CN115239077A - Low-voltage transformer district electricity stealing user identification method based on improved whale optimization algorithm - Google Patents
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Abstract
The invention belongs to the technical field of power distribution, and relates to a low-voltage transformer district electricity stealing user identification method based on an improved whale optimization algorithm, which comprises the following steps: calculating the total power consumption value of the distribution room in the time period; establishing an objective function by utilizing the calculated value of the total power consumption of the distribution room and the measured value of the total power consumption of the distribution room; solving the objective function by improving a whale optimization algorithm; and analyzing the electric energy loss rate of each user obtained by solving by using a distance-based abnormal point detection algorithm, and outputting the users with the suspicion of electricity stealing. According to the method, a dynamic change convergence factor, a random position updating coefficient and a directional search behavior are introduced to improve a traditional whale algorithm, then the improved whale optimization algorithm is utilized to estimate the electric energy loss rate of each user in a platform area, and finally the abnormal users with the electric energy loss rate are identified through an abnormal point detection algorithm based on distance.
Description
Technical Field
The invention belongs to the technical field of power distribution, and particularly relates to a low-voltage transformer district electricity stealing user identification method based on an improved whale optimization algorithm.
Background
With the rapid development of social economy, the demand of society on electric energy is rapidly increased, and the electric energy is not only an important support for the development of national economy, but also an important guarantee for the maintenance of self development of electric power companies. The abnormal electricity utilization of the users in the transformer area not only damages the benefits of the power company and seriously influences the health development of the power company, but also brings great hidden dangers to the safety and the electricity utilization of a power grid.
The traditional manual inspection mode has low efficiency, high difficulty and large consumption of manpower and material resources. Most of the existing electricity stealing detection models rely on huge data sets, and low-voltage electricity stealing work orders in a power grid marketing system are few, so that the model training requirements are difficult to meet.
CN110824270A discloses a method for identifying electricity stealing users by combining line loss and abnormal events in a transformer area, which comprises the following steps: the method comprises the steps that the transformer area and user data of at least one transformer area to be checked are obtained, wherein the transformer area and user data comprise transformer area line loss data and basic data of all power users in the transformer area; determining that the abnormal line loss transformer area of the electricity stealing suspected user exists in the specified electricity utilization period by applying a transformer area line loss abnormal detection method and transformer area line loss data of the at least one transformer area to be inspected; aiming at any abnormal line loss transformer area with electricity stealing suspected users, determining a K-means clustering electricity stealing suspected user set, a support vector machine electricity stealing suspected user set and a Bayesian algorithm electricity stealing suspected user set; and determining a list of electricity stealing suspicion users in the abnormal line loss area after comprehensive evaluation.
CN109947815A is a method for identifying electricity stealing based on outlier algorithm, comprising the following steps: the method comprises the steps of obtaining daily power consumption data of a user, preprocessing the data, calculating sample fluctuation rate CV, determining a centroid and parameters p and D, performing power stealing judgment through an outlier algorithm, determining a power stealing sample point and setting a power stealing alarm. The patent combines the power fluctuation rate and an improved distance-based outlier mining algorithm to complete the identification of the electricity stealing of the user.
Whale Algorithm (Whale Optimization Algorithm) is an Algorithm proposed based on the behavior of Whale preys. Whales are a group of mammals that also work in concert to repel and trap prey when hunting. Whale algorithm is an emerging optimization algorithm, and the research and application cases are few. In the whale algorithm, the position of each whale represents a feasible solution. During the process of catching a colony of whales, each whale has two behaviors, one is to surround the prey, and all whales advance towards other whales; the other is a steam bag net, and whales swim circularly to eject air bubbles to drive preys. In each generation of swim, whales will randomly choose these two behaviors for hunting. In the act of whale surrounding prey, the whale will randomly choose whether to swim towards the optimal whale or randomly choose a whale as its target and approach it.
Whale algorithm has less application research in the field of electric power, and CN113281620A discloses a fault section positioning method, system and medium based on adaptive whale algorithm, which are used for positioning fault sections. CN110110930A discloses a recurrent neural network short-term power load prediction method for improving whale algorithm, which is used for power load prediction. In the prior art, no application report of whale algorithm in the aspect of electricity larceny prevention is available.
