identification of energy theft and tampered meters using a central observer meter: a mathematical...

7/30/2019 Identification of Energy Theft and Tampered Meters Using a Central Observer Meter: A Mathematical Approach

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alternatives to indicate installations with problems justwatching the central observer and the registers of all theconsumers.The investigation of metering faults by analysis of themetering readings have already been reported in the literature[ 6 ] .Chambers,R.G. [6]shows a systematic procedure with thepurpose of discovering discrepancies between main metersand another meter readings focused on large generators. Onthe other hand, in the present paper the main target isrecognizing frauds or energy theft.

11. OBJECTIVEThe main objective of this paper is to propose a methodologythat indicates problematic metering installations. Thealgorithms developed here associate the measurements of agroup of consumers under investigation with a centralobserver meter, registering the total energy of that set ofconsumers.This method is particularly inexpensive, as it uses a singleobserver meter for a large number of consumers. In addition,the inspections of the consumers' premises by specializedteams can be better focused as the technique showed here iscapable of identifying metering installations that present verystrong probability of presenting troubles. The number ofinspections can be reduced. Therefore, this procedure is moreeffective and less costly than inspecting the whole set ofconsumers.

m. ESCRIPTIONF THE PROBLEMAs mentioned previously, our interest is to identify, in asecondary distribution network, one or more consumers wherethe energy measurement is not correct. This may occur due tothe following reasons: either the meter is tampered, that is, it isoperating out of its accuracy class, or the consumer is gettingsome energy that is not being measured (through a conductorthat bypasses the meter).To allow this identification in a cost-effective way, it will benecessary to install a unique watthour meter (central observer)close to the secondary terminals of the distributiontransformer. The methodology will be applied to the group ofmeters of the consumers that are connected to this secondarydistribution network. See Fig. 1.

IV. REDUCEDODELINGWe will admit that there are N consumers in this group andthat for each consumer there is a watthour meter that accuracyclass is m. The accuracy class indicates that the errorcommitted by the meter should be smaller than or equal to mtimes the energy actually consumed. For example, a watthourmeter whose accuracy class is -2% should produce, as aresult of the measurement of l O OW h , a value between 98Whand 102Wh.

Fig. 1 . Exemplification of the central observer meter installationWe will also admit that another watthour meter is installed in apoint where it is possible to measure the total energy suppliedto the N consumers mentioned above. This meter will becalled central observer meter (In practical terms, that metershould be installed close to the secondary terminal of thedistribution transformer). See Fig. 2., J J!!

ObserverMeterUFig. 2. Block diagram of the metering systemThus, for a certain period of time, is possible to say that theenergy registered by the central observer meter and the energyregistered by each of the N meters should satisfy the followingequation:

Where:E ~ T U energy registered by the central observer meter (itsupposes that the central observer measurement error is well-known);ki =a constant relative to the accuracy class of the meterofthe i-* consumer (if the accuracy class is 2%, for example, thevalue of ki must be between 0,98 and 1,02);Ei=energy registered by the meter of the i-*consumer;l l i 5 N .Since (1) is valid for any period of time, if we get N values ofenergy (from each of the N meters and the central observermeter) during N periods of time, the next equations should besatisfied:

Thus, admitting that the constants ki (1 I 5N ) are unknownquantities (which are related to the accuracy classes of themeters), we have a set of N equations with N unknown

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According to this method, the unknown values of amathematical model should be calculated so that the sum of Where:the squares of the differences between the measured values The expression in boldface is the error between the estimatedand the estimated values multiplied by constants that measure and the measured value of the central observerthe degree of precision, should be minimum. Expression (3 ) W(N) =a weight arrayshows the formulation of minimum least squares called P(N)=degree of precision of the measurement

qT=measurementsegression model.I =identity matrixFrequently, the matrix P is initialized with P(O)= k*I, where kis a high value constant andI is the identity matrix.For time-varying systems, it may be necessary to introduce away to reduce the influence of old values. In this situation, itcan be introduced a forgetting factorh as shown below:

