Identification of electricity theft perpetrators in the low-voltage distribution network

. Correlation analysis proves its effectiveness in pinpointing the culprits behind electricity theft, as demonstrated by the comprehensive data obtained from measurement snapshots taken in an actual distribution network over the course of a month. The analysis relied on various methods of theft simulation that correspond to attacks on meters, communication lines, and measurement data.


Introduction
The technical and non-technical losses of electricity in a low-voltage distribution network (DN) can be assessed using the phase measurements for active powers and voltage magnitudes.These values are measured by smart meters (SM) installed at the power supply node of the network and at the points where consumers are connected to it.A significant support in determining the actual losses is a balance smart meter installed at the power supply node of the distribution network, which measures the electricity transmitted to the phases.The comparison of the electricity transmitted with the total energy received by the consumers of each phase makes it possible to find out the unmeasured electricity consumption in the phases, which corresponds to the sum of technical and nontechnical losses.Determining technical losses using the contribution method [1] by measuring active power and voltage of the consumer does not require information about the topology and parameters of the network.The difference between the actual and technical losses in the phases, corresponding to large non-technical losses, is an indicator of the electricity theft in the network.
According to the literature review [2,3], the perpetrators of electricity theft are normally detected using clustering methods, state methods, and game theory methods.It is also possible to use correlation analysis [4 -6], the performance of which was proven in [7,8] when separating the SM measurements into phases corresponding to the phases of the balance meter.
The 30-minute measurement snapshots made in a real-world DN during a month exemplify the use of the correlation analysis method in detecting the perpetrators of electricity theft.The total number of simultaneously performed complex measurements, each of which includes the measurement of active power and voltage magnitude, is 3 measurements at the power supply node and 39 measurements at consumption points.Measurements were made by 18 single-phase and 7 three-phase smart meters placed at 10 DN supports and by a three-phase balance smart meter installed at the feeder power supply node.The information from the smart meters is transferred to the data collection and processing system by the automated metering system, which is a measuring infrastructure that connects the DN with a communication network and a modern measurement structure.

Determination of phases of complex measurements at the consumption points
The first step in the theft identification algorithm is to determine the phase of each complex measurement in which it was performed.This is done using the correlation analysis [7,8], which involves the study of voltage magnitudes measured simultaneously over a long period of time in known phases of the power supply node and at the points where meters are connected to consumers, whose phases must be identified.In our case, the total number of consumers K in three phases is 39.Phase Х of the consumer connection is identified using the maximum value of the cross-correlation coefficients between the measurement vectors of the voltage magnitudes at the node of feeder supply and the k -th consumer conclusions can be obtained for measurements performed in phases B and C.
After the phase of smart meter connection is determined, the number and list of consumers are found out for each phase.For each consumer, the measurement vectors of the voltage magnitudes and active powers of the loads are generated with the number T of measurement snapshots.For the lowvoltage DN considered in our case, 11 consumers were identified in phase A, and 14 consumers in phases B and C, in each.

Determination of technical energy losses by the contribution method
Consider the contribution method [1] for an open-loop network, which is the distribution network, for one of the measurement snapshots of phase f .(1) A current equal to the current load of the consumer flows to this consumer from the feeder supply node.The product of the current load of the n -th consumer and the voltage at the feeder supply node f U sup , measured by balance smart meter, determines the active power transmitted to the n -th consumer from the power supply node

Measurements of active power of load
The sum of the powers transferred from the feeder supply node to each of the f N consumers determines the total power transmitted to all consumers of the phase If the power of the n -th consumer load is subtracted from the power transmitted to this consumer from the feeder supply node, it is possible to find out the power losses that occur along the path of its transmission.These are the so-called technical losses, the sum of which for f N consumers of the phase for each of the T measurement snapshots equals

Determination of technical energy losses by the contribution method
For each of the measurement snapshots, a comparison of the power measured by the balance meter, which is transmitted to the feeder from the supply node snapshot, allows estimating the total losses in the feeder, which are also called actual losses.These losses for each of T measurement snapshots can be represented as Non-technical energy losses, which are of the greatest interest in this study, are determined for each of the measurement snapshots as the difference between actual and technical losses tech -non Non-technical losses include unmetered electricity consumption, measurement errors, as well as errors in the method of determining technical losses.

Determination of the perpetrators of non-technical losses
In this work, using the recommendations given in [6] to detect the consumers stealing electricity, we calculate the absolute values of coefficients f хР K of correlation between the vector of non-technical losses and each of the load power vectors of the consumer.In doing so, it is assumed that the maximum coefficients correspond to consumers guilty of stealing electricity.The number of components of the non-technical loss vector Honest consumers in this case can be identified using normalized correlation coefficients , where An important indicator of the absence of electricity theft in the network is the coincidence of the correlation coefficients f K 1 and f K 2 for each relation.The first correlation coefficient characterizes the relationship between the voltage loss vector and the vector of current in the lines, which is calculated considering the nodal currents that flow in the direction from the power supply node to the end nodes of the network.The second correlation coefficient establishes the relationship between the vector of voltage loss and the vector of current in the lines, which is calculated based on the nodal currents running in the opposite direction.To determine the nodal parameters, each support of the main feeder is assigned a load node.When several smart meters are installed at the support, the total load power and the average value of the voltage magnitude are calculated at this node.

