An Optimal Sizing Methodology for a Wind/PV Hybrid Energy Production System for Agricultural Irrigation in Skikda, Algeria

Abstract

This paper presents an innovative solution to address agricultural irrigation needs through a hybrid renewable energy system (HRES) that was specifically designed for a farm located in the Skikda region of Algeria. This system is tailored to irrigate 830 fruit trees spread across 3 hectares with a total perimeter of 770 m. The proposed approach integrates two main renewable energy sources (while eliminating the use of traditional batteries for electrical energy storage): solar and wind. Instead, a large water reservoir is employed as an energy storage medium in the form of potential energy. Utilizing gravity, this reservoir directly powers the irrigation system for the fruit trees, thereby reducing the costs and environmental impacts associated with conventional batteries. This innovative design not only enhances sustainability, but also improves the system’s energy efficiency. To ensure precise and customized sizing of the system for the irrigation area, a detailed mathematical modeling of the key system components (solar panels, wind turbines, and reservoir) was conducted. This modeling identifies the critical design variables required to meet technical specifications and irrigation needs. A multi-objective optimization approach was then developed to determine the optimal configuration of the HRES, and this was achieved by considering both technical and economic constraints. The optimization algorithm used was tailored to the formulated problem, ensuring reliable and applicable results. The robustness of the optimization approach was shown by the precise match between energy production (24 kWh at 16,119.40 $) and the minimum demand. This alignment prevents over- or under-designing the system, which increases costs and reduces energy use. The findings highlight the relevance and effectiveness of the proposed methodology, demonstrating its practical utility and significant potential for generalization and adaptation to different agricultural zones with varying conditions. This work paves the way for sustainable and innovative solutions for agricultural irrigation, particularly in remote areas or regions lacking traditional energy infrastructure.

1. Introduction

Energy storage is a crucial component in the design and performance of HRESs, particularly in agricultural applications [1]. While conventional electrical storage systems, such as batteries (e.g., lead-acid and lithium-ion), are widely used and remain essential for general-purpose electricity storage in HRESs [2], alternative approaches like water tank storage—gravitational storage through elevated water reservoirs—have gained attention for specific applications like irrigation. In these cases, the stored energy is directly utilized in the form of water pressure or gravitational flow. Water tank storage offers a context-appropriate, economically viable, and environmentally sustainable solution, especially for irrigation systems. Its integration into rural agricultural energy models can reduce dependency on costly battery systems and enhance long-term system resilience, particularly in regions with limited financial and technical resources.

The increasing global demand for sustainable and reliable energy sources has intensified research on HRESs. These systems, which integrate multiple renewable energy sources, such as photovoltaic (PV) and wind energy, provide a promising solution for energy supply in remote and off-grid areas. One of the key applications of HRESs is in agricultural irrigation [3], where energy demand is variable and depends on seasonal water needs. Given the challenges associated with grid extension in rural areas, standalone renewable energy systems have emerged as an effective alternative to ensure sustainable irrigation. Despite the potential benefits of HRESs, their implementation poses several challenges, including optimal system sizing, cost-effectiveness, and energy reliability. A well-designed HRES must balance the trade-offs between initial investment costs, energy generation efficiency, and environmental impact. In this context, optimization techniques play a crucial role in determining the most suitable system configuration that can ensure a stable energy supply while minimizing costs.

Hybrid renewable energy systems (HRESs) have gained significant attention in agricultural applications, particularly for irrigation [4]. The integration of solar photovoltaic (PV) and wind energy has been widely studied as a means to provide reliable power to irrigation systems, especially in regions with high solar radiation and wind availability. Several studies [5,6,7] have explored different HRES configurations for agricultural use. Some researchers have focused on optimizing energy efficiency and economic feasibility, while others have emphasized reducing carbon emissions and environmental impact. Many of these studies have demonstrated that hybrid systems can significantly reduce reliance on fossil fuels, lower operational costs, and improve sustainability. However, optimizing system design for specific geographical locations remains a challenge due to variations in climate, energy demand, and resource availability.

