Optimizing Hybrid Renewable Energy Systems for Isolated Applications: A Modified Smell Agent Approach

Abstract

This paper presents the optimal sizing of a hybrid renewable energy system (HRES) for an isolated residential building using modified smell agent optimization (mSAO). The paper introduces a time-dependent approach that adapts the selection of the original SAO control parameters as the algorithm progresses through the optimization hyperspace. This modification addresses issues of poor convergence and suboptimal search in the original algorithm. Both the modified and standard algorithms were employed to design an HRES system comprising photovoltaic panels, wind turbines, fuel cells, batteries, and hydrogen storage, all connected via a DC-bus microgrid. The components were integrated with the microgrid using DC-DC power converters and supplied a designated load through a DC-AC inverter. Multiple operational scenarios and multi-objective criteria, including techno-economic metrics such as levelized cost of energy (LCOE) and loss of power supply probability (LPSP), were evaluated. Comparative analysis demonstrated that mSAO outperforms the standard SAO and the honey badger algorithm (HBA) used for the purpose of comparison only. Our simulation results highlighted that the PV–wind turbine–battery system achieved the best economic performance. In this case, the mSAO reduced the LPSP by approximately 38.89% and 87.50% over SAO and the HBA, respectively. Similarly, the mSAO also recorded LCOE performance superiority of 4.05% and 28.44% over SAO and the HBA, respectively. These results underscore the superiority of the mSAO in solving optimization problems.

1. Introduction

Renewable energy sources have been utilized to decrease reliance on fossil fuels and reduce greenhouse gas emissions [1]. However, to address the intermittency issues of renewable sources, such as solar and wind, hybrid renewable energy systems (HRESs) have been introduced as a solution. These systems not only meet electricity demand but also lower greenhouse gas emissions, providing an efficient, sustainable, and eco-friendly approach. This contributes significantly to the development of smart grid environments. Various configurations are integrated to develop a hybrid renewable energy system, either in grid-connected or stand-alone mode, using multiple energy sources to meet energy demand. The system utilizes multiple storage devices to balance energy fluctuations, storing excess energy in the short term with batteries and supercapacitors and in the long term with hydrogen tanks [2].

The optimal design of stand-alone hybrid renewable energy systems requires effective capacity planning and sizing to minimize investment costs and maximize the efficient use of hybrid energy resources. This design process must account for the coordination between energy sources, storage systems, and load demand patterns. To address sizing challenges in these systems, optimization techniques have been explored in the literature, involving mathematical modeling of components and the use of hourly weather data for the chosen location [3]. Additionally, these models focus on specific objective functions. In Ref. [4], the authors applied the PSO algorithm and an Artificial Neural Network to estimate PV panel parameters, with simulation results demonstrating a 3.5% improvement in convergence speed.

Recent research has focused on the application of meta-heuristic algorithms for renewable energy system sizing. Several optimization techniques have been explored, including the smell agent optimization (SAO) algorithm, a novel meta-heuristic inspired by the human sense of smell, which operates in three distinct modes, sniffing, trailing, and random mode, as described in Ref. [5]. The authors proposed an enhanced SAO algorithm for sizing hybrid renewable energy systems using photovoltaic panels, wind turbines, and batteries. This approach optimized the system for the lowest annual cost and minimized the loss of power supply probability (LPSP), with improvements of 79% and 53.4%, respectively. The research in Ref. [6] presents an approach to optimizing hybrid renewable energy systems by integrating various generation and storage technologies under a multi-objective framework. Through the assessment of seven optimization algorithms across different operational scenarios, the research identifies an effective strategy for balancing cost, reliability, and power management in isolated microgrids. A method for optimally sizing hybrid renewable energy systems for remote areas, specifically Lavan Island, considering both cost and the intermittent nature of these sources, is developed in Ref. [7]. The study introduces a novel mathematical approach incorporating PV, wind, hydrogen, battery, and fuel cell systems, aiming for off-grid electricity while offering scalability. By employing fuzzy logic and advanced optimization algorithms like the SFLA, GOA, and HBA, the research demonstrates a superior method for achieving a cost-effective and reliable energy supply. The study in Ref. [8] introduces two new optimization algorithms, QOBL-SAO and LFQOBL-SAO, and evaluates their effectiveness against standard SAO. The algorithms were tested on benchmark functions and real-world engineering problems, specifically optimizing hybrid PV/wind/battery systems for a Nigerian healthcare center. Results from simulations indicate that the new variants outperform SAO in minimizing the cost and improving the convergence of hybrid energy system optimization, with LFQOBL-SAO demonstrating superior accuracy. The research in Ref. [9] also addresses the growing need to integrate renewable energy sources with traditional fossil fuel power generation due to rising costs and environmental concerns. It introduces a new hybrid optimization method for the generation scheduling problem, specifically considering wind, solar, and electric vehicle integration alongside thermal units. The proposed heuristic approach effectively handles various operational constraints and is tested on a 10-unit thermal system with increasing renewable and EV penetration. The study in Ref. [10] introduces a novel Nested Identical Control (NIC) method for load frequency control in multi-area microgrids, utilizing two new enhanced versions of the Chameleon Swarm Algorithm (CSA): QCSA and QLCSA. These CSA variants incorporate quasi-oppositional-based learning and Levy flight to improve exploration and avoid local optima, demonstrating superior performance against standard CSA and other algorithms on benchmark functions. The NIC strategy, with controller parameters mirrored across areas, aims for rapid stabilization of frequency fluctuations under uncertainties, and simulations on a two-area microgrid validate the effectiveness of the proposed approach. Similarly, in Ref. [11], the authors analyzed and compared the energy performance of different configurations, testing fuel cells (FCs), electrolyzers, and hydrogen tanks as backup storage systems alongside photovoltaic (PV) panels and wind turbines (WTs). The optimization results indicated that the PV/WT/FC configuration was the most cost-effective, achieving the lowest Total Annual Cost (TAC). In Ref. [12], Shuang Wang et al. demonstrated that while the original SAO algorithm is reliable for solving numerical problems, they improved the algorithm by incorporating the jellyfish swarm’s active–passive mechanism and a novel random operator. This modified SAO (mSAO) improved solution quality by 10–20% over the basic SAO when applied to constraint benchmarks and engineering problems.

