Optimal Design and Sizing of Hybrid Photovoltaic/Fuel Cell Electrical Power System

Abstract

Renewable energy solutions play a crucial role in addressing the growing energy demands while mitigating environmental concerns. This study examines the techno-economic viability and sensitivity of utilizing solar photovoltaic/polymer electrolyte membrane (PEM) fuel cells (FCs) to meet specific power demands in NEOM, Saudi Arabia. The novelty of this study lies in its innovative approach to analyzing and optimizing PV/PEMFC systems, aiming to highlight their economic feasibility and promote sustainable development in the region. The analysis focuses on determining the optimal size of the PV/PEMFC system based on two critical criteria: minimum cost of energy (COE) and minimum net present cost (NPC). The study considers PEMFCs with power ratings of 30 kW, 40 kW, and 50 kW, along with four PV panel options: Jinko Solar, Powerwave, Tindo Karra, and Trina Solar. The outcomes show that the 30 kW PEMFC and the 201 kW Trina Solar TSM-430NEG9R.28 are the most favorable choices for the case study. Under these optimal conditions, the study reveals the lowest values for NPC at USD 703,194 and COE at USD 0.498 per kilowatt-hour. The levelized cost of hydrogen falls within the range of USD 15.9 to 23.4 per kilogram. Furthermore, replacing the 30 kW Trina solar panel with a 50 kW Tindo PV module results in a cost reduction of 32%. The findings emphasize the criticality of choosing optimal system configurations to attain favorable economic outcomes, thereby facilitating the adoption and utilization of renewable energy sources in the region. In conclusion, this study stands out for its pioneering and thorough analysis and optimization of PV/PEMFC systems, providing valuable insights for sustainable energy planning in NEOM, Saudi Arabia.

1. Introduction

Access to reliable and safe power is crucial for the socioeconomic development of any country. It fosters innovation and encourages investment in new business ventures, serving as a catalyst for job creation, prosperity, and the overall well-being of society [1,2]. The power availability plays a vital role in facilitating commercial activities and supporting global economies [3]. However, conventional power plants are frequently located far away from areas with high electricity demand [4]. Consequently, a long transmission and distribution (T&D) infrastructure needs to be established to deliver power to these areas. The construction cost of these extensive T&D networks is eventually passed on to consumers, influencing their final price [5]. Considering the adverse environmental impact of fossil-based power generation methods [6], there is a global transition toward more sustainable alternatives. However, most of these sources are intermittent, with gaps between energy availability and end-user consumption [7]. This drawback must be acknowledged as one of the challenges of sustainable alternatives. To overcome these issues, the development of appropriate microgrids and energy storage systems for the power grid becomes imperative. These advancements can effectively bridge the gaps and ensure a reliable and continuous energy supply from renewable sources. In this context, microgrids (MGs) are emerging as a viable solution. Microgrids consist of distribution units and distributed energy resources such as fuel cells (FCs) and solar panels, supplemented by various storage mediums like mechanical storage (flywheels) and chemical storage (batteries) [8]. By adopting microgrids, countries can facilitate the shift from traditional electricity systems to more sustainable ones, promoting a greener and more efficient power generation approach [9].

Microgrids can be operated manually or automatically, but their overall performance can be significantly enhanced through efficient regulation. These microgrids play a crucial role in smart grids, considered the future of electricity distribution in both urban and rural areas. One notable advantage of microgrids is their ability to function independently from the main grid, enabling them to operate autonomously and mitigate grid disturbances. Moreover, microgrids contribute to faster response times and facilitate swift recovery. They are also instrumental in ensuring supply security and enhancing grid resilience. As a result of their enhanced controllability, microgrids are now commonly integrated into low- and medium-voltage distribution units. The significance of distributed energy resources (DERs) was validated through laboratory-scale examinations, affirming the benefits of microgrids [10]. Furthermore, research projects have investigated both hybrid alternating-current and direct-current microgrids [11]. Microgrids draw upon various energy sources such as hydropower, solar photovoltaics (PVs), and wind energy. Ongoing studies are exploring innovative approaches to constructing and utilizing microgrids, driving advancements in this field.

