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SPECIAL SECTION ON EVOLVING TECHNOLOGIES IN ENERGY STORAGE SYSTEMS
FOR ENERGY SYSTEMS APPLICATIONS
Received February 13, 2021, accepted February 23, 2021, date of publication March 1, 2021, date of current version March 31, 2021.
Digital Object Identifier 10.1109/ACCESS.2021.3062675
Abnormal Detection of Electricity Consumption of
User Based on Particle Swarm Optimization and
Long Short Term Memory With the
Attention Mechanism
JIAHAO BIAN 1, LEI WANG 1,4, RAFAŁ SCHERER 2, (Member, IEEE), MARCIN WOŹNIAK 3,
PENGCHAO ZHANG 1, AND WEI WEI 4, (Senior Member, IEEE)
1Shaanxi Key Laboratory of Industrial Automation, Shaanxi University of Technology, Hanzhong 723001, China
2Institute of Computational Intelligence, Czestochowa University of Technology, 42-200 Czestochowa, Poland
3Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
4Shaanxi Key Laboratory of Network Computing and Security Technology, Xi’an University of Technology, Xi’an 710048, China
Corresponding author: Lei Wang (leiwang@xaut.edu.cn)
This work was supported in part by the National Natural Science Foundation of China under Grant 61773314, in part by the Shaanxi
Provincial Natural Science Basic Research Program under Grant 2019JZ-11, in part by the Scientific Research Project of Education
Department of Shaanxi Provincial Government under Grant 19JC011, in part by the Key Research and Development Program of Shaanxi
Province under Grant 2018ZDXM-GY-036, and in part by the Shaanxi Key Laboratory of Intelligent Processing for Big Energy Data under
Grant IPBED7.
ABSTRACT In the process of power transmission and distribution, non-technical losses are usually caused
by users’ abnormal power consumption behavior. It will not only affect the dispatch and operation of the
distribution network, bring hidden dangers to the security of the power grid, but also damage the operating
costs of power companies and disrupt the operation of the power market. Aiming at users’ abnormal
electricity consumption behavior, this paper proposes a model based on particle swarm optimization and
long-short term memory with the attention mechanism (PSO-Attention-LSTM). Firstly, according to the
actual electricity theft behavior, six typical electricity theft modes are summarized, and 4 composite modes
are obtained by combining them, so as to comprehensively test the detection performance of the model for
various electricity theft behaviors. Secondly, a detection model based on PSO-Attention-LSTM is proposed,
and the model is built using the TensorFlow framework. The model uses the attention mechanism to give
different weights to the hidden state of LSTM, which reduces the loss of historical information, strengthens
important information and suppresses useless information. Use PSO to solve the difficult problem of model
parameter selection, and optimize the hyperparameters to improve the model performance. Finally, the
data set of the University of Massachusetts was used for simulation and compared with convolutional
neural network-long short term memory (CNN-LSTM), attention mechanism-based long short term memory
(Attention-LSTM), LSTM, gated recurrent unit (GRU), support vector regression (SVR), randomforest (RF)
and linear regression (LR) to verify the effectiveness and accuracy of the method used in this article. In this
paper, Matlab software is used to analyze and visualize the detection result data.
INDEX TERMS Abnormal detection, LSTM, particle swarm optimization, attention mechanism, electricity
theft modes.
I. INTRODUCTION
There are often losses in power grid transmission and dis-
tribution transmission. The losses are mainly divided into
technical loss (TL) and non-technical loss (NTL). The main
The associate editor coordinating the review of this manuscript and
approving it for publication was Eklas Hossain .
cause of non-technical loss is abnormal electricity consump-
tion by users’ behaviors such as stealing electricity, fraud,
etc [1]. Abnormal electricity consumption behavior of users
will affect the dispatch operation of the regional power grid,
interfere with the safety management of power supply, and
bring hidden dangers to the security of the power grid. At the
same time, with the reform of the national power market,
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J. Bian et al.: Abnormal Detection of Electricity Consumption of User Based on PSO-Attention-LSTM
independent power sales and distribution companies appear,
and users’ power theft would directly damage the profits of
the power companies and disrupt the operation of the power
market [2]. Abnormal electricity consumption behaviors of
users are general in various countries. According to incom-
plete statistics, non-technical losses in China, India, Brazil
and Mexico account for 6.42%, 26.2%, 16.85% and 15.83%
of the national power consumption [3]. China has a large
population base, a large demand for electricity, and increasing
electricity consumption. The annual economic loss due to
electricity theft across the country can reach several billion
yuan [4]. Therefore, the research on the detection of abnormal
electricity consumption of users is an urgent problem to be
solved.
With the updation and development of smart grid and
advanced metering infrastructure (AMI), smart meters have
also begun to be widely used. Compared with traditional
electricity meters, smart electricity meters can collect user
data more accurately and efficiently, and can obtain mas-
sive amounts of user electricity consumption data, provid-
ing sample support for the analysis and detection of users’
abnormal electricity consumption behavior. In contrast, using
smart meters for data transmission is also vulnerable to
attacks in communications and networks. Nowadays, elec-
tricity thief can use digital storage technology and network
communication technology to attack smart meters, thereby
tampering with data to reduce electricity bills, and attacks
on smart meters are more ‘‘invisible’’ [5]. The traditional
methods for detecting abnormal electricity consumption of
users mainly use manual on-site verification of electricity
meter information, judgment through experience, installation
of monitoring equipment, etc [6]. These methods have low
detection efficiency and high cost, cannot quickly and accu-
rately determine abnormal electricity consumption behavior,
and it is difficult to detect tampering in communications and
networks [7].