Elkadeem et al. [8] assessed the viability and economic considerations of a hybrid renewable energy system designed for agricultural and irrigation applications in Dongola, Sudan. They evaluated combinations of solar panels, wind turbines, diesel engines, batteries, and converters to determine the best economical and eco-friendly arrangement. The ideal configuration achieved a 95% reduction in emissions and fuel consumption, with a net present cost of 24.16 $ million and a levelized cost of energy of 0.387 $ per kWh. Moreover, they illustrated, via sensitivity analysis, a reliance on solar radiation, wind velocity, and interest rates, emphasizing the significance of renewable energy in rural advancement.

Al-Rawashdeh et al. [9] introduced a hybrid renewable energy system (HRES) designed for the sustainable irrigation of a farm situated in a remote region of Al-Jafr, Jordan. It amalgamated solar and wind resources with sophisticated optimization methodologies to improve energy efficiency. It highlighted the reduction in carbon emissions while presenting comprehensive modeling and performance evaluation across diverse environmental situations. The study probably depended on particular environmental situations, thereby constraining the generalizability of the findings. It inadequately addressed economic viability, maintenance difficulties, or large-scale deployment concerns, which are essential for practical implementation.

Ghosh et al. [10] expanded the topic of smart energy networks by introducing sophisticated approaches for maximizing the integration of renewable energy and enhancing power generation and consumption predictions. It emphasized advanced computational methodologies, including IoT and multi-level reconfiguration frameworks for solar trackers and wind turbines, aimed at improving grid efficiency and sustainability. The project highlighted pragmatic applications, including measures to minimize energy waste and enhance distribution networks. Nonetheless, the constraints were possible difficulties in scalability, elevated implementation expenses, and the heightened complexity arising from the incorporation of sophisticated technologies.

Kose et al. [11] concentrated on the design and optimization of autonomous hybrid renewable energy systems that integrate wind, solar, and battery storage for irrigation purposes. The research assessed the technical and economic efficacy of these systems by examining various configurations under certain local conditions. Significant contributions encompassed the identification of suitable sizing solutions to guarantee reliability and cost-effectiveness, especially in areas with fluctuating renewable energy potential. The research emphasized the need for precise demand forecasting and localized resource evaluation in attaining sustainable energy solutions. Nonetheless, the research exhibited certain shortcomings. It mostly concentrated on particular case studies and did not thoroughly examine scalability for larger systems or varied geographical regions. Furthermore, it presumed consistent operational and maintenance expenses, disregarding possible variations during the system’s existence.

Tarife et al. [12] investigated the design of an off-grid hybrid renewable energy microgrid (HREM) specifically for rural agricultural areas. The study employed a modified multi-objective particle swarm optimization (MOPSO) method to optimize the integration of solar photovoltaic systems, run-of-the-river hydropower, battery storage, and diesel backup, aiming to balance cost, reliability, and environmental impact. It highlighted local economic advantages by incorporating the microgrid with agricultural technology to improve production, especially in abaca fiber processing, which is a vital regional endeavor. The study offered a framework for sustainable rural electrification, but it was constrained by its dependence on particular local data, the intricacy of its optimization algorithm, and the omission of alternate renewable sources such as biomass or wind. Moreover, its scalability to more extensive regions or metropolitan environments poses a hurdle.

Yan et al. [13] introduced a multi-objective optimization approach for the design of a hybrid photovoltaic, wind, fuel cell, and battery system. The optimization was predicated on three models: energy supply reliability, electricity efficiency, and the capital cost of the hybrid system. The Elephant Herding Optimization (BEHO) algorithm was employed to address the multi-objective optimization problem and was validated against various algorithms and benchmark functions. The primary objective was to identify the Pareto surface, encompassing a range of potential design choices to assist decision makers in achieving the global optimum solution. The final results demonstrated that the proposed method is a viable way for constructing the hybrid system. Consequently, they proposed a novel methodology for the design of a hybrid renewable energy system that decision makers might employ to achieve a global optimal solution.

Over the past decade, numerous studies have focused on the optimal sizing of hybrid renewable energy systems for agricultural electrification and irrigation [14,15], as well as on system optimization [16,17,18,19] and the development of optimization algorithms [20,21,22,23,24,25].