Several algorithms have been developed to solve complex problems, including discrete, constraint, dynamic, and non-differentiable issues, as highlighted by Mariye Jahannoosh et al. in Ref. [13]. The hybrid Grey Wolf Optimizer-Sine Cosine Algorithm (HGWOSCA) was compared with the SCA, GWO, and Particle Swarm Optimization (PSO) methods for designing various combinations of hybrid systems under varying reliability constraints. The results demonstrated that the PV/WT/FC combination was the most cost-effective and reliable, particularly in terms of the lowest levelized supply cost of energy (LSCS) and the highest Load Instantaneous Power (LIPmax) for meeting the demand of remote communities. Additionally, the same system was analyzed using the Jaya algorithm and compared with the Genetic Algorithm, Backtracking Search Algorithm, and PSO. The simulation results, as shown in Ref. [14], revealed that the PV-FC system was the most cost-effective method, outperforming the PV-WT-FC and WT-FC combinations when the maximum loss of power supply probability (LPSP) was set at 0% and 2%. Recent studies have also led to the development of novel hybrid algorithms, such as the smell agent optimizer (SAO) combined with symbiosis organism search (SOS), as described in Ref. [15], for optimal control of microgrid operations. The findings suggest that the SASOS algorithm is a promising solution for engineering optimization and improving the control systems of autonomous microgrids. The study in Ref. [16] analyzes hybrid renewable energy systems (HRESs) with solar PV panels, diesel, and batteries for reliable off-grid power. It highlights their techno-economic advantages over single sources, especially in areas with solar potential and grid issues. The integration of solar and diesel proves consistently effective across different regions, offering key insights for energy policy. The study in Ref. [17] explores powering remote Mexican homes using autonomous hybrid renewable energy and photovoltaic systems, utilizing HOMER Pro 3.16.1 software for a year-long analysis. The optimal configuration identified a solar system with a converter and a diesel/battery backup as the most viable and reliable option, achieving over 80% renewable energy. Muhammad et al. in Ref. [18] present an off-grid hybrid renewable energy system for electrifying a remote area in Abuja, Nigeria. The optimization problem was addressed using the Optimal Foraging Algorithm (OFA), and the results were compared with those from the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Additionally, in Ref. [19], the authors propose a Power Management and Control (PMC) system for energy optimization in sustainable environments. This system combines GA and PSO to balance energy consumption and the Occupant Comfort Index (OCI). The PMC system outperformed existing models by achieving an ideal OCI of 1 while using less energy. It was validated through simulations using actuators to control the indoor environment, demonstrating its effectiveness in reducing energy consumption while maintaining or enhancing comfort. Yan Cao et al. in Ref. [20] introduced a new model of the Elephant Herding Optimization (BEHO) Algorithm to solve multi-objective optimization problems. The algorithm was validated through various benchmark functions and algorithms for a proposed hybrid system based on PV, wind, fuel cell, and battery technologies. Recently, global attention has focused on optimizing energy management strategies for hybrid renewable energy systems, requiring careful coordination of design state, geophysical conditions, load demand, and parametric constraints. Effective implementation ensures project longevity and cost-efficiency and promotes sustainable development. Studies [19,21,22,23,24,25] highlight the technical and economic evaluation of excess electricity management beyond optimal storage capacity for off-grid renewable systems.

The main contributions of this paper are highlighted as follows:

• The paper presents a modified version of the smell agent optimization (SAO) algorithm, which uses a time-dependent approach to adapt the control parameters dynamically as the algorithm progresses. This modification improves convergence and search efficiency, addressing the limitations of the original SAO algorithm.
• The paper applies the modified and standard SAO algorithms to design a hybrid renewable energy system (HRES) for an isolated residential building in Annaba, Algeria. The system includes photovoltaic panels, wind turbines, fuel cells, batteries, and hydrogen storage, all integrated with a DC bus microgrid.
• The paper compares the modified SAO against the standard SAO, and both SAO variants are validated against the honey badger algorithm (HBA).
• Through simulations, the paper demonstrates that modified SAO (mSAO) significantly outperforms both the standard SAO and HBA in economic performance. It achieves a substantially lower loss of power supply and levelized cost of energy compared to the results obtained with the standard SAO and HBA.

The paper is organized as follows: First, the introduction is provided. Section 2 presents the mathematical descriptions of all components in the DC multisource system, along with the problem formulation, including the objective function and constraints. In Section 3, the optimization approaches are defined. Section 4 discusses the energy management system of the proposed framework, utilizing the SAO, mSAO, and HBA optimization techniques. The simulation results and corresponding discussion are covered in Section 5. Finally, conclusions and future research directions are suggested in Section 6.

2. Configuration of the System Under Study

This study focuses on a residential application using a multi-source hybrid renewable energy system (MHRES) connected to a DC bus to supply an AC dynamic load based on daily load data, with a maximum power of 4.9 kW. The primary goal is to enhance the system’s resilience by ensuring continuous power delivery to meet demand [26,27]. The system includes photovoltaic (PV) panels and a wind turbine to supply the load, along with a storage system consisting of batteries and a hydrogen storage tank. The parameters related to the components are presented in

Table A1. HRES component specifications and economic parameters.

Component Systems	Parameters	Specifications
PV	Nominal PV power Pr-PV	120 W
	PV cost CPv	USD 216
	Surface area A	1.07 m2
	PV efficiency ηPV	12%
	PV lifetime	20 years
Wind Turbine	Nominal WT power Pr-Wt	1 kW
	Vcut-in	3 m/s
	Vcut-out	20 m/s
	Vr	9 m/s
	CWind	USD 1804
	Maintenance cost CMntWind	USD 100
	WT lifetime	20 years
FC	Nominal FC power	3 kW
	FC efficiency (ηFC)	50%
	FC lifetime	5 years
	FC cost (CFC)	USD 20,000
	Replacement cost (CMnt-FC)	USD 1400
Battery	Energy capacity (Eb,u)	1000 Wh
	Maximum discharge power (b,max)	1000 W
	Maximum charge power (Pb,min)	1000
	Maximum SoCb	0.9
	Minimum SoCb	0.24
	Capital cost (CCb)	USD 2000
	Equivalent full cycles (Ncycles,b)	471
	Maintenance cost (Com,)	5% CCb USD/year
Electrolyzer	Nominal electrolyzer power	3 kW
	Electrolyzer efficiency (hEle)	74%
	Electrolyzer lifetime	5 years
	Electrolyzer cost (CEle)	USD 20,000
	Replacement cost (CMnt-Ele)	USD 1400
H2Tank	Reservoir tanks cost (CHT)	USD 2000
	Nominal capacity of THE hydrogen tank	0.3 kW
Converter	Power converter	3 kW
	Inverter efficiency (η conv/inv)	95%
	Converter/inverter lifetime	10 years
	Converter/inverter cost	USD 1583
Other parameters	Interest rate of project i	5%
	Lifespan of the project n	20 years

, Appendix A. The proposed system is shown in Figure 1, while the data used for modeling are shown in Figure 2.