In view of the shortcomings of traditional methods, some
scholars have carried out a series of studies. At present,
the detection methods for abnormal electricity consump-
tion mainly include statistical models [8], [9], data-driven
methods, and game theory-based methods [10]. With the
improvement of user-side online monitoring systems and
power information management systems, data-driven detec-
tion methods have received attention [11]. For power grid
lines, Shah et al. in [12] proposed an algorithm that uses
smart meter measurement technology to update the network
cable impedance, detects and classifies technical losses and
non-technical losses when errors occur in smart meters,
and estimates the resulting losses. Wang et al. in [13] uses
different clustering algorithms to detect 10kV non-technical
losses based on the average loss, line loss variation coef-
ficient and ammeter open-circuit records collected by the
meter, and finally analyzes and compares the detection effects
of various clustering algorithms. For electricity users, the
data-driven detection method is mainly based on the dif-
ference between abnormal users’ electricity consumption
behavior characteristics and normal users, and analyzes and
judges abnormal points through massive electricity consump-
tion data. Zhang et al. in [14] proposed a detection model
based on real-valued deep belief network (RDBN), which
uses the firefly algorithm (FFA) to solve the local optimum,
and uses undersampling and lasso algorithm to solve the data
imbalance problem. Finally, The detection model achieves
higher accuracy. Xu et al. in [15] constructed a random forest
model, using sparseness combined with anomalous cumulant
index to judge the anomaly of the sample, and the detection
effect is good. Zhao et al. in [16] uses long short-term mem-
ory networks to extract sequence features, classifies sequence
features through a full connected network (FCN), and judges
abnormal users through classification. Buzau et al. in [17]
uses all data recorded by smart meters (energy consumption,
alarms and electrical magnitudes) to detect non-technical
losses through supervised learning. The method has been
developed and tested based on real smart meter data from
Endesa’s industry and customers. Buzau et al. in [18] uses
a long and short-term memory network and a multi-layer
perceptron hybrid deep neural network to detect anomalies
and frauds in the electricity meter by analyzing daily energy
consumption and geographic information, and finally tested
it in the Spanish power company. Ghori et al. in [19] evalu-
ated 9 types and 15 existing machine learning classifiers, and
analyzed and compared the detection performance of various
classifiers using the Pakistan Power Supply Company data
set.
In the data-driven method, the regression method for
anomaly detection method can consider user consump-
tion behavior, and has a good detection effect for users
with different consumption behaviors. The accuracy of the
regression-based anomaly detection method is affected by
the accuracy of user power consumption prediction. Com-
pared with other methods, the LSTM model can better model
dynamic time series data and has advantages for time series
forecasting. But for too long time series, the LSTM model
is easy to lose the sequence information. In addition, the
adjustment of model hyperparameters depends on experi-
ence, which is complicated to adjust parameters and affects
model prediction and detection accuracy.
Based on the above considerations, this paper introduces a
PSO-Attention-LSTM model abnormal user power consump-
tion detection. Based on the electricity consumption data of
normal users and the corresponding weather characteristics,
this paper uses Tensor Flow to establish an LSTM predic-
tion model based on the attention mechanism, and predicts
the future electricity consumption of normal users with a
sliding window of 24 unit steps. According to the 6 kinds
of electricity theft modes and the combination in reality,
we obtain 4 kinds of compound electricity theft modes, and
the normal user power consumption data is simulated as
abnormal user data. We judge the time period of abnormal
behavior according to the abnormality of the user power curve
and the detection threshold. This paper uses the electricity
data set of the University of Massachusetts as a simulation
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J. Bian et al.: Abnormal Detection of Electricity Consumption of User Based on PSO-Attention-LSTM
example, and combines the PSO-optimized LSTM model
based on the attention mechanism (PSO-Attention-LSTM)
with CNN-LSTM, Attention-LSTM, LSTM, GRU, SVR,
RF and LR Compare. Finally, confusion matrix, detection
rate, false detection rate and radar chart are used to evalu-
ate detection accuracy. The result proves that the detection
model can accurately detect the user’s abnormal behavior
time period, which verifies the feasibility and accuracy of this
method. This method can more accurately predict the change
of user power consumption, and has certain reference value
for the research of abnormal power consumption detection of
users [20]–[31]. The main contributions to this paper are as
follows.
1)According to the actual law of stealing electricity,
we have constructed 6 stealing modes. And through the com-
bination of these 6 power stealing modes, 4 composite modes
are obtained. According to these 10 power stealing patterns,
a data set of abnormal users is generated. Experiments have
proved that the PSO-Attention-LSTM model has good detec-
tion performance for various power theft modes.
2)Using the LSTM model can fully consider the time series
characteristics of user power consumption, and has a good
time series data fitting regression ability. At the same time,
the Attention mechanism is introduced to give different prob-
ability weights to the hidden states of LSTM, and strengthen
the influence of important information, so that the model has
better prediction accuracy and detection effect.
3)Use PSO optimized model hyperparameters and obtain
optimal parameters, so that the model has more accu-
rate detection performance. Through the establishment of
comparative experiments, comparing with CNN-LSTM,
Attention-LSTM, LSTM, GRU, SVR, RF and LR, it is proved
that the model used in this paper has higher anomaly detection
ability.
The rest of this paper is organized as follows. In Section II,
the related work of the paper is introduced. Section III
the principle of abnormal power consumption detection
and the principle of LSTM sliding window prediction are
introduced. Section IV introduces LSTM network, attention
mechanism and particle swarm algorithm. Analyze and sum-
marize 10 abnormal power consumption patterns. Section V
introduces the simulation data and simulation settings, and
conducts simulations to verify the accuracy and validity of
the model. Finally, Section VI summarizes the work of this
article and future work.
II. RELATED WORK
A. DETECTION METHOD BASED ON STATISTICS MODEL
The statistical model-based detection method mainly com-
bines user-side smart meter electricity data, distribution net-
work voltage, current, power and other network status data
and network topology to establish a statistical model for
abnormal electricity use detection. It is difficult for most users
to perform data tampering to achieve data coordination to
detect abnormalities. For example, Lo et al. in [32] uses the
weighted least squares method to estimate the system state
through the topology of the distribution system, the voltage of
each node and the reactive power, and establishes the system
objective function for anomaly detection. This method has
high detection accuracy and low false detection rate. How-
ever, this method depends on the topology and parameters
of the distribution network, and the topology and parameters
of the distribution network are not constant. It is noted that,
the functional relationship of the parameters changes after
data tampering, and the model may have convergence prob-
lems [4].