Various studies have investigated the optimal operating conditions for different microgrids, considering their specific demand requirements, running costs, and peak-shaving considerations [12]. Bui et al. [13] proposed an optimal microgrid dispatch system that can determine the most suitable dispatch strategy for various applications. This study introduced an auto-configuration system for microgrids employing a multiagent approach. The auto-configurator agent handles device authorization, registration, and status updates, while the energy management system (EMS) agent ensures optimal microgrid operation through re-optimization after any changes. Modern power systems face the challenge of managing the upward trend in peak loads. Oprea et al. [14] performed an analysis and evaluation of strategies focused on optimizing power consumption while considering the impact of the load curve. The study examined electricity consumption optimization in smart grids, emphasizing householders’ interest in cost reduction through advanced tariff schemes. The effects of Renewable Energy System (RES) distributed generation and storage devices (SDs) on consumption curves were investigated, leading to sustainable development and substantial peak consumption reduction. The results revealed that the incorporation of smart appliances, sensors, actuators, and electricity home control applications enabled the evaluation of demand response strategy benefits. The development of communication-based systems has been employed to address system control, as highlighted by Imran and Wang [15], as well as by Almadhor [16]. Moreover, Bunker and Weaver [17] investigated a multi-dimensional control system, exploring the potential of wind electricity generation in microgrids for modern electric power systems. The study introduces a novel droop control strategy that optimizes the droop surface in multiple dimensions. Simulation and hardware-in-the-loop experiments demonstrate increased wind power utilization without the need for communication between microgrid components, while maintaining bus voltage stability. Zoulias et al. [18] conducted a techno-economic analysis on standalone microgrids in Kythnos, Greece, exploring the substitution of diesel generators with fuel cells, hydrogen storage tanks, and electrolyzers. The study assessed the feasibility of hydrogen-based systems for remote communities without grid access, revealing that although technically feasible, the current economic viability requires cost reductions in hydrogen technologies for widespread adoption. Papaioannou et al. [19] conducted an analysis to examine the impact of distributed energy resources on the overall system performance of a microgrid situated near Athens, Greece. The study examined two real microgrids, one interconnected and one autonomous, located at a seaside camping site. Utilizing HOMER power optimization software, the analysis suggested integrating new distributed generators or adjusting the operation patterns of existing ones to improve microgrid efficiency.

Over the past decade, countries in Sub-Saharan Africa, the Middle East, and other regions have witnessed the progressive development of microgrids in rural electrification initiatives. This progress has significantly extended access to sustainable electricity throughout the year, even in areas that are not connected to the main power grid. These advancements in microgrid deployment are expected to have a holistic impact in mitigating the concerns raised by the International Energy Agency’s World Energy Outlook. Specifically, this progress aims to address the alarming statistic that approximately one out of six people globally lack access to electrical power [20]. The primary reason behind the lack of power access in certain rural communities is attributed to the absence of sufficient revenue and their remote locations, which makes it challenging to connect them to existing microgrids. As a result, the initial capital costs of implementing a comprehensive power scheme are significantly increased. However, with the availability of sustainable energy sources, microgrids have emerged as the preferred option for off-grid purposes, as acknowledged by the research community.