This paper presents a methodology to optimize the sizing of a self-sustaining hybrid wind and solar power system. The approach employs metaheuristic techniques to determine the most suitable type and quantity of solar panels and wind turbines from a range of commercially available components. The objective is to minimize overall system costs while ensuring a stable energy supply, which is achieved through the integration of large water reservoirs for energy storage. Metaheuristic methods, such as genetic algorithms (GAs) and particle swarm optimization (PSO), are used to solve complex multi-objective optimization problems. Inspired by natural phenomena—such as biological evolution and swarm behavior—these techniques effectively explore large search spaces to identify optimal or near-optimal solutions. The main contributions of this work are as follows.

• Hydraulic Energy Storage Strategy: A novel energy storage concept, replacing conventional electrochemical batteries with a high-capacity water reservoir, is proposed. In this approach, excess solar or wind energy is utilized to pump water into an elevated tank, thereby converting electrical energy into hydraulic potential. This storage method offers a cost-effective and environmentally friendly solution, making it particularly well suited to agricultural applications where the stored water simultaneously serves as a vital resource for irrigation.
• Gravity-Driven Irrigation: During periods of low solar irradiance or wind availability, the system uses the stored hydraulic energy to deliver water purely through gravitational flow, entirely avoiding the need for electrical input. This contributes to improved energy autonomy and operational reliability, especially in off-grid rural settings.
• The integrated system modeling framework explicitly incorporates the reservoir’s storage capacity and hydraulic dynamics, enabling simulation and quantification of the impacts of the storage strategy. The results demonstrate that this framework effectively reduces dependence on electrical storage, improves irrigation reliability, and significantly lowers total system costs over the project’s lifetime.
• Multi-Objective Optimization Framework: A multi-objective optimization model was implemented to design and size the hybrid renewable energy system. This model concurrently minimizes system component costs and maximizes renewable electricity production while adhering to defined technical and operational constraints. The approach enables the generation of design configurations that are both economically efficient and technically robust.

The rest of this paper is structured as follows: Section 2 presents the sizing methodology for a hybrid energy system in Skikda, Algeria. Section 3 presents the results. Section 4 provides a detailed discussion of the obtained results. Finally, Section 5 concludes this paper.

2. Materials and Methods

2.1. Proposed Sizing Methodology for a Hybrid Energy System

Figure 1 illustrates the sizing methodology for a wind/PV hybrid energy production system for agricultural irrigation, which should be followed to determine the optimal number of PVs and wind turbines.

2.2. Case Study of the Selected Area: The Skikda Region

The study area is the isolated rural village of “Salah Bouchaour”, located in Skikda Province, Algeria (Latitude: 36.7° N, Longitude: 6.86° E). Situated at an elevation of approximately 120 m above sea level, the village is home to some 600 inhabitants who rely primarily on small-scale agriculture (olives, cereals, and vegetables). The local climate is Mediterranean semi-arid, with hot, dry summers (average daily solar irradiation of roughly 5 kWh/m²) and mild, wetter winters. Annual mean wind speeds of 4–6 m/s make the site suitable for small wind turbines, while irrigation water is drawn from a shallow aquifer fed by seasonal rainfall. Access to the nearest grid connection is over 15 km away, so the community currently depends on diesel generators for electricity—highlighting the potential impact of a hybrid solar–wind–hydraulic storage system.

2.2.1. Load Modeling (Energy Required)

Table 1. Irrigation requirements for the cultivated fruit trees (spring and summer seasons).

Tree Type	Water Need (1st Year)	Water Need (2nd Year)	Water Need (>2nd Year)	Number of Trees	Area Occupied (%)
Olive	100 L (2–3 times/ week)	80 L (1–2 times/week)	50 L (1 time/week)	225	≈27%
Fig	100 L (2–3 times/week)	80 L (1–2 times/week)	50 L (1 time/week)	150	≈18%
Almond	100 L (2–3 times/week)	80 L (1–2 times/week)	50 L (1 time/week)	120	≈14.45%
Prune	100 L (2–3 times/week)	80 L (1–2 times/week)	50 L (1 time/week)	335	≈40.3%

presents detailed information on the irrigation requirements of the cultivated fruit trees. It outlines the water needs by tree type and growth stage, along with their respective spatial distribution within the field. These irrigation requirements are particularly concentrated during the spring and summer seasons, when water demand is at its peak. The data have been incorporated into the system model to estimate both weekly and seasonal irrigation demands, which, in turn, enables a more accurate calculation of the energy required for water pumping. This approach provides a clearer and more realistic assessment of the hybrid energy system’s overall load profile and underscores the critical role of water storage and pumping efficiency in its design.