B. DETECTION METHOD BASED ON GAME THEORY
This method assumes that each user’s decision-making
behavior is to maximize their own interests, and detects
abnormal users based on the difference between the
decision set of the stealing user and the normal user.
Saurabh et al. in [10] established a user-distribution com-
pany game model for anti-theft. Amin et al. in [33] applied
the likelihood ratio test to anomaly detection, and established
a game model by discussing more parameters such as elec-
tricity price and the proportion of stealers. This method has
only undergone theoretical simulation, and has not yet been
verified.
C. DATA-DRIVEN DETECTION METHOD
With the improvement of user-side online monitoring systems
and power information management systems, data-driven
detection methods have received more and more atten-
tion. Data-driven detection methods are mainly divided
into three types: classification-based, clustering-based, and
regression-based.
1)Classification-based approach: The classification-based
method uses the characteristics of electricity consump-
tion data to classify normal and abnormal. For example,
Zhang et al. in [14] uses the detection model of real-valued
deep confidence network, uses the firefly algorithm to solve
the local optimum, and finally detects anomalies through
classification. Xu et al. in [15] uses a sparse random for-
est model to classify the electricity consumption behavior
on the electricity consumption side and detect abnormal
behavior. Zhao et al. in [16] used LSTM for feature extrac-
tion and classified it through a fully connected network
(FCN). Buzau et al. in [17], the XGBoost classifier is used
for non-technical loss detection. Buzau et al. in [18] uses
long-term and short-term memory networks and multilayer
perceptron hybrid deep neural networks, which have higher
accuracy than other classifiers. Ghori et al. in [19], using the
data set of Pakistan Electric Power Company, the detection
performance of 15 classifiers was tested. Zheng et al. in [34]
used deep convolutional neural network (CNN) to classify
data sets to detect abnormal electricity consumption. Ibrahem
et al. in [35] proposed the ETDFE scheme, which can use the
machine learning classifier model for electricity theft detec-
tion while protecting user privacy. This method exploited the
inner-product operations on encrypted readings to evaluate
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a machine-learning model to detect fraudulent consumers.
This method has good detection accuracy, but the modeling
is complicated and requires label data.
2)Cluster-based method: This method mainly divides the
data set into different sub-data sets according to the charac-
teristics through a specific algorithm. Wang et al. in [13] uses
different clustering algorithms to detect 10kV non-technical
losses, and compares the detection effects of various algo-
rithms. Passos Júnior et al. in [36] use an optimal path
forest clustering method for detection. Tian et al. in [37]
used the density-based spatial clustering of applications with
noise (DBSCAN) clustering algorithm to cluster the fluctua-
tion interval of the user’s electricity load curve, and divided
all data points into core points, reachable points and abnor-
malities point. This method does not require label data and is
widely used, but there are problems in parameter selection,
the detection performance is poor.
3)Regression-based method: This method mainly uses
short-term load forecasting for users, and judges abnormal
points based on the deviation between the actual power
consumption and the predicted amount. Liu et al. in [38]
uses an attention mechanism-based convolutional neural
network-long short-term memory model for abnormality
detection. In the case of protecting user privacy, feature
extraction is used to predict time series data to detect abnor-
malities such as failure or shutdown of the electricity meter.
This model conforms to the timeliness of industrial anomaly
detection, and can quickly detect the failure or shutdown of
edge devices. This method optimizes the feature extraction
of the convolutional neural network through the attention
mechanism, and uses the long and short-term memory model
to learn the consumption characteristics, so as to accurately
detect the abnormality of the industrial edge equipment. This
article focuses on the detection of abnormal electricity con-
sumption behavior of residential users. The attention mech-
anism is used to strengthen the long and short-term memory
model’s learning of important information, suppress useless
information, and improve prediction accuracy. The particle
swarm algorithm is used to optimize the hyperparameters
of the long and short-term memory model, which solves
the complexity of manual parameter adjustment and further
improves the prediction accuracy. This method can more
accurately predict the consumption behavior of residential
users and accurately detect abnormal behaviors of users.
III. PROBLEM DESCRIPTION
The abnormal user electricity consumption detection mainly
judges abnormal users through the abnormal degree of the
user power consumption data. A user’s abnormal electricity
consumption behavior will cause differences in electricity
consumption data from the electricity consumption data of
normal users of the same type. The electricity consumption
curve, current curve, voltage curve, power curve and other
electricity consumption data during these abnormal behavior
periods will all change. The abnormality can be judged by
the degree of difference between the abnormal electricity
usage data and the normal electricity usage data. In this paper,
anomaly detection is carried out through user electricity
consumption. In order to reduce electricity costs, abnormal
users adopt various methods of stealing electricity to tamper
with the user’s electricity consumption. Therefore, the user
electricity consumption data is abnormal, and the user elec-
tricity consumption is available, which can effectively detect
abnormal users.
Nowadays, the number of electricity users is huge, so the
research on abnormal electricity consumption detection
mainly focuses on the high-efficiency detection ability of
large-scale users, which can quickly and effectively screen
out suspected abnormal users among the same types of users.
However, there are some users with relatively large electricity
consumption characteristics among normal users, and their
detection methods are easy to ignore the individual user’s own
power consumption habits, which are prone to misjudgment,
and rapid investigation of anti-electricity stealing personnel
increases difficulty. Therefore, this article considers the user’s
electricity consumption habits, customizes the model for the
user, and detects abnormal users by predicting the degree of
deviation between the user’s electricity consumption data for
a period of time in the future and the actual electricity con-
sumption. This method can make up for each other with the
abnormal detection of large-scale users, detect the suspected
abnormal users after large-scale detection, and eliminate
the misdetection caused by special electricity consumption
habits. At the same time, the prediction performance of
the attention mechanism model is adopted, and the particle
swarm optimization is used to optimize the adjustment of
model hyperparameters to improve the accuracy of anomaly
detection.
For abnormal user detection, first of all, it is necessary
to accurately predict the user’s electricity consumption data
in the future period. For this time series with massive data,
LSTM has certain advantages. LSTM can dig out the user’s
electricity consumption characteristics and laws from his-
torical information, has a long-term memory function, and
more accurately predicts the electricity consumption data in
the future when considering the user’s electricity consump-
tion habits. At the same time, particle swarm optimization
and attention mechanism are used to improve the prediction
accuracy and detection performance of the LSTM model.