The economy of the Kingdom of Saudi Arabia (KSA) relies heavily on fossil-based commodities [21]. Accordingly, there has been a substantial increase in carbon emissions from 47.02 million to 586.4 million tons between 1970 and 2021, indicating a significant rise of more than 11 times since 1970 [22]. The significant increase in carbon emissions can be attributed to the manufacturing and industrial sectors, which contributed 40% of the total annual emissions in KSA [23]. It is important to highlight that the main outcome of COP25 was a global recommendation to actively pursue comprehensive reductions in carbon emissions worldwide. Kapen et al. [24] investigated the techno-economic feasibility of two hybrid system scenarios for energy and hydrogen production in Maroua, Cameroon, using HOMER Pro. Scenario 1 includes PV/Fuel Cell/Electrolyzer/Biogas, and scenario 2 includes PV/Battery/Fuel Cell/Electrolyzer/Biogas. Different system architectures were optimized for low-, medium-, and high-consumer communities. The results indicate the potential for providing electricity in the Far North region, with levelized costs of energy (LCOEs) ranging from USD 0.071/kWh to USD 1.524/kWh for scenario 1 and USD 0.15/kg to USD 3.06/kg for scenario 2. The proposed systems show promise as an alternative solution for meeting electricity demands in the region. Arsalis et al. [25] presented a comprehensive review of hybrid photovoltaic–regenerative hydrogen fuel cell (PV-RHFC) microgrid systems, analyzing their components, modeling methods, and control strategies. Different application options were discussed, considering scale, purpose, and integration with other energy technologies. Critical analysis highlighted the need for cost reduction in the RHFC subsystem and integrated energy management control to ensure flexible and reliable energy flow for commercializing hybrid PV-RHFC microgrid systems. Qandil et al. [26] examined the feasibility of using a hybrid PV, fuel cell, and battery system to power various loads in Jordan’s Al-Zarqa governorate. Solar energy potentials in the Al-Hashemeya area, with irradiation levels between 4.1 and 7.6 kWh/m²/day, were analyzed. Homer software was employed to optimize and size renewable and nonrenewable energy sources and storage methods. The results showed that the PV-diesel generator with a battery was the most suitable solution for the residential building, while the PV-FC-diesel generator-electrolyzer hybrid with a battery was ideal for the school and factory, with load profiles significantly impacting the system’s power production.

The drive to replace energy derived from fossil-based products arises from the detrimental environmental effects associated with these commodities, as well as the rapid depletion of fossil fuel reserves [27]. It is worth noting that positioned within the sunbelt, KSA benefits from clear skies for 80–90% of the year. This geographic advantage allows the country to receive a plentiful supply of thermal energy from the Sun, with the estimated annual average solar radiation level reaching 2400 kWh/m² [28,29]. Therefore, the KSA has established a goal of achieving a 130 metric ton reduction in carbon emissions by the year 2030. This necessitates an accelerated development of renewable energy systems in the country over the coming years. The goal is to supplement existing energy generation methods and gradually transition toward more robust and sustainable energy sources by 2030 [30].

The KSA is actively exploring proactive measures to harness energy using solar photovoltaic (PV) technology, taking advantage of its favorable geographical location [31]. Research on harnessing solar energy through various technologies can be traced back to 1977 [32]. When assessing wind resources in Saudi Arabia, it is important to consider two primary regions: the Arabian Gulf coastline and the red sea [33]. The average wind speed for most locations in the country ranges between 6 and 8 m/s, with the northeast, central, and western zones experiencing the most prevalent wind speeds [34]. The KSA has established its largest wind farm, located in ‘Dumat Al Jandal’. As part of the country’s vision for 2030, efforts to reduce emissions are being realized through the development of ‘NEOM’, a city designed to incorporate diverse renewable energy sources and significantly decrease carbon emissions [35]. However, renewable energy systems harnessing wind and solar power exhibit inherent variations in energy production. To optimize energy generation, hybrid systems that combine multiple renewable energy sources are often recommended [36]. These systems aim to meet specific energy loads while offering benefits such as a lower levelized cost of energy and the absence of toxic emissions [37].

Numerous studies have been conducted to investigate the optimal performance of various hybrid energy sources in the Gulf region [38,39,40]. Al-Shamma’a [41] conducted a study to optimize the performance of different hybrid energy systems in various locations in northern Saudi Arabia. The study employed genetic algorithms and considered different fuel costs to determine the best design for three hybrid systems. The findings indicated that a hybrid system consisting of solar photovoltaic panels, batteries, and diesel was recommended as the most efficient option at a wind speed of 6.75 m/s. For the diesel unit, it was observed that the system performed best when the wind speed was 5.6 m/s and the solar radiation was 1500 W/m². Rezk et al. [35] conducted a study using the HOMER software to determine the most suitable configuration for 150 m³ reverse osmosis desalination plants in NEOM city. The study recommended a configuration that included a hydrogen storage unit, photovoltaics, fuel cells, and battery storage. This configuration was chosen based on its favorable outcomes, such as a net present cost of USD 438,657 and an energy cost of USD 0.117/kWh.

