AU2011284588B2

AU2011284588B2 - Determination of the fundamental frequency of a periodic signal including harmonic components

Info

Publication number: AU2011284588B2
Application number: AU2011284588A
Authority: AU
Inventors: Gwladys Chanedeau; Jean-Paul Gaubert; Laurent Rambault
Original assignee: Itron Global SARL
Current assignee: Itron Global SARL
Priority date: 2010-07-30
Filing date: 2011-07-05
Publication date: 2014-07-03
Anticipated expiration: 2031-07-05
Also published as: WO2012013883A1; EP2598898A1; BR112013002288A2; FR2963433B1; AU2011284588A1; FR2963433A1

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

1 Determination of the fundamental frequency of a periodic signal including harmonic components The present invention relates to a method of very precise determination of the fundamental frequency of a periodic signal including harmonic components. The invention also relates to a software product enabling the implementation of the method, as well as an electricity meter including such a software product. A field of application which is envisaged particularly in the invention, although non-limiting, is that of electrical meters used in private or industrial premises in order to account for the electricity delivered by an electrical power distribution network and actually used by a user. Nowadays, the known electrical networks use a sinusoidal alternating current, monophase or three-phase, at a defined fundamental frequency, equal to 50 Hz for European networks, and 60 Hz for American networks. Nevertheless, the signals transiting through an electricity distribution network are subject to interference, and some of them are continuous and known under the name of harmonic pollution and may be very inconvenient. Thus the electrical signals of the network are not pure sinusoidal signals at the fundamental frequency, but periodic signals comprising not only the fundamental frequency but also harmonics, i.e. multiples of the fundamental frequency, generated by network-connected electronic or electrical equipment (domestic appliances: televisions, computers, printers, microwave ovens, discharge lamps..., industrial loads: speed governors, arc furnaces, welding stations...). In order to be able to determine the presence of harmonic pollutants, certain electrical meters are provided with software means which make it possible to perform a harmonic analysis, typically by discrete Fourier transform, of the network current and voltage signals received on each of their phases, and to deduce a value known as a distortion rate or THD (English initials for Total Harmonic Distortion), representing the ratio of the effective value of the harmonics to the value of the alternative fundamental variable (current or voltage). Nowadays, it would be desirable to go further in the analysis in such a way as to be able in particular to discriminate between the polluting equipment and the polluted equipment. This 2 can only be effected by determining precisely the amplitudes and above all the phases at all the harmonic frequencies. In order to to determine the harmonic frequencies present in a signal, the fundamental frequency of the signal should be determined very precisely in advance. Today certain meters may estimate the fundamental frequency on the basis of a detection of zero crossings of the signal. This technique guarantees maximum precision to the nearest tenth of a Hertz. This is nevertheless insufficient for determining the amplitudes, and above all the phases of the harmonics with the necessary precision. The object of the present invention is to propose a method which makes it possible to determine more precisely the fundamental frequency of a periodic signal having a harmonic content. For this purpose the invention relates to a method of determination of the fundamental frequency of a periodic signal including harmonic components, characterised in that it includes the following successive steps: - a first step of sampling and of weighting of the said signal at a predefined sampling frequency in order to deliver a specified 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 samples of the signal, the first value being expressed in a frequency unit chosen in such a way that the integer part of the first estimated value includes at most three digits; - A third step of estimation to the nearest tenth, in the said unit, of the fundamental frequency in which a second value estimated to the nearest tenth, in the said unit, of the fundamental frequency is determined from the said first value, the third step consisting of: o searching, among a first set of possible frequency values corresponding to variations, by constant steps of 0.1, of the first estimated value, for a first frequency value for 3 which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the second value estimated to the nearest tenth, in the said unit, correspond to the said first frequency value. Thus, in the case where the rough estimation only makes it possible to obtain a decimal fundamental frequency value with at most one digit after the decimal point, the process according to the invention offers the possibility of refining the result and determining the fundamental frequency to the nearest tenth, in the relevant unit. In a preferred implementation, the step of searching for the first frequency value of the third step of estimate to the nearest tenth, in the said unit, will advantageously include the following successive sub-steps: 1) Initialisation of the current value of the fundamental frequency at the first estimated value and a possible frequency value of the said first set at the said first estimated value incremented by 0.1; 2) Calculation of a first amplitude of the signal at the current value and of a second amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 3) Comparison of the first amplitude and the second amplitude which have been calculated; 4) If the second amplitude is greater than the first amplitude, 4i) replacement of the current