According to the periodicity and trend of users’ electricity
consumption behavior [39], [40], this paper uses one-day
data to do window sliding processing, that is, the data of the
previous 24 time steps predict the data of the next time point.
The specific prediction principle is shown in Figure 1.
IV. THE ANOMALY DETECTION MODEL
A. INTRODUCTION TO LSTM
LSTM network is a special recurrent neural network(RNN).
By adding a new memory unit c, it solves the problems of
gradient disappearance and gradient explosion in RNN, and
improves the reliability of the model [41]. It has a feedback
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FIGURE 1. LSTM sliding window prediction principle.
structure, can mine data characteristics in historical infor-
mation, and has advantages in time series forecasting. The
LSTM network structural unit is shown in Figure 2.
LSTM is mainly divided into input gate, forget gate and
output gate. The input gate controls the input at the current
moment, the output gate controls the output at the current
moment, and the forget gate controls the state at the previous
moment. Formula (1) is the specific calculation of the forget
gate, formulas (2)-(3) is the specific calculation of the input
gate, formula (4) is the update formula of the memory unit,
and formula (5)-(6) is the specific calculation of the output
gate [42].
ft=σ(Wf[ht−1,xt]+bf) (1)
it=Sigmoid(Wi[ht−1,xt]+bi) (2)
c0
t=tanh(Wc[ht−1,xt]+bc) (3)
ct=ct−1·ft+it·c0
t(4)
ot=Sigmoid(Wo[ht−1,xt]+bo) (5)
ht=tanh(ct)·ot(6)
In the formula, ht−1and htare the output at the previous
moment and the current moment respectively, xtis the input
at the current moment, Wand bare the weight matrix and bias
in the network respectively, ftis the output of the forget gate,
and itis the input gate output, otis the input of the output
gate, c0
tand ctare the current state of the input and output
memory unit.
B. ATTENTION-LSTM MODEL
The attention mechanism [43] is a resource allocation mech-
anism that simulates the attention of the human brain.
It mainly changes the attention to information, thereby
increasing useful information and ignoring useless infor-
mation. Focus on important information, get more detailed
information, suppress and ignore useless information. The
attention mechanism is used to effectively highlight the key
features that affect the user’s power consumption in the pre-
diction results of the LSTM layer, and improve the prediction
performance and detection effect of the model.
The Attention-LSTM model mainly includes the input
layer, LSTM layer, Attention layer, and Output layer. In this
paper, the Attention layer is added behind the LSTM layer,
and the input layer of the Attention layer is the feature vector
output by the LSTM layer. The probability distribution value
FIGURE 2. LSTM network structure unit.
FIGURE 3. Attention-LSTM model structure.
of the feature vector is calculated by the features learned by
the LSTM layer according to the weight distribution princi-
ple, and better weight parameters are obtained by updating
iteratively. Finally, through the fully connected layer, the
final user power consumption forecast value is output. The
structure of the Attention-LSTM model is shown in Figure 3.
Among them, the calculation formula of Attention’s weight
coefficient is as follows:
et=utanh(wht+b) (7)
at=exp(et)
Pn
i=1exp(ei)(8)
st=Xn
t=1etat(9)
In the formula, etis the important feature of the LSTM
layer output vector htat the t-th time. uand ware the weight
coefficients, and bis the bias coefficient. stis the output of
attention at time t.
C. INTRODUCTION TO PSO
The particle swarm optimization mainly seeks the optimal
solution through information exchange and mutual cooper-
ation between individuals among groups. In the algorithm,
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each individual is called a particle. All particles have their
fitness value, and the quality of the particles is judged based
on the fitness value. Each particle has two variables: speed
and position, which are mainly updated based on the optimal
position in the group and the optimal position in the individual
history.
Suppose there are m particles in a d-dimensional space,
and the update formula for the velocity and position of each
particle is:
vn+1
id =ωvn
id +c1r1(pn
id −xn
id )+c2r2(pn
gd −xn
id ) (10)
xn+1
id =xn
id +vn+1
id (11)
where vn
id is the velocity of the d-th dimension component
of the i-th particle in the n-th iteration. xn
id is the position
of the d-dimensional component of the i-th particle in the
n-th iteration. pn
id is the individual optimal d-th dimension
component of the i-th particle in the n-th iteration. pn
gd is the
d-th dimension component of the optimal population of the
i-th particle in the n-th iteration. nis the number of iterations.
c1and c2are learning factors. r1and r2are random numbers
between 0 and 1. ωis the weight of inertia.
D. THE OVERALL FRAMEWORK OF ANOMALY DETECTION
MODEL
This paper is based on the PSO-Attention-LSTM model to
detect abnormal electricity consumption of users. Firstly,
predict the user’s electricity consumption curve in the future
based on the user’s historical electricity consumption data
and weather attributes, and then calculate the degree of
abnormality between the actual electricity consumption curve
and the predicted electricity consumption curve, and finally
determine abnormal users according to the threshold. The
overall framework of the specific user abnormal electricity
consumption detection model is shown in Figure 4:
The main steps of the abnormal power consumption detec-
tion model based on PSO-Attention-LSTM are as follows:
Step 1: Construct a normal user data set with the processed
user electricity consumption and corresponding weather data
as the input data of the PSO-Attention-LSTM model. Accord-
ing to the 6 types of electricity theft modes and the charac-
teristics of abnormal users’ electricity consumption curves,
10 electricity theft patterns are combined and established.
Finally, the data set simulated according to the electricity
stealing patterns is used as the actual output data of abnormal
users.
Step 2: According to the normal user data set output in
step 1, build an PSO-Attention-LSTM model. The particle
swarm algorithm is used to optimize model hyperparameters.
The attention mechanism retains important information in
the data, suppresses useless information, and improves model
performance.
Step 3: Calculate the degree of deviation between the elec-
tricity consumption prediction curve of the PSO-Attention-
LSTM model and the actual electricity consumption curve in
FIGURE 4. Overall flow chart of anomaly detection.
the abnormal user data set, and finally detect whether the user
has abnormal behavior.