Fuel cells are highly efficient devices used for converting the chemical energy stored within fuel sources into electrical energy. Fuel cells can be classified into various types based on the fuel they utilize, cell temperature, ion exchange electrolyte/membrane, and other factors [42]. This categorization allows for a diverse range of fuel cell technologies to meet different energy needs and operational requirements. By considering these factors, researchers and engineers can select the most suitable fuel cell type for specific applications, optimizing performance and efficiency. Proton exchange membrane fuel cells (PEMFCs) are recognized as one of the most promising options among the various types of fuel cells. Their distinguishing feature is the ability to operate at low temperatures, making them suitable for a wide range of applications. Despite their low operating temperature, PEMFCs maintain an acceptable energy conversion efficiency and demonstrate high durability, making them an attractive choice for many energy conversion needs [43]. After conducting a comprehensive survey of published articles, it is evident that the field of hybrid photovoltaic/fuel cell systems is continuously evolving due to ongoing research and development efforts and significant technological advancements. Advanced control strategies, incorporating innovative algorithms and machine learning techniques, are being extensively explored to optimize system performance and enhance energy management efficiency. In parallel, researchers are diligently investigating the integration of energy storage technologies, such as advanced batteries, supercapacitors, and hydrogen storage, which enables the smooth incorporation of intermittent renewable energy sources, thereby enhancing system flexibility and reliability [44,45]. The development of diverse optimization models and simulation tools, considering factors like weather conditions, load profiles, and component characteristics, is a key focus area, with the goal of achieving an optimal design and sizing of hybrid systems, leading to notable improvements in efficiency and cost-effectiveness [46,47,48].

This study aims to address the existing research gap concerning the techno-economic viability and sensitivity analysis of utilizing solar photovoltaic/polymer electrolyte membrane fuel cells (PEMFCs) to fulfill specific power demands in NEOM, Saudi Arabia. This study highlights the need for comprehensive research that investigates the optimal configuration and economic efficiency of such hybrid systems within the NEOM city. The study has two primary objectives. Firstly, it aims to determine the optimal size of the PV/PEMFC system based on two crucial criteria: the minimum cost of energy (COE) and the minimum net present cost (NPC). By considering these criteria, the study seeks to identify the most economically viable and sustainable system configuration capable of meeting the power demands in NEOM effectively. Secondly, the study intends to assess the economic efficiency of various system configurations by evaluating the performance of different PEMFC sizes and PV panel options. The novelty of this study lies in its comprehensive analysis of the techno-economic viability and sensitivity of solar PV/PEMFC systems in NEOM city. It considers multiple factors, including the power ratings of PEMFCs, various PV panel options, COE, NPC, and the levelized cost of hydrogen. By taking these factors into account and conducting a rigorous evaluation, the study offers valuable insights into the optimal system configurations that yield the most favorable economic outcomes for NEOM city. Furthermore, the study introduces the innovative concept of incorporating hydrogen storage units alongside photovoltaics, fuel cells, and battery storage in the hybrid system. This integration of hydrogen storage represents a novel aspect of the study, as it explores the potential benefits and economic feasibility of utilizing hydrogen as an energy storage medium.

