Note: Descriptions are shown in the official language in which they were submitted.
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Method for the determination of illegal connection or tampering of meters
of a power line
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.
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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
Ptri(t)= 1),(1 ) Iõ,ed Pirr(t)
,
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wherein P,(7) is the total power fed into the line, dmed is the average
percentage dispersed by the Joule effect and P,(7) is the power measured
by the i-th counter.
If one is working in terms of energy, the formula becomes, in an
equivalent manner:
EIN =EE1+dõ,õ11Ens,
,
wherein El, -=.1./3,,Och is the total energy input on the line, dined is the
average percentage dispersed by the Joule effect and E,= SP,(t)dt It is
the energy measured by the i-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 k,(7), relevant to each counter.
This proportionality factor is a confidence in the measurements obtained
by the i-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 Pthr('t)Q(0, wherein ON is the contribution of illegal
connection to be estimated in advance. The factor Pdõ.(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 A(i), which is equal to dmed in the case that the dispersion is actually
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the one predicted theoretically. With these corrections, the above equation
is rewritten as
1'IN(1)= Ek,(i)P,(1)+ Pd,02(o)-1" AOPIN(t)
,
wherein the unknowns of the problem are the functions k(J), Pd,,(1) and A
(0. The equation can be simplified by replacing the unknown functions with
unknown values k,, P di,- and A, which are constant over time. These values,
as will be clearer in the following, can be held constant piecewise:
PIN(t).= P; PA.Q0+ API NO
,
The measures are considered discrete, i.e. carried out in
successive instants of time, during which the values P IN of power, entered
on the line are measured or consumed by each counter Pi, 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 j = 1, ...
(N) =Ek,(P),+ *INA (1)
i
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 Pdir related to any illegal connection and the
parameter A which takes account of the dispersions by Joule effect).
A rough estimate of Of can be obtained from equation (1) by making
Q., explicit with respect to the parameters and values of Pm, and P, and
setting for the unknown parameters the ideal values ki = I, Pdõ.= 1 and A =
0. In this way, one gets a first estimate 01.,, defined as the total shortfall
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between the power fed on the line and the total resulting from the sum of
the individual counters consumption:
Q1,= (PIN), ¨Z(19,), (2)
r I
This estimate, and similar estimates, are always function of PIN and
Põ 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. 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 y and a-, one gets g
by setting to zero all the values of O'j below a threshold ti+sa , with s> /,
e.g. s = 3. The estimate of g, 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 z3= 0, wherein
zj =Zk,(1),),+ Pdõ-Q,-F
as:
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arg min { E Pch,Q, *IN), (PrN)j (3)
KiPdirAEIk
wherein 4 is the definition interval of parameters k,, Pd,,. 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). Ik It is a characteristic of the used model. By definition, the
parameters
k, 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 kõ,--= 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 = 10. For
Pchr the
definition range limits are by construction Pdirm = 0 and Pchnlf = 1, for
estimate (2), or P
- &Hi ¨ 2 for estimate (9). For A, the limits are given by
those theoretically expected for the electric line under examination, termed
and dmax, respectively the minimum and maximum dispersion
percentage provided by the Joule effect on the line, the definition of the
boundaries of A are Aõ,= dmm and A' m= dmax, but such limits can be
extended by placing = 0 or Am =
I. The thus defined minimum and
maximum values of k, Pchr and A represent the interval of definition
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 kõ Pdir and A
may deviate from ideal values (1, 0 and dmed), 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)
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in L submatrices, each still containing a number of equations NUM such to
being able to be, hypothetically, 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 /0. 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 K,(T), Pd,r(T) and AN, 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 k, thus obtained for each counter i, we can
describe the distribution by statistical indicators, such as using various
kind of momentums and quartiles.
We define a momentum feature of order in for a discrete set of n
values x, and average as (other definitions are possible):
momento(m, x,)= ¨ E (x, - (4)
nil
wherein põ,= 0 for m5/ and Aim= it for m>/. With this definition, the zero-
order momentum is always /, the first-order momentum corresponds to the
average y of the set, that of order 2 to the variance 0-2, the higher orders
are related to the skewness (m = 3) 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 I), 25% (q2), 50% (q3), 75% (q4) and
100% (q3) of the set, q3 is commonly termed the median, the difference q4-
q2 is the interquartile range, which is a measure of the dispersion of the
values, and the values q I and q3 are the minimum and maximum. We
,
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define the m-th quartile function for a discrete set of values xi (with m
ranging from 1 to 6) the six values (other definitions are possible):
quartile(m, x, )=ql,q2,q3,q4,q5 , ___________________ 1
}
{
(5)
q4 ¨ q2
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 i-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 (G)õõ besides (G)oa"-1, for each counter i, with (G,),õ= momentum
(m, (P)) (m = I. .S/2), and to these we add the corresponding relationships
between the same (G), and the related momentums calculated for PIN. For
each of the S indicators, we choose in advance a weight gõ,. For example,
if one wantas to use the only media to statistically describe the values of
the Pi, given S = 4 indicators (G)õ, we will define g,õ= (0,0,1,0,0), m = 0,
... 4.
vs , ,\
This makes it possible to use a single scalar value L nr. -13' 6mµir:L' i, ,
associated
to each counter i, to describe the statistical weight. We describe the
distribution of values obtained for the parameters kõ i.e. we build a set of T
indicators (11),5, besides (1-4)0-------1, with T positive integer and in = 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,õ to be used as the
previous g, to obtain a single scalar value representative of the statistical
weight of the distribution of lc, for the i-th counter.
