The present invention relates to a method for the determination of illegal connection or tampering of meters of a power line.

More precisely, the present invention relates a method which allows to detect any fraud on a power line, or any loads connected to the electrical line without the presence of a counter, and/or individual tampered or malfunctioning counters, by statistical analysis and processing of the measured data, taking into account the equations of power on the line.

Prior art

Systems are known to measure energy losses on electrical lines.

To the inventors, no methods are known to determine whether these losses are due to the illegal connection to the electric line or to individual tampered or malfunctioning counters, nor methods for associating the losses to specific counters are known.

The object of the present invention is to provide a method for the determination of non-technical losses in a power line which solves the problems left open by the prior art.

An object of the present invention is to provide a method and a system for the determination of tampered or badly working counters and direct sockets, without counter, in a power line, according to the annexed claims, which form an integral part of the present description.

The invention will be now described, for illustrative but not limitative purposes, with particular reference to the figures of the accompanying drawings, in which:

- Figure 1 shows an overall flow chart of the method;

- Figure 2 shows a detailed flow chart of what is indicated as block C in figure 1 ;

- Figure 3 shows an example of a system that implements the method of the invention. Detailed description of examples of the invention

The invention is based on the analysis of data collected on the electrical grid through the usual electricity meters and other line electrical parameters meters (by electricity meters it is understood electronic meters or electric meters).

By electrical line it is to be understood not the whole electrical grid, but a single branch of it.

The aim of the method is to determine a confidence on the measures of individual counters, and on the assumption of an illegal connection with respect to the measure, deemed reliable, of the total energy on the line, taking into account the energy losses due to the Joule effect.

The meter normally operates in the following way:

it detects current, voltage and phase angle of the power line; it performs the product between current, voltage and phase angle, it integrates said product in time and gets a measure of energy, amnd makes it visible on the terminal. What one wants to get, after having applied the method of the invention, it is the identification of electrical losses of a power line in terms of energy; however, the method works both in case that its input data are expressed in terms of power, and in case they are expressed in terms of energy.

In practice, it is easier to work on the input data in terms of power, and convert all into input energy at the end of the calculations performed by the algorithm. Ideally, every time t, the total introduced on the line, once the dispersion by the Joule effect is subtracted, should be equal to the sum of the consumption measured by the individual counters, then for N counters, in a balanced line, we expect wherein P, _N (T) is the total power fed into the line, d _med is the average percentage dispersed by the Joule effect and P _t (T) is the power measured by the /-th counter.

If one is working in terms of energy, the formula becomes, in an equivalent manner:

N

1

wherein E _1N = P _m (t)di is the total energy input on the line, d _med is the average percentage dispersed by the Joule effect and E- = P, (t)dt It is the energy measured by the /-th counter.

In the following, we will describe the method with reference to the input data expressed in terms of power, being understood that, wishing to work with input data expressed in terms of energy, simply replacing the powers with the integrals of the powers in the time domain, or with their energies, will be sufficient.

In real cases, therefore, the power balance of a line cannot be realized, either because of measurement discrepancies for individual counters, or due to illegal connection, which are present on the line and not counted by the individual counters, or for any discrepancy of the dispersions due to the Joule effect compared to what theoretically expected for the line. The first of these effects is described by a multiplicative factor, the time-dependent ki(T), relevant to each counter. This proportionality factor is a confidence in the measurements obtained by the /-th counter and is close to 1 when the counter detects the actual power consumption.