Disclosure of Invention
The invention aims to solve the problem of identifying electricity stealing users in a low-voltage transformer area, and provides a low-voltage transformer area electricity stealing user identification method based on an improved whale optimization algorithm, which has the core idea that the improved whale optimization algorithm is used for estimating the electric energy loss rate of each user, and then an abnormal point detection algorithm based on distance is used for screening users with abnormal electric energy loss rate; the electric energy loss rate of each user is analyzed, so that the high-efficiency identification of electricity stealing users in the low-voltage distribution room is realized.
The technical scheme adopted by the invention is as follows: a low-voltage transformer district electricity stealing user identification method based on an improved whale optimization algorithm comprises the following steps:
and 4, analyzing the electric energy loss rate of each user obtained in the step 3 by using a distance-based abnormal point detection algorithm, and outputting the users with suspicion of electricity stealing.
Further preferably, in step 1, the power consumption of the users is corrected by using the power consumption rate of the users, and the corrected power consumptions of all the users in the distribution room are added to obtain a calculated value of the total power consumption of the distribution room:
M 0 ＝M 1 θ 1 +M 2 θ 2 +…+M n θ n (1)
in the formula, theta 1 ，θ 2 ，…， θ n 1,2, 8230, n user electric energy loss rates, M 1 ，M 2 ，…，M n Respectively 1,2, 8230, n user electric energy meter metering values;
the metering values of the electric energy meters of each user in 95 time periods in one day are respectively substituted into the formula (1), and the calculated value of the total power consumption of the distribution area in 95 time periods can be obtained
In the formula (I), the compound is shown in the specification,
respectively representing the 1 st, 2 nd, \8230thand n user electric energy meter metering values in the 1 st period;
respectively representing the 1 st, 2 nd, \ 8230;, n user electric energy meter metering values in the 2 nd period;
respectively representing the 1 st, 2 nd, \ 8230st, n user electric energy meter metering values in the 95 th period.
Further preferably, in the step 2, a calculated value of the total power consumption of the distribution room in 95 time periods is used
And measured value of total power consumption of distribution room in 95 time periods
Establishing an objective function:
in the formula: f is the error of the calculated value sequence of the total electric energy of the distribution area in 95 time periods a day and the measured value sequence of the total electric energy of the distribution area in 95 time periods a day after the electricity consumption of the user is corrected;
in order to correct the calculated value array of the total electricity consumption of the distribution area in 95 time periods in one day after the electricity consumption of the user,
the measured value of the total electricity consumption of the station area is measured for 95 time periods in a day.
Further preferably, in the step 3, the process of solving the objective function by improving the whale optimization algorithm is as follows:
parameters a of the basic whale optimization algorithm:
A＝2a*r 1 -a (4)
r 1 is [0,1 ]]A is a dynamic change convergence factorA seed;
t is the current iteration number, t max Is the maximum number of iterations;
in order to make full use of the location of the prey, i.e. the optimal solution θ * (t) proposing a random position update coefficient m as follows:
θ(t+1)＝m·θ * (t)-A·K|A|＜1，p＜05 (7)
θ(t+1)＝m·θ rand -A·K|A|≥1，p＜0.5 (8)
θ(t+1)＝K’·e bl ·cos(2πl)+(1-m)·θ * (t)p≥0.5 (9)
K＝|C·θ rand -θ(t)| (10)
K’＝|θ rand -θ(t)| (11)
C＝2·r 2 (12)
wherein theta (t) is the position of the whale individual in the current iteration, theta (t + 1) is the new position of the whale individual in the next iteration, and theta rand To represent the randomly chosen position vector of whale, m is
Random number between, p and r 2 Are all [0,1]B is a constant, which defines the shape of the logarithmic spiral, where 1,l is taken to be [0,1%]The random number b and the random number l jointly control a spiral position updating mode of whale individuals, K is a moving step length, and C is [0,2 ]]A random number in between;
in addition, in order to enlarge the algorithm search space and further improve the optimization capability of the algorithm, the invention also provides a directional search behavior, which is as follows:
Firstly, initializing the position of a whale individual in a whale optimization algorithm; initializing the position state of whale individuals into a vector theta = (theta) 1 ，θ 2 ，…，θ n )，θ 1 ，θ 2 ，…θ n Respectively setting a group of possible user electric energy loss rates of corresponding users, setting the initial parameter population size N and the maximum iteration number t of the whale optimization algorithm corresponding to the error in the objective function, wherein the current fitness of the whale individual is f = f (theta) max (ii) a Randomly generating individual whales, wherein each whale represents a group of possible user electric energy loss rates;