This modeling accounts for the supply of a water reservoir used to irrigate a total of 830 fruit trees distributed over an area of 30,000 m² (3 hectares), with a perimeter of 770 m. The reservoir has a total volume of 36 m³ (dimensions: $4\times 6\times 1.5$ = 36 m³), as illustrated in Figure 2. Water is distributed through a pumping system operating at a flow rate of 3 m³/h with an energy consumption of 2 kWh. Based on this configuration, the estimated energy load for irrigation is approximately 24 kWh. The irrigation system components and accessories used in this setup are detailed in Appendix B.

2.2.2. System Components

The studied hybrid system comprises wind turbines, solar panels, converters, control systems, communication devices, and excludes batteries. Figure 3 illustrates the schematic diagram of the system.

A comprehensive description of the main components—including photovoltaic panels, wind turbines, and associated accessories—utilized in the proposed hybrid energy system is provided in the Appendix B. This includes technical specifications of each element within the system architecture.

In this context, the energy consumption calculation is assumed to exclusively refer to the end-use appliances powered by the HRES—specifically, the water pumps and associated control systems—excluding the generation components, such as PV modules, wind turbines, and inverters.

The energy consumed by these devices is given by the following formula:

$$E_{consumed}=\sum _{i=1}^n{N}_i{P}_{i}t,$$

(1)

where:

• $N_i$: The number of devices.
• $P_i$: The rated power of each device.
• t: Number of hours of use.
• $E_{consumed}$: Energy consumed by these devices (energy requested by the system).
• The total energy consumed was 24 kWh.

Model Assumptions

In the system model, several simplifications are imposed.

• The pump is assigned a constant overall efficiency of 70%. This single efficiency value (power out versus power in) is used for every operating point rather than modeling the pump’s performance curve or efficiency variation with flow or age.
• Open-water evaporation from the reservoir is accounted for by subtracting a fixed depth (in mm/day) for each time-step. This rate is taken from local climatic averages (for example, a hot, arid reservoir may typically lose an order of 3–5 mm of water per day).
• Equipment aging (such as PV module degradation over years of service) is not applied to the simulated time-series output. Instead of gradually reducing solar conversion or pump efficiency over time, the model treats all components as ‘new’ throughout. (In practice, one would budget for end-of-life replacement; for example, PV modules lose on the order of 0.5% of output per year, but this degradation is implicitly captured only in the financial life-cycle cost analysis, not in the operational model itself.)
• All meteorological forcing (solar irradiance, temperature, wind, etc.) is drawn from a multi-year historical dataset (e.g., a long-term weather station record or reanalysis data). By design, the model, therefore, assumes that future weather will be statistically similar to the past and does not explicitly include any rare or unprecedented weather extremes beyond those contained in the historical record.

Note: A solution is proposed to address the challenges associated with operating a renewable energy system without batteries. Specifically, the implementation of grid-forming inverters with virtual inertia control was planned, providing a synthetic inertial response similar to that of synchronous machines. This approach helps maintain frequency stability during load fluctuations and enables the inverter to operate in grid-forming mode, generating voltage and frequency references in off-grid conditions and thereby ensuring a stable power supply to all connected loads without relying on an external grid or batteries. To address the reactive power needs of the pump’s inductive motor, we included power factor correction—either through the motor drive or with a dedicated capacitor bank or static reactive compensator—to avoid excessive reactive power consumption, energy losses, or voltage drops. These enhancements maintain a focus on renewable integration while improving the system’s technical feasibility and reliability, particularly in applications such as irrigation, where service continuity is essential.