value by the possible frequency value, then incrementation of the possible frequency value of the said first set by 0.1; 4ii) calculation of a third amplitude of the signal at the current value and of 4 a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 4iii) reiteration of sub-steps 4i) h 4ii) as long as the calculated 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) calculation of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 5iii) as long as the calculated fourth amplitude is greater than the calculated third amplitude, replacement of the current value by the possible frequency value, decrementation of the possible frequency value of the said first set by 0.1 and reiteration of the sub-step 5ii); 6) Making the first frequency value sought correspond to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive. Thus the number of calculations necessary is optimised. In the case where it is desired to refine the result still further, the method according to the invention advantageously includes a fourth step of estimation to the nearest hundredth, in the said unit, of the fundamental frequency in which a third value estimated to the nearest hundredth, in the said unit, of the fundamental frequency is determined from the said second value estimated to the nearest tenth, in the said unit, the fourth step consisting of: o searching, among a second set of possible frequency values corresponding to 5 variations, by constant steps of 0.01, of the second value estimated to the nearest tenth, in the said unit, for a second frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the third value estimated to the nearest hundredth, in the said unit, correspond to the said second frequency value. The step of search for the second frequency value of the fourth step of estimation to the nearest hundredth, in the said unit, will advantageously include sub-steps similar to those implemented for the third step of estimation, again in this case in such a way as to optimise the number of calculations necessary. A precision to the nearest thousandth, in the said unit, can also be advantageously obtained by providing a fifth step of estimation to the nearest thousandth, in the said unit, of the fundamental frequency in which a fourth value estimated to the nearest thousandth, in the said unit, of the fundamental frequency is determined from the said third value estimated to the nearest hundredth, in the said unit, the fifth step consisting of: o searching, among a third set of possible frequency values corresponding to variations, by constant steps of 0.001, of the third value estimated to the nearest hundredth, in the said unit, for a second frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the fourth value estimated to the nearest thousandth, in the said unit, correspond to the 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 relates to the determination of the fundamental frequency of the phase voltage and the phase and neutral currents of an electrical power 6 distribution network including at least one phase and one neutral. To this end, the invention also relates to an electricity meter receiving a voltage between at least one phase and one neutral as well as phase and neutral currents of an electrical power distribution network, characterised in that it includes anaogue/digital means for conversion of the phase voltage and currents, a microcontroller and software means for implementing the method according to the invention for the determination of the fundamental frequency of the phase voltage and the phase and neutral currents. The present invention will be better understood in the light of the following description with reference to the appended drawings, in which: - Figure 1 shows in synoptic form the different steps of the method according to the invention for the determination of the fundamental frequency to the nearest thousandth, in the relevant unit; - Figure 2 shows simulation results; - Figure 3 shows in synoptic form the different sub-steps preferably implemented for the determination of the fundamental frequency to the nearest tenth, in the relevant unit; - Figure 4 shows in synoptic form the different sub-steps preferably implemented for the determination of the fundamental frequency to the nearest hundredth, in the relevant unit; - Figure 5 shows in synoptic form the different sub-steps preferably implemented for the determination of the fundamental frequency to the nearest thousandth, in the relevant unit; - Figure 6 shows a example of samples of a signal with harmonic content for which it is desired to determine the fundamental frequency with great precision; - Figure 7 shows schematically an electricity meter implementing the method according to the invention. The present invention is based on the known principle that it is possible to obtain a discrete spectral representation of any signal sampled, periodic or not, on the basis of a discrete Fourier transform. Thus the signal can be broken down in the form of a sum of pure signals (sine and cosine) weighted by coefficients known as Fourier coefficients. For a periodic signal at a given fundamental frequency and having a harmonic content, the 7 two discrete Fourier coefficients of level h may be expressed according to the following relations: 1 N-12T ah(F)= - eS(i)cos(2xhFiT,) NT j=O T (Relations (1)) 1 N-12T bh (F) =- 1 -=-eS(i)sin(27hFiTe) NT i=0 T in which: - ah(F) and bh(F) represent the level h discrete Fourier coefficients at the frequence F; - T is the period of the signal, the inverse of the frequency F; - Te is the sampling period; - N is the total number of samples considered; - NT is the total number of periods of the signal over which the samples have been taken; - i is the reference of a current sample; - S(i) is a sample of the signal. The amplitude A(Fo) of the signal at the fundamental frequency Fo can be expressed as a function of the level 1 discrete Fourier coefficients calculated for this frequency according to the relation: 2 2