calculating the optimal individual and recording the optimal individual into a bulletin board; selecting a distribution area general table and n electric power users for 95 time periods of a day, acquiring a power data acquisition sequence, calculating the fitness according to a target function, comparing the fitness corresponding to each individual, taking the optimal individual with the minimum error value, and recording the current position and the fitness of the optimal individual into a bulletin board;
after each individual respectively carries out random simulation of enclosing prey, foaming net attack, searching predation and directional search, the fitness of the current position of the individual is checked and compared with the value recorded by the bulletin board, and if the fitness is better than the value recorded by the bulletin board, the bulletin board is updated. Then judging whether the maximum iteration number is reachedIf the number is equal to the preset value, outputting a result to obtain a group of user electric energy loss rates theta meeting the requirements 1 ，θ 2 ，…，θ n 。
Further preferably, in the step 4, if the number of neighbors of a sample point is greater than the set threshold, the sample point is a normal point, and if the number of neighbors is less than the set threshold, the sample point is an abnormal point; calculating the Euclidean distance D between the sample point and all other points, comparing the Euclidean distance D with a distance threshold value r, if D < r, the sample point is a neighbor, and if D > r, the sample point is not a neighbor; it is determined whether the analyzed sample point is an outlier.
The invention has the beneficial effects that: the method comprises the steps of firstly introducing dynamic change convergence factors and random position updating coefficients to improve a traditional whale algorithm, then estimating the power loss rate of each user in a platform area by utilizing an improved whale optimization algorithm, and finally identifying the users with abnormal power loss rates through an abnormal point detection algorithm based on distance.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 shows the power consumption rate of each user.
Fig. 3 shows the identification result of the electricity stealing subscriber.
Detailed Description
The invention is explained in further detail below with reference to the drawings.
Referring to fig. 1, a low-voltage transformer district electricity stealing user identification method based on an improved whale optimization algorithm comprises the following steps:
Correcting the power consumption of the users by utilizing the power consumption rate of the users, and adding the corrected power consumption of all the users in the distribution room to obtain a total power consumption calculation value of the distribution room:
M 0 ＝M 1 θ 1 +M 2 θ 2 +…+M n θ n (1)
in the formula, theta 1 ，θ 2 ，…， θ n 1,2, 8230, the power loss rate of n users, M 1 ，M 2 ，…，M n Respectively 1,2, 8230, n user electric energy meter metering values;
the metering values of the user electric energy meters in 95 time periods in one day are respectively substituted into the formula (1), and the calculated value of the total power consumption of the distribution area in 95 time periods can be obtained
In the formula (I), the compound is shown in the specification,
respectively representing the 1 st, 2 nd, \8230thand n user electric energy meter metering values in the 1 st period;
respectively representing the 1 st, 2 nd, \8230thand n user electric energy meter metering values in the 2 nd period;
respectively representing the 1 st, 2 nd, \ 8230st, n user electric energy meter metering values in the 95 th period.
And 2, establishing an objective function by utilizing the calculated value of the total power consumption of the transformer area and the measured value of the total power consumption of the transformer area.
Calculating the total power consumption of the distribution room in 95 time periods
And measured value of total power consumption of distribution room in 95 time periods
And establishing an objective function, and considering both the overall error and the error offset of each dimension.
In the formula: and F is the error between the calculated value sequence of the total electric energy of the distribution area in 95 time periods of a day and the measured value sequence of the total electric energy of the distribution area in 95 time periods of a day after the electricity consumption of the user is corrected.
In order to calculate the number sequence of the total electricity consumption of the distribution area in 95 time periods of a day after the electricity consumption of the user is corrected,
the measured value is a measured value sequence of the total power consumption of the station area of 95 time periods in a day.
And 3, solving the objective function by improving a whale optimization algorithm.
