EJEEE
https://doi.org/10.62909/ejeee.2024.006 Edison Journal for Electrical and Electronics Engineering
Article
Load Frequency Control for Hybrid Power System by Modified
PSO-PID Controller
Mahmood Hasan Alhafadhi 1, , Mustafa Jamal Ahmed 2, and Husam Hamid Ibrahim 3, *,
1 Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary;
femmahmood@uni-miskolc.hu
2 Department of Biomedical Engineering, Institute of Applied Sciences, Faculty of Engineering, Near East
University, Cyprus; 20227121@std.neu.edu.tr
3 Department of Electrical, Electronic and Systems Engineering, Faculty of Engineering and Built Environ-
ment, Universiti Kebangsaan Malaysia (UKM), Selangor, Malaysia; p97884@siswa.ukm.edu.my
* Correspondence; Tel.: +60 172804671
Abstract: With a proportional integral derivative (PID) controller, the effectiveness of load fre-
quency control (LFC) for separated a variety of electric power-generating devices is described. In
the structure under study, a thermal and hydro power producing unit is combined. In order to
maintain system efficiency in the event of an unexpected demand on the power structure, the PID
controller is suggested as a secondary regulator. The suggested PID controller's optimum gain set-
tings are found using the modified particle swarm optimization (MPSO) technique. The controller
increase settings were optimized using a variety of expense processes, namely integral time absolute
error (ITAE), integral absolute error (IAE), integral squared error (ISE), and integral time squared
error (ITSE). Additionally, the efficiency evaluation of traditional PID controllers for a comparable
system utilizing the differential evolution (DE) algorithm and genetic algorithm (GA) demonstrates
the improvement of the MPSO approach. The findings demonstrate that in an electrical crisis, the
MPSO-PID controller provides a quicker stabilized reaction and that the suggested technique's per-
cent increase over the traditional way is over GA and over DE.
Keywords: proportional integral derivative (PID); modified particle swarm optimization (MPSO);
Load Frequency Control (LFC)
1. Introduction
Distribution of electricity and output, or the production and distribution of electricity
based on user load demand, make up the electric energy system. Globalization and tech-
nological development have led to a daily increase in consumer appetite for power. By
building new power plants and renovating old ones, the producing capacity is boosted to
meet load demand. The power grid faces a number of problems when a complex power
network is implemented, including voltage and frequency deviation [1].
The way that consumers utilize power is not linear. To guarantee stable system op-
eration, power generation so changes proportionately with load demand. Rapid increases
in power demand have an effect on the stability of the whole power-generating unit in a
system or any linked system [2].
One of the most important factors affecting the grade of the energy strategy is fre-
quency, and the LFC technique takes care of frequency fluctuation. A secondary controller
should be involved into the strategy in order to implement the LFC scheme, which will
increase performance and recover the specified power supply [3]. Because the secondary
controllers aren't able to achieve the required outcome, the controller gain has to be im-
proved. The literature research in this study included a variety of optimal methodologies
Citation: Hasan Alhafadhi, M., M.
Jamal Ahmed, and H. Hamid Ibra-
him, Load Frequency Control for Hy-
brid Power System by Modified PSO-
PID Controller. Edison Journal for
Electrical and Electronics Engineer-
ing, 2024. 2: p. 35-41.
Academic Editor: Assoc. Prof. Dr.
Mojgan Hojabri
Received: 13/6/2024
Revised: 15/7/2024
Accepted: 2/8/2024
Published: 9/8/2024
Copyright: © 2024 by the authors.
Submitted for possible open access
publication under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/license
s/by/4.0/).
EJEEE 2024, Vol.2 36 of 41
to enhance the controller gain parameters. The reaction of secondary controllers and op-
timization techniques that have been tried and tested are covered in the sections that fol-
lowing [4].
