A hybrid approach of artificial neural network-particle swarm optimization algorithm for optimal load shedding strategy

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 4, August 2022, pp. 4253~4263
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i4.pp4253-4263  4253
Journal homepage: http://ijece.iaescore.com
A hybrid approach of artificial neural network-particle swarm
optimization algorithm for optimal load shedding strategy
Nghia Trong Le1
, Tan Trieu Phung2
, Anh Huy Quyen1
, Bao Long Phung Nguyen1
, Au Ngoc Nguyen1
1
Department of Electrical and Electronics Engineering, University of Technology and Education, Ho Chi Minh City, Vietnam
2
Department of Electrical and Electronics Engineering, Cao Thang Technical college, Ho Chi Minh City, Vietnam
Article Info ABSTRACT
Article history:
Received Jun 12, 2021
Revised Dec 17, 2021
Accepted Jan 1, 2022
This paper proposes an under-frequency load shedding (UFLS) method by
using the optimization technique of artificial neural network (ANN)
combined with particle swarm optimization (PSO) algorithm to determine
the minimum load shedding capacity. The suggested technique using a
hybrid algorithm ANN-PSO focuses on 2 main goals: determine whether
process shedding plan or not and the distribution of the minimum of
shedding power on each demand load bus in order to restore system’s
frequency back to acceptable values. In the hybrid algorithm ANN-PSO, the
PSO algorithm takes responsible for searching the optimal weights in the
neural network structure, which can help to optimize the network training in
terms of training speed and accuracy. The distribution of shedding power at
each node considering the primary control and secondary control of the
generators’ unit and the phase electrical distance between the outage
generators and load nodes. The effectiveness of the proposed method is
experimented with multiple generators outage cases at various load levels in
the IEEE-37 Bus scheme where load shedding cases are considered
compared with other traditional technique.
Keywords:
Artificial neural network
Hybrid ANN-PSO
Optimal load shedding
Particle swarm optimization
Phase electrical distance
This is an open access article under the CC BY-SA license.
Corresponding Author:
Nghia Trong Le
Department of Electrical and Electronics Engineering, University of Technology and Education
1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, 71313, Vietnam
Email: trongnghia@hcmute.edu.vn
1. INTRODUCTION
Load shedding in an electrical system is a very complex and fast process. Operational failures are
unpredictable and the time required to implement load shedding is also very short. Therefore, traditional load
shedding methods using under-frequency load shedding relays (UFLS), or under voltage load shedding relays
(UVLS) [1]–[5] are not fast enough for emergencies. The actual load shedding system takes place in real
time, and in this part, the fast response of the neural network can provide the optimal and responsive load
recognition and shedding under instantaneous conditions. This method of adaptive load shedding using
neural networks has been developed in [6], [7]. Furthermore, the literature [5] indicated that the response
speed of the artificial neural network (ANN) algorithm is faster than other methods. However, ANN also has
limitations such as system type, system dimension, impact function, learning factors, and amount of training
sets [8].
At present, intelligent computing techniques have been widely implemented in the power system.
This is due to the robustness and flexibility of these algorithms in solving nonlinear problems. Meta-heuristic
algorithms such as: ANN [9]–[12], genetic algorithm (GA) [13], and particle swarm optimization (PSO) [14],
have been proposed to determine the lowest amount of shedding power that maximizes the benefit of the
system.