(6)( ~ , N )(112) x N t = l hN-1 .E2(t)The value of h is between 0 and 1. The lower the value of A,the larger is the weight of more recent measurements, ascompared with older measurements. Recursive equations are:

y( t ) =ql.el+e. +...+pw , (3 )Where:y - observed variable;0 - unknown parameters;cp - measurements;t - time period in which the measurements were done.Quantities cp and y are measured for several instants of time.If we do not know the exact parameters, they can be estimated,obtaining expression (4).ye( t )=pI.&]+Where:&=estimated parametersy e = value of the observed variable as a function of the

+... +q,,.&, (4)0(t) =0(t-1) +Q(t).[y(t) - cpT(t).e(t-l)]W(t) =P(t).cp(t)=P(t-l).cp(t)[h +cpT(t).P(t-l).cp(t)]-lP(t) =[ -W(t).cpT (t)] .P(t-1) / h

(7)mere:estimated parameters

The problem of the least squares is to determine theIt is possible to demonstrate that minimum error is obtainedwhen:Parameters so that Y e ( t ) agrees as clOselY as possible with Y ( t ) . The application of the least squares algorithm in a set of 12was studied and the results are shown in thissection.

Where:&=array of estimated parameters;Q =matrix composed by the measurements in several instantsof time;Y =matrix composed by the observed variablesy( t ) in severalinstants of time.The squared matrix(QT.Q)should be non singular.At first, this method also needs a matrix inversion. Thenumber of lines and columns of this matrix is the same as thenumber of observations. Thus, the higher is the number ofobservations, the higher is the computational effort. However,there is an alternative method, denominated Recursive LeastSquare Method, in which, to obtain new coefficients, it isenough to know the values of more up-to-date measurements.This means that Recursive Least Square Method needs lesscomputational effort than the Matrix Inversion Method. TheRecursive Least Square Method can be expressed by thefollowing equation:@(N+1)=e(N)+w(N)[yN+i q(N+1) e(N)] ( 5 )W(N) =P(N+l) cpT(N+l)W(N) =P(N) cpT(N+l)[lq(N+l)P(N) cpT(N+l)]-P(N+l)= I-W(N) ~p(N+l) P(N)

Consumer 1had his meter tampered, so that only the third partof the energy delivered to the consumer was effectivelycomputed by the meter. So,his coefficient should change from1 to 3. Figure 6 presents a simulation of the behavior ofthe coefficient of meter 1, as a function of the measurements.In measurement 6, we have introduced a modification in themeter. The algorithm theoretically needs 12 measures to adaptitself. So, we can observe that, in the 18 measurement, thecoefficient value is 3, that is, the algorithm has identified thefraud.

-34Fig. 6. Identification process results

C. Main DificultiesAn intrinsic difficulty present in the methods described aboveis obtaining the N linearly independent equations. When weobserve the consumption of the N consumers for T units oftime, we will obtain an equation. If we do N-1 otherobservations, each one for T units of time, there is a greatprobability that the new obtained equations be linearlydependent. This is due to the fact that, during the observationperiod of T units of time, the consumers may keep their

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consumption pattern approximately invariable, making thenew generated equations very close to each other. To avoidthis difficulty, the algorithm should identify the singularity ofthe matrix ((DT.@) n order to choose a convenient set ofequations. of the consumers.

consideration two factors:a) The technical losses that occur along the distributionnetwork, among the central observer meter and the meters

Another difficulty of the method is in the finite resolution ofthe watthour meters generally used by the utility. Most ofthese meters are electromechanical with lkWh of resolution.In other words, quantities lower than lkWh will be truncated.This fact can cause evaluation mistakes, when the equationssystem is being solved. Thus, the methodology shouldconsider the finite resolution of the meters.To exemplify this problem, we have simulated a hypotheticalcase with 12 electromechanical meters (each one withresolution of lkWh ). In this example, at any time, all of theconsumers have the same consumption except for a nullmeasure. This null measure is needed to keep the squaredmatrix (aT.@)rom being singular. The shape of the matrix ispresented in Fig. 7.