As illustrated in Figure 2, Figure 2a displays the 24 h load profile of a residential building in Anaba, Algeria. This profile exhibits a fluctuating energy demand throughout the day, with periods of low consumption during the early morning hours (approximately 0–6 h), followed by increasing demand in the morning, a significant peak around midday (approximately 12–14 h reaching nearly 5 kW), and subsequent fluctuations with a generally decreasing trend toward the late evening.

Figure 2b presents the corresponding 24 h profiles for solar radiation and wind speed in Annaba. The blue line, plotted against the left y-axis, shows the solar radiation (in W/m²). It indicates a typical daytime solar irradiance pattern, starting at zero during the night, gradually increasing after sunrise, reaching a peak intensity around midday, and then decreasing back to zero as the sun sets. The orange line, plotted against the right y-axis, depicts the wind speed (in m/s). This profile shows more variability throughout the day, with periods of relatively low wind speeds and instances of higher wind speeds occurring at different times within the 24 h. These solar and wind profiles capture the availability of the required natural resources for the design of the hybrid system.

2.1. System Modeling

The model examined in this study is a hybrid system comprising a solar system, a fuel cell, and a wind turbine integrated with an electrolyzer and cell stacks (wind/solar/fuel cell) for prolonged energy utilization with stored energy for specific durations. During operation, excess electrical energy generated by the photovoltaic (PV) panels and wind turbine is utilized to charge the battery when the SOC of the battery is less than SOC min or to produce hydrogen via electrolysis. Subsequently, the produced hydrogen is stored in hydrogen reservoir tanks, which are then utilized to generate electricity by providing fuel cell stacks with hydrogen.

The mathematical models of all components included in the proposed hybrid system are briefly presented as follows:

A.

PV model

The electrical power generated from series-connected several PV cells is expressed as follows (1):

$$p_{PV}(t)=I(t)\times A\times {\eta }_{PV}$$

(1)

where I(t) is the solar radiation, A denotes the PV area, $p_{PV}$ is the power produced by each PV cell, and η_PV is the efficiency of the PV system and the converter system with $N_{PV}$ number of PV panels, the total produced power is as follows (2):

$$P_{PV}(t)=N_{PV}\times p_{PV}(t)$$

(2)

B.

Wind turbine model

The power of the wind turbine at a specific wind speed v can be formulated as (3) [27,28]:

$$P_{WT}(t)=\left\{\begin{array}{l}0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}v(t)\le v_{cut-in}\\ P_r{\displaystyle \frac{v(t)-v_{cut-in}}{v_r-v_{cut-in}}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{1em}\hspace{1em}\hspace{1em}{v}_{cut-in}<v(t)<v_r\\ P_r\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{v}_r<v(t)<v_{cut-in}\end{array}\right.$$

(3)

where v is the wind speed, P_r is the rated power of the WT, and v_cut-in, v_cut-out, and v_r are the c_ut-in, c_ut-out, and rated speed of the WT, respectively. If the number of WTs is $N_{WT}$, the overall produced power is as follows (4):

$$P_{WT}(t)=N_{WT}\times p_{WT}(t)$$

(4)

where $P_{WT}(t)$ is the total power produced by the wind turbines.

C.

Energy Storage

To maintain a continuous balance between energy sources and load, the Energy Storage System (ESS) can provide a regulating reserve. In our work, battery banks with fully integrated electrolyzers, fuel cells, and hydrogen tank systems are complemented to meet the required load.

The power balance $P_B(t)$ is calculated as the difference between the total power generated ($P_{ren}(t)$) by both the PV $P_{PV}(t)$ and wind $P_{WT}(t)$ and the power load $P_{Load}(t)$. This value indicates whether there is a surplus or deficit of energy relative to the demand (5).

$$\begin{array}{l}{P}_B(t)=P_{ren}(t)-P_{Load}(t)\\ P_{ren}(t)=P_{PV}(t)+P_{WT}(t)\end{array}$$

(5)

C.1 Battery storage

This potentially leads to a positive $P_B(t)$ (excess energy) and the $P_B(t)$ could be negative, indicating an energy deficit. The charging and discharging schedule of the battery is expressed in Equations (6)–(9) in References [5,29].

• Charging mode, when there is excess energy, i.e., $P_{ren}(t)>P_{Load}(t)$

$$P_{ch}(t)=\min \left\{P_B(t),{\displaystyle \frac{1}{{\eta }_{chb}}}\times \left(E_{bat}^{\max }-E_{bat}(t-1)\right)\right\}$$

(6)

The energy stored in the batteries can be calculated as the expression (7):

$$E_{ch}(t)=E_{bat}(t-1)\times \left(1-\sigma \right)+P_{ch}(t)\times {\eta }_{chb}$$

(7)

where $P_B(t)$ is the battery power, $E_{bat}^{\max }$ is the maximum energy capacity of the battery, $E_{bat}$ is the present energy of the battery, $\sigma$ is the dept of discharge, and ${\eta }_{chb}$ is the charging efficiency of the battery.