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Int J Elec & Comp Eng, Vol. 12, No. 4, August 2022: 4253-4263
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In particular, the ANN is an information processing template that is modelled based on the activity
of the people nervous system. In an ANN, the weight represents the importance (strength) of the input data to
the information processing. Learning processing of ANN is actually the process of adjusting the weights of
the input data to get the desired result. Back-propagation (BP) is the most commonly used learning method.
To solve problems in power systems, ANN often use network types such as general regression neural
network (GRNN), back propagation neural network (BPNN). In particular, back propagation neural network
(BPNN) is an algorithm that is effectively used to improve training of artificial neural networks (ANNs). Its
performance at a large scale depends on the structure of the different learning model and algorithms used to
compute and reduce its error in the learning process. However, BPNN has two major drawbacks: low
convergence speed and instability. Today, some recent researches had been studied to limit the disadvantages
of BPNN networks by improving the network structure. In [15], the author had proposed to improve the
connection weights of the neural network by combining the ant colony optimization algorithm (ACO) with
ANN. The results of this method can be given in a high performance but the algorithm also has limitations
such as long training time, and the performance of the algorithm is highly dependent on the settings. Unlike
ACO, PSO algorithm is a search algorithm based on swarm regression, it does not require any data structure
information and highly effective in global search problems [16].
The objective of this paper is to show the efficiency of hybridizing PSO algorithm with ANN
network. With the support of the PSO algorithm, the proposed method can determine the link weights in the
ANN faster to shorten the computational process of setting the appropriate weights in the network. That
saves the time to train the network but still generates the neural network with high accuracy. Load shedding
control strategies consider to the primary and secondary control of generators to minimize the capacity of
load reduction. The distribution of the capacity of load reduction at each load node of the system is made
based on the phase electrical distance between the loads and the outage generator.
2. METHOD
2.1. Optimal quantity of load reduction capacity
The frequency response of the power system when a generator failure occurs, includes the following
processes: primary frequency control and secondary frequency control. In this paper, the frequency response
of the power grid takes into account the influence of frequency dependent loads [16]. After this process end,
if the frequency is even not within the allowable parameter, then load reduction have to perform. Details of
these processes have been presented in [17]. Computing the minimum shedding power helps to minimize
damage to customers while restoring the frequency to the allowable value. In [17], the optimum amount of
load reduction capacity is expressed as (1):
∆𝑃𝐿𝑆𝑚𝑖𝑛 = ∆𝑃𝐿 +
∆𝑓𝑎𝑙𝑙𝑜𝑤
𝑓0
. 𝛽 − ∆𝑃𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑚𝑎𝑥 (1)
In which,
∆𝑃𝐿 =
−∆𝑓1
𝑓𝑛
. 𝛽 is status of power balance
𝛽 = 𝑃𝐿. 𝐷 + ∑
𝑃𝐺𝑛,𝑖
𝑅𝑖
𝑛−1
𝑖=1 (𝑃𝐺𝑛,𝑖
is the rated power of the ith
generator)
𝑅 =
∆𝑓
∆𝑃𝐺
is the drop of the adjustment characteristic
∆𝑃𝐺 =
−𝑃𝐺𝑛
𝑅
.
∆𝑓
𝑓𝑛
is the relationship between power variation and frequency variation
D is the percentage characteristic of the change of load according to the percentage change of frequency [18].
∆𝑓𝑎𝑙𝑙𝑜𝑤 = 𝑓0 − 𝑓𝑎𝑙𝑙𝑜𝑤 is the allowable frequency attenuation.
∆𝑃𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑚𝑎𝑥 = ∑ (𝑃𝐺𝑚,𝑗
− ∆𝑃𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙.𝑗)
𝑚
𝑗=1 is the maximum amount of secondary
control power generated by the power system.

Int J Elec & Comp Eng ISSN: 2088-8708 
A hybrid approach of artificial neural network-particle swarm optimization … (Nghia Trong Le)
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Where, ∑ ∆𝑃𝑃𝑟𝑖𝑚𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 = ∑
−𝑃𝐺𝑛,𝑖
𝑅𝑖
𝑛−1
𝑖=1 .
∆𝑓1
𝑓0
𝑛=1
𝑖=1 is the primary control power of the jth
generator; 𝑃𝐺𝑛,𝑖
is the
rated power of the ith
generator; ∆𝑓1 = 𝑓1 − 𝑓0 is the frequency attenuation; f0 is the rated frequency of the
power system; 𝑃𝐺𝑚,𝑗
is the maximum generating power of the secondary frequency control generator j.
2.2. Phase electrical distance and its application in load shedding
The definition of the phase electrical distance (PED) between two buses is defined as in (2)[19], [20]:
1 1 1 1
( , ) ( ) ( ) ( ) ( )
D i j J J J J
p P ii P jj P ji P ij
   
   
    (2)
As shown in (2) can be written as (3):
1 1 1 1
( , ) ( ) ( ) ( ) ( )
P P P P
D i j J J J J
p jj ij ii ji
   
   
    (3)
where, 1 1
( ) ( )
J J
P jj P ij
 
 
 is the phase angle between 2 nodes j and i due to the power P injected into node j.
1 1
( ) ( )
J J
P ii P ji
 
 
 is the phase angle between 2 nodes i and j due to the power P injected into node i.
As shown in (2) can be written as (4):
1 1 1 1
( , ) ( ) ( ) ( ) ( )
D i j J J J J
p P jj P ji P ii P ij
   
