Numéro 
Sci. Tech. Energ. Transition
Volume 79, 2024
Decarbonizing Energy Systems: Smart Grid and Renewable Technologies



Numéro d'article  66  
Nombre de pages  9  
DOI  https://doi.org/10.2516/stet/2024068  
Publié en ligne  24 septembre 2024 
Regular Article
Optimal planning of energy microgrid with multiobjective functions in independent mode
^{1}
Department of Electrical Engineering, University of TechnologyIraq, Baghdad 10066, Iraq
^{2}
Department of Energy, Universidad de la Costa, Barranquilla, Colombia
^{3}
Department of Electrical and Electronics Engineering, School of Engineering and Technology, JAIN (Deemed to be University), Bangalore, Karnataka, India
^{4}
Marwadi University Research Center, Department of Electrical Engineering, Faculty of Engineering & Technology, Marwadi University, Rajkot 360003, Gujarat, India
^{5}
Department of Mechanical Engineering, Chandigarh College of Engineering, Chandigarh Group of Colleges, Jhanjeri, Mohali 140307, Punjab, India
^{6}
NIMS School of Electrical and Electronics Engineering, NIMS University Rajasthan, Jaipur, Rajasthan, India
^{7}
Head of the Department Physics and Chemistry, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, National Research University, Tashkent, Uzbekistan
^{8}
Scientific Researcher, University of Tashkent for Applied Sciences, Str. Gavhar 1, Tashkent 100149, Uzbekistan
^{9}
Scientific Researcher, Western Caspian University, Baku, Azerbaijan
^{10}
Faculty of Electrical and Electronics Engineering Technology, Universiti Malaysia Pahang AlSultan Abdullah, 26600 Pekan, Pahang, Malaysia
^{11}
Department of computers Techniques engineering, College of technical engineering, The Islamic University, Najaf, Iraq
^{12}
Department of Computers Techniques Engineering, College of Technical Engineering, The Islamic University of Al Diwaniyah, Al Diwaniyah, Iraq
^{13}
Department of Computers Techniques engineering, College of technical engineering, The Islamic University of Babylon, Babylon, Iraq
^{14}
Manipur International University, Imphal, Manipur, India
^{*} Corresponding author: harikumarpallathadka@gmail.com
Received:
12
June
2024
Accepted:
16
August
2024
Energy storage systems are crucial in managing the uncertainties associated with power generation from renewable sources like wind turbines (WTs) and photovoltaic (PV) systems. This article presents the most effective sizing of energy resources within a microgrid, which includes hydrogen storage, PV, battery systems, and WT in the independent mode of the main grid. The study aims to minimize installation costs, maximize the penetration of WT and PV systems in meeting demand, and reduce load shedding. To tackle the intricacies of the planning process, the research utilizes the modified sunflower optimization (MSFO) algorithm. Through comparative experiments, the study confirms the efficacy of this method, showcasing its capacity to deliver enhanced outcomes. The findings indicate that the proposed method efficiently optimizes resource allocation at an optimal pace.