O a a a a a a a a a a aa O a a a a a a a a a aa a O a a a a a a a a aa a a O a a a a a a a aa a a a O a a a a a a aa a a a a O a a a a a aa a a a a a O a a a a aa a a a a a a O a a a a Ia a a a a a a O a a aa a a a a a a a a O a aa a a a a a a a a a O aI a a a a a a a a a a O

Fig. 7. A hypothetical consumption matrix

These technical losses are due, mainly, to the resistanceof theconductors that connect the consumer to the distributionnetwork.In order to get a more accurate model of the distributionsystem, it is necessary a realistic estimation of the technicallosses. This can be done through the knowledge of theelectrical characteristics of the distribution network.Simulations of the system should be done in order to get atable, as precise as possible, relating the amount of energyflowing through the distribution network and thecorresponding losses. Then, the energy measured by thecentral observer meter should be corrected, in order tocompensate for the losses. For example, supposing that for agiven situation the amount of losses iS 5%, EToTKj should bemultiplied by 0.95 to obtain the energy actually delivered tothe consumers.b) Frauds that are external to the meter, usually

accomplished through bypasses.The external fraud can be estimated adding a term to (1)originating (8) as shown following:EmTa =klE1 +k2E2+. +kiEi+. +kNEN +EF~ (8)Equation (8 ) will be called expanded model and to correctlyidentify kl, k2, ...,kN he coefficients EF~,m, ...,Em must bediscovered at first moment.

The value of a hypothetical measurement value) wasswept in intervals of 50Wh around 25kWh, 50kWh and1OOkWh. For example, with regard to lOOkWh, the value ofa as swept from 99499 to 100499. We assumed idealconditions, that is, accuracy class equal to zero for the metersand technical losses equal to zero, too. The obtainedcoefficients values should be unitary. However, due to thefinite resolution of the meters, in kWh, the obtained values aredifferent from 1.Table 1shows the biggest differences. Noticethat, for low consumption, the effect of the finite resolution ofthe meters becomes more critical.

TABLEDIFFERENCES DUE TO FINITE RESOLUTION OF THE METER

Consumption Maximum Differences

1OOkWh 10%VI. EXPANDED ODELING

The modeling described in section IV does not take into

A possible solution for this problem is carries out intelligentprocessing of the measurements of the consumers meters andof the central observer.One way to achieving that is by providing a historical databasewith the consumption values of each consumer and thecorresponding consumption of the central observer meter.When the deviation between central observer and the sum ofthe consumers changes significantly and this alterationcoincides with the alteration of the behavior of some specificconsumer, this indicates that this consumer (or consumers)may be doing a fraud by energy deviation.For example, we will present a simulated case where thedifference between the measurement of the central observerand the sum of the consumers changes, being increased of200kWh, as shown in Fig. 8.It should be investigated which consumers changed theirbehaviors of consumption at that same instant. For example, inthis case a certain consumer changed his behavior,as shown inFig. 9.

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averageI Months I

2 4 6 8 10 12Fig. 8. Difference between the s um of all consumer meters and the observermeter.

kWh I~ .- .- . .300

2 5 0 .

200 -1 5 0 .

100 -

50 -I Months I

2 4 6 8 10 12Fig. 9. Hypothetical consumer load curve with an alteration of behaviorThe change of the consumption level is about 200kWh, hatmay correspond to the unknown term EFj . Thus, alreadyknowing this term, we would do the following composition inorder to obtain an equation with the shape like the reducedmodel one:

W. ONCLUSIONSIn this paper, a new approach for identification of frauds oradulterations in measurement systems in distribution networkshas been presented.The methodology includes the utilization of a central observermeter installed close to the secondary terminals of thedistribution transformer, the energy measurements of thismeter, the energy measurements of the meters of the eachconsumer served by this secondary distribution network, andconvenient mathematical methods.It has been demonstrated that it is possible to identify, in alarge number of the cases, which consumer (or consumers) is(are) committing frauds.The methodology is based on an equations system where theunknown quantities are the accuracy classes (normalized) ofthe meters.The possible methods for the solution of the system can usestatistic or deterministic approaches.