A(F

0 ) = a 1

(F

0 )+ b 1

(F

0 ) (Relation (2)) with, according to the relations (1) above: 1 N-12T ai (F0)= - - S(i)cos(27cFoiTe) NT i=0 To (Relations (3)) 1 N-12T bi (F0) =- L -- e-S(i)sin(27cFoiTe) -NT i =0 TO In a preferred implementation, the method according to the invention consists, as will be seen with reference to Figure 1, of effecting a first rough estimation of the fundamental frequency of the signal, expressed in a unit of frequency chosen so that the integer part of the first 8 estimated value includes at most three digits, then of successively searching for a more precise estimation, typically to the nearest tenth, in the relevant unit, then to the nearest hundredth, in the relevant unit, then to the nearest thousandth, in the relevant unit, by searching each time for the frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients according to the relations (2) and (3) above, is the maximum. The following notations are used appropriately in the description below: - s(t) represents the periodic signal having a harmonic content, of which the fundamental frequency is to be determined; - Flo~' is an estimation of the fundamental frequency to the nearest tenth, in the relevant unit; - Fo2 is an estimation of the fundamental frequency to the nearest hundredth, in the relevant unit; - Fo3 is an estimation of the fundamental frequency to the nearest thousandth, in the relevant unit; In accordance with the simplified synoptic diagram shown in Figure 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 Fe in such a way as to deliver a specified number N of samples of the signal. The purpose of the weighting is to limit the signal in time. A Hanning type weighting window is preferably used which makes it possible to obtain the required limitation with little influence on the signal. A second step of rough estimation of the fundamental frequency is then carried out in which a first estimated value F of the fundamental frequency is calculated from the said samples of the signal. The detection of the zero crossings is preferably used for this second step. In accordance with this known method, a test is performed on two successive signal samples in order to to determine if they have opposing signs. The zero crossings on the rising edge and the falling edge are recorded on the horizon of a second one. In order to refine the result 9 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. However, this value is not very precise (maximum precision at the tenth of the relevant unit). For the sake of understanding it is important to note that the first value F is expressed in a frequency unit chosen in such a way that the integer part of this first estimated value comprises at most three digits. Thus for a signal of fundamental frequency of the order of 50 or 60 Hertz, the relevant unit in the rest of the method is the Hertz. On the other hand, if the signals are of the order of 50 000 Hertz, the relevant unit in the rest of the method will be the KiloHertz. A third step 300 of estimation to the nearest tenth, in the relevant unit, of the fundamental frequency is then performed; During this step 300, a second value estimated to the nearest tenth, in the relevant unit, of the fundamental frequency is determined from the said first estimated value F from the first step 200. More precisely, in accordance with the invention, the third step 300 consists of: - searching, among a first set of possible frequency values corresponding to variations, by constant steps of 0.1, of the first estimated value, for a first frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and - making the second value estimated to the nearest tenth, in the relevant unit, correspond to the said first frequency value. Thus the third step 300 consists of searching, among all the possible values F, 1 0 j such that Fp,10-1 =Fx+pxO,1 p = 0 ;1 ; i 2 ... the value for which the following relation is obtained: 10 Max[A(Fp, 1 0 1 )]=Max raF +b rF V JJ relation (4) By way of example, if a rough frequency of 51.3 Hz is found at the end of the step 200, the relevant unit is the Hertz, and the first set of possible frequency values, in which a search is performed for an estimation to the tenth of a Hertz, of the fundamental frequency, will comprise at most the following 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. During this step 300, a second value Flo~] estimated to the nearest tenth, in the relevant unit, of the fundamental frequency is delivered. The method according to the invention can stop at this level in all the cases where greater precision is not sought. In the other cases the method continues with a fourth step 400 of estimation to the nearest hundredth, in the relevant unit, of the fundamental frequency. This fourth step 400 is similar to the third step 300, except that the initial value of the frequency which is to be refined corresponds here to the second