E. ABNORMAL USER DATA SET BASED ON ELECTRICITY
THEFT MODE
Because the data set used in the article is the electricity
consumption data of normal users, the data needs to be trans-
formed according to the electricity theft mode to simulate
and generate the electricity consumption data set of abnor-
mal users. Abnormal power usage behavior of users is not
stochastic, and its ultimate goal is to reduce the electricity
bill that needs to be paid, so its abnormal behavior has a
certain law. The typical electricity consumption curve of a
user who steals electricity is a small amount of electricity
used continuously for a long time, and the curve is stable [44],
that is, it has the characteristics of continuous, small amount,
and stability.
Based on the characteristics of the electricity consumption
curve of users who steal electricity and the fact that there
are 6 typical electricity theft modes [45], [46], this paper
establishes a data set of abnormal users under typical elec-
tricity theft modes. Through the analysis and combination
of 6 typical electricity theft modes, a data set of abnormal
users under 4 compound modes is finally established. Typ-
ical electricity theft modes are shown in formulas (7)-(12).
Among them, Pi:jand P0
i:jare the electricity consumption data
of the normal user and the simulated abnormal user from the
i-th hour to the j-th hour, and ¯
Pis the average electricity con-
sumption of the normal user in the previous month. In mode
2 and mode 3, min(Pi:j)<P<max(Pi:j). In mode 4, i<m<n<j.
In mode 5 and mode 6, 0<α(t)<1, i≤t≤j.
Mode 1: P0
i:j=α·Pi:j,{0< α < 1}(12)
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FIGURE 5. Comparison chart of 10 power stealing modes.
Mode 2: P0
i:j=(Pi:jPi:j≤P
P Pi:j>P(13)
Mode 3: P0
i:j=max(Pi:j−P,0) (14)
Mode 4: P0
i:j=f(t)·Pi:j,
f(t)=(0t∈[m,n]
1t∈(i,m)∪(n,j)(15)
Mode 5: P0
i:j=Pi:j·α(t) (16)
Mode 6: P0
i:j=¯
P·α(t) (17)
Among the above-mentioned 6 typical electricity theft
modes, mode 1 and mode 5 have similarities, and it is of
little significance to combine with each other, so only one of
them is selected to be combined with other modes. Modes 2,
3, and 4 also have similarities, and only one of them is
selected for combination. Therefore, the 6 typical electricity
theft modes can be divided into mode 1, mode 5, mode 2,
mode 3, mode 4, mode 6 three types, each of which selects
one mode and combines them to create a total of 4 composite
modes. Among them, composite mode 1 is a combination of
mode 2 and mode 5, composite mode 2 is a combination of
mode 3 and mode 6, composite mode 3 is a combination of
mode 5 and mode 6, and composite mode 4 is a combination
of mode 4, mode 5 and mode 6. The compound mode is shown
in formulas (13)-(16).
CM 1: P0
i:j=(P(t)P(t)≤P
P P(t)>P(18)
where P(t) is consistent with mode 5, 0<α(t)<1, i≤t≤j
and min(P(t))<P<max(P(t)).
CM 2: P0
i:j=max(P(t)−P,0),(19)
where P(t) is consistent with mode 6, 0<α(t)<1, i≤t≤j
and min(P(t))<P<max(P(t)).
CM 3: P0
i:j=(¯
P·α(t)t∈[m,n]
Pi:t+t:j·α(t)t∈[i,m)∪(n,j](20)
Among them, 0.6<α(t)<0.8, i<m<n<j.
CM 4: P0
i:j=
Pi:m·f(t)t∈[i,m)
Pm:n·α(t)t∈[m,n]
¯
P·α(t)t∈(n,j]
(21)
where P(t) is consistent with mode 4, i≤t<m,i<m<
n<jand 0.6<α(t)<0.8.
According to the above-mentioned electricity theft mode,
the power consumption data of abnormal users is simulated.
Figure 5 shows the selected normal power consumption curve
from Dec 8th, 2016 to Dec 14th , 2016, and the abnormal
electricity consumption curve under 6 electricity theft modes
and 4 combined modes.
F. ANOMALY DETECTION MODEL CONSTRUCTION
The data set is divided into historical electricity consumption
data and current electricity consumption data. The historical
electricity consumption data is used to train the model, and
the PSO-Attention-LSTM prediction model is established to
predict the current electricity consumption data of the user.
The abnormal user electricity consumption data simulated
above is used as the actual electricity consumption data at
the current moment, and compared with the predicted current
electricity consumption data, the abnormal point is judged
by the threshold. The specific construction process of the
detection model based on PSO-Attention-LSTM is shown in
Figure 6.
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FIGURE 6. PSO-Attention-LSTM model construction process.
V. EXPERIMENTAL RESULTS
A. DATA ACQUISITION AND PROCESSING
The data used in this article comes from the public data
set of the University of Massachusetts [47], which records
user electricity consumption records from Oct 7th, 2014 to
Dec 15th, 2016. The weather data record corresponds to the
weather changes from Jan 1st , 2014 to Dec 31st , 2016, mainly
hourly temperature, humidity, body temperature, etc.
The original data comes from the electricity consumption
data of real users, so the data will be affected by external
influences and there will be missing and ‘‘noise’’. In order
to ensure the accuracy and reliability of the simulation, for
the existing missing data and wrong data, linear interpolation
is used to fill in the data. The paper selects hourly electricity
consumption data for a total of 793 days from Oct 14th, 2014
to Dec 14th, 2016. The weather data is selected to correspond
to the user’s temperature, humidity, and body temperature,
totaling 19,932 data.
In order to ensure the stability and speed of model training,
the data stochastic is normalized. The specific normalization
formula is shown in formula (17).
˜
P=P−Pmin
Pmax −Pmin
(22)
In the formula, ˜
Pis the user’s electricity consumption after
normalization, Pis the user’s electricity consumption before
normalization, and Pmax and Pmin are the user’s maximum
and minimum electricity consumption respectively.