Key words: Effective sizing / Microgrid / Independent mode / Hydrogen storage / Installation costs / Load shedding
© The Author(s), published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nomenclature
n, N : Number of energy sources (Number)
C_{O&M, CA, CRP} : Maintenance and operation, Capital and replacement costs ($)
f, IR: Inflation and interest values (%)
P_{load} : Electrical demand in microgrid (kw)
h_{r}, h : Height and height WT, Meter (m)
V_{r}, V, V_{c}, V_{co} : Rate of wind speed, Wind speed, Wind speed in cutin state and Wind speed in cutout (m/s)
p_{r} : Power generated by WT (kW)
Y_{PV} : Power capacity by PV (kW)
${\overline{G}}_{\mathrm{rsrc}},{\overline{G}}_{\mathrm{r}}$ : Solar radiation in under test and Solar radiation (Kw/m^{2})
P_{EL} : Power injected to electrolyzer (kW)
η_{bat}, μ_{EL} : Efficiency of battery and electrolyzer (%)
e_{Tank} : Hydrogen tank capacity (kg)
y, c, Q, Q_{1} : Power exponent of battery, Battery capacity, Total power of battery and Power of battery (kw)
1 Introduction
1.1 Amis and motivations
Research has been heavily concentrated on enhancing energy sources to provide energy to consumers, reducing operational expenses and technical indicators, and considering technical limitations [1]. Energy hybrid systems have been implemented to address economic, environmental, and reliability requirements, while also taking into account consumer behavior, in order to achieve this objective. Energy hybrid systems combine different sources of energy, such as solar, wind, and battery storage, to create a more efficient and reliable energy system. By integrating multiple sources of energy, these systems can better meet the varying demands of consumers while also reducing costs and environmental impact [2]. One of the key benefits of energy hybrid systems is their ability to provide a more stable and reliable energy supply. By combining different sources of energy, these systems can ensure that power is always available, even when one source is not producing energy. This can help to prevent blackouts and other disruptions to the energy supply [3]. In addition to improving reliability, energy hybrid systems can also help to reduce costs for consumers. By using a combination of renewable energy sources, such as solar and wind power, these systems can lower energy bills and reduce reliance on expensive fossil fuels. This can help to make energy more affordable for consumers while also reducing greenhouse gas emissions and other environmental impacts. The latest advancements in energy systems are highlighted by these systems, which make use of communication links connecting consumers and generation resources to enhance and simplify consumer participation in load profile transformation. The modifications to the load profile significantly influence the efficient distribution of energy, leading to a more flexible system that lowers generation expenses, decreases emissions, and enhances dependability. Additionally, through the utilization of ideal resource dimensions, energy production can be significantly decreased in energy markets, all the while promoting collaboration between energy providers and consumers to regulate demand and prevent the necessity for extra units. The increasing diversity of hybrid loads will undoubtedly require careful consideration of optimal sizing, which will play a crucial role in future energy management [3, 4].
1.2 Related studies
Several research studies have been carried out on different aspects of microgrid energy systems. The study highlighted in reference [5] emphasizes the importance of shortterm optimal scheduling for a hybrid energy system, with a specific focus on considering risk constraints. The optimal energy management approach for microscale energy hybrid presented in [6] takes into account various factors including resource availability, prices, and demand. Employing an iterative algorithm, this approach aims to minimize costs effectively. The examination of the scheduling issue within the energy hybrid system, utilizing multistep modeling and optimal sizing through various multiplication methods, is discussed in reference [7]. The emphasis in [8] is on optimizing the operation of the energy system using probabilistic optimization techniques in order to maximize the profit of the energy hybrid system. The scheduling strategy proposed in [9] focuses on the energy hybrid system, taking into account conditional valueatrisk and highlighting the importance of optimal sizing modeling in order to minimize generation costs efficiently. A novel approach to energy management has been introduced in [10] to improve the security of load supply. Furthermore, the study in reference [11] delves into the energy transfer process and aims to minimize overall energy expenses within an energy hybrid setup. The study in [12] analyses an energy hybrid system optimization model, which considers peak clipping of thermal and cost reduction. The assessment of energy flow within energy networks of energy systems involves conducting load flow analysis to optimize the energy hybrid system, as outlined in [13]. Additionally, the study in [14] presents an efficient scheduling framework for the energy hybrid system, taking into account the constrained optimization of uncertainties in energy sources in order to reduce system investment expenses. The paper in [15] introduces a variety of techniques for energy management, focusing on essential methods for demandside management and load forecasting aggregation. The study in [16] delves into the examination of maximizing anticipated advantages within an energy hybrid system, taking into account energy market prices and uncertainties related to wind generation, using stochastic optimization analysis. The research conducted in [17] focuses on the stochastic optimization framework within the energy hybrid system, incorporating risk modeling approaches. The shortterm scheduling framework for an energy hybrid system, as proposed in [18], is established on energy pricing through information gap decision theory. The study in [19] delves into the development of an energy hybrid system for resource sizing, taking into account the variability of energy sources through the utilization of the Benders algorithm. The research carried out in [20] centers on investigating how the weight sum method can be used to optimize energy usage, operational costs, and reduce emission pollution. In [21] and [22], an assessment is conducted on a multiobjective issue that takes into consideration energy efficiency and economic aspects in order to enhance the operation of the system. In [23], the focus is on examining the most suitable design for the energy hybrid system, with careful consideration of economic factors and environmental impacts.