The second effect, i.e. illegal connection, is described by an unknown function P _dir (t)Q(t), wherein Q(t) is the contribution of illegal connection to be estimated in advance. The factor P _dir (T) is 0 when the illegal connection is absent. The change compared to the dispersion provided by the Joule effect, is described by a factor dependent on the time Aft), which is equal to d, _md in the case that the dispersion is actually the one predicted theoretically. With these corrections, the above equation is rewritten as

( =∑ *, (to (t)+ p _lllr (t)Q(t) ⁺ )Pm (0

wherein the unknowns of the problem are the functions kj(T), PdirfT) and A (t). The equation can be simplified by replacing the unknown functions with unknown values k _h P _dir and A, which are constant over time. These values, as will be clearer in the following, can be held constant piecewise:

The measures are considered discrete, i.e. carried out in successive instants of time, during which the values P _lN of power, entered on the line are measured or consumed by each counter P with respect to the previous instant. In this way, said M the number of measurements taken, the previous equation is replaced by a system of M equations (one for each instant _, / = /, ... ):

The number of unknown parameters of such a system is N+2 (the N parameters k which are the multipliers of the contribution by the N counters, the parameter P _dir related to any illegal connection and the parameter which takes account of the dispersions by Joule effect).

A rough estimate of Q _j can be obtained from equation (1 ) by making Qi explicit with respect to the parameters and values of P _lN and P, and setting for the unknown parameters the ideal values A¾ = 7, P _dir = 1 and A = 0. In this way, one gets a first estimate Q _j ' , defined as the total shortfall between the power fed on the line and the total resulting from the sum of the individual counters consumption:

This estimate, and similar estimates, are always function of P _IN and P they cannot be used directly in the equation (1) since, by construction, the latter would be automatically balanced from the values used to derive Q _j ' . We extract, instead, from this estimate, a significant contribution, which cannot be considered noise in the measurement signal, for example by applying a filter on the values of Q , thanks to which, once average and standard deviation of Q are respectively indicated by μ and σ, one gets Q _j by setting to zero all the values of O below a threshold μ+sa , with s> 1, e.g. s = 3. The estimate of Q _j , in the course of the application of the method, is then possibly refined with the equation (9) and the subsequent filter.

The thus constructed system, is an over-determined system of linear equations if the equations are linearly independent and if M > N + 2. In the following, it will be clear that the method is statistically more significant when M is bigger than N by approximately an order of magnitude.

For over-determined systems such as the one shown in equation (1), it is not said that there are exact solutions, but we can look for solutions that best approximates the balance equation, i.e. we indicate the generic solutions of a system of equations z _j = 0, wherein as: wherein h is the definition interval of parameters k,, P _dir and A which is to be constructed closed and limited in such a way to guarantee the existence of at least one solution to the problem described by the equation (3). I _k It is a characteristic of the used model. By definition, the parameters ki are multiplicative, indicating that non-technical losses are presumed to be proportional. The limits of these parameters express confidence about the measurement characteristics of the individual counters. If it is assumed that the single meter cannot measure a power greater than the amount actually consumed, we define a minimum k _m = 1. Similarly, if it is assumed that a tampered or malfunctioning meter cannot measure less than 1/10 of the actually consumed power, we define a maximum k,u = 10. For P _dir the definition range limits are by construction P _dirm = 0 and P _dirM = 1 , for estimate (2), or P _dirM = 2 for estimate (9). For A, the limits are given by those theoretically expected for the electric line under examination, termed d _mi „ and d _max , respectively the minimum and maximum dispersion percentage provided by the Joule effect on the line, the definition of the boundaries of A are A _m = d _min and A ' _M = d _max , but such limits can be extended by placing A ' _m = 0 or A _M = 1. The thus defined minimum and maximum values of k, P _dir and A represent the interval of definition I _k .

With these definitions, for an equation of the type (3), we can assure the existence of a solution, but we cannot define a priori its uniqueness, which should be assessed on a case by case basis. In fact, a crucial point of the method is that, by neglecting the solutions of the problem and seeking, rather, information on the likelihood that k _h P _dir and A may deviate from ideal values (1 , 0 and d _med ), one can get around the theoretical limit and neglect the problem of the uniqueness of the solution.