estimated value Flo~' from the step 300. In this case a third estimated value F 1 -2 is determined from the second value Flo~' by: - searching, among a second set of possible frequency values corresponding to variations, by constant steps of 0.01, of the second estimated value Flo~, for a second frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and - making the third estimated value F 1 o-2 correspond to the second frequency value resulting from the search. Thus the third step 400 consists of searching among all the possible values F, 10-2 such that 11 F =F _1 +qxO,01 q,10 2 10 q = 0 1 2 ; 2 ... the value for which the following relation is obtained: Max A(F q 2)] =Max a 2!F q12 +b1 F qi2 relation (5). By way of example, if a frequency estimated to the nearest tenth of a Hz at 51.3 Hz is found at the end of the step 300, the second set of possible frequency values in which a search wil be performed for an estimation to the nearest hundredth of a Hertz, of the fundamental frequency, will comprise at most the following nineteen 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. Thus at the end of the step 400, a third value F 1 0 -2 estimated to the nearest hundredth, in the relevant unit, of the fundamental frequency is delivered. If the precision obtained is not satisfactory for the envisaged application, the method can continue with a fifth step 500 of estimation to the nearest thousandth, in the relevant unit, of the fundamental frequency. Here too, the fifth step is very similar to the two steps 300 and 400 described above, except that the initial value of the frequency which is to be refined corresponds to the third estimated value Fo-2 from the step 400. Consequently a fourth estimated value Flo 3 is determined from the third value Flo 2 by: - searching, among a third set of possible frequency values corresponding to variations, 2 by constant steps of 0.001, of the third estimated value Flo- , for a third frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and 12 - making the fourth estimated value F 1 3 correspond to the third frequency value resulting from the search. Thus the fourth step 500 consists of searching, among all the possible values Fk, 1 )3 such that F =F -2 +kx,001 k,10-3 10 k = 0 1 2 ... the value for which the following relation is obtained: Max[A(F )j =Max a 2 F + b r F relation (6). By way of example, if a frequency estimated to the nearest hundredth of a Hz to 51.32 Hz is found at the end of the step 400, the third set of possible frequency values in which a search wil be performed for an estimation to the nearest thousandth of a Hertz, of the fundamental frequency, will comprise at most the following nineteen 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. Thus at the end of the step 500, a fourth value F 1 3 estimated to the nearest thousandth, in the relevant unit, of the fundamental frequency is delivered. It might be thought that the method could continue in this way. Nevertheless, the simulations effected by the applicant have made it possible to show that the method of estimation has a limit, typically to the nearest thousandth, in the relevant unit. In fact, the estimation of the fundamental frequency depends upon the different parameters below: 13 - the period T of the signal of which the fundamental frequency is sought; - the variation x over T corresponding to the precision - the sampling period Te - total number NT of periods of the signal over which the samples have been taken; - the total number N of samples considered, given by the relation N =- x NT Te Simulations have been performed for a sinusoidal signal of fundamental frequency equal to 50Hz and for a sampling period Te equal to 256 p seconds, in order to measure the influence of the total number N of samples considered on the precision of the estimation. More precisely, Figure 2 shows the variation of the precision over the fundamental frequency of the periodic signal (close to 50Hz) identified at the frequency giving the maximum amplitude of the discrete Fourier transform at the fundamental level, as a function of the number of samples constituting the window for acquisition of the said sampled signal at a sampling period Te, the weighting window applied being a Hanning window. The following relation is noted: Tf =NTxT=NxTe with: T, the duration in seconds of the acquisition window NT, the number of periods of the real fundamental of period T and N, the number of samples acquired at the sampling period Te Thus, if N is equal to 1250, the following is obtained: T = 1250 x 256 p s = 0.32 s which corresponds to a number NT de 16 periods of 50 Hz, and for N equal to 5000, the following is obtained: T = 5000 x 256 p s = 1.28 s which corresponds to a number NT of 64 periods of 50 Hz, On the graph of Figure 2, the Y axis is shown on a logarithmic scale of 1 Hertz to 10-9 Hertz, and the X axis is linear, from 0 to 6000 samples.