2.2.3. Problem Formulation Based on a Multi-Objective Optimization Approach

Multi-objective optimization is defined as the task of identifying a vector of decision variables that satisfies a set of constraints while optimizing a vector-valued objective function (Osyczka [26]). Each component of this function represents a distinct performance criterion, which is typically in conflict with the others. In this context, “optimization” refers to finding a solution that yields values for all objectives that are acceptable to the designer. In mathematical terms, a multi-objective optimization problem can be represented as follows:

• Find a vector $X^{*}$ that:
• Minimize $F(X)={[f_1(P),f_2(X),\dots ,f_k(X)]}^T$
• subject to $g_m(X)\le 0$ (m inequality constraints).
• and $h_l(X)=0$ (l equality constraints).
• $X^{*}\in {\mathbf{R}}^n$: Vector of the decision variables.
• $F(X^{*})\in {\mathbf{R}}^k$: Vector of the objectives function.

In this study, the decision variables are represented by the vector X, which is defined as follows:

$$X=(x_1,x_2),$$

(2)

where:

• $x_1$: Number of PV panels.
• $x_2$: Number of wind turbines.

The primary focus in designing the hybrid power system is to determine the optimal sizing of each component to ensure the load is met both economically and reliably. The renewable energy sources considered include PV panels $(E_{pv})$ and wind turbines $(E_e)$, along with the unit costs of each component, $C_{pv}$ and $C_e$.

The optimization model intrinsically incorporates site-specific meteorological inputs—hourly wind-speed and solar irradiation time series from previous studies (see references [3,27])—which feed directly into the annual energy-yield simulations and, in turn, inform our equipment cost estimates.

Therefore, two objective functions can be defined:

• The aim to maximize the electrical energy produced by the hybrid system, which is represented by $F_1$ and is defined as follows:

  $$F_1(x)=E_{pv}{x}_1+E_e{x}_2.$$

  (3)
• The purpose to minimize the total cost represented by $F_2$, which is defined as follows:

  $$F_2(x)=C_{pv}{x}_1+C_e{x}_2.$$

  (4)

The constraints that can affect the system are defined as follows:

• Number of PV: $x_{1_{min}}\le x_1\le x_{1_{max}}$.
• Number of wind turbines: $x_{2_{min}}\le x_2\le x_{2_{max}}$.
• Unit cost of PV: $C_{pv}=$$161.19$ $.
• Unit cost of wind turbine: $C_e=1492.54$ $.
• Maximum energy produced by a PV: $E_{pv}=0.240$ kWh.
• Maximum energy produced by a wind turbine: $E_e=0.900$ kWh.
• Minimum load to be satisfied $E_D=24$ kWh.

Determination of ${\mathit{x}}_{{\mathbf{1}}_{\mathit{min}}}$, ${\mathit{x}}_{{\mathbf{1}}_{\mathit{max}}}$, ${\mathit{x}}_{{\mathbf{2}}_{\mathit{min}}}$, ${\mathit{x}}_{{\mathbf{2}}_{\mathit{max}}}$.

These extreme values are determined using the complementarity study, and, according to

Table A2. The accessories intended for this operation.

Number	Designation	Unit Price in $	Quantity	Total Price in $
1	Pipes ∅ 75	95.52	45	4298.40
2	Pipes ∅ 400	37.13	16	594.08
3	Gutters	0.075	1600	120.00
4	Flanges ∅ 75	1.34	65	87.10
5	Valves ∅ 20 threaded	0.36	65	23.40
6	Plugs ∅ 20	0.11	65	7.28
7	Valves ∅ 63	5.97	1	5.97
8	Valves ∅ 75	11.94	1	11.94
9	Reed Plugs ∅ 75	6.72	1	6.72
10	Teflon	1.49	1	1.49
		Total		4298.51

(see Appendix B.2), it can be seen that the following apply:

• The temperature is important during the period from March to September. Hence, the electrical energy produced by the PVs is at the maximum (maximum efficiency), whereas the electrical energy produced by the wind turbines is negligible. In the interest of satisfying the load of the system in this period, the energy produced will be based solely on the PVs, which allows us to determine the maximum number of PVs:

  $$x_{1_{max}}={\displaystyle \frac{systemload}{E_{pv}}}={\displaystyle \frac{24}{0.24}}=100.$$