• Discharging mode, when there is an energy deficit, i.e., $P_{ren}(t)<P_{Load}(t)$

$$P_{dis}(t)=\min \left\{|P_B(t)|,{\eta }_{disb}\times (E_{bat}(t-1)-E_{bat}^{\min }\right\}$$

(8)

The energy stored in the battery can be calculated using Equation (9):

$$E_{dis}(t)=E_{bat}(t-1)\times \left(1-\sigma \right)-{\displaystyle \frac{1}{{\eta }_{disb}}}\times P_{dis}(t)$$

(9)

The SoC_b can be expressed in a discrete form in (10) [26]:

$$So{C}_b(K+1)=So{C}_b(K)-{\displaystyle \frac{P_b\left(K\right)}{n_b{E}_{b,u}}}\Delta t$$

(10)

where SoC_b is the state charge of the battery and P_b is the battery power in (W), E_bat is the nominal energy capacity in (Wh) of each elemental battery unit, N_b is the number of batteries, $E_{dis}$ is the discharging energy of the battery and ${\eta }_{disb}$ discharge efficiency.

C.2 Water Electrolyzer

When there is excess energy, hydrogen is produced. The power output delivered from the electrolyzer to the tank of the hydrogen is illustrated as follows (11) [29]

$$P_{el}(t)={\eta }_{el}\times P_{ren-el}(t)$$

(11)

where P_el is the electrolyzer output power (kW), P_{ren_el} is the electrolyzer input power (kW), and η_el is the efficiency of the electrolyzer assigned a constant value.

The amount of renewable energy available $P_{ren-el}(t)$ is determined by the amount of excess energy and the amount of energy used to charge the batteries (12).

$$P_{ren-el}(t)=P_B(t)-P_{ch}(t)$$

(12)

Taking into account the rated power of the electrolyzer P_Eln and the charge level of the hydrogen tank, the following equation determines the actual amount of hydrogen produced $P_{H2-P}(t)$ in Equation (13) [25,27]:

$$P_{H2-P}(t)=\min \left\{E_{\tan k}^{\mathrm{m}\mathrm{a}\mathrm{x}}-E_{\tan k}(t-1),\min (P_{ren-el}(t),P_{ELn})\times {\eta }_{el}\right\}$$

(13)

where, $E_{\tan k}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum energy capacity of the tank, $P_{ren-el}$ is the replacement cost of the electrolyzer, ${\eta }_{el}$ is the efficiency of the electrolyzer, $P_{ELn}$ is the power produced by the electrolyzer and $P_{H2-P}$ is the hydrogen power.

C.3 Modeling H2 Tank

The electrical energy stored inside the tank $E_{\tan k}(t)$ can be expressed as follows (14):

$$E_{\tan k}(t)=E_{\tan k}(t-1)+\left\{P_{el}(t)-{\displaystyle \frac{P_{H2-FC}(t)}{{\eta }_{storage}}}\right\}$$

(14)

The amount of hydrogen stored in kilograms can be obtained from Equation (15) in [30]:

$$M_{tank}(t)={\displaystyle \frac{E_{\tan k}(t)}{HH{V}_{H2}}}$$

(15)

where $HH{V}_{H2}$ is the hydrogen gas’s higher heating value, which is usually taken as $39.7\hspace{0.17em}{\mathrm{kWh}/\mathrm{m}}^2$.

C.4 Fuel Cell model

Proton Exchange Membrane Fuel Cells (PEMFCs) are one of the most widely utilized fuel cell technologies. This type of fuel cell generates only electricity, water, and heat.

The energy output of fuel cells is directly related to the hydrogen consumed from the hydrogen tank and the efficiency of the fuel cell, as expressed in Equation (16) as, in Ref. [30].

$$P_{FC}(t)={\eta }_{FC}\times P_{H2-FC}(t)$$

(16)

In addition, the produced thermal power of the FC $P_{THFC}$ is achieved using Equations (17) and (18):

$$P_{THFC}=r_{THFC}\times P_{FC}$$

(17)

$$r_{THFC}=\left\{\begin{array}{l}0.6801\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}PLR\ge 0.05\\ 1.0785\times PL{R}^4-1.9739\times PL{R}^3+1.5005\times PL{R}^2\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}PLR<0.05 \\ -0.2817\times PLR+0.6838\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}otherwise\end{array}\right.$$

(18)

D.

Inverter model

The inverter model is expressed in terms of the output power delivered to the load as follows in (19):

$$\left\{\begin{array}{l}{P}_{invn}\ge P_{PV}\left(t\right)+P_{dis}\left(t\right)+P_{FC}\left(t\right)\\ P_{invn}=K\times \max \left(P_{PV}\left(t\right)+P_{dis}\left(t\right)+P_{FC}(t)\right)\end{array}\right.$$

(19)

2.2. Problem Formulation

The meta-heuristic algorithms, standard SAO, and modified mSAO algorithms are applied to generate the optimal design and sizing of the proposed systems. The objective function describing the entire system and all of the relevant constraints are presented in this section.

2.2.1. Objective Function

The optimal design of the hybrid systems is proposed to minimize the levelized cost of energy (LCOE), the loss of power supply probability (LPSP), and excess energy (EE). The corresponding mathematical expression is given by Equations (20)–(22) in Ref. [24]:

$$\min F=\min (\lambda LCOE+\lambda LPSP+\lambda EE)$$

(20)

The objective functions can be expressed in Equations (21)–(29)

$$LCOE={\displaystyle \frac{TAC}{E_{total}}}$$

(21)

$$TAC={\displaystyle \sum _{i=1}^{N}AMC}+{\displaystyle \sum _{i=1}^{N}ACC}+{\displaystyle \sum _{i=1}^{N}REPC}$$

(22)

where in Total Annual Cost (TAC), $E_{total}$ represents the total energy produced, N stands for the overall number of hours considered, ACC stands for the annualized capital cost, AMC stands for the annual maintenance, and REPC stands for the replacement cost. The AMC is calculated using Equation (23):

$$AMC=N_{PV}\times C{m}_{PV}+N_{WT}\times C{m}_{WT}+N_{EL}\times C{m}_{EL}+C{m}_{FC}+C{m}_{Bat}$$

(23)

The ACC, on the other hand, is calculated using Equation (24):

$$ACC=CRF\times \left[N_{PV}{C}_{PV}+N_{WT}{C}_{WT}+C_{FC-EL}+N_{Bat}{C}_{Bat}+N_{\mathrm{Tan}k}{C}_{\mathrm{Tan}k}+N_{inv}{C}_{inv}\right]$$

(24)

where $N_{PV},N_{WT},N_{Bat},N_{\mathrm{Tan}k,}{N}_{inv}$ represent the number of PV panels, wind turbines, batteries, hydrogen tanks, and converters, respectively, while $C_{PV},\hspace{0.17em}\hspace{0.17em}{C}_{WT},\hspace{0.17em}\hspace{0.17em}{C}_{FC-EL},\hspace{0.17em}\hspace{0.17em}$ $C_{Bat},\hspace{0.17em}\hspace{0.17em}{C}_{\mathrm{Tan}k},\hspace{0.17em}\hspace{0.17em}{C}_{inv}$ denote the unit costs of the PV panels, wind turbines, fuel cells, electrolyzers, batteries, and converters, respectively. CRF is the Capital Recovery Factor is modeled as follows (25):

$$CRF={\displaystyle \frac{i{(1+i)}^n}{{(1+i)}^n-1}}$$

(25)

where i (5%) is the annual interest rate and n denotes the system’s lifetime (20 years).