2. Site and Load Demand

NEOM city is a planned cross-border mega-city project that is being developed in the northwest of Saudi Arabia, along the Red Sea coast. The city is strategically located in proximity to the borders of Egypt and Jordan. NEOM aims to be a model for future sustainable cities, with a strong emphasis on renewable energy sources and green technologies. It is intended to be a hub for innovation, technology, and advanced industries, with a focus on various sectors such as energy, water, biotechnology, and tourism. The development of NEOM city represents a bold vision for sustainable urban living and a commitment to environmental and ecological preservation. NEOM city is considered the first and pioneering project that achieves large-scale implementation and complete reliance on renewable energy sources [49]. In addition to reducing carbon emissions, this project will pave the way for global sustainability initiatives. Moreover, the accessibility of renewable energy for both industries and citizens is an encouraging advancement that fosters fair access to clean energy resources. NEOM city is located at latitude 29°08′ and longitude 34°55′ in Saudi Arabia. Figure 1a presents the average monthly daily clearance index and sun radiation levels on a horizontal surface. The radiation levels are highest during the months of June and July, while they are lowest in December and January. The average monthly daily temperature is also depicted in Figure 1b. Electricity in NEOM city serves multiple purposes, including domestic consumption. Figure 2 represents the monthly load variance, showcasing the utilization of alternating-current (AC) electricity for the case study’s load, which primarily powers the commentary buildings in NEOM City. The average daily load amounts to 250 kWh, with a peak power of 31 kW.

3. PV/PEM Fuel Cell System

The integration of various energy systems can lead to the development of an optimal design that minimizes the levelized cost. The utilization of HOMER software proves valuable in designing and evaluating technically and financially optimal energy systems. This tool empowers us to conduct system optimization and sensitivity analysis, ensuring well-informed decision making while reducing costs. The determination of the best value for the decision-making process is critical during the optimization process. The input data, such as solar data and load demand for NEOM, as well as specific system components, should be considered. The software facilitates the calculation of capital, replacement, and operational and maintenance (O&M) costs for individual components. As depicted in Figure 3, the solar PV system is connected to the direct current (DC) bus to utilize its output power. A DC-AC converter is employed to transform the generated power from DC to AC for application in the AC bus. By applying this approach within HOMER and integrating the cost analysis of the individual system components, making informed decisions regarding the optimal system becomes much more straightforward and efficient. Figure 3 illustrates the configuration of a PV/PEMFC hybrid system, where a hybrid power unit comprising solar PV, a fuel cell unit, and a hydrogen source can fulfill the load demand in NEOM. It should be noted that fuel cells and hydrogen storage tanks are particularly suitable for off-grid hybrid power systems.

3.1. PV Array

The calculation of power generated by solar PV can be determined using Equation (1), which represents a correlation between solar radiation and temperature [50].

$$P_{pv}=P_{PV,STC}{f}_{PV} \frac{G_T}{G_{STC}}[1+{\alpha }_P\left(T_c-T_{c,STC}\right)]$$

(1)

where the standard solar radiation is represented as $G_{STC}$, while the actual solar radiation is denoted as $G_T$. Similarly, the standard temperature is indicated as $T_{c,STC}$ and the actual temperature is represented as $T_c$. The derating factor for the PV system is denoted as $f_{PV}$, and ${\alpha }_P$ signifies the coefficient. It is important to note that HOMER determines the tilt angle. The calculation of $P_{PV,STC}$ is derived using Equation (2). The PV modules are connected in series denoted by $N_s$ and in parallel denoted by $N_p$. The maximum power at standard operating conditions is represented as $P_{mSTC}$, while the actual power $P_{PV}$ is calculated using Equation (3). The efficiency of the panels is determined using Equation (4). In this study, four different PV modules are utilized to identify the optimal module.

Table 1. The electrical specification of the PV modules.

Parameter	PV Module Type
	Jinko Solar-JKM415M-54HL4	Powerwave-PW-390-BMD-HV	Tindo Karra-330P	Trina Solar TSM-430NEG9R.28
Maximum power, Pmax, (W)	415	390	330	430
Voltage at maximum power (V)	30.79	30.59	33.25	43.2
Current at maximum power (A)	13.48	12.78	9.93	9.96
Open-circuit voltage, Voc, (V)	37.31	36.90	40.93	51.4
Short-circuit current, Isc, (A)	14.01	13.40	10.93	10.59
Efficiency (%)	21.25	19.88	19.8	21.5
No of cells	108	108	60	144
Nominal operating cell temperature	45 ± 2 °C	45 ± 2 °C	44	43 °C
Temperature coefficients of Pmax	−0.35%/°C	−0.35%/°C	−0.37	–0.30%/K
Temperature coefficients of Voc	−0.28%/°C	−0.27%/°C	−0.30	–0.24%/K
Temperature coefficients of Isc	0.048%/°C	+0.05%/°C	+0.06	0.04%/K
Price (USD)	310	280	265	235

provides the electrical specifications of the PV modules.