  (5)
• The wind speed is very important between the months of January to April; therefore, the electrical energy produced by the wind turbines is at the maximum (maximum efficiency). On the other hand, the electrical energy produced by the PVs is negligible. In order to satisfy the load of the system in this period, the energy produced will be based solely on the wind turbines. This allows us to determine the maximum number of wind turbines:

  $$x_{2_{max}}={\displaystyle \frac{Charge}{E_e}}={\displaystyle \frac{24}{0.9}}=27.$$

  (6)

Finally, the problem can be formulated as follows:

Find the vector $X=[x_1,x_2]$ that

$$\left\{\begin{array}{cc}max{E}_p=E_{pv}{x}_1+E_e{x}_2\hfill & \hfill \\ min{C}_{tot}=C_{pv}{x}_1+C_e{x}_2\hfill & ,\hfill \end{array}\right.$$

(7)

such as

$$\left\{\begin{array}{cc}{E}_{pv}=0.24\hfill & \hfill \\ E_e=0.9\hfill & \hfill \\ C_{pv}=1492.54\hfill & \hfill \\ 0\le x_1\le 100\hfill & \hfill \\ 0\le x_2\le 27\hfill & \hfill \end{array}.\right.$$

3. Results

3.1. Meteorological Conditions and Irrigation Demand in the Selected Region

An analysis of Figure 4 and Figure 5 reveals that the peak irrigation demand occurs between the months of May and October. This period is characterized by minimal precipitation, elevated solar irradiation levels, and relatively low wind speeds.

The meteorological data, including solar irradiation, wind speed, and ambient temperature, were sourced from the NASA Surface Meteorology and Solar Energy (SSE) database [28]. The data were obtained by inputting the geographic coordinates of the study area into the SSE web interface, which generated monthly averaged climatic parameters for a specified time frame.

Figure 4 presents the monthly mean values of the wind speed, solar irradiation on a tilted surface, and ambient temperature. The solar radiation data represent monthly averages over a 20-year period (2001–2022). During the May–October window, solar irradiation varied between 3.82 kWh/m²/day and 6.41 kWh/m²/day, with a maximum value of 7.34 kWh/m²/day recorded in July.

In contrast, the wind speed demonstrated limited variability throughout the year, with an average of approximately 4.35 m/s, and this was calculated over a 22-year period (2001–2022). These observations highlight a temporal complementarity between solar and wind resources, thereby supporting the hybrid integration of photovoltaic (PV) and wind turbine systems. Nonetheless, solar energy remained the predominant renewable source during the irrigation-intensive months.

Precipitation patterns are inherently location-dependent. The climate of northern Algeria—typical of Mediterranean regions—is marked by hot and arid summers. As illustrated in Figure 5, precipitation in the selected study area ranged between 32.83 mm and 49 mm during May and October, with the lowest monthly average of 4.76 mm observed in July. These values are insufficient to meet the agricultural water requirements, thereby necessitating the implementation of supplemental irrigation strategies.

Note: In his work, Kasbadji [27] established a wind map of Algeria. His results showed that, in Algeria, wind speeds vary between 1 and 5.5 m/s at 10 m from the ground, and the latter increases from 1 to 7 m/s at 25 m from the ground. From an energy point of view, he concluded that installing wind turbines at altitudes greater than or equal to 25 m from the ground makes energy applications interesting.

3.2. Resolution Method for the Multi-Objective Optimization Problem

Solving a multi-objective optimization problem with inequality constraints, which involves simultaneously addressing conflicting objectives, yields a set of optimal compromise solutions—commonly known as Pareto-optimal solutions—rather than a single optimal solution, as is the case in single-objective optimization. Each solution in the Pareto set is considered non-dominated, meaning no solution in the set is universally better than the others. Therefore, selecting a final solution requires additional preference information from the decision maker.

To solve the optimization problem presented in Equation (7), evolutionary algorithms offer an effective alternative as they can compute the entire Pareto front, even for non-convex problems. Moreover, they help overcome the challenge of local extrema. In particular, we propose using the Integer gamultiobj function (available in the MATLAB R2024b environment), which implements a controlled, elitist genetic algorithm (a variant of the NSGA-II algorithm [29] specifically).