The replacement cost (REPC) is calculated using Equations (26)–(27):

$$REPC=C_{rep}\times {\displaystyle \frac{i}{{(1+i)}^{nr}-1}}$$

(26)

$$REPC=C_{REP}^{FC}\times {\displaystyle \frac{i}{{(1+i)}^{15}-1}}+C_{REP}^{Elz}\times {\displaystyle \frac{i}{{(1+i)}^{15}-1}}+C_{REP}^{Bat}\times {\displaystyle \frac{i}{{(1+i)}^{10}-1}}+C_{REP}^{Con/inv}\times {\displaystyle \frac{i}{{(1+i)}^{10}-1}}$$

(27)

where nr is the lifetime of the replaced component.

The loss of power supply probability (LPSP) is a criterion used for evaluating the reliability of the proposed energy system. The equation below is used to calculate the value of the LPSP (28).

$$LPSP={\displaystyle \frac{{\displaystyle {\sum }_0^T{P}_{Load}-P_{WT}\left(t\right)-{\eta }_{inv}\times \left(P_{PV}\left(t\right)+P_{FC}\left(t\right)+P_{dis}\left(t\right)\right)}}{{\displaystyle {\sum }_0^T{P}_{Load}}}}$$

(28)

The following mathematical equation can be used to express the excess energy:

$$EE={\displaystyle \frac{{\displaystyle \sum _0^T{P}_{Load}}-P_{PV}-P_{WT}-\left(P_{ch}(t)+P_{el}(t)\right)}{P_{PV}+P_{WT}}}$$

(29)

where $C_{REP}^{FC}$ is the replacement cost of the fuel cell, $C_{REP}^{Elz}$ is the replacement cost of the electrolyzer, $C_{REP}^{Bat}$ is the replacement battery, and $C_{REP}^{Conv/Inv}$ is the replacement of converter.

2.2.2. Different Constraints

The tri-objective function must be optimized considering system components minimum and maximum number N Lower ≤ Ni ≤ N Upper as decision variable constraints related to the optimal design and sizing of the HRES that should be satisfied:

$$\begin{array}{l}{N}_{pv}^L\le N_{pv}\le N_{pv}^U\\ N_{wt}^L\le N_{pv}\le N_{wt}^U\\ N_{Bat}^L\le N_{Bat}\le N_{Bat}^U\\ N_{EL}^L\le N_{EL}\le N_{EL}^U\\ N_{FC}^L\le N_{FC}\le N_{FC}^U\\ N_{\mathrm{Tan}k}^L\le N_{\mathrm{Tan}k}\le N_{\mathrm{Tan}k}^U\\ Soc(t_{\min })\le Soc(t)\le Soc(t_{\max })\\ E_{\tan k}^{\min }\le E_{\tan k}\le E_{\tan k}^{\max }\end{array}$$

(30)

where $N_{pv}^L$ and $N_{pv}^U$ are the lower and upper bounds for the number of PV panels, $N_{wt}^L$ and $N_{wt}^U$ are the lower and upper bounds for the number of wind turbines, $N_{bat}^L$ and $N_{bat}^U$ are the lower and upper bounds for the number of batteries, $N_{EL}^L$ and $N_{EL}^U$ are the lower and upper bounds for the number of electrolyzers, $N_{FC}^L$ and $N_{FC}^U$ are the lower and upper bounds for the number of fuel cells, and $N_{\mathrm{Tan}k}^L$ and $N_{\mathrm{Tan}k}^U$ are the lower and upper bounds for the number of hydrogen tanks.

3. Optimization Approaches for Microgrid Energy Management

The majority of new meta-heuristic algorithms focus on the foraging behaviors of the agents through a constant parameterization. The SAO is one such algorithm whose performance is significantly influenced by the choice of its control parameters, like the olfaction capacity and step size. In our study, we proposed a dynamic method for selecting these parameters and eventually proposed a modified SAO, called the mSAO. Both the mSAO and the original SAO were used to obtain optimal results for sizing the hybrid renewable energy system based on established reliability, technico-economical, and stability criteria.

3.1. Smell Agent Optimizer

Smell agent optimization (SAO) is a cutting-edge meta-heuristic algorithm inspired by the intelligent behaviors of agents trailing the source of a smell molecule. This modern optimization technique mimics the natural process of smell detection and tracking, whereby agents navigate through a complex search space to identify the optimal solution. The SAO combines swarm intelligence, machine learning, and dynamic optimization principles to efficiently explore and exploit the search space, ensuring a robust and adaptive search process. The parameters related to the SAO algorithm are given in

Table A2. SAO meta-heuristic algorithm-related parameters.

Parameter	Symbol	Value
Number of smell molecules	N	50
Number of the decision variables	D	4
Temperature	T	3
Mass	M	2.4
Boltzmann’s constant	K	1.38 × 10−23
Maximum iteration	itr	100

of Appendix A. Detailed theoretical information on the SAO algorithm can be found in References [15,28].

The SAO algorithm is defined by a set of equations in three main phases, which model the behavior of agents as they search for optimal solutions. The SAO begins by initializing a population of smell molecules, represented as candidate solutions:

$$n^{(t)}=\left[\begin{array}{ccc}{n}_{1,1}& \dots & n_{1,d}\\ n_{2,1}& \dots & n_{2,d}\\ ⋮& \dots & ⋮\\ n_{N,1}& \dots & n_{N,d}\end{array}\right]$$

(31)

where $n^{(t)}$ denotes the matrix of current solutions, and d is the number of control variables in the problem domain.