$$P_{PV,STC}=\left(N_s\times N_p\right)P_{mSTC}$$

(2)

$$P_{PV}=\left(N_s\times N_p\right)P_m$$

(3)

$${\eta }_{mpSTC}=\frac{P_{PV,STC}}{A_{PV}{G}_{T,STC}}$$

(4)

3.2. Fuel Cell

A fuel cell is a device that converts chemical energy from hydrogen into electricity by utilizing an oxidant. The by-products of this electrochemical reaction process are water and heat. Although some references may refer to fuel cells as batteries, it is important to distinguish between the two. While batteries serve as energy storage devices, fuel cells act as energy conversion devices. Fuel cells typically have a longer lifespan as the reactants are connected externally, unlike batteries, which experience significant losses even when not discharging any current or voltage, due to the reactants being embedded internally. Additionally, fuel cells are considered more environmentally friendly than batteries, as there are concerns regarding the disposal of batteries after their end-of-life. Fuel cells also exhibit higher efficiency, typically around 60%, compared to traditional internal combustion engines [51].

It is worth noting that fuel cells have an average lifetime of approximately 5000 h, equivalent to about 200 days [52]. Conversely, batteries display a wide range of lifespans, varying from 11.6 to 26.5 years [53]. Moreover, advancements in technology allow for the recycling of retired batteries through the precise and fast identification of micro-health parameters [54]. Considering this information, it becomes clear that batteries typically boast longer lifespans than fuel cells, which contributes to their superior overall economic benefits. However, despite their shorter lifespans compared to batteries, the unique advantages of fuel cells in terms of efficiency and environmental impact should not be disregarded. Fuel cells remain a compelling choice for specific applications. Hence, careful consideration of these factors is essential when selecting the most suitable energy storage solution to meet diverse needs [55].

The integration of fuel cells with intermittent renewable systems like solar PV has shown promising system performance in the literature. The combination of fuel cells and solar PV, whether in grid-connected systems or standalone setups, has been extensively explored [56]. In the current study, proton exchange membrane fuel cells (PEMFCs) are chosen due to their favorable operating temperature range, high efficiency, and rapid response time [57].

3.3. Hydrogen Tank

To mitigate the seasonal and daily variations in energy demand and availability, the storage of hydrogen plays a crucial role, as it is widely recognized as one of the most recommended energy carriers. Hydrogen storage offers advantages over lead–acid batteries, especially for long-term storage requirements. Pressurized tanks are still commonly employed for hydrogen storage in various applications [58]. Standalone systems often necessitate the implementation of energy storage mechanisms to ensure uninterrupted power supply during instances of intermittent or system failure. The autonomy of the hydrogen tank is defined as the ratio between the energy capacity of the tank and the electric load. The hydrogen tank autonomy ($A_{\mathrm{htank}}$) can be calculated using Equation (5).

$$A_{\mathrm{htank}}=\frac{Y_{\mathrm{htank}}LH{V}_{H_2}(24\mathrm{h}/\mathrm{d})}{L_{prim,ave}(3.6\mathrm{M}\mathrm{J}/\mathrm{k}\mathrm{W}\mathrm{h})}$$

(5)

where $Y_{\mathrm{htank}}$ denotes the capacity of the hydrogen tank (kg) and $L_{prim,ave}$ denotes the average primary load (kWh/d). The lower heating value ($LH{V}_{H_2}$) is the amount of heat released when a fuel undergoes complete combustion, considering that the water produced during combustion remains in a liquid state rather than being vaporized. In the case of hydrogen, the LHV is 120 MJ/kg.