   
    (4)
where,
1 1
( ) ( )
J J
P jj P ji
 
 
 is the phase angle change at j due to the active power transferred from j to i.
1 1
( ) ( )
J J
P ii P ij
 
 
 is the phase angle change at i due to the active power transferred from i to j.
In power system, the goal is to concentration on the priority of load shedding at nearby the outage
generator location. To do this, the idea of the PED between node i and node j is applied. Two nodes that are
close to each other will always have a very small PED between them. The smaller PED between the load
node and the generator, the closer the load node is to the faulty generator. Therefore, when a fault occurs in
an area on the grid, the adjustment of the grid at the faulty area will achieve the best effect. Therefore,
minimizing the control error in the faulty area will cause less effect on other areas of the system. In load
curtailment, zoning a serious fault and shedding loads around the faulty area will make the impact of the fault
on the system smaller, the load shedding plan will be more effective. When a generator failure occurs at node
n, the quantity of shedding power at m different load nodes based on PED can be distributed according to the
principle: the closer the load node of the failed generator, the greater the amount of shedding power and vice
versa. The expression to calculate the load reduction capacity at load nodes according to PED is shown in
expression (5) [21]:
𝑃𝐿𝑆𝑖 =
𝐷𝑃,𝑒𝑞
𝐷𝑃,𝑚𝑖
. 𝑃𝐿𝑆𝑚𝑖𝑛 (5)
with
𝐷𝑃,𝑒𝑞 =
1
∑
1
𝐷𝑃,𝑚𝑖
𝑖≠𝑚
(6)
In which: m is the quantity of generators; i is quantity of bus; PLSi is the load reduction capacity at ith
bus
(MW); PLSmin is the minimum load reduction capacity to restore the frequency back to acceptable range
(MW); DP,mi is the PED of the load to the failure generator m; DP,eq phase angle sensitivity of all load buses
and generators. The PED between load buses and generator is shown in Figure 1.
2.3. Particle swarm optimization (PSO) algorithm and back-propagation neural network (BPNN)
BPNN proposed by Rumelhart, Hinton and Williams in 1986 is applied in research fields such as
pattern recognition, data prediction, problem recognition, image processing and many more other areas [22],
[23] based on the ability to self-learn from mistakes. To overcome the disadvantages of BPNN networks, the
PSO algorithm is one of the optimal search techniques to help solve the problems posed above. It allows
searching for optimal solutions over large spaces.
The PSO algorithm, which modeled the flight of birds in searching for food, was introduced by
Kennedy et al. [24]. PSO is set with a random group of particles (solutions) and then in processed of finding

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optimal solution by updating generations. In each generation, each instance is updated to the two best values.
The first value is the best solution obtained so far, called Pbest. Another optimal solution that this individual
follows is the global optimal solution Gbest, which is the best solution that the individual neighbor of this
individual has achieved so far. In other words, each individual in the population updates their position
according to its best position and that of the individual in the population up to the present time, which is shown
in Figure 2 [24]. The flowchart of the PSO algorithm is shown in Figure 3.
Figure 1. Describe the PED between generator 8 and the load buses
Figure 2. The position of the individuals in the convergence of the PSO algorithm
Velocity and position of each particle is updated as (7):
𝑣𝑖
𝑘+1
= 𝑤. 𝑉𝑖
𝑘
+ 𝑐1. 𝑟1(𝑃𝑏𝑒𝑠𝑡 − 𝑋𝑖
𝑘
) + 𝑐2𝑟2(𝐺𝑏𝑒𝑠𝑡 − 𝑋𝑖
𝑘
) (7)
After each cycle the location of each instance will be updated as (8):
𝑋𝑖
𝑘+1
= 𝑋𝑖
𝑘
+ 𝑉𝑖
𝑘+1
(8)
In which:
Vi
k
, Xi
k
: the velocity and position of each particle i at iteration k.
𝑊 : inertia weight.
c1, c2: acceleration coefficients, whose range are between 1.5 and 2.5.