The literature that is relevant to the proposed work is included in the description,
like deferential evaluation algorithm [5, 6], novel optimized fuzzy logic control [7], opti-
mal fractional-order fuzzy PID controller [8], moth flame optimization algorithm [9], hy-
brid bacteria foraging optimization algorithm [10] fitness dependent optimizer [11], frac-
tional order [12] particle swarm optimization [13] and it demonstrates how many experts
adjust the controller gain settings using the MPSO optimization approach. Furthermore,
a backup PID controller was built for the suggested power supply. To demonstrate the
MPSO's superiority, comparisons with other widely used techniques, including the con-
ventional, GA, and DE algorithms, were made.
The primary benefit of MPSO is its ability to provide high-quality solutions while
avoiding premature convergence to local minima. The primary benefit of MPSO is that it
has fewer tuning parameters. By using a high-dimensional search space and particle in-
teractions, MPSO finds the optimal solution.
In this study, the MPSO–PID controller was used with various expense processes.
The system's effectiveness was assessed by comparing its response to a PID controller for
an identical power system that had been modified using a conventional, genetic, and dif-
ferential evolution method. This study's key objectives were to improve the suggested
system's performance and preserve system stability in urgent circumstances so that all
customers could get high-quality electricity. In order to overcome the crisis, a PID con-
troller that was adjusted using MPSO and four distinct expense processes was used to
enhance the system parameters. Using the same criteria, the MPSO-PID response was also
evaluated in comparison to traditional, GA, and DE-based PID controller comebacks.
In this research, expected traditional generation sources were combined with an iso-
lated power system. Only one expense processes were considered in the design and ex-
ploration of the present work. By examining the effectiveness of the suggested controller
and optimization strategy in the addressed power system with four different expense pro-
cesses, this research, in contrast, narrows this disparity. A thorough analysis was done to
ascertain the exact advantages of the recommended upgraded controller.
2. Materials and Methods
2.1 Computational Simulation of the Power System
Three different types of power-generating units—thermal and hydro units—are in-
cluded in the planned power network. In addition, a PID controller has been added to
control the fluctuation and all three units were seen as the source of a single system. Figure
1 displays the Simulink model of the suggested system configuration. The suggested sys-
tem's mathematical formulation is as follows, as covered in [5, 14]:
Components of the thermal power system:
(3)
Components of the hydropower system:
EJEEE 2024, Vol.2 37 of 41
where Tsg, Tr, and Tt stand for the duration characteristics of the steam generator,
the reheater, and the regulator, correspondingly. The duration characteristics for the gov-
ernor, drop reimbursement, penstock turbine, and hydro power station are Tgh, Tr, Trh,
and Tw, in that order. Employing the MATLAB/Simulink framework for frequency con-
trol, a Simulink model was created for analysis based on the transfer functions of the in-
tended energy system. A step load perturbation (SLP) of 0.99% was applied throughout
the research.
Using the MATLAB/Simulink software to simulate frequency control, a Simulink
model was created for analysis based on the transfer functions of the planned energy sys-
tem [5, 14].
Figure 1 shows the suggested system's mathematical framework.
2.2 Method of Regulation
In the realm of technology and control, the PID controller is a widely used device.
The PID controller is minimal to develop, install, and operate. It is capable of self-adjust-
ing to the chosen value. As per references [15, 16], the PID controller's mathematical equa-
tion is:
where the increases of the proportional, integral, and derivative controllers are, re-
spectively, Kp, Ki, and Kd.
2.3 Traditional Technique of Tuning
The traditional technique of test and error-tuning was employed to get the ideal con-
troller increase ratio. In this tuning manipulate, the initial integral increase rate (KI) has
been adjusted by trial and error. The ideal benefit value for KI was established as an on-
going amount when it was discovered. After that, similar to the integral increase value,
the proportional increase rate (KP) has been adjusted to reach its ideal value. Then, as
recommended by [15, 16], the derivative controller increase rate (KD) was modified after
the KI and KP were set as constants. The curves corresponding to the effectiveness mark-
ers for the IAE, ISE, ITAE, and ITSE.
Applying the many price functions that were researched, the ideal rate of the PID
controller increase were determined at the conclusion of the adjusting procedure and are
displayed in Table 1.
