ii) calculating (309) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the value of possible frequency, from the discrete Fourier coefficients of rank 1;

5iii) as long as the fourth amplitude is greater than the third calculated amplitude, replacing (311) the current value by the possible frequency value, decrementing (311) the possible frequency value of said first set of 0.1 and reiterating sub-step 5ii);

6) Match (307; 312) the first desired frequency value to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

Method according to any one of the preceding claims, characterized in that it comprises a fourth step (400) of estimate to the nearest hundredth, in said unit, of 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 (400) consisting in: searching for, among a second set of possible frequency values corresponding to variations, by not constant 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 to match the third value estimated to the nearest hundredth in said unit to said second frequency value.

4. Method according to claim 3, characterized in that the step of finding the second frequency value of the fourth step (400) of estimate to the nearest hundredth, in said unit, of the fundamental frequency comprises the following successive sub-steps:

1) initializing (401) the current value of the fundamental frequency to the second value estimated to within a tenth, in said unit, and a possible frequency value of said second set to said second estimated incremented value of 0.01;

2) calculating (402) a first amplitude of the signal at the current value and a second amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

3) comparing (403) the first amplitude and second amplitude calculated;

4) If the second amplitude is greater than the first amplitude,

4i) replacing (404) the current value by the possible frequency value, then incrementing (404) the possible frequency value of said second set of 0.01;

4ii) calculating (405) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

5) Otherwise,

5i) replacing (408) the possible frequency value by the current value decremented by 0.01;

5ii) calculating (409) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the value of possible frequency, from the discrete Fourier coefficients of rank 1;

5iii) as long as the fourth amplitude is greater than the third calculated amplitude, replacing (411) the current value by the possible frequency value, decrementing (411) the possible frequency value of said second set of 0.01 and reiterating sub-step 5ii);

6) Match (407; 412) the second desired frequency value to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

A method according to any one of claims 3 and 4, characterized in that it comprises a fifth step (500) estimate to one thousandth, in said unit, the fundamental frequency in which a fourth value estimated to one thousandth, in said unit, fundamental frequency is determined from said third estimated value to the nearest hundredth in said unit, the fifth step (500) consisting of: searching for a third set of possible frequency values corresponding to variations by a constant pitch of 0.001 of the third value estimated to the nearest hundredth in said unit, a third frequency value for which the corresponding amplitude of the signal, calculated from the discrete Fourier Fourier coefficients of rank 1, is maximum, and o matching the fourth estimated value to one thousandth in said unit to said third frequency value.

Method according to Claim 5, characterized in that the step of searching for the third frequency value of the fifth step (500) estimate to the nearest thousandth, in said unit, of the fundamental frequency comprises the following successive sub-steps:

1) initializing (501) the current value of the fundamental frequency to the third value estimated to the nearest hundredth, in said unit, and a possible frequency value of said third set to said third estimated incremented value of 0.001;

2) calculating (502) a first amplitude of the signal at the current value and a second amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

3) comparing (503) the first amplitude and second amplitude calculated;

4) If the second amplitude is greater than the first amplitude,

4i) replacing (504) the current value by the possible frequency value, then incrementing the possible frequency value of said third set of 0.001;

4ii) calculating (505) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the possible frequency value, from the discrete Fourier coefficients of rank 1;

5) Otherwise,

5i) replacing (508) the possible frequency value by the current value decremented by 0.001;

5ii) calculating (509) a third amplitude of the signal at the current value and a fourth amplitude of the signal at the value of possible frequency, from the discrete Fourier coefficients of rank 1;

5iii) as long as the fourth amplitude is greater than the third calculated amplitude, replacing (511) the current value by the possible frequency value, decrementing (511) the possible frequency value of said third set of 0.001 and reiterating the step 5 (ii);

6) Match (507; 512) the third desired frequency value to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

7. Method according to any one of the preceding claims, characterized in that the second step (200) of rough estimation consists in detecting the number of zero crossings of the signal.

8. Method according to any one of the preceding claims, characterized in that the first step (100) of sampling and weighting of said signal comprises a weighting by a Hanning type window.

9. Method according to any one of the preceding claims, characterized in that said periodic signal is constituted by an input signal of an electric energy meter in a distribution network of electrical energy at a fundamental frequency close to 50 Hertz or 60 Hertz.

10. Software product intended to be implemented by a microprocessor or microcontroller, characterized in that it carries out the method according to any one of claims 1 to 9.

11. Counter (1) of electrical energy receiving a voltage between at least one phase and one neutral and phase and neutral currents of an electric power distribution network, characterized in that comprises means (10) for analog-to-digital conversion of the voltage and phase currents, a microcontroller (12) and software means (11) implementing the method according to any one of claims 1 to 9 for the determination the fundamental frequency of the voltage and the phase and neutral currents.