14 Figure 2 shows clearly that, in order to obtain a finer precision than 0.1 Hertz, it is necessary to choose a number of samples greater than a certain threshold denoted No.], corresponding here to 150 samples. In order to obtain a finer precision than 0.01 Hertz, it is necessary to choose a number of samples greater than a threshold denoted No 01 , corresponding here to 400 samples. In order to obtain a finer precision than 0.001 Hertz, it is necessary to choose a number of samples greater than a threshold denoted N 0

.

001 , corresponding here to 600 samples. It is apparent in particular from this graph that a precision to the nearest thousandth of a Hertz for a signal of fundamental frequency 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 should be recalculated for each fundamental frequency to be estimated and for each sampling frequency provided, as a function of the desired precision. In the steps of the method which are described with reference to Figure 1, each of the steps 300, 400 and 500 comprise a sub-step during which a search is performed for a more precise value among respectively a first, second and third set of at most nineteen possible frequency values. A preferred implementation of the sub-step of searching within the steps 300, 400 and 500 which makes it possible to reduce the number of calculations performed will now be described with reference to Figures 3 to 5: With reference first of all to Figure 3, the search for the first frequency value Flo~' estimated to the nearest tenth, in the relevant unit, of the fundamental frequency includes a first sub step of initialisation 301 wherein the current value Fo of the fundamental frequency is initialised at the first estimated value F, resulting from the step 200, and a possible frequency value of the first set, denoted below as Flo', is initialised at the first estimated value F incremented by 0.1.

15 For these two values Fo and Flo~', a calculation is then performed (sub-step 302) of the two amplitudes A(Fo) and A(Flo~') obtained from the level 1 discrete Fourier coefficients, i.e., according to the aforementioned relations (2) and (3):

A(F

0 )= a (FO )+b (FO) A(F =al F+b FO 10 10 10 These two amplitudes are then compared (sub-step 303). In the case where the amplitude A(Flo~') is greater than the amplitude A(Fo), this means, in accordance with the invention, that the valeur Flo~' constitutes a better estimation of the fundamental frequency than the value Fo. Therefore the current value Fo is replaced (sub-step 304) by the possible frequency value Flo', then a search iis performed as to whether, in the first set, an even better value exists by incrementing the possible frequency value Flo~' of the said first set by 0.1. This may be expressed by the relations: Fo = Fio Fio~' = Flo~' + 0.1 For these two new values Fo and Flo~', a calculation is then performed (sub-step 305) of the two amplitudes A(Fo) and A(F 1 o~') obtained from the level 1 discrete Fourier coefficients, and a new comparison (sub-step 306) of the amplitudes obtained is performed. The sub-steps 304 and 305 are reiterated as long as the amplitude A(Flo~') is greater than the calculated amplitude A(Fo). The search is stopped as soon as the result of the comparison (sub-step 306) is negative. In this case, the value sought corresponds to the previous current value at the end of the sub-steps 304 to 306, for which the comparison was positive, i.e. the value before incrementation. This leads to again decrementing the current value by 0.1 (sub-step 307). If on the other hand at the end of the sub-step of comparison 303 the amplitude A(Flo~') is less than the amplitude A(Fo), this means, in accordance with the invention, that the value Fo constitutes a better estimation of the fundamental frequency than the value Flo~] It is 16 unnecessary in this case to seach for the values of the first set which are greater than Flo~. Therefore a current value equal to Fo is retained, but the possible frequency value Flo~' is replaced (sub-step 308) by the current value Fo decremented by 0.1. This may be expressed by the relations: Fo -Fo Fio~- = Fo~ For these two new values Fo and Flo~', a calculation is then performed (sub-step 309) of the two amplitudes A(Fo) and A(F 1 o~') obtained from the level 1 discrete Fourier coefficients, and a new comparison (sub-step 310) of the amplitudes obtained is performed. In the case where the amplitude A(Flo~') is greater than the amplitude A(Fo), this means, in accordance with the invention, that the valeur Flo~' constitutes a better estimation of the fundamental frequency than the value Fo. Therefore the current value Fo is replaced (sub-step 311) by the possible frequency value Flo', then a search iis performed as to whether, in the first set, another even better value exists by decrementing the possible frequency value Flo~ of the said first set by 0.1. This may be expressed by the relations: Fo = Fio~' Fio-' = Fio~' -0.1 The sub-steps 309 and 310 are reiterated as long as the amplitude A(F 1 o~') is greater than the calculated amplitude A(Fo). The search is stopped as soon as the result of the comparison (sub-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, i.e. the value before decrementation. This leads to again decrementing the current value by 0.1 (sub step 312). Figures 4 and 5 illustrate a preferred implementation of the step of search for a frequency value, respectively to the nearest hundredth, and to the nearest thousandth, in the relevant unit. The implementation is similar to that presented with reference to Figure 3, and thus will not be described in detail.