Given the so constructed indicators aldm and ('Wm, it is possible,
with a weight function f (i'Gi'lli) which can for example take the form:
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( r
f(i,G,,H,)=(Zgõ, (6,),õ E hõ, (H,)õ, (6)
m 0 P.,m 0
to reorder the counters for decreasing confidence, so that the value off is
greater for those counters for which k is probabilistically more distant from
I and which are also more significant as the average of P,. In other words,
we define a new index cõ which indicates the counter of the sequence of
values off(i,Gõ H,), ordered in such a way that
f(cõ..,Gdo Ha) (7)
Once the counters are ordered by confidence, we can point to at
least the first Ivo counters in the list as "to be checked' in such a way that
this number Ivo 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(w)-h(Y(w)-B) (8)
wherein B is the shortfall percentage on the line given by
B=(i- dmed)-E(G,)sõ..,
in which (Gd5,2f-/ corresponds, as defined, to the average value of the
measures of the i-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 (G)a with a an integer such that the above relation
is selected), W(w) is a function defined as a non-decreasing
W(w)= Ek' (G,
cu 2u)S 2 = I
n I
or a function of the sum of the contributions of the first w counters taken in
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the order defined by (7); k',õ 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 1, 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)= N
or
Y(w)= Z(14) I N)+ B
where Z = W (N), with W(w) as previously defined, and B is the percentage
shortfall.
In addition:
, {x
h(x)=
0 x < 0
The function C(w) is highest in wo 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 wo 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 Pau-,
we can define a confidence on the likely presence of illegal connection.
For example, building up a dichotomous distribution with the obtained
values of Pthr, and defining "absence" (0) the illegal connection in cases
where Pth,.= 0 and "presence" (I) 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
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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) dim, dmed) dnical the vector of weights g,õ of the
general
parameters of the distribution of the individual signals (G)õõ the vector of
weights hi, of the parameters of the distribution of elementary signals aid.
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, Pd,,. 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 Pi the vector
consisting of the i-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/\., so it is possible to complete the matrix with a
column comprising the technical losses proportional to PIN and a further
column 0 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 Cl, solving the minimization problem
described with the equation (3). In the case of non-unique solution,
choosing only one.
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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. 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 0" using also the values of
k, and A just obtained, for example with the following expression:
Q", = (PO, - *IN), (9)
1 I
Filtering this estimate as done with the previous, for example by
applying a filter on the values of Q",, thanks to which, termed Ai and cr,
respectively, average and standard deviation of T., one obtains Qj by
setting all the values of Q", below a threshold At + s'u, with 0 <s' <s, e.g.
s' =
/, 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 Q and considering the contribution of direct
connection (Pdx,.= 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 Cl 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 (H)õ, as described in the equations (4) and (5).
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Referring to Figure 1, block E, ordering with the weight function (6),
or building a new sequence cõ for the counters, so that they are ranked by
decreasing probability to deviate from the ideal value of km, as described
in (7).
Referring to Figure 1, block F, calculate the maximum wo 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 Pthr
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 P1, P2, P3, the measurements on individual
counters and on the line meter Pi ,v are shown in the following table.
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I PI P2 P3 Piu 1 PI P2 P3 Pt 77 PI P2 P3 Phi
1 I 4-18 :144 144 9:16 :13 I 132 210 272 620 65
652 216 119 9$4
2 I 824 296 180 1300 34 I 112 120 164 396 60 636 204 92 932
3 1 856 161 180 1200 35 308 220 100 696 67 688
201 141 1036
4 600 168 180 948 30 :176 204 124 704 08 752 140 104 1056
604 204 136 1024 37 220 204 136 560 69 028 64 160 1152
6 710 268 132 1110 38 176 144 100 480 TO 520 64 156 7411
7 480 260 128 868 39 420 64 168 652 71 420 04 140 632
0 268 260 128 050 40 352 64 136 552 72 304 208 164 676
9 148 216 92 456 41 136 64 164 364 73 404 212 160 776
524 04 128 730 42 210 212 104 592 74 812 204 164
1 ISO
11 472 6-1 124 660 43 100 212 168 540 75 592 216 140 948
12 -168 64 120 652 44 412 208 140 760 70 724 224 104 1132
13 476 172 96 744 45 408 196 156 760 77 1004 144 216 1364