Each molecule’s position is based on upper and lower bounds:

$$n_{i,j}^{(t)}=r_1\times (u{b}_j-l{b}_j)+l{b}_j$$

(32)

where $r_1$ is a random number between 0 and 1, and ub and lb are the upper and lower bounds of the variable.

• Sniffing Mode: Initial exploration of the search space.

Through Brownian motion with each molecule having a velocity given by

$$w^{(t)}=\left[\begin{array}{ccc}{w}_{1,1}& \dots & w_{1,d}\\ w_{2,1}& \dots & w_{2,d}\\ ⋮& \dots & ⋮\\ w_{N,1}& \dots & w_{N,d}\end{array}\right]$$

(33)

The molecules update their positions using:

$$n^{(t+1)}=n^{(t)}+w^{(t+1)}$$

(34)

where is updated by

$$w^{(t+1)}=w^{(t)}+r_2\times \sqrt{\left({\displaystyle \frac{kT}{m}}\right)}$$

(35)

where w is the velocity of the molecules, k is Boltzmann’s constant (smell constant), T is the temperature of molecules, m is the mass of molecules, and r₂ is a random value.

2.

Trailing Mode: Agents follow the best solution found.

Agents adjust their positions to move toward promising solutions. The new position is computed using

$$n^{(t+1)}=n^{(t)}+r_D\times olf\times (n_{best}^{(t)}-n^{(t)})-r_J\times olf\times (n_{worst}^{(t)}-n^{(t)})$$

(36)

where $r_D$, $r_J$, are random numbers between [0, 1], olf is the olfaction capacity, $n_{best}^{(t)}$ is the best solution found, and $n_{worst}^{(t)}$ is the worst solution.

3.

Random Mode: Random exploration to avoid local optimum.

If the algorithm fails to improve fitness using sniffing or trailing modes, the random mode is activated:

$$n^{(t+1)}=n^{(t)}+r_K\times step$$

(37)

where step is an arbitrary constant step size and $r_K$ is a random number between [0, 1].

3.2. Modified Smell Agent Optimizer (mSAO)

The unique features of the SAO, such as dynamic sniffing, trailing, random phases, and agent communication, enable the algorithm to balance exploration and exploitation effectively, leading to improved convergence and solution quality. Despite these positive features of the algorithm, the performance of each phase of the algorithm is highly dependent on the proper choice of its control parameters. For example, in the sniffing phase of the algorithm, the evaporation of smell molecules is penalized by the temperature (T), mass (M), and Boltzmann’s constant (K). In the trailing phase, the ability of the agent to trail the smell molecule is penalized by the constant olfaction capacity of the agent (olf), whereas the random phase is penalized by a constant step size (S). Poor choices of these parameters may result in inadequate exploration and exploitation of the search space, leading to insufficient diversity in solutions and reduced chances of finding global optima. This could also result in scalability problems, as the algorithm may not scale well with increasing problem dimensions or agent populations, leading to decreased performance and efficiency. To address these challenges, this paper introduces a mathematical procedure to adapt the selection of the control parameters as the algorithm progresses through the hyperspace. For example, the olfaction capacity and the step movement of the agent are mathematically determined using Equations (31) and (32), respectively.

$${\displaystyle \sum _{t=1}^{T_{\max }}f(t)=(f_L-f_H)\times ((T_{\max }-t)/t)+f_H}$$

(38)

$${\displaystyle \sum _{t=1}^{T_{\max }}s(t)=(s_L-s_H)\times ((T_{\max }-t)/t)+s_H}$$

(39)

where $f_L$ and $f_H$ are the lowest and highest possible values of olfaction capacity, $s_L$ and $s_H$ are the lowest and highest possible steps an agent can take during a random search, $T_{\max }$ and $t$ are the maximum and current iterations, respectively.

The SAO modification in Equations (31) and (32) is implemented to linearly decrease with time. This means that, for the initial stages of the search process, large values are selected to enhance global exploration, and searching new areas is recommended, while, for the later stages, the parameter values are reduced for local exploration, fine-tuning the current search area effectively. The flowchart for the implementation of the modified SAO is shown in Figure 3.

4. Multisource Model Energy Management Strategy

In our study, the proposed energy management used for the integrated multisource-based PV and WT generators and using batteries, with green hydrogen for energy storage, was investigated. The primary objective is to ensure power balance and to minimize the operating costs of the system. Additionally, extending the life cycle is essential for system components, especially the fuel cell stack, by reducing the FC power dynamics and conserving hydrogen use. However, the battery is fully charged to manage excess energy when the hydrogen storage tank is filled, and the load demand is minimal. This approach ensures a consistent and reliable energy supply to meet demand. The proposed EMS optimization mechanisms are illustrated in Figure 4, following the definition of the system’s constraints and objective function.

5. Results and Discussion

This section presents the study of the simulation results of the proposed systems carried out on hourly weather and load demand data.

Optimization Technique Analysis

The results in

Table 1. HRES components sizing results.

	Metrics	Scenario 1 (All Components)			Scenario 2 (No Hydrogen)			Scenario 3 (No Battery)
		SAO	mSAO	HBA	SAO	mSAO	HBA	SAO	mSAO	HBA
	NPV	8	5	8	13	5	6	20	5	6
	NWT	3	2	3	2	2	2	2	2	2
	NBat	7	2	3	2	2	2	--	--	--
	NTank	3	2	2	--	--	--	2	2	2
	NConv	5	5	5	4	4	4	4	4	4
Total annual cost (USD)	Best	619,464.60	619,464.60	622,492.68	613,685.57	613,685.57	614,275.39	616,910.51	616,910.51	617,395.86
	Avg	622,376.43	620,531.70	622,734.79	615,217.04	614,288.80	614,647.84	618,031.01	617,649.14	617,743.82
	Std	3.568 × 10−3	1.914 × 10−3	6.51 × 10+02	1.558 × 10−3	1.111 × 10−3	4.083 × 10+02	1.446 × 10−3	1.212 × 10−3	4.46 × 10+02
Time (s)		2.88	4.26	2.79	2.96	2.85	1.92	2.97	2.85	2.38

outline the sizing of renewable energy components obtained using the modified smell agent optimization (mSAO) algorithm compared to the original smell agent optimizer (SAO) and honey badger algorithm (HBA). The HBA is a meta-heuristic algorithm developed to mimic the intelligent foraging behavior of honey badgers [31]. The performance of the developed techniques was evaluated under three test scenarios. In the first scenario, all of the system components, including the two storage types (battery and hydrogen tank), are interconnected in the EMS. In the second scenario, the hydrogen is disconnected, leaving only the battery system as the energy storage device, while in the third scenario, the battery system is disconnected, leaving only the hydrogen tank as the storage system. The best, average, and standard deviation were calculated based on the results of the 50 executions. The modeling and simulation of the optimization problem were accomplished using the MATLAB R2023b program. All simulations were carried out on an HP computer system, with Windows 11 OS, 16 GB of RAM, and Intel CORE i7, 10^th Gen.