Methods for simulating electricity theft
To confirm the effectiveness of the considered approaches to detecting the perpetrators of electricity theft, the research relied on the methods for simulating the perpetrators of theft, which are offered in various literature sources [6,9,10].These methods involve: 1. Multiplying the power of consumer ) (t P n by the randomly generated number  , within the range 0.1 - 0.9, for all snapshots of power measurements * .with the product of the average load of the consumer and a randomly generated number  , in the range 0.1 -0.9. 7. Replacing all power measurement snapshots of consumer ) (t P n with the average load value over the analyzed period of time.

Illustration of theft detection methods
Figure 1 shows the daily graphs of active power of consumers in the phases of a real-world distribution network, which are built using 39 measurements taken from the automated metering system protocols.Table 1 indicates the values of the total energy consumption according to the measurements of the balance meter and consumer meters, as well as the values of the energy loss components for January 2023 for 1488 30minute measurement snapshots.An assessment of the contribution of power of the consumer of each phase to non-technical losses, in the form of graphs of correlation coefficients between the vectors of non-technical losses and each of the consumer load vectors for the three phases of January 2023 (Figure 2) indicates a weak correlation.This gives us hope for a theft-free period at issue, which is additionally evidenced by the coincidence of the graphs of the correlation coefficients presented in Figure 3.
Let us simulate a decrease in the power of load for consumer 220 of phase C by 5%, 10%, 30%, 50%, 70%, 90%, corresponding to the first method of theft, for  equal to 0.95, 0.9, 0.7, 0.5, 0.3, and 0.1.Table 2 shows that in this case, for a constant value of the electricity supplied to the phase, equal to 45437.52 kWh, the total electricity consumption and technical losses go down, while the actual and nontechnical losses go up.As for the accusation of the consumer of the electric energy theft, in all cases, the theft is proved by the maximum correlation coefficient С хР K , which rises with an increase in the share of stolen electricity in the range of 0.809 ÷ 0.998, Figure 4.An almost identical result, pointing to consumer 220 as the culprit of the electricity theft, was also obtained for the maximum values of the correlation coefficients С xI K of the vectors of total current unbalances and vectors of current loads of consumers.Figure 5 demonstrates the graphs of correlation coefficients С K 1 and С K 2 , showing how, with an increase in the amount of electricity stolen by consumer the difference between the ordinates of the graphs rises.In addition, the intersection of the graphs corresponding to the fifth node or the fifth support, at which the smart meters of consumers 218 and 220 are located, indicates that at least one of them is associated with the electricity theft.

Fig. 3. Graphs of correlation coefficients
Two columns of graphs, Figure 6, illustrate seven ways of simulating theft with the load of consumer 220 as an example.The left column shows the daily load curve and the daily non-technical loss curve corresponding to the simulated theft.The right column shows graphs of correlation coefficients for phase C consumers.The maximum load of consumer 220 for 1,488 measurement snapshots in January is 4.112 kW, and the average load is 1.789 kW.

K
presented in Figure 7, allows in both cases of theft to successfully detect the thieves.

Conclusion
The problem of identifying the consumers stealing electricity in the phases of the low-voltage distribution network is solved considering technical losses that do not require knowledge of the topology and parameters of the network.The findings suggest that in order to detect theft, there is no need to analyze the correlation between the vector of non-technical losses and the vectors of load powers of consumers, instead, one should investigate the correlation of the vector of current unbalances with the vectors of current loads.To assess the absence of theft in the network, it is proposed to check the coincidence of the correlation coefficients between the voltage loss vector and the current vectors in the lines, when they are calculated considering the nodal currents that flow from the power node to the end of the feeder and in the opposite direction.The example of a real-world distribution network feeder illustrates how correlation analysis can effectively identify simulated perpetrators of different types of theft.

U
of the n -th consumer, where the number of consumers in phase f , equal to the number T of measurement snapshots.Honest consumers can be identified using normalized correlation coefficients between the vector of the balance meter measurements reduced by the value of technical losses allow confidently identifying the culprits of theft.Another, alternative way to determine the perpetrators of theft, which does not require the calculation of either technical or non-technical losses, can be the calculation of the maximum correlation coefficients f xI K between the current unbalance vector f I unb in phase f and each of f N vectors of current loads f n I calculated using expressions (1).Unbalance currents caused by the unmetered loads, including their theft, for each measurement snapshot are equal to the difference between the current supplied to the network from phase f of power supply source f I sup and the sum of consumer load currents RSES 2023 https://doi.org/10.1051/e3sconf/202346101029E3S Web of Conferences 461, 01029 (2023) bI K is correlation coefficients relating the vector of power supply source currents f sup I with each of f N vectors of current loads f n I .Even in the absence of theft, the correlation coefficients f хР K and f хI K , which correspond to different consumers and do not exceed the values of weak correlation, can differ significantly from each other.

Fig. 1 .
Fig. 1.Graphs of daily active power loads of consumers in phases A, B, C.

Fig. 2 .
Fig. 2. Correlation coefficients A хР K , B хР K , C хР K in phases A, B, C for January 2023.

Fig. 4 .
Fig. 4. Change in the correlation coefficient С хР K , with an increase in the percentage of electricity stolen by consumer 220.

Figure 7 (
Figure 7 (1.3 and 2.3) shows scatter plots, with ordinates С hР K , and abscissas С хР K .The points with minimum ordinates and maximum abscissas, which are marked with arrows, correspond to consumers guilty of energy theft.
The research was carried out under State Assignment Project (no.FWEU-2021-0001) of the Fundamental Research Program of Russian Federation 2021-2030.

Table 1 .
Values of total energy consumption and losses in phases A, B, and C of the distribution network for the month of January 2023.

Table 2 .
Influence of the percentage of electricity stolen by consumer 220 of phase C on the total consumption and losses.