EJEEE
https://doi.org/10.62909/ejeee.2024.007 Edison Journal for Electrical and Electronics Engineering
Article
A Fresh Manner Cuckoo Search Algorithm for Handling Hy-
drothermal Scheduling in Short Term
K. S. Khalaf 1, *, , Jaafar M. Mahdy 2, and Mohammed Adnan Mohammed 3, 4,
1 School of Electrical and Electronic Engineering, Engineering campus, Universiti Sains Malaysia, Penang, Ma-
laysia; kaesarkhalaf@student.usm.my
2 Electronic Engineering Department, Faculty of Engineering, University of Hull, Hull, United Kingdom;
jaafar.mm@yahoo.com
3 Computer engineering Department, National Engineering School of Sfax, Sfax University, Sfax city, Tunisia;
mohammed.adnan@enis.tn
4 Computer Engineering and Systems Department, Faculty of Engineering, Mansoura University, Mansoura
city, Egypt
* Correspondence: Tel.: +60-149263901
Abstract: The main goal of the short-term hydrothermal scheduling (HS) challenge is to drastically
reduce the large fuel charge of producing power by preparation the hydrothermal energy producers
while taking power balance restrictions, the reservoir's storage restrictions, the water's gross dis-
charge, and the thermal power producers' and hydropower stations' operating restrictions into ac-
count. Many algorithms have been used to crack this similar issue, and relevant research have been
published in the literature; nevertheless, their scope is limited in terms of the number of iterations
required to accomplish the solution state and the solution state itself. To crack the HS issue, this
article suggests applying a new trend cuckoo search algorithm known as the fresh manner cuckoo
search (FMCS) algorithm, an altered variant of the conventional CS. The suggested FMCS reduces
the number of iterations associated with the CS and enhances the solution condition. The motion's
lengths are broken down into a variety of stages that can be taken, offering an endless amount of
variation. The hydrothermal power system has been utilized to verify the efficacy of FMCS. The
outcomes show that FMCS performs better than any other comparative method that has lately been
applied to the HS problem. Additionally, it has been shown that compared to one other methods,
the FMCS methodology has achieved minimum gross costs. As a result, the suggested FMCS
emerges as a very practical and successful strategy for resolving the HS issues.
Keywords: short-term hydrothermal scheduling; hydropower plants; cuckoo search algorithm;
minimizing fuel cost
1. Introduction
By arranging the running of the thermal generators and hydropower generators in
the most efficient manner for a predetermined amount of time, short-term hydrothermal
scheduling, or HS, seeks to minimize the gross fuel charge of thermal generators. The best
scheduling is accomplished by a variety of methods, and a large body of research has been
done in the literature. Because the HS goal function is not linear, gradients methods and
Lagrange multipliers have to be used. However, taking into account the transformed na-
ture results in suboptimal methods that manifest as enormous losses in revenue creation;
this was also accomplished through planned operations [1]. By carefully scheduling the
hydrothermal system's functioning, the power sharing demands in the HS have been
properly allocated between thermal generators and hydropower components, satisfying
one of the HS's primary requirements—minimum fuel cost [2, 3].
Citation: Khalaf, K.S., J.M. Mahdy,
and M.A. Mohammed, A Fresh Man-
ner Cuckoo Search Algorithm to Hy-
drothermal Scheduling in Short
Term. Edison Journal for Electrical
and Electronics Engineering (EJEEE),
2024. 2: p. 42-49.
Academic Editor: Asst. Prof. Wurod
Qasim Mohamed
Received: 27/8/2024
Revised: 2/10/2024
Accepted: 11/10/2024
Published: 17/10/2024
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 43 of 49
Numerous studies have employed optimization strategies to tackle the HS issue, as
previously indicated. A thorough synopsis of those investigations and a succinct explana-
tion of numerous optimization methods and algorithms can be found in ref. [4, 5]. Aside
from those, there are a few other recent studies on the HS issue utilizing genetic algo-
rithms [6], enrich GA, particle swarm optimization (PSO), and enrich PSO [7], as well as
fast evolutionary programming (FEP), classical evolutionary programming, and im-
proved FEP (IFEP) [8], grasshopper optimization algorithm [9], adaptive particle swarm
optimization (APSO), modified APSO [10], modified differential evolution, improved
PSO [11, 12], teaching learning-based optimization (TLBO) [13], one rank cuckoo search
algorithm [14], running IFEP (RIFEP) [15], gradient search techniques [16], simulated an-
nealing approach [17], clonal selection royal [18], krill herd algorithm [19], and sequential
quadratic programming [20].