The results for the optimal sizing with the EMS are summarized in Table 1.

It can be seen from Table 1 that the analysis reveals that the mSAO algorithm consistently outperforms SAO and the HBA across all configurations, as evidenced by the reduced number of components required and the associated decrease in the average total annual cost. The installed PV power is reduced with the mSAO in all configurations; this is mainly caused by the optimal distribution of power and the prediction capacity of the mSAO algorithm. However, wind turbines serve the same dimension in all configurations, except in the first scenario in which mSAO attained a lower sizing. The energy capacity of batteries is also reached with mSAO in scenario 1 but fixed in scenario 2.

Figure 5 illustrates the convergence of the three algorithms throughout 100 iterations, wherein the most optimal outcome is observed in the second configuration utilizing the battery, contrasting with the other two configurations. Moreover, the efficiency of the mSAO algorithm in attaining optimal solutions by iteration number 29 correlates with a total annual cost of 614,288.8 (USD), as demonstrated by its consistently superior performance over a total of 50 runs, as shown in Figure 6 and Figure 7.

The results of different scenarios show the response of the proposed method to variations in input parameters. From the results shown in

Table 2. Results of the statistical study for the three proposed hybrid configurations using SAO and mSAO algorithms.

Configuration	Index		SAO	mSAO	HBA
PV/WT/Battery/Hydrogen	LCOE	Best	0.1846	0.4828	0.8740
		Average	0.6714	0.6986	0.8973
		StD	1.15 × 10−01	5.46 × 10−01	1.66 × 10−02
	LPSP	Best	1.69 × 10−02	8.48 × 10−03	1.91 × 10−02
		Average	2.01 × 10−02	1.44 × 10−02	2.73 × 10−02
		StD	2.76 × 10−03	7.14 × 10−02	3.56 × 10−03
	Excess Energy	Best	16.1358	15.340	18.96401
		Average	16.4176	17.1639	26.4235
		StD	2.76 × 10+03	4.25 × 10−01	3.10 × 10+00
PV/WT/Battery	LCOE	Best	0.3510	0.3583	0.6669
		Average	0.6868	0.7021	0.7409
		StD	7.72 × 10−02	1.07 × 10−02	7.31 × 10−02
	LPSP	Best	1.69 × 10−02	7.14 × 10−03	1.76 × 10−02
		Average	1.74 × 10−02	1.22 × 10−02	1.93 × 10−02
		StD	2.55 × 10−03	7.75 × 10−02	1.89 × 10−03
	Excess	Best	16.5794	17.1407	18.0397
		Average	17.0788	17.3042	19.2992
		StD	2.73 × 10−01	7.74 × 10−02	1.75 × 10+00
PV/WT/Hydrogen	LCOE	Best	0.3997	0.6866	0.7241
		Average	0.8857	0.7176	0.9115
		StD	7.13 × 10−02	9.87 × 10−03	4.78 × 10−02
	LPSP	Best	1.68 × 10−02	5.68 × 10−03	1.81 × 10−02
		Average	17.37 × 10−02	1.05 × 10−02	1.97 × 10−02
		StD	2.56 × 10−03	7.14 × 10−02	2.43 × 10−03
	Excess Energy	Best	14.120	17.141	18.729
		Average	17.069	17.322	19.619
		StD	6.33 × 10−01	5.68 × 10−02	1.99 × 10+00

, it can be observed that the mSAO reached the optimal objective function value in all cases, much better than the standard SAO and the HBA. The insignificant difference between the best and average values proved the convergence of the 50 implemented runs, demonstrating the stability and accuracy of the mSAO technique.

The analysis of the result shows the superior performance of the mSAO algorithm compared to the SAO algorithm across the key performance indicators. For the PV/WT/Battery/Hydrogen configuration, the average LCOE achieved by mSAO was slightly higher than that achieved by SAO but twice as low as that obtained with the HBA. The average LPSP with mSAO was significantly lower at 0.0144, compared to 0.020 for SAO and 0.027 for the HBA. This represents a substantial reduction of roughly 38.89% and 87.50% with respect to SAO and the HBA, respectively. The SAO, however, attained a better LPSP value of 35.58% over the HBA. The average excess energy was slightly higher for mSAO at 17.164 GWh compared to 16.418 kWh for SAO, an increase of about 4.6%, but lower in comparison with the HBA. For the PV/WT/Battery configuration, the average LCOE for mSAO was about 2.22% higher than that of SAO and 5.52% lower than the HBA. The average LPSP for mSAO was significantly lower, with 136.59% and 146.33% improvement over SAO and the HBA, respectively. The average excess energy for mSAO was marginal with mSAO −1.3% when compared with SAO, but lower by 11.53% when compared with the HBA. For the PV/WT/Hydrogen configuration, the average LCOE for mSAO was lower by 23.43% and 27.03% than that obtained with SAO and the HBA, respectively. Similarly, the average LPSP obtained with mSAO was 63.95% and 87.65% better than that obtained with SAO and the HBA, respectively. The average excess energy was slightly higher for mSAO at 17.322 kWh compared to 17.069 kWh for SAO and 19.619 kWh for the HBA, respectively. This constitutes an increase of 1.5% with respect to SAO and a decrease of 13.26% with respect to the HBA. These comparative studies across all configurations consistently highlight the significant improvements offered by the mSAO algorithm, more importantly, in the LCOE and the LPSP.