B. SIMULATION SETTINGS
In the data set used in this article, 18,696 pieces of data with
a total of 779 days from Oct 14th, 2014 to Dec 1st , 2014
are used as the training set for PSO-Attention-LSTM model
training. The remaining 168 pieces of data for a total of 7 days
from Dec 1st , 2016 to Dec 7th, 2016 are used as the test
set. Use the data from Dec 8th, 2016 to Dec 14th , 2016 to
simulate abnormal user electricity consumption data. Among
them, select Dec 9th where the curve ‘‘peak’’ and ‘‘valley’’
are obvious and Dec 12th where the curve is relatively stable
perform abnormal behavior simulation to test the model’s
ability to detect abnormal users in different states. Compare
the electricity consumption curve predicted by the model
with the simulated abnormal electricity consumption curve to
determine the abnormal point. This article uses Tensor Flow
to build a detection model based on PSO-Attention-LSTM.
The model uses MSE loss function and Adam optimizer,
and uses particle swarm optimization to optimize the number
of hidden layers, iterations, and batch samples. In partical
swarm optimization, the inertia weight ωis set to 0.5, the
learning factors c1and c2are both set to 2, the population
size is set to 20, and the maximum number of evolutionary
iterations is set to 100.
C. SIMULATION RESULTS AND ANALYSIS
1) PSO-ATTENTION-LSTM MODEL PREDICTION RESULTS
To accurately detect abnormal electricity consumption behav-
ior of users, first accurately predict the electricity consump-
tion of normal users, and judge the abnormal points based
on the deviation between the predicted electricity consump-
tion data and the actual abnormal behavior electricity con-
sumption data. This paper uses the historical usage data of
normal users and the corresponding weather attributes (air
temperature, humidity, apparent temperature) to predict the
electricity consumption curve of users in the future. In this
paper, root mean square error (RMSE), mean absolute error
(MAE), mean absolute percentage error (MAPE) and abso-
lute error (AE) are used to evaluate model performance. Con-
fusion matrix, positive rate (PR) and false positive rate (FPR)
are used to evaluate detection performance. The specific eval-
uation formula is as follows.
RMSE =v
u
u
t
1
n
n
X
i=1P0
i−Pi
2(23)
MAE =1
n
n
X
i=1P0
i−Pi(24)
MAPE =1
n
n
X
i=1P0i−Pi
|Pi|(25)
AE =P0
i−Pi(26)
M=TP FP
FN TN (27)
PR =TP
TP +FN (28)
FPR =FP
FP +TN (29)
where, iis the label of the data sample, that is, hourly time; n
is the total number of data samples; Piis the actual electricity
consumption of normal users; P0
iis the normal user electricity
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FIGURE 7. Forecast value of electricity consumption of 8 models.
FIGURE 8. Comparison chart of absolute error of 8 models.
consumption predicted by the model; TP is the actual abnor-
mal electricity consumption data is detected as an abnormal
point; FN is the actual abnormal electricity consumption data
is detected as a normal point; FP is the actual normal elec-
tricity consumption data is detected as an abnormal point; TN
is the actual normal electricity consumption data is detected
as a normal point.
This article uses SVR, RF, LR, GRU, LSTM, CNN-LSTM
and Attention-LSTM for comparison. Figure 7 shows the
predicted curves and actual electric consumption curves of
the five methods. Figure 8 shows the absolute error curves of
the five methods. Table 1 shows the error indicators of the
five methods.
Figure 7 shows the actual electricity consumption curve
from December 1st to December 7th, 2016, and the forecast
curves of the five models. Table 1 and Figure 8 show the cor-
responding error curves and error indicators. Table 1 shows
the MAE, MRE and RMSE of the 8 methods. The three error
indicators of PSO-Attention-LSTM are all the smallest, and
RF has the largest error. It can be seen in Figs. 7 and 8 that
PSO-Attention-LSTM has high individual point errors, but
the error curve is relatively lowest, the prediction curve is the
best, and the RF error curve is the highest. The data used in
this article are residential electricity consumption data, the
electricity consumption is small, the fluctuation is large, and
there are certain errors in data collection and transmission,
so there is a certain ‘‘burr’’ in the error curve. Most of
the ‘‘burrs’’ in the PSO-Attention-LSTM error curve are the
errors of the ‘‘peak’’ and ‘‘valley’’ points of the electricity
consumption curve, and the overall error is small. In sum-
mary, the PSO-Attention-LSTM model has better accuracy
than other models and can accurately predict the electricity
consumption curve.
2) SIMULATION RESULTS AND ANALYSIS OF ABNORMAL
ELECTRICITY CONSUMPTION DETECTION MODEL
The electricity consumption of users in the future period
predicted by the model is compared with the actual value of
abnormal electricity consumption in 10 simulated power theft
modes, and abnormality is evaluated through absolute error
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TABLE 1. 8 methods of prediction error indicators.
FIGURE 9. 6 electricity consumption curve test results of electricity theft
modes (Dec 9th, 2016).
and relative error, and finallythe abnormal point is judged
according to the threshold. For the setting of the threshold,
setting too small will cause frequent false detections, and
setting too large will result in failure to detect. In order
to prevent as much as possible the misdetection caused by
model errors caused by the randomness of users’ electricity
consumption, the threshold should not be set too small, and
users’ electricity consumption habits need to be considered.
At the same time, in order to detect as many abnormal user
behaviors as possible, the threshold setting should not be
too large, and the threshold needs to be set according to the
user type. Combining the proportion of residents’ electricity
stealing and the average electricity consumption of residents,
the relative error threshold is set to 0.2, and the absolute
error threshold is set to 0.39kW·h. There is a certain error
in the detection of the ‘‘peak’’ value generated by the user’s
randomness in the detection model, that is, the ‘‘burr’’ in the
error curve, and only using the absolute error threshold is
prone to misjudgment. At the same time, since the ‘‘valley’’
value of the electricity consumption curve is less than 1,
the relative error is relatively large. Only using the relative
error threshold is easy to misjudge the ‘‘valley’’ value of the
electricity consumption curve. In summary, two thresholds
are used in the article to prevent false detections as much
as possible. Figures 9 and 10 show the detection results of
the 6 single power theft modes of the LSTM detection model
from Dec 8th to Dec 10th, 2016 and from Dec 11th to Dec
13th, 2016. Figures 11 and 12 show the relative error curves
and absolute error curves of the 6 power theft modes from
Dec 8th to Dec 14th, 2016.