Parameter a of basic whale optimization algorithm:
A＝2a*r 1 -a (4)
a＝2-2t/t max (5)
r 1 is [0,1 ]]A is a convergence factor, and the value of the parameter a is determined by the change of the convergence factor a. The convergence factor is larger, so that the overall search of the basic whale optimization algorithm is facilitated, the possibility of trapping in local optimum is reduced, the local search of the basic whale optimization algorithm is facilitated when the convergence factor is smaller, and the convergence speed of the basic whale optimization algorithm is accelerated. In the basic whale optimization algorithm, the convergence factor decreases linearly with the increase of the iteration number, so that the convergence speed of the basic whale optimization algorithm is slow. Therefore, the invention provides a dynamically-changing convergence factor, which improves the convergence speed of the whale optimization algorithm and does not influence the global search and local search performance of the algorithm. The concrete formula is as follows:
t is the current iteration number, t max Is the maximum number of iterations. The convergence factor produces a larger parameter during early iterationThe number A is beneficial to the global search of the whale optimization algorithm, and the convergence speed of the algorithm is improved; and a convergence factor generates a small parameter A in later iteration, and local search of the whale optimization algorithm is facilitated.
In addition, to take full advantage of the location of the prey, i.e. the optimal solution θ * (t) improving the optimizing precision of the whale optimizing algorithm, and providing a random position updating coefficient m which is as follows:
θ(t+1)＝m·θ * (t)-A·K|A|＜1，p＜0.5 (7)
θ(t+1)＝m·θ rand -A·K|A|≥1，p＜0.5 (8)
θ(t+1)＝K’·e bl ·cos(2πl)+(1-m)·θ * (t)p≥0.5 (9)
K＝|C·θ rand -θ(t)| (10)
K’＝|θ rand -θ(t)| (11)
C＝2·r 2 (12)
in the formula, theta (t) is the position of the whale individual in the current iteration, theta (t + 1) is the new position of the whale individual in the next iteration, and theta rand Is a position vector representing random whale selection, m is
Random number between, p and r 2 Are all [0,1 ]]B is a constant, which defines the shape of the logarithmic spiral, where 1,l is taken to be [0,1 ]]The random number b and the random number l jointly control a spiral position updating mode of whale individuals, K is a moving step length, and C is [0,2 ]]A random number in between.
m is the position updating coefficient of the optimal solution, when p is less than 0.5, the whale optimization algorithm is in a prey surrounding and immediate searching stage, and the position updating coefficient at the moment is increased along with the increase of iteration times, so that the optimal solution fully plays a role; when p is larger than or equal to 0.5, the whale optimization algorithm is in a spiral updating position stage, along with the continuous iteration of the whale optimization algorithm, whales are close to the prey continuously, the positions of the prey are changed by adopting a small updating coefficient of 1-m, the local searching capacity of the whale optimization algorithm is effectively improved, and the optimizing precision is further improved.
In addition, in order to enlarge the algorithm search space and further improve the optimization capability of the algorithm, the invention also provides a directional search behavior, which is as follows:
θ i next ＝θ i +step i＝1，2，3 (13)
The positions of individual whales in the whale optimization algorithm are initialized. Initializing the position state of whale individuals into a vector theta = (theta) 1 ,θ 2 ,…,θ n ),θ 1 ,θ 2 ,…θ n Respectively setting a group of possible user electric energy loss rates of corresponding users, setting the initial parameter population size N and the maximum iteration times t of a whale optimization algorithm corresponding to the error in the objective function, wherein the current fitness of the whale individual is f = f (theta) max (ii) a Individual whale individuals are randomly generated, and each whale represents a group of possible user power consumption rates.
Calculating the optimal individual and recording the optimal individual into a bulletin board; selecting a distribution area general table and n electric power users in 95 time periods of a day, acquiring a numerical sequence of electric energy data, calculating the fitness according to an objective function, comparing the fitness corresponding to each individual, taking the optimal individual with the minimum error value, and recording the current position and the fitness of the optimal individual into a bulletin board.
When whale individuals randomly simulate surrounding prey, foaming net attack, searching predation and directional searching behaviors respectively, the fitness of the current positions of the individuals is checked and compared with the value recorded by the bulletin board, and if the fitness is better than the value recorded by the bulletin board, the bulletin board is updated. Judging whether the maximum iteration times are reached, if so, outputting a result to obtain a group of user electric energy loss rates theta meeting the requirements 1 ，θ 2 ，…，θ n 。
And 4, analyzing the electric energy loss rate of each user obtained in the step 3 by using a distance-based abnormal point detection algorithm, and outputting the users with suspicion of electricity stealing.