To obtain an indication of probability on deviations from the ideal values of the parameters, we can divide the problem in a number L of elementary units, by subdividing the matrix associated to the equation (3) in L submatrices, each still containing a number of equations NUM such to being able to be, hypothetical^, over-determined or at least determined, i.e. NUM > N + 2, and use the distribution of the solutions of L units to estimate the deviations from the ideal values of the parameters (in this case the number of functions z _} is equal to NUM). It should be, therefore, that the number of units and the resulting solutions are in sufficient numbers to be significant in statistical terms, i.e. L > about 10. The division of the problem into elementary units, besides providing subsequently a distribution of the parameters, allows, as anticipated, to operate on a piecewise linear system, in which the unknown parameters are to be considered the average values for each single unit of the unknown functions Kj(T), Pdi _r ( ) and A(t), better approximating a possible non- constant trend of these parameters. Moreover, the distribution in L smaller dimension problems allows a reduction of the computational costs and an easy implementation of the method by parallel algorithms.

Given the set of values thus obtained for each counter , we can describe the distribution by statistical indicators, such as using various kind of momentums and quartiles.

We define a momentum feature of order m for a discrete set of n values x _; and average μ as (other definitions are possible):

1 "

momento(m, x, )= -∑(*, - μ„, )"' (4) n I , wherein μ„= 0 for m≤l and μ _η = μ for m>l. With this definition, the zero- order momentum is always 1, the first-order momentum corresponds to the average μ of the set, that of order 2 to the variance er ² , the higher orders are related to the skewness (m = J) and to the kurtosis (m = 4), etc. The quartiles are the values that divide the set into four parts of equal amount, they are five values that mark the 0% {q,), 25% (q ₂ ), 50% (q ₃ ), 75% (q ₄ ) and 100%) (q ₅ ) of the set, q ₃ is commonly termed the median, the difference q ₄ - q ₂ is the interquartile range, which is a measure of the dispersion of the values, and the values q, and q ₅ are the minimum and maximum. We define the w-th quartile function for a discrete set of values xi (with m ranging from 1 to 6) the six values (other definitions are possible):

At the end of the calculation, as long as one always choose an only a value in each of the L units for each of the N + 2 parameters (also in the case that for the above unit the solution is not unique), through the two functions defined in (4) and (5) we can obtain an indication of the probability that the single counter z ^' -th is malfunctioning or tampered, as described below.

We use equation (4) to describe the measured values of the individual counters P i.e. we build up a set S (even positive integer) of indicators (Gi) _m , besides (G,) ₀ ≡l, for each counter , with momentum (m, (Pj) _j ) {m = 1, .5/2), and to these we add the corresponding relationships between the same (G) _m and the related momentums calculated for P^. For each of the S indicators, we choose in advance a weight g _m . For example, if one wantas to use the only media to statistically describe the values of the Pj, given S = 4 indicators (Gj) _m , we will define g _m = (0, 0, 1, 0, 0), w = 0, ... 4.

This makes it possible to use a single scalar value ∑ ^» '=<> , associated to each counter /, to describe the statistical weight. We describe the distribution of values obtained for the parameters k _h i.e. we build a set of T indicators ¾)„„ besides (Hj)o≡l, with T positive integer and m = 0, ... T, which contains values obtained by the equations (4) and (5). For each of the T indicators we choose in advance a weight h _m to be used as the previous g _m to obtain a single scalar value representative of the statistical weight of the distribution of k _t for the z ^' -th counter.

Given the so constructed indicators (¾)„, and (Gj) _m , it is possible, with a weight function ^ ¹ · °·' which can for example take the form: to reorder the counters for decreasing confidence, so that the value of / is greater for those counters for which k is probabilistically more distant from / and which are also more significant as the average of P In other words, we define a new index c _u which indicates the counter of the sequence of values of /(/,G„ Hi), ordered in such a way that f(c _} ,G _el , H _cl ) > f(c ₂ , G _c2 , ¾)> ...> f(c _N , G _N , H _cN ) (7)