Figures 9 and 10 respectively select Dec 9th and Dec 12th
for electricity theft. It can be seen from Figure 9-10 that the
method used in the article can well detect the time period of
abnormal behavior for the abnormal electricity consumption
curve under the 6 electricity theft modes. The misjudgment
points in the figure are mainly due to the sharp rise and fall
of the curve, which makes the LSTM unable to accurately
FIGURE 10. 6 electricity consumption curve test results of electricity theft
modes (Dec 12th, 2016).
FIGURE 11. Absolute error curve of 6 electricity theft modes.
FIGURE 12. Relative error curve of 6 electricity theft modes.
predict, so they are judged as abnormal points. But overall,
the method used in this article can accurately detect abnormal
behavior. Figures 11 and 12 are the absolute and relative
error curves of the six electricity theft modes. The two error
curves of Mode 4 have the highest degree of abnormality,
so the detection effect is the best. In mode 4, the electricity
consumption is randomly set to zero, resulting in a relative
error curve of 1 in the abnormal period, and a larger absolute
error curve, so the detection accuracy of abnormal points is
the highest. The error curve of mode 5 is relatively low, and
its anomaly detection effect is the worst. Mode 5 modifies the
current month’s electricity consumption based on the average
electricity consumption of the previous month. Therefore, its
electricity consumption curve is relatively flat and fluctuates
above and below the average value. The error is relatively low,
which makes it impossible to accurately detect abnormalities.
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FIGURE 13. 4 kinds of composite mode electricity consumption curve test
results(Dec 9th, 2016).
FIGURE 14. 4 kinds of composite mode electricity consumption curve test
results(Dec 12th, 2016).
Figure 13 and Figure 14 show the detection results of the
four composite electric stealing modes of the PSO-Attention-
LSTM detection model from Dec 8th, 2016 to Dec 10th , 2016
and from Dec 11th to Dec 13th, 2016. Figures 15 and 16 show
the relative error curves and absolute error curves of the four
power theft modes from Dec 8th to Decr 14th, 2016.
It can be seen from Figure 15 and 16 that the two abnormal-
ity curves during the period of compound mode 1 abnormal
behavior are the lowest. In Figure 13 and 14, it can also be
seen that composite mode 1 detects the least abnormal points.
Therefore, composite mode 1 has the worst anomaly detec-
tion effect. It can be seen from the above that the absolute
error of mode 5 at the ‘‘valley’’ point is relatively small,
and the detection effect of mode 5 is the worst compared
to other modes. The mode 2 is mainly to steal electricity by
modifying the ‘‘peak’’ point, so the detection effect of the
‘‘valley’’ point of the compound mode 1 is poor. The confu-
sion matrix was used to count the detection results of PSO-
Attention-LSTM and compared with the detection results
of GRU, SVR, RF, LR, CNN-LSTM and Attention-LSTM.
Table 2 is the confusion matrix of the detection results of the
abnormal points of the 6 power theft modes, and Table 3 is
the confusion matrix of the detection results of the abnormal
points of the 4 composite modes. According to the confusion
matrix, the detection rate and false detection rate are used to
evaluate the detection accuracy. Figure 17 is a radar chart of
the positive rate and false positive rate of the 10 electricity
theft modes for 5 detection methods.
It can be seen from Table 2 and Table 3 that the LSTM
detection model in the electricity stealing mode and the com-
pound stealing mode both detects more abnormal points and
fewer false detection points. Figure 17 also shows that the
FIGURE 15. Absolute error curve of 4 compound modes.
FIGURE 16. Relative error curve of 4 compound modes.
FIGURE 17. Radar chart of model positive rate and false positive rate.
positive rate is the largest and the false positive rate is the
smallest. LSTM has advantages in processing time series
data, and can learn users’ electricity consumption habits,
so the forecasting electricity consumption curve is accurate
and the detection performance is good. Compared with the
LSTM model, the PSO-Attention-LSTM model further opti-
mizes the parameters, and the detection effect is the best.
Relatively speaking, the positive rate of RF is relatively the
smallest, the false positive rate is the largest, and the detection
effect is the worst. Electricity consumption data has noise
due to the randomness of electricity consumption, and RF is
prone to over-fitting, resulting in the worst detection effect.
GRU also has advantages in processing time series data,
so the detection effect is stronger than SVR, RF and LR.
It can also be seen in Figure 17 that the positive rates of
SVR and LR are basically the same, and the false positive
rate of SVR is slightly lower than that of LR, and the detec-
tion effect is similar. The positive rate of CNN-LSTM and
Attention-LSTM is similar to that of LSTM, but the false
positive rate is lower than that of the LSTM model, which
reduces false detections. In summary, the detection model
based on PSO-Attention-LSTM has better anomaly detection
capabilities than the model. The detection results of this
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TABLE 2. 6 kinds of typical electricity theft mode abnormal point detection results.
TABLE 3. 4 kinds of compound mode abnormal point detection results.
model can provide auxiliary decision-making functions for
power grid anti-stealing personnel to find abnormal users, and
also provide a certain reference for the research on reducing
non-technical losses and grid abnormal detection.
VI. CONCLUSION
In order to investigate suspicious abnormal users and reduce
the non-technical losses of the power grid, this paper proposes
an abnormal user electricity detection method based on the
PSO-Attention-LSTM model. Firstly, we establish a power
theft mode, and generate a data set of abnormal users, then
build a PSO-Attention-LSTM prediction model based on his-
torical power consumption data and corresponding weather
characteristics, and finally determine the detection perfor-
mance of the model through the set threshold and abnormal
user data set. This method has the following advantages:
1)Constructed 6 actual electric stealing modes and 4 com-
posite modes, the detection performance of the detection
model for different kinds of abnormalities can be more
comprehensively evaluated through these 10 electric stealing
modes.