17 In fact, the steps 401 to 407 on the one hand, and 408 to 412 on the other hand, of Figure 4 are identical in all points to the steps 301 to 307, and 308 to 312 described above, except that the values Flo~] and the steps of incrementation/decrementation by 0.1 have been replaced by values F 1 o-2 and steps of incrementation/decrementation by 0.01. Likewise, the steps 501 to 507 on the one hand, and 508 to 512 on the other hand, of Figure 5 are identical in all points to the steps 301 to 307, and 308 to 312 described above, except that the values Flo~] and the steps of incrementation/decrementation by 0.1 have been replaced by values F 10 3 and steps of incrementation/decrementation by 0.001. An example of application of the method according to the invention, and more specifically the steps according to Figures 1, 3, 4 and 5 will now be described with reference to Figures 6 and 7. Figure 6 partially shows samples obtained at the end of the step 100 (Figure 1) from a signal coming from a voltage source. The signal s(t) in question is for example a voltage signal of a phase of an electrical distribution network received between a phase and a neutral of a meter 1 shown schematically in Figure 7. This could also be any phase and neutral current of the electrical power distribution network. The meter includes analogue/digital conversion means 10 and software means 11 which make it possible, under the control of a microcontroller 12, to implement the method of determination of the fundamental frequency of the signal s(t) to the nearest thousandth of a Hertz. In this example, 5000 samples at a sampling period of 256 seconds are available at the output of the conversion means 10 at the end of the step 100. The step of rough estimation 200, performed by the method of detection of zero crossings, makes it possible to obtain a first estimated value of 51.3 Hz. Therefore the relevant unit here is the Hertz. The table below indicates the intermediate results found, in accordance with the steps of Figures 3, 4 and 5: 18 Step 301 Step 302 Fo = 51.3 Hz A(Fo) = 1477.54 LSB Fo = 51.4 Hz 1 1467.82 LSB The comparison of amplitudes (step 303), which here gives a negative result, is continued according to the step 308. Step 308 Step 309 Step 312 FO = 51.3 Hz A(Fo) = 1477.54 LSB Flo-' = 51.2 Hz 1 (Flo~' = 1456.19 LSB F Flo = 51.3 Hz Therefore the value of 51.3 Hz constitutes the best estimation to the nearest tenth of a Hertz pres which it is possible to obtain. The search for an estimation to the nearest hundredth of a Hertz is then performed: Step 401 Step 402 Fo = 51.30 Hz A(Fo) = 1477.54 Hz Fo~ 2 = 51.31 Hz A(FIo~2 = 1477.97 LSB The comparison of amplitudes (step 403), which here gives a positive result, is continued according to the step 404: Step 404 Step 405 Fo = 51.31 Hz A(Fo)= 1477.97 LSB F Fo~ 2 = 51.32 Hz 1 A(FIo~ 2 ) = 1478.09 LSB The comparison of the amplitudes (step 406), which here gives a positive result, is reiterated in the steps 404 to 405: 19 Step 404 Step 405 Step 407 Fo = 51.32 Hz A(Fo) = 1478.09 LSB Fo~2 = 51.33 Hz A(Flo~2) = 1477.89 LSB Fo-2 = 51.32 Hz Therefore the value of 51.32 Hz constitutes the best estimation to the nearest hundredth of a Hertz which it is possible to obtain. The search for an estimation to the nearest thousandth of a Hertz is then performed: Step 501 Step 502 Fo = 51.320 Hz A(Fo)= 1478.0926 Hz Flo~ = 51.321 Hz A(Fro3) 1477.0872 LSB The comparison of amplitudes (step 403), which here gives a negative result, is continued according to the step 408. Step 408 Step 409 Fo = 51.320 Hz A(Fo)= 1478.0926 Hz Flo~3= 51.319 Hz A(Flo~ 3 ) = 1478.0948 LSB The comparison of amplitudes (step 410), which here gives a positive result, is continued according to the step 411: Step 411 Step 409 Step 412 Fo = 51.319 Hz A(Fo)= 1478.0948 Hz Flo~3= 51.318 Hz A(Flo~3 1478.0940 LSB Fio 51.319 Hz Therefore the value of 51.319 Hz constitutes the best estimation to the nearest thousandth of a Hertz which it is possible to obtain.