Once the counters are ordered by confidence, we can point to at least the first w ₀ counters in the list as "to be checked" in such a way that this number w ₀ entails the maximum gain downstream of the checks with the minimum number of necessary checks, via a suitable maximum gain function C (w) defined as c{w )= w (M> y h (y (w B ) (8) wherein B is the shortfall percentage on the line given by

in which (Gj) _S /2 ₊ i corresponds, as defined, to the average value of the measures of the -th counter in relation to the average value of the input power PIN (here S is meant as an even integer, but in general can also be odd, and then one uses (Gj) _a with a an integer such that the above relation is selected), W (w) is a function defined as a non-decreasing or a function of the sum of the contributions of the first w counters taken in the order defined by (7); k' _cu is a function of the values of the statistical indicators of k, obtained for each counter, in particular the standard deviation of the median or mean from the ideal value /, or the same mean and median; Y(w) is a cost function, increasing in w, for which some simple expressions are (but other expressions are usable with similar effectiveness):

Y(w) = w/ N

or

Y(w) = Z(w/ N) + B where Z = W (N), with W(w) as previously defined, and B is the percentage shortfall.

In addition:

The function C(w) is highest in w ₀ when such a number of counters balances the initial shortfall and does not involve an excessive growth of Y(w). It is here to be specified that with w ₀ the method identifies the minimum number of faulty meters, but nothing impedes to go checking the next n counters of the sequence (7) (n is a positive integer).

In addition to statistical considerations on the obtained values of P _di we can define a confidence on the likely presence of illegal connection. For example, building up a dichotomous distribution with the obtained values of Pd _ir , and defining "absence" (0) the illegal connection in cases where P _dir = 0 and "presence" (1) in the other cases. With this definition, termed n the number of "presence" cases, we expect a binomial distribution with a probability of "presence" p=n/L, and with this construction, given the obtained dichotomous values, we perform a hypothesis test obtaining a confidence result on the presence of illegal connection.

In detail, the method is applied as described in Figures 1 and 2 and explained in the following. Initial data: M measures for each of the N counters on the line and M measures for the total power input on the line are given.

Fixing the initial values: the minimum, average and maximum dispersion theoretical contribution (Joule effect) (percentage of the total entered on the line) d _mil1 , d _me(l , d _max , the vector of weights g _m of the general parameters of the distribution of the individual signals (GJ _m , the vector of weights h„, of the parameters of the distribution of elementary signals (Hi),,,, any Lagrange multipliers and associated constraint parameters to be used in a more complete version of the equation (3), and the existence limits of the unknown parameters k _h P _c n _r and A to be used in (3).

The data are supposed as collected in column for each single counter, defining a matrix D in which the column index corresponds to the single counter and the row index to the single time measurement.

Referring to Figure 1 (block A), it is indicated with P, the vector consisting of the -th column of the matrix D (containing N columns) obtaining the vector of the likely direct connections as defined in equation (2)·

By assumption, the technical losses (Joule effect) are proportional to the input power P _IN , so it is possible to complete the matrix with a column comprising the technical losses proportional to P _m and a further column O with values proportional to any non-technical losses (illegal connection).

Referring to Figure 1 , block B, splitting the data into elementary units. Calculating the number NUM of rows of the said matrix D so that NUM> N + 2 and divide the matrix in L submatrices (L * NUM <= M).

Referring to Figure 2, block C1 , solving the minimization problem described with the equation (3). In the case of non-unique solution, choosing only one. Referring to Figure 2, block C2, checking the obtained value of direct connection with a statistical evaluation on the extent of non-technical losses (illegal connection) given by P _dir and technical losses (Joule effect) given by A. In its assessment, performing a hypothesis test to determine whether what has been obtained as a direct drive can be considered a true signal or just noise. Also determining whether the value of technical losses is compatible with what is theoretically expected.

Referring to Figure 2, block C4, in the case where the direct connection is likely (technical losses above the theoretical threshold or signal not conceivable as noise), recalculating the vector Q with a less conservative mode, by making a new estimate O" using also the values of kj and A just obtained, for example with the following expression:

Q"rM _J -∑k,P _l - A(P _m ) _j (9)

; 1

Filtering this estimate as done with the previous, for example by applying a filter on the values of Q" thanks to which, termed μ and σ, respectively, average and standard deviation of <9" one obtains Q _j by setting all the values of Q"- below a threshold μ + s'a, with 0 <s' <s, e.g. s' = J, where s is the threshold value used to filter the previous estimate (2).