2)Using the LSTM network can fully consider the time
series characteristics of the user’s power consumption, has a
good time series data fitting regression ability. At the same
time, the attention mechanism is used to solve the prob-
lem of long-sequence data information loss, and it can also
enhance important information and suppress useless infor-
mation. Use the PSO to optimize the hyperparameters of the
Attention-LSTM model, obtain the optimal parameters, and
further improve the performance of the model.
3)By setting up comparative experiments, comparing with
LSTM, GRU, SVR, RF, LR, CNN-LSTM and Attention-
LSTM, it is verified that the PSO-Attention-LSTM model
has advantages in positive rate and false positive rate, and has
stronger anomaly detection ability.
The detection model established in this paper has a poor
detection effect on ‘‘burr’’ points caused by large noise and
strong randomness, and does not consider the related prob-
lems of practical application. Therefore, in future work, this
paper will eliminate the bad detection effect of ‘‘burr’’ points,
further improve the detection accuracy of the model, and
study the application of the detection model in practice.
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JIAHAO BIAN is currently pursuing the degree
with the School of Electrical Engineering, Shaanxi
University of Technology. His research interests
include artificial intelligence and power big data.
LEI WANG received the B.S. and M.S. degrees in
computer science and technology from the Xi’an
University of Technology, Xi’an, China, in 1994
and 1997, respectively, and the Ph.D. degree in
electronic science and technology from Xidian
University, Xi’an, in 2001. He is currently a Pro-
fessor with the Faculty of Shaanxi Key Laboratory
of Industrial Automation, Shaanxi University of
Technology, Hanzhong, Shaanxi, China. His cur-
rent research interests include evolutionary algo-
rithms, neural networks, and big data.
RAFAŁ SCHERER (Member, IEEE) received
the M.S. degree in electrical engineering from
the Department of Electrical Engineering and the
Ph.D. degree in computer science (Methods of
Classification Using Neuro-Fuzzy Systems) from
the Department of Mechanical Engineering and
Computer Science, Czestochowa University of
Technology. He is currently an Associate Professor
with the Institute of Computational Intelligence,
Czestochowa University of Technology. He was a
Principal Investigator of the Polish Ministry of Science and Higher Edu-
cation project Computational Intelligence Methods in Data Mining and
a Researcher in the Polish-Singapore Research Project (Development of
Intelligent Techniques for Modeling, Controlling and Optimizing Complex
Manufacturing Systems). He is a Co-coordinator of the Microsoft Dynam-
ics Academic Alliance Program, Czestochowa University of Technology.
He authored a book on multiple classification techniques published in
Springer. He authored more than 80 research articles. His research inter-
ests include developing new methods in computational intelligence and
data mining, ensembling methods in machine learning, and content-based
image indexing. He was a Reviewer for major computational intelli-
gence journals. He co-organizes every year or two years the International
Conference on Artificial Intelligence and Soft Computing in Zakopane
(http://www.icaisc.eu/) which is one of the major events on computational
intelligence. He is also a Co-Editor of the Journal of Artificial Intelligence
and Soft Computing Research (http://jaiscr.eu/).
MARCIN WOŹNIAK received the M.Sc. degree
in applied mathematics from the Silesian Uni-
versity of Technology, Gliwice, Poland, in 2007,
and the Ph.D. degree in computational intelligence
and the D.Sc. degree in computational intelligence
from the Czestochowa University of Technology,
Czestochowa, Poland, in 2012 and 2019, respec-
tively. He is currently an Associate Professor with
the Faculty of Applied Mathematics, Silesian Uni-
versity of Technology. He is a Scientific Supervi-
sor in editions of The Diamond Grant and The Best of the Best programs
for highly talented students from the Polish Ministry of Science and Higher
Education. He participated in various scientific projects (as Lead Investi-
gator, Scientific Investigator, Manager, or Participant) at Polish and Italian
universities. He was a Visiting Researcher with universities in Italy, Sweden,
and Germany. He has authored/coauthored more than 100 research papers
in international conferences and journals. His current research interests
include neural networks with their applications together with various aspects
of applied computational intelligence. He was a Session Chair at various
international conferences and symposiums, including the IEEE Symposium
Series on Computational Intelligence and the IEEE Congress on Evolu-
tionary Computation. He was the Editorial Board member or an Editor
of Sensors, IEEE ACCESS,Frontiers in Human Neuroscience,PeerJ CS,
the International Journal of Distributed Sensor Networks,Computational
Intelligence and Neuroscience, the Journal of Universal Computer Science,
and so on.
PENGCHAO ZHANG received the B.Eng. degree
in automation from the Shaanxi University of
Technology (SNUT), Hanzhong, China, and the
M.Eng. degree in traffic control engineering from
Northwestern Polytechnical University (NPU),
Xi’an, China, where he is currently pursuing the
Ph.D. degree. He is also an Associate Professor
with SNUT. His current research interests include
industrial robot and mobile robotics.
WEI WEI (Senior Member, IEEE) received the
M.S. and Ph.D. degrees from Xi’an Jiaotong Uni-
versity, Xi’an, China, in 2005 and 2011, respec-
tively. He is currently an Associate Professor with
the School of Computer Science and Engineering,
Xi’an University of Technology, Xi’an. He ran
many funded research projects as a principal inves-
tigator and technical members. He has published
around 100 research papers in international con-
ferences and journals. His current research inter-
ests include wireless networks, wireless sensor networks application, image
processing, mobile computing, distributed computing, pervasive computing,
the Internet of Things, and sensor data clouds. He is a Senior Member of
the China Computer Federation. He is a TPC member of many conferences.
He is an Editorial Board Member of the Future Generation Computer
System, IEEE ACCESS,Ad Hoc & Sensor Wireless Sensor Network, the
Institute of Electronics, Information and Communication Engineers, and
KSII Transactions on Internet and Information Systems. He is a Regular
Reviewer of the IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
the IEEE TRANSACTIONS ON IMAGE PROCESSING, the IEEE TRANSACTIONS ON
MOBILE COMPUTING, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, the
Journal of Network and Computer Applications, and many other Elsevier
journals.
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