The HS issue has been greatly helped by all of the aforementioned methods; none-
theless, they have limitations in terms of the solution phase and the amount of iterations
required to achieve the solution state. Although Yang and Deb employed the Cuckoo
Search (CS) Algorithm to solve optimization issues for the initial time during 2009, the CS
has recently been suggested for usage in economic dispatch problems [20]. One of the
metaheuristic methods that supports multiple rule parameters is CS. By laying their eggs
in the nests of other kinds of cuckoos, it imitates the parasitic relationship of multiple
cuckoo species.
Following its discovery of CS's benefit in addressing optimization problems, irregu-
lar and economical dispatch problems were subsequently resolved using it [21]. To ad-
dress the HS issue, the CS was actually hired more lately; for specifics, see ref [22]. The
findings of reference [22]. indicated that, in comparison to all other scenarios involving
high-rate nonlinear behavior, such as valve point loads, CS is a workable strategy with
superior performance. Nevertheless, step-length fluctuation is a shortcoming of the con-
ventional CS method that is critical to achieving the answer. Thus, in order to solve the
HS problem, this paper suggests applying an improved CS known as the fresh manner
cuckoo search algorithm (FMCS), an altered version of the conventional CS.
2. Materials and Methods
2.1. Hydrothermal treatment System computational model
The hydrothermal power system mathematical framework that we utilized for im-
provement is presented in this section. Because water is free to use, the input fuel cost of
hydropower producing equipment is minimal when compared to thermal and hydro pro-
ducers. Because it differs from thermal power plants, nonetheless, our primary goal was
to produce energy by utilizing water resources extensively while minimizing the overall
input fuel cost of thermal energy-producing equipment. We chose the objective variable
represented in Equation (1) in light of the aforementioned need. Equations (2) through (9)
[7, 11, 22] also include the restrictions that were taken into consideration when fixing the
HS issue.
- Objective function
(1)
- Limitations:
The restriction pertaining to the equilibrium of power generation and load is articulated
as follows:
(2)
The hydropower production (PH(i,j)) is a process of the water discharge rate and is de-
fined as follows: (3)
The volume of water contained in the reservoir can be expressed as:
(4)
EJEEE 2024, Vol.2 44 of 49
The functional times of thermal energy producers were limited owing to
(5)
The operating times of hydropower producers have been limited due to
(6)
The limitations pertaining to the water discharge amount are denoted by:
(7)
The limitations pertaining to the starting and final water capacity of the reservoir are spec-
ified by (8)
The limitations pertaining to water storage capacity of the reservoir are specified
(9)
2.2. Comprehensive methodology for addressing the HS issue through the sug-
gested FMCS
Stage 1: Choose FMCS variables, which include the sum of host nests (Np), the likelihood
of a host bird detecting a strange egg in its nest (Pa), and the highest amount of repetitions
(Gmax).
Stage 2: Set up the number of Np host nests as outlined in limitations.
• Compute the surplus discharge of water and the slack heat unit one utilizing For-
mulas (12) and (13).
• Compute all the hydroelectric drives utilizing Equation (1).
Stage 3: Assess the fitness functions utilizing Equations (2 to 9) to identify the optimal nest
(current best solution) associated with the minimum fitness function price, Xbest.
• Establish the initial repetition as G equal to one.
Stage 4: Produce a fresh group of remedies through as outlined in paragraph and rectify
any infringed remedies utilizing Equation (10).
Stage 5: Compute the derelict water release and the corresponding derelict thermal unit
number one for the fresh group of remedies utilizing Eqs. (11) and (12).