Referring to Figure 2, block C3, in the case the direct connection is unlikely, resetting the vector 0 and considering the contribution of direct connection (? _<¾ -= 0) as absent.

Referring to Figure 2, block C5, solving again the problem of the minimum described with the equation (3). In the case of non-unique solution, choosing only one of them.

Referring to Figure 2, block C6, choosing the minimum solution, i.e. the one that best approximates the balance equation, between those obtained in the previous blocks C1 and C5.

Referring to Figure 1 , block D, analyzing the individual solutions and describing them with statistical and quartiles moments, i.e. calculating the parameters (Hi) _m as described in the equations (4) and (5). Referring to Figure 1 , block E, ordering with the weight function (6), or building a new sequence c _u for the counters, so that they are ranked by decreasing probability to deviate from the ideal value of k _cu , as described in (7).

Referring to Figure 1 , block F, calculate the maximum w ₀ Equation (8), which indicates the minimum number of the first counter of the new sequence to be indicated as suspects.

Referring to Figure 1 , block G, transforming the values of P _dir obtained in the L units into a dichotomous sequence of presence/absence of illegal connection and evaluating, by a hypothesis test, the probability of illegal connection, as previously defined.

Application example

Given a series of 96 measurements on a power line that supplies power to three consumptions Pi, P , P3, the measurements on individual counters and on the line meter P _/iV are shown in the following table.

P I P2 P3 Pin u P I P2 P3 Pin PI P2 P3 Pin

I 448 344 144 936 33 1 2 216 272 620 6 652 216 J 111 984

8 4 296 1 0 1300 34 1 12 120 164 396 60 036 204 92 932

3 856 161 I SO 1 2O0 35 308 220 168 696 67 688 2 1 11 1 1036

4 168 .1 ⁽ 1 948 36 876 204 124 704 68 75° 140 .164 1056

5 684 204 136 1024 37 220 204 136 560 09 92.8 64 160 1152

6 71 268 132 1 116 38 1 6 144 160 480 70 520 64 1 6 740

7 480 260 128 868 39 420 64 168 652 71 420 64 148 632

8 268 260 128 650 40 352 64 136 552 72 304 208 164 676

9 118 216 92 456 41 1 6 64 164 364 73 404 212 160 776

J O 524 S4 1.28 736 42 216 212 164 592 74 812 204 164 .1 180

.1.1 472 04 124 600 43 160 212 168 540 75 592 210 140 948

12 408 64 120 652 44 41 2 208 140 760 76 724 224 1 4 1 132

13 476 172 96 744 45 408 196 156 760 77 1004 144 216 1364

11 380 216 121 720 10 296 61 161 521 78 2528 152 100 2810

15 208 208 128 544 47 1 76 64 144 381 79 3000 1 8 140 326S

10 300 204 1 16 620 48 356 64 104 524 80 2270 288 1 2 2716

17 228 184 96 508 49 676 156 96 928 1 2304 344 168 2816

18 172 64 .128 304 50 648 212 116 970 82 1 152 524 164 1840

19 470 64 124 664 51 492 208 120 820 83 1 152 548 140 1840

20 292 64 1.16 472 52 52 204 1.1 868 84 7.10 544 152 14.12

21 296 180 104 580 53 508 1 1 2 708 85 764 1296 100 2220

22 368 21.2 124 704 54 660 64 116 840 86 556 596 1.24 1276

23 352 204 128 684 544 64 1 16 724 87 808 252 96 1 156

24 60 204 136 400 56 472 8 116 670 88 1220 200 120 1540

25 176 88 1 6 4 0 7 330 224 100 660 89 1 164 316 124 1.904

26 250 64 2.16 536 58 392 208 100 700 90 1468 388 124 1980

27 312 60 224 596 59 6.1.6 208 120 944 91 1444 392 96 1932

28 288 1 4 264 676 00 584 170 116 876 92 1 168 396 168 1732

29 504 212 108 884 61 576 68 108 752 93 1 128 372 172 1072

.10 472 208 184 804 62 852 64 96 1012 94 956 320 1 8 1424

31 60 1 204 176 084 63 720 64 1 0 904 95 152 228 104 784

32 492 140 1 78 ⁽ 1 64 650 168 1 0 944 96 50;- 232 132 872

On the basis of these data, we perform the following steps:

1 . Figure 1 Block A. We use as minimum and maximum values k _m = 1 , KM = 10 for counters and P _dirm = 0, P _dirM = 1 and A _m = 0.06, A _M = 1 respectively for P _dir and A. We set the minimum, average and maximum dispersion of the line (A) d _mi „= 0.06, d _med = 0.07, d _max = 0.08. In this simplified case, we will use the only median as weight of values (Hj) _m , then we will have a single value H corresponding to the median of the values calculated for each counter and only one value h„,= 1. Even for the vector (Gj) _m , we will use only 2 values: the 0 order moment, by definition (G,) ₀ =l and (Gj)i as ratio between the averages of the values of (P^ and (Pm) _j , which on the basis of the previous table are

0. 12. For the construction of the weight function (6), we will use only the first of the two values, consequently g _m = (1.0) , we will use the second only in the maximum gain function. We calculate the likely direct connection by first defining a vector Q as the difference between the amount detected by the meter (or "power meter") (P _m ) and what is the sum of the individual counters:

2. for Q _j ' we calculate the average (μ = 240.08) and the standard deviation (σ = 309.46);

3. we build up a new vector Q _j = Q', if and only if O > μ + 3σ, otherwise (¾ = 0 this vector is an estimate of non-technical losses for illegal connection.

4. By assumption, the technical losses (dispersion by Joule effect) are proportional to the input power, so we can build up a matrix comprising columns P„ a column including possible illegal connections Q and technical losses proportional to _/ , _v :

D = (P, P ₂ P ₃ QP _IN )

5. Figure 1 block B. We divide the matrix D into L = 8 submatrices of M = 12 measures. For example for the second and the third sub-matrix we obtain:

PI P2 P3 Q Pin I P2 P3 Q Pin

476.00 1 2.00 96.00 0.0!) 76.76 176.00 88.00 176.00 0.00 508.46

380.00 216.00 124.00 0.00 860.07 256.00 64.00 216.00 0.00 607.76

208.00 208.00 128.00 0.00 059.98 31 2.00 60.00 224.00 0.00 677.07

300.00 204.00 116.00 0.00 744.93 288.00 124.00 264.00 0.00 916.33

228.00 1 S4.00 96.01) 0.00 614.82 504.00 212.00 168.00 0.00 1040.90

1 72.00 64.00 128.00 0.00 419.23 472.00 208.00 184.00 0.00 101 6.50

476.00 64.00 124.00 0.00 756.49 604.00 204.00 176.00 0.00 1176.48

292.00 64.00 1 16.00 0.00 541 .21 492.00 140.00 148.00 0.00 905.86

296.00 180.00 104.00 0.00 694.22 132.00 216.00 272.00 0.00 739.80

368.00 212.00 124.00 0.00 883.62 1 12.00 1 0.00 104.00 0.00 505.23

352.00 204.00 128.00 0.00 81 .20 308.00 220.00 168.00 0.00 969.62

60.00 204.00 1 6.00 0.00 496.69 370.00 204.00 124.00 0.00 838.88 6. For each of the 8 sub-matrices, we apply the method described in the flow chart in Figure 2, that is, we find the corresponding coefficients k fa, fa, fa = di fa = A solutions of the system of equations:

then we check if what is obtained as a direct connection is acceptable in terms of randomness (i.e. that can not be considered noise), or that the value obtained for the technical losses (leakage by the Joule effect) does not exceed the maximum allowed d _max . In the positive, we recalculate with a less conservative direct connection, as in equation (9), also by relaxing the constraints on k, in the negative we recalculate without direct connection (¾„■= 0). Finally we accept, as useful values k, those values that make minimum the function in (3), among those calculated in the previous steps. For the second sub-matrix, we obtain a non-acceptable or absent value for direct connection, then we recalculate the equation by eliminating the contribution of direct connection. For the third sub-matrix, initially we obtain the vector 0 given in the table, then, once the limits have been relaxed, we obtain for Q the new values:

Q = (0; 0; 0; 121.76; 0; 0; 0; 0; 0; 0; 124.37; 0) with which the minimum is recalculated and accepted.