1.3 Novelties and contributions
The current research seeks to explore the most effective layout of energy sources in a microgrid, with particular emphasis on integrating energy storage systems like batteries and hydrogen systems. The goals of this research include reducing expenses linked to resource setup, enhancing the adoption of photovoltaic (PV) and wind turbine (WT) technologies, and decreasing the frequency of load shedding. This research employs the modified sunflower optimization (MSFO) algorithm to address the issue at hand. By utilizing this algorithm, we can identify the most effective rates for the objective functions, all the while taking into account the limitations imposed by the microgrid. The study seeks to discover the most efficient and effective energy resource combination to achieve desired outcomes through the use of the MSFO algorithm. After determining the optimal parameters, the research delves into optimizing the resource count of the microgrid. It is necessary to increase the size of energy resources to improve their performance and efficiency. The study focuses on maximizing the efficiency of resource allocation to guarantee that the microgrid has the right amount and type of energy sources to fulfill the system’s requirements. The objective of this research is to concentrate on the design of resources within a microgrid, specifically highlighting the integration of energy storage systems. Through the application of the MSFO algorithm and resource count optimization, the study strives to attain the intended results of cost reduction, increased WT and PV penetration, and decreased load shedding.
2 System configuration
The microgrid model illustrated in Figure 1 has been developed to integrate a range of resources in order to fulfill the energy requirements of the load. These resources encompass WT, PV, batteries, and hydrogen storage systems. The microgrid model also facilitates the transfer of energy in both directions, from the AC bus to the DC bus. This twoway energy transfer is employed to replenish the battery and hydrogen storage system. Surplus energy produced by the resources can be converted from AC to DC and stored in the battery and hydrogen storage tanks for future consumption. The microgrid model is designed to facilitate bidirectional energy transfer through the use of bidirectional inverter and rectifier converters. The converters are essential for converting energy from AC to DC and vice versa, facilitating efficient energy transfer in two directions. The microgrid model’s design permits the integration of different resources and supports bidirectional energy transfer to fulfill energy demands and store surplus energy for later use.
Fig. 1 Microgrid configuration. 
Fig. 2 Pareto front in Case 1. 
Fig. 3 Pareto front in Case 2. 
Fig. 4 Pareto front in Case 3. 