11 380 216 121 720 16 296 61 161 521 78 2528 152 160 2810
19 208 208 128 544 47 176 64 144 304 79 3000 128 140 3260
6 300 204 116 620 48 356 64 10-1 524 80 2276 260 152 2716
17 228 184 96 508 49 076 156 96 928 81 2304 344 108 2816
18 172 64 128 364 50 648 212 116 976 82 1152 524 164 18-10
19 476 04 124 60-1 51 402 208 120 820 83 1152 54-8 14(1 1840
202 64 116 -172 52 552 204 112 868 84 710 544 152 1412
206 I8O 104 180 53 500 112 OS 708 85 764 1200 160 2220
22 368 212 124 704 54 660 64 116 810 89 550 590 124 1270
23 352 904 128 684 55 544 64 116 724 87 808 252 90 1156
24 00 204 136 400 56 472 08 116 676 88 1220 200 120 1540
23 176 SS 176 4-1(1 57 336 224 100 660 09 1404 :110 124 1.904
.)0 950 64 210 536 392 208 100 700 90 140.8 388 124 19940
27 312 60 224 596 59 I 616 208 120 944 91 1444
302 96 19:32
2S 288 12-1 204 676 60 I 384 176 116 876 92
11118 :396 168 1732
21-4 , 504 912 168 884 61 576 100 732 93 112s 372 172
1672
472 208 184 864 62 052 (14 90 1012 94 956 32)) 14-, 142-1
31 094 204 17(1 084 63 1 720 64 120 904 95
452 228 1(1-1 784
32 I 492 140 148 780 0-1 I 656 168 120 944
131 508 232 132 872
On the basis of these data, we perform the following steps:
1. Figure 1 Block A. We use as minimum and maximum values kõ, = I,
km = 10 for counters and Pdirn, = 0, PdirM = 1 and Aõ, = 0.06, Am = 1
respectively for Pd,,- and A. We set the minimum, average and maximum
dispersion of the line (A) d,,,15= 0.06, dmed= 0.07, dmax= 0.08. In this
simplified
case, we will use the only median as weight of values (111)57, then we will
have a single value Hi corresponding to the median of the values
calculated for each counter and only one value hõ,- I. Even for the vector
(G,)õ,, we will use only 2 values: the 0 order moment, by definition (G)0=1
and (G,), as ratio between the averages of the values of (P,,) and Wildi,
which on the basis of the previous table are (Gth= 0.56, (G2)1= 0-17, (G3)1=
0.12. For the construction of the weight function (6), we will use only the
first of the two values, consequently gm= (1.0), we will use the second only
in the maximum gain function. We calculate the likely direct connection by
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first defining a vector Q as the difference between the amount detected by
the meter (or "power meter") (Pi,v)j and what is the sum of the individual
counters:
(P.),
2. for Q.,. we calculate the average (p = 240.08) and the standard
deviation (0- = 309.46);
3. we build up a new vector Qi = Q1; if and only if 0,- > p + 3a,
otherwise g = 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 Põ a column including possible illegal connections Q and
technical losses proportional to PIN:
D = (P1 P2 P3 QPIN)
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 Q Pin P1 P2 P3 Q Pin
476.00 172.00 96.00 OM 876.76 176.00 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
208.00 208.00 126.00 0.00 659.98 312.00 60.00 224.00 0.00 677.07
300.00 204.00 116.00 (LOU 744.93 288.00 124.00 264.00 0.011 916.33
228.00 184.00 96.00 0,00 614.82 504.00 212.00 1(18.00 (1.00 1040.90
172.00 04.00 198.00 0.00 419.23 472.0(1 208.00 184.00 0.00 1016.511
476.00 64.00 124.00 0.00 756.49 604.00 204.00 176.00 0.00 1176.48
292.00 64.00 116.00 0.00 541.21 492.00 140.00 148.00 0.00 905.86
996.00 180.00 104.00 0.00 604.29 1:32.00 216.00 972.00 0.00 739.80
368.00 212.00 124.00 (LOU 883.62 112.00 120.00 104.00 (1.00 5(15.23
359.00 204.00 198.00 0.00 816.20 308.00 220.00 168.00 0.00 969.62
60.00 904.00 136.00 (1.00 496.00 376.00 204.011 124.00 0.00 838.88
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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
k2, k3, k4 = Pd,r, k5 = A solutions of the system of equations:
k= arg minE ki(13,), *IN), - (PIN),
K k I
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 dm,. 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 (Pdõ.= 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:
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K1 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, )1 (Median) for each counter:
(I1)= 1.05, (H2)1= 1.29, (H3)1= 1.00.
8. Figure 1, Block E. We construct a weighting function as in (6). In
this simplified case, for the chosen values of h,õ and gõõ the weight function
is identically equal to the median. As in (7), we construct a new sequence
cõ for the counters:
c.õ- {2,1,3}
9. Figure 1 block F. Once the maximum gain function is defined as in
(8):
C (w) = W (1,v) - h (Y (w) - B)
so that such function is maximum when the gain probability with the
minimum number of tests, wherein:
W(w)= k' (u ), Y(w)= w I N
wherein k' in this case corresponds to the median of the values of k found
in every elementary unit for the single counter, and
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{X
B = (1¨ clined)¨Z0,),, h(x)= X 0
0 x < 0
For the function C(4), we get the following values:
C (w)
1 0.02
2 0.23
3 0.01
The maximum of C(w) is obtained in correspondence of wo = 2, then
we accept tampered and/or malfunctioning meters P2 and P1 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)
VVherefrom 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
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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.