3.4. Electrolyzer

Water electrolyzers are structured as interconnected cells arranged in series, aiming to generate hydrogen as their primary output. These devices utilize two distinct electrodes, separated either by a liquid electrolyte or a solid polymer electrolyte. The process involves the dissociation of water using electricity, resulting in the production of hydrogen and oxygen. In the current study, a PEM electrolyzer is considered as the preferred electrolysis technology [59].

4. Economic Considerations

Economic considerations play a crucial role when designing a renewable energy system. It involves selecting optimal component sizes and minimizing the total net present cost and cost of energy through a careful evaluation of various economy-related factors. These factors include capital costs, operating and maintenance costs, expected system lifetime, and energy costs. By optimizing these aspects, a renewable energy system can offer a reliable and cost-effective energy supply.

The net present cost (NPC) is a crucial financial evaluation metric employed in HOMER software to assess the economic feasibility of a renewable energy system. It quantifies the net present value (NPV) of all costs associated with the system over its lifetime, encompassing initial capital expenses, maintenance and operating costs, as well as the salvage value at the end of its useful life [60]. Through the calculation of NPC, a comprehensive assessment of the long-term financial sustainability of a renewable energy system can be achieved.

HOMER employs discounted cash flow analysis to determine the NPC of a renewable energy system. This analysis involves discounting all future costs and revenues to their present value using a discount rate, which represents the opportunity cost of capital [61]. The NPV of the project is then computed by subtracting the total present value of costs from the total present value of revenues. If the NPV is positive, the project is considered economically feasible, while a negative NPV indicates the project is not financially viable. The NPC can be estimated using the following relationship.

$$NPC=\frac{C_{ann,tot}}{{CRF}_{(i,N)}}$$

(6)

where C_ann,tot represents the annual cost; i denotes the discount rate, which is also referred to as the interest rate or rate of return; and N represents the number of years for which the annuity is paid.

The capital recovery factor (CRF) is a ratio utilized to compute the present value of a sequence of equal annual cash flows. Mathematically, the CRF can be expressed as follows:

$$CRF\left(i,N\right)=\frac{{i(1+i)}^N}{{(1+i)}^N-1}$$

(7)

The CRF formula incorporates the concept of the time value of money by discounting future cash flows to their present value. The numerator of the equation represents the discounted cash flows, while the denominator comprises the present value of the annuity factor based on the payment period and discount rate. The CRF is typically used to calculate the annual payment required to repay a loan or to determine the annual cost of an investment throughout its useful life. The CRF can be obtained by dividing the discount rate by the quantity of 1 minus the inverse of the present value of the annuity factor. To calculate the annual cost of an investment, the CRF is multiplied by the initial cost of the investment.

In HOMER software, the levelized cost of energy (COE) is a key metric that measures the operating cost of a renewable energy system. It represents the total net cost of the system over its operational life, divided by the total useful electrical energy generated during that period [62]. The COE encompasses all costs associated with the renewable energy system, including capital expenses, operating and maintenance costs, and fuel expenses, if applicable. By calculating the COE, HOMER facilitates the comparison of different system configurations, fuel resources, and financing options to determine the most economically viable and cost-effective solution for a specific energy project [63]. The COE is a crucial metric used in designing and optimizing renewable energy systems and is widely employed in industry and policy analysis to assess the financial feasibility of renewable energy investments.

To calculate the levelized cost of energy (COE), the total annualized cost is divided by the total electric load served. The formula is as follows:

$$COE=\frac{Total Annualized Cost }{Total Electric Load}$$

(8)

The total annualized cost refers to the overall annualized cost of the renewable energy system, which incorporates capital costs, operating expenses, and maintenance costs. On the other hand, the total electric load represents the cumulative electric load served by the system throughout its lifespan.

By dividing the annualized cost of electricity generation by the total electric load served, the COE reflects the average cost per kilowatt-hour (kWh) of useful electrical energy produced by the system. The COE serves as a valuable metric for assessing the competitiveness of a renewable energy system in comparison to other energy sources. It also helps in identifying opportunities for cost reduction and performance enhancement within the system.