2.1 PV modelling
The phenomenon of the photoelectric effect takes place when sunlight photons interact with the surface of the PV cells, resulting in the liberation of electrons and the generation of an electric current. The quantity of electricity produced by the PV system is directly linked to the intensity of light, where greater intensity results in higher power production. Nevertheless, the ambient temperature also has a notable impact on the effectiveness of the PV system. The PV system is represented as follows [24]:$${P}_{\mathrm{PV}}\left(t\right)={Y}_{\mathrm{PV}}\xb7{f}_{\mathrm{PV}}\frac{G\left(t\right)}{{G}_{\mathrm{STC}}}.$$(1)
2.2 WT modelling
The WT modeling process encompasses various essential elements and equations that elucidate the turbine’s behavior and functionality. These models play a critical role in comprehending and forecasting the turbine’s power output, efficiency, and overall operation. The WT is depicted in the following manner [24]:$${V}_{\mathrm{W}}\left(t\right)={V}_{\mathrm{r}}\left(t\right){\left(\frac{h}{{h}_{r}}\right)}^{y}$$(2) $${P}_{\mathrm{WT}}\left(t\right)=\{\begin{array}{cc}0& {V}_{\mathrm{w}}\left(t\right)\le {V}_{\mathrm{c}}\\ {p}_{r}\left(\frac{{V}_{\mathrm{w}}\left(t\right){V}_{\mathrm{c}}}{{V}_{\mathrm{r}}{V}_{\mathrm{c}}}\right)& {V}_{\mathrm{c}}\le {V}_{\mathrm{w}}\left(t\right)\le {V}_{\mathrm{r}}\\ p& {V}_{\mathrm{r}}\le {V}_{\mathrm{w}}\left(t\right)\le {V}_{\mathrm{c}0}\\ 0& {V}_{\mathrm{w}}\left(t\right)\ge {V}_{\mathrm{c}0}\end{array}.$$(3)
Here (2) and (3) depict the modeling of wind speed at the specified height and the generation of power by the wind turbine.
2.3 Battery modelling
The modeling of the battery can be described as a dynamic procedure that includes the monitoring of the battery’s state of charge, voltage, current, and temperature. This data is essential for determining the best discharge rate and duration to guarantee efficient and effective utilization of the battery. The battery management system is crucial for overseeing the discharge process, preventing overdischarging and overcharging of the battery, and ultimately preserving its longevity and efficiency. Through precise battery behavior modeling and the application of suitable control strategies, the battery can effectively be used in discharging mode to fulfill the surplus load requirements and uphold a consistent power supply. Furthermore, the battery modeling considers variables like battery capacity, efficiency, and aging effects, which can influence the battery system’s overall performance. It is crucial to consistently monitor and analyze these variables in order to make necessary adjustments for maximizing battery usage and extending its lifespan. In general, developing a battery model is vital for guaranteeing the dependable and effective performance of renewable energy systems like wind turbines and solar panels. This involves integrating battery storage efficiently to address changing energy needs and uphold grid stability. The battery is represented in the following manner [25]:$${P}_{\mathrm{bat}\u2010\mathrm{ch}}^{\mathrm{max}}=\frac{k{Q}_{1}{e}^{k\Delta t}+\mathrm{Qkc}(1{e}^{k\Delta t})}{1{e}^{k\Delta t}+c(k\Delta t1+{e}^{k\Delta t})},$$(4) $${P}_{\mathrm{bat}\u2010\mathrm{dh}}^{\mathrm{max}}=\frac{\mathrm{kc}{Q}_{\mathrm{max}}+{Q}_{1}k{e}^{k\Delta t}+\mathrm{Qkc}(1{e}^{k\Delta t})}{1{e}^{k\Delta t}+c(k\Delta t1+{e}^{k\Delta t})},$$(5) $${P}_{\mathrm{bat}\u2010\mathrm{ch}}=\frac{{P}_{\mathrm{bat}\u2010\mathrm{ch}}^{\mathrm{max}}}{{\eta}_{\mathrm{bat}}},$$(6) $${P}_{\mathrm{bat}\u2010\mathrm{dh}}={P}_{\mathrm{bat}\u2010\mathrm{dh}}^{\mathrm{max}}{\eta}_{\mathrm{bat}}.$$(7)
The battery’s peak power capacity for charging and discharging is denoted by equations (4) and (5) correspondingly. Equations (6) and (7) illustrate the charging and discharging processes of the battery.