2.4 Modified Particle Swarm Optimization Tuning Method
EJEEE 2024, Vol.2 38 of 41
A better MPSO method for the issue of hydrothermal scheduling
The following phases may be used to characterize the computational operations of
the MPSO technique:
• Stage 1: Enter the system's parameters and designate the upper and lower bounds
for each variable.
• Stage 2: Only the number of population particles and the initializer.
• Stege 3: Assign the trial vector Qp = [q11, q12, ..., q1m; q21, q22, ..., q2m ,...,qn1,
qn2, ..., qnm] to represent the population particles that need to develop. The reservoir
turbine outflows at different periods, according to their capacity limitations, are the com-
ponents of qij. Among the committed m intervals, qid, which depends on output of ith
hydroelectric plant at dth interval, is chosen at randomness. Next, the storage contents of
reservoirs Vij are computed given the hydro discharges. Next, PHij is computed using.
• Stage 4: Compare the assessment score for every single particle (24 - 4) with its
Pbest. Between Pbest, the best assessment score is shown by gbest.
• Stage 5: Restart the loop with k = k+1; modify the location, velocity, and weight of
gravity.
• Stage 6: Only after all restrictions are met is each particle's revised position as-
sessed. if each particle's assessment value outperforms the prior Pbest. Pbest is the value
that is currently set. The value is set to gbest if the best Pbest outperforms gbest.
• Stage 7: Using equations (12) and (13), the dynamic search-space squeezing ap-
proach is triggered to modify the top and lower limits of the particles in relation to the
most recent gbest.
• Stage 8: Display the outcome and end if the halting requirement is met; if not, con-
tinue with Stages 2.
Following the tuning stage, the PID controller's proper boost constants were estab-
lished in order to preserve power system stability in the face of unanticipated load varia-
tions or emergency case configurations [17]. The increase values derived via MPSO tweak-
ing are shown in Table 2.
Table 1. shows the traditional PID controller's boost
settings.
Optimized Increase
Kp
Ki
Kd
IAE
0.99
0.39
0.01
ISE
1.19
0.39
0.12
ITAE
0.59
0.35
0.99
ITSE
0.99
0.39
0.29
Table 2. Increases rates of the MPSO to optimal PID
controller parameters
Optimized Increase
Kp
Ki
Kd
IAE
1.00
1.00
0.11
ISE
1.00
1.00
0.14
ITAE
0.81
1.00
0.19
ITSE
0.98
1.00
0.09
3. Model Outcome
The suggested system's simulator was created using MATLAB 2016a. The traditional,
GA, DE, and MPSO–PID controller answers are examined in this section for their respec-
tive capabilities. The system's efficiency was assessed for several optimization methods
employing 0.99% SLP. In the end, the MPSO performance has been evaluated by con-
trasting it with a PID controller's performance that was tuned using a traditional, GA, and
DE method. It demonstrates the frequency reaction is compared with different expense
processes. The traditional, GA, DE, and MPSO-tuned PID controller replies correspond-
ingly. Table 3 provides the equivalent regulated statistical rates to the frequency deviation
(delF), where Ts stands for settling duration, POS for maximum overshoot, and PUS for
maximum undershoot.
EJEEE 2024, Vol.2 39 of 41
Table 3. Manipulated factors of delF using the ISE ex-
pense processes
Methods
Ts (S)
POS (Hz)
×10−3
PUS (Hz)
× 10−3
Traditional
90
0.3
6.7
GA
47
0.2
6.6
DE
53
0.3
6.6
MPSO
42
0.3
6.8
Table 4. Manipulated factors of delF using the IAE ex-
pense processes
Methods
Ts (S)
POS (Hz)
×10−3
PUS (Hz)
× 10−3
Traditional
59
0.2
11.3
GA
49
0.1
10.6
DE
43
0.1
10.6
MPSO
37
0.1
6.9
Analysis was done on the frequency deviation's reaction for various expense pro-
cesses. The MPSO–PID controller with the ISE price function produced superior outcomes
than the other methods, according to the thorough investigation. Compared to the others,
the MPSO–PID with ISE calmed the oscillation faster, at 44.9 s. The suggested controller
outperformed the traditional model by 98%, the GA by 6.9%, and the DE by 19.9%. It il-
lustrates the delF evaluation for the IAE expense processes, and Table 4 reports the math-
ematical outcomes.