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

Claims

1. Method of determination of the fundamental frequency of a periodic signal including harmonic components, characterised in that it includes the following successive steps: - a first step (100) of sampling and of weighting of the said signal at a predefined sampling frequency in order to deliver a specified number N of samples of the signal; - A second step (200) of rough estimation of the fundamental frequency wherein a first estimated value of the fundamental frequency is calculated from samples of the signal, the first value being expressed in a frequency unit chosen in such a way that the integer part of the first estimated value includes at most three digits; - A third step (300) of estimation to the nearest tenth, in the said unit, of the fundamental frequency in which a second value estimated to the nearest tenth, in the said unit, of the fundamental frequency is determined from the said first value, the third step (300) consisting of: o searching, among a first set of possible frequency values cofresponding to variations, by constant steps of 0.1, of the first estimated value, for a first frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the second value estimated to the nearest tenth, in the said unit, correspond to the said first frequency value.

2. Method as claimed in Claim 1, characterised in that the step of searching for the first frequency value of the third step (300) of estimating to the nearest tenth, in the said unit, of the fundamental frequency includes the following successive sub-steps: 1) Initialisation (301) of the current value of the fundamental frequency at the first estimated value and a possible frequency value of the said first set at the said first estimated value incremented by 0.1; 22 2) Calculation (302) of a first amplitude of the signal at the current value and of a second amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 3) Comparison (303) of the first amplitude and the second amplitude which have been calculated; 4) If the second amplitude is greater than the first amplitude, 4i) replacement (304) of the current value by the possible frequency value, then incrementation (304) of the possible frequency value of the said first set by 0.1; 4ii) calculation (305) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 4iii) reiteration of sub-steps 4i) to 4ii) as long as the fourth amplitude is greater than the calculated third amplitude; 5) Otherwise, 5i) replacement (308) of the possible frequency value by the current value decremented by 0.1; 5ii) calculation (309) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 5iii) as long as the calculated fourth amplitude is greater than the calculated third amplitude, replacement (311) of the current value by the possible frequency value, decrementation (311) of the possible frequency value of the said first set by 0.1 and 23 reiteration of the sub-step 5ii); 6) Making the first frequency value sought correspond (307; 312) to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

3. Method as claimed in any one of the preceding claims, characterised in that it includes a fourth step (400) of estimation to the nearest hundredth, in the said unit, of the fundamental frequency in which a third value estimated to the nearest hundredth, in the said unit, of the fundamental frequency is determined from the said second value estimated to the nearest tenth, in the said unit, the fourth step (400) consisting of: o searching, among a second set of possible frequency values corresponding to variations, by constant steps of 0.01, of the second value estimated to the nearest tenth, in the said unit, for a second frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the third value estimated to the nearest hundredth, in the said unit, correspond to the said second frequency value.