2.4 Hydrogen system modeling
The electrolytic cells play a crucial role in the separation of water molecules into hydrogen and oxygen using electrolysis. The resulting hydrogen is subsequently stored in tanks, which may undergo compression or liquefaction based on the intended use. The hydrogen is supplied to fuel cells to generate electricity, heat, and water as byproducts when energy is required. This hydrogen storage system model facilitates the efficient and environmentally sound storage of renewable energy sources such as solar or wind power. By converting excess electricity into hydrogen during periods of low demand, the stored hydrogen can be utilized later to generate electricity when necessary, providing a reliable and sustainable energy storage solution. Moreover, hydrogen fuel cells have the potential to be utilized in a wide range of applications such as transportation, stationary power generation, and backup power systems [26].$${P}_{\mathrm{EL}}\left(t\right)={\mu}_{\mathrm{EL}}\left({P}_{\mathrm{WT}}\left(t\right)+{P}_{\mathrm{FC}}\left(t\right)+{P}_{\mathrm{PV}}\left(t\right)+{P}_{\mathrm{bat}\u2010\mathrm{dh}}\left(t\right)\right){P}_{\mathrm{load}}\left(t\right),$$(8) $${e}_{\mathrm{Tank}}\left(t\right)={e}_{\mathrm{Tank}}\left(t1\right)+\left({P}_{\mathrm{EL}}\times t\right),$$(9) $${P}_{\mathrm{FC}}=\frac{{e}_{\mathrm{Tank}}\left(t\right)}{t}{\beta}_{\mathrm{FC}}.$$(10)
Equations (8)–(10) illustrate the power input to the electrolyzer, the amount of hydrogen stored, and the power generated by the fuel cell, respectively.
3 Objective functions modelling
The system planning is assessed in accordance with the following objective functions:
3.1 Cost of resources
The first objective is to lower the installation costs of the resources:$$\mathrm{min}{f}_{1}=\sum _{n=1}^{N}{C}_{{\mathrm{CA}}_{n}}+{C}_{{\mathrm{RP}}_{n}}\sum _{n=1}^{N}{F}_{{\mathrm{RP}}_{n}}\left(N\right)+{F}_{\mathrm{O}\&M}\sum _{n=1}^{N}{C}_{\mathrm{O}\&M}$$(11)where:$${F}_{\mathrm{RP}}\left(N\right)=\frac{1}{{\left(1+\mathrm{IR}\right)}^{n}},$$(12) $${F}_{\mathrm{O}\&\mathrm{M}}=\sum _{n=1}^{N}\frac{1}{{\left(1+\mathrm{IR}\right)}^{n}}.$$(13)
Equations (12) and (13) outline the factors related to costs of replacement, operation, and maintenance (O&M), respectively.
3.2 Penetration of resources
The second objective is to enhance the utilization of PV and WT technologies to fulfill the energy demand effectively.$$\mathrm{min}{f}_{2}=\left\sum _{t=1}^{T}\frac{{P}_{\mathrm{WT}}\left(t\right)+{P}_{\mathrm{PV}}\left(t\right){P}_{\mathrm{load}}\left(t\right){P}_{\mathrm{bat}\u2010\mathrm{ch}}\left(t\right){P}_{\mathrm{EC}}\left(t\right)}{{P}_{\mathrm{WT}}\left(t\right)+{P}_{\mathrm{PV}}\left(t\right){P}_{\mathrm{load}}\left(t\right)}\right\times 100.$$(14)
3.3 Demand shedding
The last objective is to reduce demand shedding, which is represented in the following manner:$$\mathrm{min}{f}_{3}=\left\sum _{t=1}^{T}\frac{{P}_{\mathrm{load}}\left(t\right)+{P}_{\mathrm{bat}\u2010\mathrm{ch}}\left(t\right)[{P}_{\mathrm{PV}}\left(t\right)+{P}_{\mathrm{WT}}\left(t\right)+{P}_{\mathrm{bat}\u2010\mathrm{ch}}\left(t\right)+{P}_{\mathrm{FC}}\left(t\right)]}{{P}_{\mathrm{load}}\left(t\right)}\right\times 100.$$(15)
4 Constraints
The microgrid being evaluated is constrained by several limitations, as detailed here:$${P}_{\mathrm{WT}}\left(t\right)+{P}_{\mathrm{PV}}\left(t\right)+{P}_{\mathrm{FC}}\left(t\right)+{P}_{\mathrm{bat}\u2010\mathrm{dh}}\left(t\right)={P}_{\mathrm{load}}\left(t\right){P}_{\mathrm{load}}^{\mathrm{sh}}+{P}_{\mathrm{bat}\u2010\mathrm{ch}}\left(t\right)+{P}_{\mathrm{EC}}\left(t\right),$$(16) $$P\le {P}^{\mathrm{max}},$$(17) $$N\le {N}^{\mathrm{max}}.$$(18)
Here (16)–(18) guarantee load distribution, resource allocation, and resource quantity.