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r1, r2: random value generated for each velocity update, whose value are in range [0; 1]
𝑃𝑏𝑒𝑠𝑡, 𝐺𝑏𝑒𝑠𝑡: the best position of the ith
particle, and the best position in the corresponding population,
respectively.
Figure 3. PSO algorithm diagram
3. BUILDING HYBRID ALGORITHM: ARTIFICIAL NEURAL NETWORK-PARTICLE
SWARM OPTIMIZATION (ANN-PSO)
The working principle of the hybrid ANN-PSO algorithm is mostly based on the effectiveness of
BPNN, which is the adjustment of the weight is always in the descending direction of the error function and
requires only some local information. However, the BPNN also has limitations [16] such as low convergence
speed and instability. These limitations are due to the fact that the network cannot be trained when the
weights are adjusted to very large values. The case of error curves is so complex that there are so many local
minima that the convergence of the algorithm is very sensitive to the initial values. Inspired from [25], by
combining with PSO, the network training performance can be improved as well as helping the network
avoid the "local minima" errors during training. The only limitation of this proposed algorithm is the
necessity to set the parameters of the algorithm to match the data. The block scheme of the proposed method
is shown in Figure 4. The hybrid artificial neural network-particle swarm optimization (ANN-PSO) algorithm
implementation process is presented in Figure 5.
Figure 4. The block diagram of proposed method
The steps to implement the ANN-PSO hybrid algorithm are as:
Step 1: Initialize the network structure with input and output data.
Step 2: Carry out the implementation of the PSO algorithm to find a suitable new W weight for the neural
network according to the following objective function:
𝑀𝑆𝐸 =
1
𝑛
∑ (𝑑𝑖 − 𝑦𝑖)2
𝑛
𝑖=1 (11)

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where: di: the ith
output of the neural network
yi: the ith
desired output
n: the output number of the neural network
Step 3: From the new weights W in the neural network proceed to train the network.
Step 4: Compare and evaluate the results.
Figure 5. The process of implementing hybrid algorithm ANN-PSO
4. SIMULATION AND RESULTS
The suggested technique is experimented on the IEEE-37 bus with 9 generators and 26 loads bus
electrical system [17], [26]. The simulation is processed on the PowerWorld 19. The flowchart of the process
of data collection, training and testing is shown in Figure 6.
In this study, the JO345#1 generator (bus 28) disconnected from the power system. Applying the
method presented in section 2.1 to estimate the smallest load reduction capacity of 17.64 MW. The PED
between the JO345#1 generator and the load nodes is shown in Figure 7.
The simulation results in Figures 8 and 9 show that the proposed load shedding method has an
improvement in power quality in terms of frequency bus POPLAR69. After distributed amount of shedding
power at each Bus based on PED (mentioned in section 2.2), the frequency increases from 59.6 to 59.7 Hz,
which is within allowable range. The proposed load shedding strategy does not have too much impact on
voltage quality.
The construction of the training dataset is done by simulating the IEEE 37-bus diagram with varying
the loads from 60% to 100% of the maximum load. Each load level will correspond to different generator
outage cases. The results obtained in 328 samples, including: 123 samples of load shedding and 205 samples
of non-load shedding. For each load shedding case, the delivery of the load reduction capacity at the load
buses is made based on the PED, presented in (5) in section 2.2 corresponding to the power level of the load
and generator location. Collected data will be normalized and divided into 85% of training, the rest is used to

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check the accuracy of ANN-PSO. Proceed to build a training neural network with a network structure of
8 hidden layer neurons with different input variables from 15-165 variables, which are the parameters of the
grid system, including: PLoad is load active power, generator power is PGenerator, power on transmission line is
PBranch, VBus is bus voltage, fBus is bus frequency and the output are 9 variables which are the powers to be
shed at the load buses when there is a generator failure from load shedding 1 to Load shedding 9. The
accuracy of the proposed method compared with the GA training method and back-propagation is presented
in Table 1.
Figure 6. Processing of proposed method flowchart
Figure 7. PED relationship between JO345#1 generator and load nodes

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The comparison of simulation results between ANN-PSO and GA-ANN methods is shown in
Figure 10. Figure 10 presents the simulation results of the proposed ANN-PSO hybrid algorithm applied to
the IEEE 37-bus, 9-generator, which has superior advantages over the GA-ANN hybrid algorithm in both
time aspects training time and accuracy. Specifically, with 120 input variables, the training and testing
accuracy of ANN-PSO is 97.4% and 100% higher than that of GA-ANN at 81.8% and 79.1%. The training
time of ANN-PSO is faster than that of GA-PSO hybrid algorithm because the PSO has a faster convergence
speed than the GA. Thus, the weight W will be updated faster during training. That shows the effectiveness of the
proposed method.
Figure 8. Comparison of frequency bus POPLAR69 between before and after the load rejection
Figure 9. Comparison of voltage bus POPLAR69 between before and after the load rejection