7. Figure 1 block D. After processing the 8 sub-matrices, the folowing is obtained: Kl K2 K3 Pdir A

1.05 1.30 1.00 0.80 0.07

1.05 1.31 1.00 0.00 0.06

1.05 1.28 1.00 1.05 0.07

1.01 1.25 1.00 1.01 0.09

1.05 1.29 1.01 0.00 0.07

1.05 1.31 1.00 0.00 0.06

1.11 1.22 1.00 1.19 0.06

1.00 1.41 1.00 1.20 0.12 from which we get the following values of (H,)i (Median) for each counter:

(Hi) 1 05, (H ₂ )i= 1.29, (H ₃ ),= LOO.

8. Figure 1 , Block E. We construct a weighting function as in (6). In this simplified case, for the chosen values of h _m and g _m , the weight function is identically equal to the median. As in (7), we construct a new sequence c„ for the counters: c„ = {2,1 ,3}

9. Figure 1 block F. Once the maximum gain function is defined as in (8):

C (w) = W (w) - h (Y (vv) - B) so that such function is maximum when the gain probability with the minimum number of tests, wherein:

a 1 wherein k' in this case corresponds to the median of the values of k found in every elementary unit for the single counter, and

For the function C(w), we get the following values:

w C(w)

1 0 2

2 0.23

3 0.01

The maximum of C(w) is obtained in correspondence of w ₀ = 2, then we accept tampered and/or malfunctioning meters P ₂ and Pi as probable, in the order.

10. Figure 1 , block G. The non-negligible values of direct connection (illegal connection) visible in the table in point 7, in five of the eight sub- matrices, are also indicative of a probable connection without counter. From these values, one obtains a dichotomous sequence 0 (absence), 1 (presence) of illegal connection:

(1 ,0,1 ,1 ,0,0,1 ,1)

Wherefrom one derives an estimated value of illegal connection probability p = 5/8 = 62.5% for a binomial distribution.

EXAMPLE OF SYSTEM REALIZING THE INVENTION

Referring to Figure 3, in a power line 50 (last part of the grid 55) to which N consumptions 10 are connected, an input power meter (40 line meter), downstream of the line transformer 45, is inserted. The data of the individual consumption Pi, detected by the N counters 20 relevant to the consumptions 10, and of PIN (total introduced on the line), detected by the line meter 40, are collected in 60 and optionally stored in a centralized database 70. The collected data can be aggregated to defined time intervals and processed using the method described. If the database 70 is present, the data can be extracted in 80 and in any case they are processed by a central processor 90 to provide the result 95.

The method and system 100 of the invention provide, in 95, indications about the presence of illegal connection and the possible tampering or malfunction of individual counters, or it ranks the entire line as balanced (absence of illegal connection and tampered or malfunctioning meters) .

ADVANTAGES

By the method of the invention, it can be determined, with a minimum cost of the measurement data collection, where there are consumption anomalies in the electrical grid. The distinguishable anomalies are on one hand the likely presence of illegal connection to the grid, and, on the other hand, the likely presence of a malfunction or a tampering of the single counter.

In this way, the grid operator may intervene in order to verify the prediction of the method without having to make a huge campaign of checks and to solve the anomalies with different methods depending on the case.

This, in turn, allows to save activities of technicians and to ensure the correct payment from users.

In the foregoing, preferred embodiments have been described and variants of the present invention have been suggested, but it is to be understood that those skilled in the art will be able to make modifications and changes, without thus departing from the related scope of protection, as defined by the attached claims.