Figure 8 illustrates the performance comparison of the two optimization algorithms, SAO and mSAO, across 50 runs for the three renewable energy system configurations: PV/WT/Hydrogen/Battery, PV/WT/Hydrogen, and PV/WT/Battery.

The mSAO exhibits improved stability and reduced fluctuations in total annual cost across all system configurations, with particular advantages in the complex PV/WT/Hydrogen/Battery setup. This improvement can be attributed to mSAO design, which incrementally narrows the range of search parameters in later iterations. By focusing more precisely on promising regions in the solution space, mSAO minimizes the occurrence of cost spikes, especially under more intricate conditions involving multiple energy storage options like hydrogen. In simpler configurations (PV/WT/Battery), while all algorithms show comparable performance, mSAO still consistently achieves marginally lower costs when compared with SAO and the HBA. This suggests a distinct robustness that favors complex system optimization in which cost minimization and reliability are paramount.

Figure 9 compares the performance of the three renewable energy system configurations using three key metrics: loss of power supply probability (LPSP), levelized cost of energy (LCOE), and excess energy. In terms of reliability, the PV/WT/Hydrogen system shows the lowest LPSP, indicating that it is the most dependable configuration with the least chance of power supply failure. The PV/WT/Battery/Hydrogen system has a higher LPSP, but it achieves the lowest LCOE, making it the most cost-effective option over its lifetime. Meanwhile, both the PV/WT/Battery and PV/WT/Hydrogen systems show a higher LCOE, which suggests that they are less cost-efficient. When assessing energy efficiency, the PV/WT/Battery/Hydrogen system also excels by producing the least excess energy, indicating better energy utilization compared to the other two configurations. The PV/WT/Battery configuration, although simpler, produces the most excess energy, which suggests that it is less efficient and incurs higher energy wastage. Overall, the PV/WT/Battery/Hydrogen system offers the best balance between cost-effectiveness and energy utilization, though the PV/WT/Hydrogen system stands out for its superior reliability.

Figure 10, which shows the results across the three scenarios—PV/WT/Hydrogen/Battery, PV/WT/Battery, and PV/WT/Hydrogen—highlights the cost distribution among key components: wind turbines (wtCost), photovoltaic panels (pvCost), batteries (batCost), and hydrogen tanks (tankCost). The optimization results show that the PV/WT/Hydrogen/Battery system generally incurs the highest total annual cost due to the inclusion of both battery and hydrogen storage, with substantial contributions from batCost and tankCost. However, this system offers the best balance for reliability due to its diversified energy storage options, making it a strong contender for projects prioritizing energy security despite higher costs. The PV/WT/Battery system has lower overall costs, particularly due to reduced tankCost, but it may be less reliable in scenarios requiring large-scale energy storage, as it relies solely on batteries.

In the first scenario (Figure 10a), mSAO exhibits an efficient approach to cost distribution by achieving a lower battery cost (18.2%) compared to both SAO (28.8%) and the HBA (23.9%). This significant reduction in batCost by mSAO, even with strategic reallocations leading to higher hydrogen tank (42.6%), photovoltaic (19.0%), and wind turbine (27.3%) costs, underscores its ability to identify highly specialized and potentially more cost-effective combinations for energy storage. This indicates mSAO’s strong exploitation phase, allowing it to pinpoint a uniquely optimal sizing for batteries that contributes to overall system efficiency. While the HBA presents a more balanced distribution, mSAO’s capacity for such a substantial reduction in a major cost component highlights its superior ability to find innovative and highly optimized solutions, even if it means a different distribution across other components.

In the second configuration, in which battery storage is the sole energy storage mechanism (Figure 10b), mSAO demonstrates its robust approach to ensuring system reliability and performance. While mSAO exhibits the highest battery cost (44.7%) among the three algorithms, this is considered a strategic allocation to ensure the necessary investment in the sole storage component for robust system operation. In a scenario constrained to a single storage technology, mSAO’s optimization prioritizes the critical sizing required for system stability and performance, even if it results in a higher percentage share for the battery. Furthermore, mSAO achieves a lower wind turbine cost (35.4%) compared to SAO (49.0%) and the HBA (47.6%), showcasing its efficiency in optimizing other generation components. This indicates mSAO’s capacity to make decisive performance-driven allocations, ensuring the microgrid’s operational integrity. In this configuration, in which hydrogen storage is the primary storage mechanism (Figure 10c), mSAO consistently demonstrates its superior optimization capabilities. It achieves slightly lower tankCost (51.0%) and wtCost (32.7%) than SAO (52.1% and 34.1%, respectively). Crucially, mSAO yields the lowest photovoltaic cost (13.8%) in this scenario, outperforming both SAO (15.2%) and the HBA (12.6%). This consistent minimization of pvCost by mSAO, alongside its efficient management of tankCost and wtCost, highlights its comprehensive optimization capabilities.

6. Conclusions

In this paper, we have successfully demonstrated the efficacy of the modified smell agent optimization (mSAO) algorithm in optimizing the design and operation of a hybrid renewable energy system (HRES) for an isolated residential building. By introducing a time-dependent adaptation of control parameters, the mSAO significantly improved upon the limitations of the standard SAO algorithm, leading to enhanced convergence and search capabilities. Through simulations and comparative analysis, the mSAO consistently outperformed the standard SAO and HBA in terms of both economic and reliability metrics. The proposed HRES, optimized using mSAO, achieved a lower total annual cost (TAC) and levelized cost of energy (LCOE) compared to the standard SAO and the benchmarked HBA. Furthermore, the system configuration comprising photovoltaic (PV) panels, a wind turbine, and a battery storage system was identified as the most effective solution, capable of delivering optimal energy performance across various operational scenarios. The findings of this research highlight the potential of advanced optimization techniques like mSAO in enhancing the economic viability and operational efficiency of renewable energy systems. Though the mSAO outperformed the traditional SAO, the former, however, involves slightly longer computational time in the optimization process. Future work could focus on real-time control strategies and demand-side management techniques that enable more responsive and adaptive power distribution. This could include the application of machine learning algorithms to predict load demand and optimize energy storage management. Also, field validation of the proposed mSAO technique in real-world HRES installations would be invaluable in demonstrating its practical viability and scalability for larger, more complex systems.