The main difficulties for solving the system are getting a setoflinearly independent equations, the finite resolution of themeters, the non-zero resistance of the energy cables, and thebypass of the energy that is not accounted by the meters.The problem of energy deviation through bypassing the meterdemands a more careful analysis, based on observation of theconsumer behavior, and will be better investigated in futureworks.

VIII. REFERENCESGama, S.Z., et alli - Uma Nova Abordagem Tecnoldgica de Combate hPerdas Comerciais - XV Seminfio Nacional de DistribuiGLo deEnergia Elttrica - SEND1 2002, Brazil, 2002.Bandim , C.J., Pin to Junior, A.V., Alvare nga, L.M., Loureiro, M.R.B.,Santos, J.C.R., Galvez-Durand, F., - Loss Evaluation in DistributionSystems - Congreso Internacional De Distribucih Eltctrica, CidelArgentina 2002Nilsson, H. , Random sampling of and a scheme for reporting ofmalfunctions in electricity meters in Sweden ,Metering and Tariffs forEnergy Supply, 1999. Ninth International Conference on (Conf. Publ.No. 462)), Aug 1999 ,Birming ham, UKMisra, R.B. Patra, S, Tamper detection using neuro-fuzzy logic [staticenergy meters] ,Metering and Tariffs for Energy Supply, 1999. NinthInternational Conference on (Conf. Publ. No. 462), Aug 1999,Birmingham, UK.Singhal, S. ,The role of metering in revenue protection ,Meteringand Tariffs for Energy Supply, 1999. Ninth International Conference on(Conf. Publ. No. 462)), Aug 1999 ,Birmin gham, UKChambers, R.G., Early diagnosis of tariff metering faults by asystematic analysis of maidcheck metering discrepancies , Meteringand Tariffs for Energy Supply, 1999. Ninth International Conference on(Conf. Publ. No. 462)), Aug 1999 ,Birmin gham, UK.Bandim, C.J., Souza, F.C., Alvareng a, L.M., Pinto Junior, A.V., L uiz,F.C., Alves Junior, J.E.R., Galvez-Durand,F., Loureiro, M.R.B., Dantas,A.R.,- Centm lized Metering System In Buildings - CongresoInternacional D e Distribucidn El6ctrica, Cidel Argentina 2002Costa, R.S. , aldas, R.P., Alvareng a, L.M., Pi nto Jr., A.V., Souza, F.C.,Pimentel, J.C.G., Bandim, C.J. - A New C oncept O f Electrical EnergyMetering In Buildings -ERE, 1994.Astrom, K.J., Wittenmark, B., - Adaptative Control - Addison-Wesley1989.

IX. BIOGRAPHIESCesar J. Bandim is a research engineer and a project manager of CEPEL -Electric Power Research Center, in Rio de Janeiro, RJ,Brazil. Mr. Bandimholds an M.Sc. degree in electrical engineering.Jose Eduardo R. Alves Jr. is a research engineer and a project manager ofCEPEL. Mr. Alves holds a D.Sc. degree in electrical engineering. Mr. Alves isalso professor of UFF - Flumineme Federal University, in N iter& RJ,Brazil.Fabio C. de Souza is a research engineer and a project manager of CEPEL.Mr. Souza holds a n M.Sc. degree in electrical engineering.Ary V. Pinto Jr. i s the manager of CEPELs R&D Program of DistributionSystems and Energy-Efficient Use. Mr. Pinto holds an M.Sc. degree inelectrical engineering.Mauro R. B . Loureiro. is an external consultant that works in cooperation withCEPEL. M r. Loureiro holds a B.Sc. degree in electrical engineering.Christiane A. MagalhFies is an external consultant that works in cooperationwith CEPEL. M s. M agalhZes holds a B.Sc. degree in electrical engineering.Federico Galvez-Durand is professor of the UFRJ - Rio de Janeiro FederalUniversity in Rio de Janeiro, RJ, Brazil. Mr. Durand holds a D.Sc. degree inelectrical engineering.

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identification of energy theft and tampered meters using a central observer meter: a mathematical...

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