It is observed that the problem mentioned above can also be solved using the $\epsilon$-constraints method. In other words, the multi-objective optimization problem is transformed into a single-objective optimization problem by retaining one objective function while treating the others as constraints. However, the key limitation of this method is the selection of the maximum values for each objective, which requires a deep understanding of the problem (given our clear awareness of the system’s cost limits).

To solve the problem of optimal sizing of the hybrid PV/wind system to meet the load with minimum cost, we used the “Integer gamultiobj” function in MATLAB.

3.3. Choice of the Final Optimized Solution

As shown in Figure 6 and Figure 7, the multi-objective optimization method provides a set of optimal solutions (Pareto front) where none can be deemed superior without applying an additional classification criterion. At this stage, several solutions are possible:

• The user’s intervention in selecting the optimized vector.
• The introduction of a new classification criterion, reflecting the user’s preference for one of the objectives.
• The incorporation of decision aid methods, which establish an ordered relationship among the various objectives.

To achieve this, the TOPSIS algorithm [30,31,32] was employed. The resulting vector of the selected objectives is presented in

Table 2. Optimization results.

${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{E}}_{\mathit{p}}$ (kWh)	${\mathit{C}}_{\mathit{tot}}$ ($)
100	0	24	16,119.40

.

3.4. Cost vs. Area vs. Energy Trade-Off Analysis

To further demonstrate the optimization potential, a parametric evaluation was conducted linking the total system cost to the number of PV panels (area coverage) and energy produced.

Table 3. System metric variation with respect to panel count.

Number of PV Panels	Area (m2)	Energy Produced (kWh)	Cost ($)
60	96	14.4	9671.40
80	128	19.2	12,895.20
100	160	24.0	16,119.00

shows the variation in the system metrics based on panel count.

As can be seen, increasing the panel count linearly scaled the area and energy but non-linearly affected the cost-efficiency trade-off. The optimal solution would balance these factors based on irrigation demand and land availability.

3.5. Sensitivity Analysis of Model Parameters

A sensitivity analysis was performed to evaluate how variations in key input parameters affect system configuration and cost. The parameters tested were as follows:

• Solar irradiance $(\pm 10\%)$.
• Wind speed $(\pm 10\%)$.
• PV panel cost $(\pm 20\%)$.
• Wind turbine cost $(\pm 20\%)$.

Figure 8 illustrates the effect of each parameter on the total system cost and the number of components required (i.e., the PV panels required). The results indicate that solar irradiance and PV cost significantly influence system design. A decrease in irradiance by 10% increases the number of PV panels by approximately 12% when meeting the same energy load. In contrast, wind speed variations have minimal effect, which aligns with the dominance of solar energy in the optimal configuration. This analysis confirms the robustness of the proposed system and reinforces the choice of PV-dominant sizing for the specific conditions of the Skikda region.

4. Discussion

The optimization results of the hybrid energy system indicate a cost-effective configuration that is specifically adapted to the environmental conditions and operational constraints of the study area. A detailed analysis of the results reveals that the algorithm consistently favors the exclusive use of photovoltaic (PV) panels, a choice primarily driven by the region’s favorable solar irradiance and climatic characteristics. The area, which is not exposed to high wind speeds, limits the effectiveness of wind turbines. This justifies their exclusion from the optimal solution. PV panels, on the other hand, are well suited for the region due to the availability of solar energy, making them a more reliable and cost-effective choice.

The solution demonstrates scalability as additional PV panels could easily be added to meet higher energy demands in the future. The modularity of PV systems makes them adaptable to changing requirements, a crucial factor in agricultural applications where energy demands might fluctuate. The precise match between the energy production (24 kWh) and the minimum requirement reflects the robustness of the optimization algorithm. This alignment ensures that the system is neither over-designed (leading to unnecessary costs) nor under-designed (leading to energy shortfalls).

• Cost vs. Performance Trade-off: The decision to exclude wind turbines highlights a critical trade-off.
• Cost Savings: Avoiding wind turbines reduces upfront capital expenditure by 1492.54 $ per turbine and simplifies system maintenance.

The total cost of 16,119.40 $ is a reasonable investment for agricultural irrigation systems in regions like northern Algeria, where agriculture forms a significant part of the economy. The solution is not only feasible, but also ensures a return on investment through reliable energy production, which is essential for uninterrupted irrigation.