5 Optimization method
The sunflower tracking system is a dependable technique utilized for assessing optimal sun exposure. It was found in the research that pollination happens randomly, especially when flowers are spaced far apart. Usually, a solitary patch of flowers can emit millions of pollen gametes, with each sunflower generating only one. The distance of a plant from the sun determines the level of radiation it absorbs, with those nearer to the sun receiving higher amounts. In contrast, plants that are situated further away experience reduced radiation exposure. This study adheres to this principle to maximize heat absorption in sunflowers. The modelling sunflower optimization (SFO) algorithm is as follows [27, 28]:$${H}_{i}=\frac{{P}_{\mathrm{s}}}{4\pi r{d}_{i}^{2}}.$$(19)
Where:
P_{s} = Strength of the source.
d_{i} = Distance from plant i.
The model presented below demonstrates how the sunflower is oriented in relation to the sun. $${\stackrel{\u20d7}{D}}_{i}=\frac{{X}^{*}{X}_{i}}{\Vert {X}^{*}{X}_{i}\Vert}.$$(20)
Where:
ith = Plantation and the current plantation are denoted by X_{i} and X ^{*}.
The sunflowers’ orientation towards the direction S_{i} can be assessed as follows:$${S}_{i}=\beta \times {P}_{i}\left(\Vert {X}_{i}+{X}_{i1}\Vert \right)\times \Vert {X}_{i}+{X}_{i1}\Vert .$$(21)
To attain optimal worldwide outcomes, it is essential to limit the maximum increment by utilizing the given equation.$${S}_{\mathrm{max}}=\frac{\Vert {X}_{\mathrm{max}}{X}_{\mathrm{min}}\Vert}{2\times {N}_{\mathrm{pop}}}.$$(22)
Where:
X_{max}= Highest rate.
X_{min}= Lowest rate.
N_{pop}= Overall population.
The new plantation is illustrated as:$${\stackrel{\u20d7}{X}}_{i+1}={\stackrel{\u20d7}{X}}_{i}+{S}_{i}{\stackrel{\u20d7}{D}}_{i}$$(23)
5.1 Modified SFO (MSFO) algorithm
The proposed algorithm proves to be efficient for tackling optimization problems; however, there are existing constraints that need to be resolved. A significant obstacle faced by the sunflower optimization algorithm is premature convergence. Individuals tend to concentrate on solutions close to the best possible outcome, disregarding exploration in other areas of the solution space because of the disparity between local and global search. The MSFO algorithm addresses this challenge by implementing a novel strategy. The problem of premature convergence, which results in extended execution durations, arises from the unintentional dispersion of the population throughout various sections of the sunflower optimization during every iteration. Incorporating Lévy flight (LF) as a parameter significantly enhances the performance of bioinspired optimization algorithms and helps mitigate premature convergence. This parameter facilitates a random walk approach that finetunes local search, effectively overcoming the challenges associated with premature convergence [27, 28].$$\mathrm{Le}\left(w\right)\approx {w}^{1\tau},$$(24) $$w=A{\leftB\right}^{1/\tau},$$(25) $${\sigma}^{2}={\left\{\frac{\mathrm{\Gamma}\left(1+\tau \right)}{\tau \mathrm{\Gamma}(\left(1+\tau \right)/2)}\frac{\mathrm{sin}\left(\pi r/2\right)}{{2}^{(1+\tau )/2}}\right\}}^{\frac{2}{r}}.$$(26)
The LF mechanism is being used for the new plantation as described below:$${\stackrel{\u20d7}{X}}_{i+1}=\left({\stackrel{\u20d7}{X}}_{i}+{S}_{i}{\stackrel{\u20d7}{D}}_{i}\right)\mathrm{Le}\left(\delta \right).$$(27)
Algorithm 1 displays the MSFO method. The primary step of this proposed algorithm involves forming a population of individuals, which can be distributed randomly or evenly. Assessing each person allows us to pinpoint the individual who can approach the sun more closely. Currently, the algorithm is designed to track a single sun, but future iterations will support multiple suns. Subsequently, the other individuals will realign their positions toward the sun, mimicking the behavior of sunflowers, by making random movements in a specified direction.