4. Method as claimed in Claim 3, characterised in that the step of searching for the second frequency value of the fourth step (400) of estimating to the nearest hundredth, in the said unit, of the fundamental frequency includes the following successive sub-steps: 1) Initialisation (401) of the current value of the fundamental frequency at the second estimated value to the nearest tenth, in the said unit, and a possible frequency value of the said second set at the said second estimated value incremented by 0.01; 2) Calculation (402) of a first amplitude of the signal at the current value and of a second amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 3) Comparison (403) of the first amplitude and the second amplitude which have 24 been calculated; 4) If the second amplitude is greater than the first amplitude, 4i) replacement (404) of the current value by the possible frequency value, then incrementation (404) of the possible frequency value of the said second set by 0.01; 4ii) calculation (405) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 4iii) reiteration of sub-steps 4i) to 4ii) as long as the fourth amplitude is greater than the calculated third amplitude; 5) Otherwise, 5i) replacement (408) of the possible frequency value by the current value decremented by 0.01; 5ii) calculation (409) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 5iii) as long as the calculated fourth amplitude is greater than the calculated third amplitude, replacement (411) of the current value by the possible frequency value, decrementation (411) of the possible frequency value of the said first set by 0.01 and reiteration of the sub-step 5ii); 6) Making the second frequency value sought correspond (407; 412) to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

5. Method as claimed in any one of Claims 3 and 4, characterised in that it includes a 25 fifth step (500) of estimation to the nearest thousandth, in the said unit, of the fundamental frequency in which a fourth value estimated to the nearest thousandth, in the said unit, of the fundamental frequency is determined from the said third value estimated to the nearest hundredth, in the said unit, the fifth step (500) consisting of: o searching, among a third set of possible frequency values corresponding to variations, by constant steps of 0.001, of the third value estimated to the nearest hundredth, in the said unit, for a second frequency value for which the corresponding amplitude of the signal, calculated from the level 1 discrete Fourier coefficients, is the maximum, and o making the fourth value estimated to the nearest thousandth, in the said unit, correspond to the said third frequency value.

6. Method as claimed in Claim 5, characterised in that the step of searching for the third frequency value of the fifth step (500) of estimating to the nearest thousandth, in the said unit, of the fundamental frequency includes the following successive sub-steps: 1) Initialisation (501) of the current value of the fundamental frequency at the third estimated value to the nearest hundredth, in the said unit, and a possible frequency value of the said third set at the said third estimated value incremented by 0.001; 2) Calculation (502) of a first amplitude of the signal at the current value and of a second amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 3) Comparison (503) of the first amplitude and the second amplitude which have been calculated; 4) If the second amplitude is greater than the first amplitude, 4i) replacement (504) of the current value by the possible frequency value, then incrementation (404) of the possible frequency value of the said third set by 0.001; 26 4ii) calculation (505) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 4iii) reiteration of sub-steps 4i) h 4ii) as long as the calculated fourth amplitude is greater than the calculated third amplitude; 5) Otherwise, 5i) replacement (508) of the possible frequency value by the current value decremented by 0.001; 5ii) calculation (509) of a third amplitude of the signal at the current value and of a fourth amplitude of the signal at the possible frequency value from the level 1 discrete Fourier coefficients; 5iii) as long as the calculated fourth amplitude is greater than the calculated third amplitude, replacement (511) of the current value by the possible frequency value, decrementation (511) of the possible frequency value of the said third set by 0.001 and reiteration of the sub-step 5ii); 6) Making the third frequency value sought correspond (507; 512) to the last current value at the end of sub-steps 4) or 5) for which the comparison is positive.

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

8. Method as claimed in any one of the preceding claims, characterised in that the first step (100) of sampling and weighting of the said signal includes weighting by a Hanning-type window. 27

9. Method as claimed in any one of the preceding claims, characterised in that the said periodic signal is constituted by an input signal of an electricity meter in a electrical power distribution network at a fundamental frequency close to 50 Hertz or 60 Hertz.

10. Software product intended to be implemented by a microprocessor or microcontroller, characterised in that it carries out the method as claimed in any one of Claims 1 to 9.

11. Electricity meter (1) receiving a voltage between at least one phase and one neutral as well as phase and neutral currents of an electrical power distribution network, characterised in that it includes anaogue/digital means (10) for conversion of the phase voltage and currents, a microcontroller (12) and software means (11) for implementing the method as claimed in any one of Claims 1 to 9 for the determination of the fundamental frequency of the voltage and the phase and neutral currents.