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Table 1. Compare the products of the suggested technique with other methods
Variable
ANN-PSO GA-ANN BPNN
Train Test Time_CPU Train Test Time_CPU Train Test Time_CPU
15 96.4 100 2.8 91.1 89.5 542.9 96.4 98.5 1.2
30 90.1 95.5 1.2 97.9 98.5 718.4 90.4 94 1.5
45 90.1 82.1 1.5 84.6 77.6 731.5 90.4 94 2.5
60 90.1 95.5 1.8 83.3 83.6 283.5 94.8 98.5 1.4
75 90.1 82.1 3.1 89.3 85.1 852.1 90.4 94 3.0
90 84.6 77.6 2.9 91.1 89.5 699.6 90.4 94 3.4
105 90.1 82.1 1.9 84.6 77.6 542.2 90.4 94 5.1
120 97.4 100 3.9 81.8 79.1 615.0 90.4 94 2.2
135 91.1 95.5 1.9 80.2 77.6 530.4 90.4 94 2.1
150 97.6 100 2.7 82.03 79.1 1213.8 90.4 94 22.8
165 90.1 82.1 2.6 89.6 85.1 907.0 90.4 94 4.4
Figure 10. Compare the training results of the proposed method with GA-ANN
5. CONCLUSION
BPNN is a network structure commonly used in identification and prediction problems. BPNN has
some drawbacks such as decelerate convergence speed and neighboring minima error, which reduce the
performance of the network. PSO is considered as a search algorithm to get the optimal weights in the ANN.
The combination of PSO algorithm and neural network with back-propagation algorithm aims to overcome
the limitations of the traditional BPNN. The bright result of this method is a network structure can learn
faster and predict with better accuracy. The efficiency of the proposed method had been compared with the
GA-ANN method to shows the superiority in accuracy and training time.
The optimization in relations of capacity, location and load reduction period takes into account
primary and secondary control factors and hybrid ANN-PSO algorithm to establish a rules base which is
constructed on the PED applied to the IEEE 37-bus, 9-generator test scheme, the generators have
accomplished efficiency in training time just as high precision. In further work, it is needed to consider the
impact of renewable energy sources in the analysis of frequency stability and load shedding.
ACKNOWLEDGEMENTS
This work belongs to the project grant No: B2020-SPK-03 funded by Ministry of Education and
Training and hosted by Ho Chi Minh City University of Technology and Education, Vietnam.
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BIOGRAPHIES OF AUTHORS
Nghia Trong Le received his Ph.D. degree in electrical engineering from Ho Chi
Minh City University of Technology and Education (HCMUTE), Vietnam, in 2020. Currently,
he is a lecturer in the Faculty Electrical and Electronics Engineering, HCMUTE. His main
areas of research interests are load shedding, power systems stability and distribution network.
He can be contacted at email: trongnghia@hcmute.edu.vn.

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Tan Trieu Phung received his M.Sc. degree in electrical engineering from Ho
Chi Minh City University of Technology and Education (HCMUTE), Vietnam, in 2020.
Currently, he is a lecturer in the Faculty Electrical and Electronics Engineering, Cao Thang
Technical College. His main areas of research interests are Artificial Neural network, load
shedding in power systems. He can be contacted at email: pttan@hcmute.edu.vn.
Anh Huy Quyen received his Ph.D. degree in power system from MPIE, Russia
in 1993. Currently, he is a professor and lecturer in the Faculty Electrical and Electronics
Engineering, HCMUTE. His main areas of research interests are modelling power systems,
pattern recognition in dynamic stability of power systems, artificial intelligence. He can be
contacted at email: anhqh@hcmute.edu.vn.
Bao Long Phung Nguyen received his Bachelor degree in Ho Chi Minh City
University of Technology and Education (HCMUTE), Vietnam, in 2020. He is currently a
research assistant in the Faculty Electrical and Electronics Engineering in Ho Chi Minh City
University of Technology and Education (HCMUTE), Vietnam. He can be contacted at email:
16142018@student.hcmute.edu.vn.
Au Ngoc Nguyen received his B.Sc. and PhD. in electrical engineering from Ho
Chi Minh City University of Technology and Education (HCMUTE), Vietnam, in 1998 and
Ho Chi Minh City University of Technology (HCMUT), in 2019, Vietnam. He is currently
lecturer in the Faculty Electrical and Electronics Engineering, HCMUTE. His main areas of
research interests are power systems stability and distribution network. He can be contacted at
email: ngocau@hcmute.edu.vn.

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