6 Numerical simulation
This section emphasizes the numerical simulation of optimal resource planning for multiple objectives, which is integral to the proposed modeling implementation. The resource input data and parameters are sourced from references [29–31]. By obtaining the Pareto front solutions for these objectives, we can identify the desired solution within them. To accomplish this, we utilize the fuzzy method outlined in references [32, 33]. In Table 1, three case studies have been included to aid in the planning of the proposed microgrid.
Case studies in microgrid.
The cases are given to optimize objective functions in microgrid. These case studies will be analyzed in the next subsection to ensure optimal operation in microgrid.
6.1 Results analysis
This section confirms the superior performance of the proposed optimization method by addressing a multiobjective capacity problem related to resources. Figure 2 displays the Pareto solutions produced by the MSFO algorithm for Case 1, demonstrating the allocation of resources. The criteria considered consist of installation cost, penetration rate, and load shedding. The preferred option, indicated in red, features installation cost, penetration rate, and load shedding values of $323,333.5, 27.3%, and 4.83% respectively. Proceeding to Figure 3, you can see the collection of Pareto solutions for Case 2. In this instance, the preferred solution involves an installation cost of $327,865.3 and a PV and WT penetration of 27.89%. The installation cost is higher in Case 2 compared to the other cases due to the absence of loadshedding and the increased sizing and number of resources. Figure 4, illustrates the collection of Pareto solutions for Case 3. In this scenario, the installation cost is $323,565.30, and the load shedding percentage is 4.43%. These results highlight the optimization algorithm’s success in addressing a multiobjective challenge. Pareto solutions present a variety of options that effectively weigh the different factors involved, empowering decisionmakers to pick the most fitting solution based on their priorities and constraints.
Tables 2–4 present the optimal number and sizing of resources for the case studies. Case 2 features the highest number and sizing of resources, while Cases 1 and 3 are nearly identical to each other.
Optimal sizing of resources in Case 1.
Optimal sizing of resources in Case 2.
Optimal sizing of resources in Case 3.
7 Conclusion
The article studied the optimal planning of energy sources in an independent microgrid. The primary objectives include lowering installation expenses, optimizing the utilization of wind turbines and solar panels to meet demand balance, and reducing power outages. The study also delves into the various parameters and constraints involved in the planning process, such as time, cost, and resource availability. By incorporating these factors into the MSFO algorithm, the study demonstrates its ability to handle complex planning scenarios and provide solutions that meet the specified objectives. Overall, the study’s findings underscore the significance of the MSFO algorithm in addressing the complexities of the planning process and its potential to revolutionize resource allocation practices across various industries. With its proven efficiency and adaptability, the algorithm offers a promising solution for optimizing planning processes and achieving better outcomes.
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All Tables
All Figures
Fig. 1 Microgrid configuration. 

In the text 
Fig. 2 Pareto front in Case 1. 

In the text 
Fig. 3 Pareto front in Case 2. 

In the text 
Fig. 4 Pareto front in Case 3. 

In the text 
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