If the number of neighbors of a sample point is greater than the set threshold, the sample point is a normal point, and if the number of neighbors is less than the set threshold, the sample point is an abnormal point. The method for calculating the number of neighbors of any sample point is to calculate the Euclidean distance D between the sample point and all other points, compare the Euclidean distance D with a distance threshold r, and if D is not the same, calculate the number of neighbors of any sample point<r is the neighbor of the sample, if D>r is not a neighbor of the sample. And finally, determining whether the analyzed sample point is an abnormal point or not according to the assumption. Since the object of the analysis studied is the user power loss rate, a one-dimensional euclidean distance is used here. For two one-dimensional sample data theta 1 And theta 2 The euclidean distance formula is defined as:
D(θ 1 ，θ 2 )＝|θ 1 -θ 2 | (15)
the one-dimensional samples are adopted, so that the complexity of data processing is greatly reduced, and the algorithm execution efficiency is improved. Therefore, the method has certain advantages compared with other electricity stealing identification algorithms.
The XX community in a certain province has 20 residents, 96-point electric energy data of the general community and each user sub-table in 12 months and 20 days in 2020 are obtained, the unit is kilowatt-hour, electricity consumption in 95 time periods is obtained after pretreatment, and part of the electricity consumption is shown in table 1.
Table 1 community partial electric quantity data
Carrying the electric quantity data of 95 time periods into (2) calculating the total electric quantity calculation value of the distribution area
Calculated value of total electric quantity of low-voltage transformer area is reused
And actual value
Establishing an objective function
Then, the whale optimization algorithm is used for solving the electric energy loss rate theta of each user, and the solving result is shown in fig. 2. As can be seen from fig. 2, the power consumption rate of some users is large, and then the abnormal point is identified by using the distance-based abnormal point detection algorithm, where the distance threshold r =0.2 and the score threshold is 0.3, and the final output result is as shown in fig. 3, where the abnormal point is marked as 1 and the normal user is marked as 0. As can be seen from the algorithm output result, the user with the number 16 is suspected to be a power stealing user.
The foregoing description is of the preferred embodiment of the present invention only, and is not intended to limit the invention in any way, so that those skilled in the art, having the benefit of this disclosure, may modify and/or adapt the same to equivalent embodiments without departing from the scope of the present invention. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are still within the protection scope of the technical solution of the present invention.
Claims (5)
1. A low-voltage transformer district electricity stealing user identification method based on an improved whale optimization algorithm is characterized by comprising the following steps:
step 1, calculating a total power consumption calculation value of a distribution area in a time period;
step 2, establishing an objective function by using the calculated value of the total power consumption of the distribution room and the measured value of the total power consumption of the distribution room;
step 3, solving the objective function by improving a whale optimization algorithm;
and 4, analyzing the electric energy loss rate of each user obtained in the step 3 by using a distance-based abnormal point detection algorithm, and outputting the users with suspicion of electricity stealing.
2. The low-voltage transformer district electricity-stealing user identification method based on the improved whale optimization algorithm as claimed in claim 1, wherein in the step 1, the power consumption of the user is corrected by using the power consumption rate of the user, and the corrected power consumptions of all users in the transformer district are added to obtain a calculated value of the total power consumption of the transformer district:
M 0 ＝M 1 θ 1 +M 2 θ 2 +…+M n θ n (1)
in the formula, theta 1 ，θ 2 ，…，θ n 1,2, 8230, the power loss rate of n users, M 1 ，M 2 ，…，M n Respectively 1,2, 8230, n user electric energy meter metering values;
the metering values of the electric energy meters of each user in 95 time periods in one day are respectively substituted into the formula (1), and the calculated value of the total power consumption of the distribution area in 95 time periods can be obtained
In the formula (I), the compound is shown in the specification,
respectively, the 1 st, 2 nd,8230, n user electric energy meters measure values;
respectively representing the 1 st, 2 nd, \8230thand n user electric energy meter metering values in the 2 nd period;
respectively representing the 1 st, 2 nd, \ 8230st, n user electric energy meter metering values in the 95 th period.