• Compute updated values for all hydroelectricity production using, for example,
equation (1).
Stage 6: Utilize Equations (10 to 12) to compute the coefficients of the recently derived
solutions.
• Evaluate the suitability of the fresh approach against the ancient explanation (at
the exact nest) to select the superior option at individually nest.
Stage 7: Produce an additional set of solutions informed by the finding and steps of the
alien egg as outlined, and rectify any violated ideas utilizing equation (10 to 12).
Stage 8: Compute the derelict water release and the associated derelict thermal component
number one for the fresh collection of explanations utilizing equations (10 to 12).
• Compute the updated values for all hydroelectric generation using equation (1).
Stage 9: Compute fitness functions for the updated set of solutions utilizing equation (10
to 12).
• Evaluate the soundness of the unexplored explanation against the existing resolu-
tion (at the exact nest) to select the superior option at every single nest.
Stage 10: Assess all revised existing explanations to identify the optimal present explana-
tion, Gbest.
Stage 11: Verify if G is less than Gmax; if so, increment G by 1 before going back to stage
4. Cease all actions.
2.2. Fresh Manner Cuckoo Search Algorithm (FMCS)
The variables pa, λ, and α involved to the CS assist the method in identifying locally
as well as globally improved explanations, accordingly. The variables pa and α are crucial
EJEEE 2024, Vol.2 45 of 49
in the acceptable modification of explanation matrices and may be utilized to change the
method's proportion of convergence.
The conventional CS method employs a constant value for both pa and can't be al-
tered throughout generations to come. The primary disadvantage of this strategy lies in
the amount of repetitions required to identify an ideal explanation. When the significance
of pa is minimal and the number of α is substantial, the method's efficiency would be
suboptimal, resulting in a significant upsurge in the amount of repetitions. If the rate of
pa is substantial and the rate of α is minimal, the rate of converging is elevated, although
it can fail to identify the optimal explanations.
The primary distinction amongst the FMCS and CS is in the method of altering pa
and α. To enhance the efficacy of the CS method and address the limitations associated
with set quantities for pa and α, the FMCS process employs adjustable parameters for pa
and α. In the early epochs, the parameters pa and α have to be sufficiently great to compel
the method to improve the variety of explanation matrices. Nevertheless, these numbers
ought to be diminished in the last rounds to achieve improved acceptable modification of
explanation matrices. The parameters pa and α are continuously altered with the output
count and are articulated in Equations (3 to 9), where NI denotes the total number of rep-
etitions and GN signifies the present repetition.
3. Results
This part presents the outcomes of a simulated annealing technique for tackling the
hydrothermal scheduling issue, utilizing a trial design of hydrothermal energy produc-
tion equipment as referenced in [9, 11]. It encompasses a consortium of 4 hydroelectric
stations and several thermal units considered as a singular similar thermal facility. The
viability of the FMCS approach for a larger hydrothermal power system has been evalu-
ated by its application on a secondary trial design including a series of 3 thermal genera-
tors and 4 hydroelectric plants.
The actual data for this design has been gathered according to references [9, 11]. The
schedule spans a duration of 24 hours, with each interval set at 1 hour. The mathematical
model was conducted on the MATLAB program 2023b on a machine equipped with a
Core i5 12th Gen cpu operating at 2.00 GHz and 16.00 GB of Memory.
3.1 Choice of Variables
Only five parameters—three main components from the original CS and a few more
modifications—could be harmonized in the FMCS. First, a few factors involving the three
main components are taken into consideration. These factors have an impact on every
recent solution that has been generated through exploration and exploitation. These are
the nest-number (NE) and the potential discovery of an extraterrestrial egg, Pa. On the
other hand, the extreme amount of repetitions ought to have a constant influence on the
best answer. Furthermore, a few other factors that affect the integration of the mining and
extraction components are taken into account. These can be changed using the fresh man-
ner power and should be pleased with the upper and lower constraints. The FMCS ap-
proach is provided by the obliged with the best solution, improving its speed of conver-
gence and performance. Conversely, the three primary parameters from the original CS
method, along with a few more in the explanation, were simple to choose since the earlier
limit equations had made them clear. Following multiple runs with different FMCS
EJEEE 2024, Vol.2 46 of 49
control parameter values, population (Np) = 200, extreme repetition = 600, and possibility
(Pa) = 0.8 were selected as the key control parameters.