Technical Viability Criteria for the Proposed Configuration

To ensure the proposed system is technically viable, we defined and validated the configuration based on the following key performance metrics.

• Energy Match Criterion: The total energy production (24 kWh/day) exactly met the irrigation demand. This was verified using component-specific generation data (24 kWh per PV panel), ensuring that no excess or deficit could compromise system operation or inflate costs.
• Component Utilization Efficiency: The design uses 100 PV panels, achieving close to maximum daily generation under average solar irradiance. The elimination of wind turbines was technically justified by the site’s low wind potential, minimizing underutilized components.
• Cost-to-Performance Ratio: The selected configuration provided the lowest total cost (16,119.40 $) that satisfies energy demand without reliance on costly battery storage. The system achieves a levelized cost of energy (LCOE) that is competitive with the grid-subsidized electricity in the region, further supporting economic viability.
• Storage Substitution Feasibility: Instead of batteries, a water reservoir stores potential energy. This design decision is technically sound as gravitational flow can reliably power the irrigation system without introducing the conversion losses that are typically found in battery-based systems.
• Environmental Suitability: Based on meteorological data and local resource assessment, solar energy was identified as the dominant viable source. The configuration aligns with seasonal solar availability and matches crop water needs during peak sun months.

These criteria collectively ensure that the final configuration is not only cost-effective, but also technically robust, sustainable, and practical for implementation in similar agricultural contexts.

5. Conclusions

This work aligns with the national energy transition strategies and contributes to the broader objective of fostering a cleaner and more sustainable future. Additionally, it highlights the significant potential of renewable energy utilization in enhancing local agricultural development, particularly through the implementation of cost-effective irrigation systems. It presents a novel approach to agricultural irrigation through the design of a HRES, combining solar and wind energy sources for a farm located in the Skikda region of Algeria. The system utilizes a large water reservoir to store energy in the form of potential energy, replacing traditional batteries and using gravity to power the irrigation system for 830 fruit trees. A detailed mathematical modeling of the system components was conducted to identify key design variables, and this was followed by the development of a multi-objective optimization approach to ensure the system’s optimal sizing and performance.

In our approach, the water reservoir serves as a central component of the energy storage strategy, offering a viable alternative to conventional batteries. Instead of relying on electrochemical storage, the system utilizes a large elevated water reservoir to store potential energy, which is later used for irrigation through gravity-driven flow. This method ensures energy-free water delivery during periods of low solar or wind energy availability. The reservoir’s capacity and operational dynamics are fully integrated into the system modeling, allowing for a comprehensive assessment of its role in reducing dependence on electrical storage, enhancing irrigation reliability, and minimizing overall system costs. The results demonstrate that leveraging pumped-water storage represents an economically attractive and technically robust alternative to battery-based storage in hybrid renewable energy-driven agricultural systems.

The results confirm the practical viability and sustainability of the proposed methodology, demonstrating its capacity to improve energy efficiency and agricultural resilience, particularly in remote areas with limited access to conventional energy infrastructure. This work paves the way for a broader adaptation of HRESs across diverse agricultural regions. To support their widespread adoption, it is essential to invest in alternative energy storage solutions, such as water reservoirs, which provide a reliable and cost-effective energy supply tailored to irrigation needs. Further efforts should include research on context-specific hybrid configurations, integration of HRESs into national agricultural strategies, and the implementation of pilot projects to assess real-world performance. Strengthening local capacities through technical training, financial support, and regional service centers will also be key. Finally, embedding HRESs in national electrification and food security policies, alongside robust monitoring and evaluation frameworks, will ensure long-term impact and scalability.

Future research will focus on enhancing the performance of hybrid energy systems by incorporating additional factors. This development will include the integration of alternative renewable energy sources, such as biomass, alongside advanced energy storage devices (e.g., water reservoirs and batteries). Moreover, further studies should explore the application of various methodologies, enabling comparison of results across different approaches. Particular attention will be given to assessing the impact and limitations of using water reservoirs as an energy storage medium in place of batteries, with emphasis being placed on scalability, maintenance requirements, and long-term reliability.