3. The method as claimed in claim 2, wherein in step 2, the calculated value of the total power consumption of the distribution area in 95 time periods is used to calculate the electricity stealing users in the low-voltage distribution area based on the optimized algorithm for whale
And the measured value of the total power consumption of the distribution room in 95 time periods
Establishing an objective function:
in the formula: f is the error of the calculated value sequence of the total electric energy of the distribution area in 95 time periods a day and the measured value sequence of the total electric energy of the distribution area in 95 time periods a day after the electricity consumption of the user is corrected;
in order to correct the calculated value array of the total electricity consumption of the distribution area in 95 time periods in one day after the electricity consumption of the user,
the measured value is a measured value sequence of the total power consumption of the station area of 95 time periods in a day.
4. The identification method for the low-voltage transformer district electricity stealing users based on the improved whale optimization algorithm as claimed in claim 3, wherein in the step 3, the process of solving the objective function by the improved whale optimization algorithm is as follows:
parameter a of basic whale optimization algorithm:
A＝2a*r 1 -a (4)
r 1 is [0,1 ]]A is a dynamically varying convergence factor;
t is the current iteration number, t max Is the maximum iteration number;
to make full use of the location of the prey, i.e. the optimal solution theta * (t), proposing a random position update coefficient m as follows:
θ(t+1)＝m·θ * (t)-A·K|A|≤1，p≤0.5 (7)
θ(t+1)＝m·θ rand -A·K|A|≥1，p≤0.5 (8)
θ(t+1)＝K′.e bl .cos(2πl)+(1-m)·θ * (t)p≥0.5 (9)
K＝|C·θ rand -θ(t)| (10)
K′＝|θ rand -θ(t)| (11)
C＝2·r 2 (12)
wherein theta (t) is the position of the whale individual in the current iteration, theta (t + 1) is the new position of the whale individual in the next iteration, and theta rand Is a position vector representing random whale selection, m is
Random number between, p and r 2 Are all [0,1]B is a constant, l is [0,1 ]]The random number b and the random number l jointly control a spiral position updating mode of whale individuals, K is a moving step length, and C is [0,2 ]]Random number in between；
A directed search behavior is proposed, as follows:
θ i next ＝θ i +step i＝1，2， (13)
Firstly, initializing the position of a whale individual in a whale optimization algorithm; initializing the position state of whale individuals into a vector theta = (theta) 1 ，θ 2 ，…，θ n )，θ 1 ，θ 2 ，…θ n Respectively setting a group of possible user electric energy loss rates of corresponding users, setting the initial parameter population size N and the maximum iteration times t of a whale optimization algorithm corresponding to the error in the objective function, wherein the current fitness of the whale individual is f = f (theta) max (ii) a Randomly generating individual whales, wherein each whale represents a group of possible user electric energy loss rates;
calculating the optimal individual and recording the optimal individual into a bulletin board; selecting a distribution area general table and n electric power users for 95 time periods of a day, acquiring a power data acquisition sequence, calculating the fitness according to a target function, comparing the fitness corresponding to each individual, taking the optimal individual with the minimum error value, and recording the current position and the fitness of the optimal individual into a bulletin board;
after each individual respectively carries out random simulation of enclosing prey, foaming net attack, predation search and directional search, the fitness of the current position of the individual is checked and compared with the value recorded by the bulletin board, and if the fitness is better than the value recorded by the bulletin board, the bulletin board is updated; judging whether the maximum iteration times is reached, if so, outputting a result to obtain a group of user electric energy loss rates theta meeting the requirements 1 ，θ 2 ，…，θ n 。
5. The identification method for the electricity stealing users in the low-voltage transformer area based on the improved whale optimization algorithm as claimed in claim 4, wherein in the step 4, if the number of neighbors of a sample point is greater than the set threshold, the sample point is a normal point, and if the number of neighbors is less than the set threshold, the sample point is an abnormal point; calculating the Euclidean distance D between the sample point and all other points, comparing the Euclidean distance D with a distance threshold value r, if D is less than r, the sample point is a neighbor, and if D is more than r, the sample point is not a neighbor; it is determined whether the analyzed sample point is an outlier.
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| CN117195090A (en) * | 2023-11-08 | 2023-12-08 | 南昌工程学院 | Method and system for detecting electricity larceny of low-voltage distribution area |
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| CN117195090A (en) * | 2023-11-08 | 2023-12-08 | 南昌工程学院 | Method and system for detecting electricity larceny of low-voltage distribution area |
| CN117195090B (en) * | 2023-11-08 | 2024-03-08 | 南昌工程学院 | Method and system for detecting electricity larceny of low-voltage distribution area |
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