3.2 Achieved Outcomes
Within the Pa limit range values of 1 dimensional to 9, the suggested FMCS was com-
pleted more than ten times with confidence, and a particular version of FMCS was accom-
plished over a hundred times with confidence. The maximum amount of repetitions and
the number of nests, on the other hand, were previously limited to specific numbers of
350 and 15, respectively. The findings, which are displayed in Tables 1 and 2, include the
lowest entire cost, average entire cost, maximum entire cost (in $), average computation
period (in seconds), and standard deviation gathered by FMCS.
Table 1. A succinct outcome of the suggested
FMCS with different Pa values
Table 2. The best results attained using the
suggested FMCS method
Pa
Min Cost
Avg. Cost
Max Cost
CPU
0.1
709,032
709,045
709,053
19
0.2
709,101
709,114
709,122
19
0.3
709,218
709,231
709,239
19
0.4
709,358
709,371
709,379
19
0.5
709,497
709,510
709,518
19
0.6
709,624
709,637
709,645
19
0.7
709,707
709,720
709,728
20
0.8
709,865
709,878
709,886
20
0.9
709,866
709,879
709,887
20
m
Pdm
Vm
qm
Psm
1
1120
89701
1839
910
2
1500
89592
3340
910
3
1100
89702
1369
912
4
1800
89593
4825
912
5
1000
89703
1178
915
6
1290
89594
2849
915
The FMCS got ideal solutions at Pa exactly equal to 0.7, while the CS found ideal
explanations at Pa ranging from 0.1 to 0.9 according to the results shown in Tables 1 and
2. Additionally, FMCS may receive a lower standard deviation, average gross cost, and
maximum net expense.
Tables 1 and 2 show the precise solution's optimum sites for the release of water and
the generation of thermal energy. Thus, it is demonstrated that the suggested FMCS
method successfully uses poured hydropower to solve the HS issue station. Figure 1
shows how much load is required and the energy output of the thermal and hydroelectric
stations for each time interval during the timetable horizon corresponding to the optimal
solution for test system 1. Figure 2 shows the reservoir capacity of all hydro plants for the
same feature as well as the recommended technique's cost converging feature.
Figure 1. hydro plant discharged hourly
Figure 2. hydro plant storage on an hourly basis
EJEEE 2024, Vol.2 47 of 49
3.4 Validation of the Proposed System
The outcomes produced from the suggested FMCS method were contrasted to mul-
tiple current methods teaching learning-based optimization (TLBO) (See ref. [13]). Only
research investigations done for test system 1 were examined to ensure the accuracy of
this comparison. The net cost acquired by FMCS was comparable to that generated by
FMCS lower than that generated through all other methods. Nevertheless, the compara-
tive results demonstrated that the suggested FMCS method is more rapid and precise in
achieving solutions for HS problems than the strategies evaluated.
5. Conclusions
In this research, the HS issues with a variety of difficult restrictions were solved using
the FMCS method. Four cascading hydroelectric facilities and one thermal plant were
used to evaluate the same system during its 24-hour planned performance with 1-hour
segments. The outcomes demonstrated that, for the HS problem, the suggested FMCS
technique outperformed the traditional CS. The FMCS technique outperformed other cur-
rent optimization strategies in achieving a suitable optimal solution, as demonstrated by
simulation results of cascading hydrothermal structures, wherein the computing time was
reduced.
Data Availability Statement: The data used will be available on request
Acknowledgments: I want to express my appreciation to the study team, which includes our uni-
versities in different countries, for their cooperative efforts in data collection and analysis. Their
knowledge has been extremely helpful to the study.
Conflicts of Interest: “The authors declare no conflict of interest.”
EJEEE 2024, Vol.2 48 of 49
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