The MPSO–PID controller outperforms the other optimization methods based on the
graphical and mathematical responses evaluation of the suggested controller with the IAE
expense processes in Table 4. For 39 seconds, it managed the oscillation. The MPSO–PID
controller outperformed the traditional regulator by 44.9%, the GA controller by 24%, and
the DE controller by 4.8%, measured in percentages. The delF contrast for the ITSE ex-
pense processes are shown in Table 5 gives the numerical data.
Table 5. Manipulated factors of delF using the ITSE
expense processes
Methods
Ts (S)
POS (Hz)
×10−3
PUS (Hz)
× 10−3
Traditional
59
0.2
10.3
GA
46
0.1
8.5
DE
43
0.1
7.6
MPSO
37
0.1
7.3
Table 6. Manipulated factors of delF using the ITAE ex-
pense processes
Methods
Ts (S)
POS (Hz)
×10−3
PUS (Hz)
× 10−3
Traditional
60
0.2
13.9
GA
52
0.1
9.4
DE
42
0.05
10.7
MPSO
31
0.04
6.4
Table 6 provide a frequency response comparison based on the ISTE expense pro-
cesses, which indicates that the MPSO–PID controller outperforms the other optimization
strategies. The oscillation was stabilized at 40 s using the MPSO-PID controller. The
MPSO–PID controller outperformed the traditional approach by 50%, GA by 14%, and DE
by 7.7%. Table 6 provide the graphical and numerical comparison of del F for the ITAE
expense processes, respectively.
In Table 6, the MPSO–PID controller's efficiency is compared with several optimiza-
tion methods; it outperforms the traditional, GA, and DE algorithms. The oscillation was
stopped after 32.8 seconds using the ITAE-based MPSO–PID controller. The MPSO–PID
controller outperformed the traditional technique by 78%, GA by 54%, and DE by 23% in
terms of percentile gain. Figure 2 shows a comparison of the four expense processes for
settling time in a bar chart.
EJEEE 2024, Vol.2 40 of 41
Figure 2. An examination of the MPSO–PID controller's settling time
Finally, a bar chart in Figure 2 contrasted the MPSO–PID controller comeback with
each of the four expense processes. It demonstrates that the rapid settled comeback over
other expense processes (IAE, ISE, and ITSE) indicates that the ITAE expense processes -
based PSO–PID controller offers a superior reaction than other expense processes.
4. Conclusions
This paper provides a comprehensive performance analysis of the LFC for a single-
area, multi-source power-generating system equipped with a supplementary PID control-
ler. The MPSO approach with four different expense processes, along with conventional
tuning, GA, and DE methods, were used to calculate the gain settings for PID controllers.
The analysis of the system performance evaluations showed that the traditional, GA, or
DE algorithm-tuned controller performance is not as well-regulated as the MPSO–PID
controller with an ITAE expense processes-based controller. In a similar vein, compari-
sons were made between the MPSO–PID controller's responsiveness with other expense
processes. In comparison to other expense processes and improvement method controller
responses, the PSO–PID controller with the ITAE expense processes has been more prev-
alent.
Author Contributions: Conceptualization, Methodology, and Supervision, M. H. Alhafadhi; Soft-
ware, Formal analysis, and Writing-Editing, M. J. Ahmed; Validation, Investigation, Resources, and
Writing-original draft, H. H. Ibrahim; Funding acquisition, all authors have read and agreed to the
published version of the manuscript.
Funding: There was no external support for this study.
Data Availability Statement: The corresponding author may provide the data from this research
upon demand.
Acknowledgments: This investigation is not supported by a grantee number.
Conflicts of Interest: “The authors declare no conflict of interest.”
43
39 37
29
0
10
20
30
40
50
ISE IAE ITSE ITAE
Settling Time S
Expense Processes
EJEEE 2024, Vol.2 41 of 41
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