5. Description and Optimization Approach of HOMER

HOMER (Hybrid Optimization Model for Multiple Energy Resources) is a powerful simulation software developed by the National Renewable Energy Laboratory (NREL) to analyze and optimize hybrid power systems. The software is widely used in the field of renewable energy to design and assess the feasibility of standalone or grid-connected systems that combine multiple energy resources, such as solar photovoltaic (PV), wind, diesel generators, batteries, fuel cells, and hydrogen storage.

The optimization process in HOMER involves evaluating different system configurations and sizing components based on techno-economic criteria. It aims to find the most cost-effective and reliable configuration for a given energy demand and available resources. HOMER utilizes an iterative optimization algorithm that explores various combinations of energy resources and system parameters to minimize the overall cost of energy while meeting the specified load demand and operational constraints.

To achieve this, HOMER performs a detailed analysis of the available energy resources, including solar radiation, wind speed, and load profiles. It considers the efficiency, cost, and performance characteristics of each energy component to determine the optimal combination that best matches the load requirements and maximizes the utilization of renewable energy sources.

The optimization model of the software also takes into consideration the dynamic and variable nature of renewable resources over time. By employing a time-stepped simulation approach, it thoroughly evaluates the system’s performance under various weather conditions and load patterns, ensuring a comprehensive assessment of system reliability and feasibility.

6. Results and Discussion

The HOMER software is designed to analyze and determine the optimal design and configuration of a renewable energy system based on specific energy demands, available resources, and cost constraints. Its primary objective is to identify the most cost-effective solution that minimizes either NPC or the COE for the system. Throughout the optimization process, HOMER systematically examines numerous potential system configurations by varying component sizes, operation modes, and dispatch strategies. Furthermore, it aims to find the combination of variables that leads to the most economically advantageous solution. During the optimization process, HOMER considers multiple factors, such as load demand, resource availability, and system capacity, to generate the optimal solution. It analyzes the interaction and influence of these factors to ensure the best possible outcome. By evaluating different scenarios, adjusting variables, and analyzing the results of each iteration, HOMER enables the identification of the most efficient solution. This iterative approach ensures that the designed renewable energy systems are cost-effective, reliable, and economically viable.

To determine the optimal size and cost-effective PV/PEMFC system, the study considers three different sizes of PEMFC: 30 kW, 40 kW, and 50 kW. Additionally, four PV panels are used: Jinko solar-JKM415M-54HL4, Powerwave-PW-390-BMD-HV, Tindo Karra-330P, and Trina solar TSM-430NEG9R.28.

Table 2. Comparative analysis of PV module types and FC sizes for optimal results.

PV (kW)	FC (kW)	Electrolyzer (kg)	H2 Tank (kg)	Converter (kW)	NPC (USD)	COE (USD/kWh)	O&M (USD/year)	Capital Cost (USD)
Jinko solar-JKM415M-54HL4
183	30	70	200	28.9	743,912	0.526	26,576	325,270
179	40	70	210	31.9	878,494	0.622	33,440	351,729
179	50	70	210	31.9	1,000,000	0.718	40,415	376,729
Powerwave-PW-390-BMD-HV
183	30	70	200	28.9	742,835	0.526	26,845	319,960
183	40	70	200	27.4	877,973	0.621	33,850	344,752
196	50	60	190	32.4	1,000,000	0.718	400,661	372,198
Tindo Karra-330P
183	30	70	200	26.6	771,097	0.546	27,694	334,856
183	40	70	200	26.6	906,187	0.641	34,682	359,856
179	50	70	210	31.9	1,040,000	0.738	41,541	386,758
Trina solar TSM-430NEG9R.28
201	30	60	180	29.3	703,194	0.498	26,458	286,423
202	40	60	180	27	837,307	0.593	33,376	311,561
202	50	60	180	27	971,097	0.687	40,282	336,561

presents the optimized outcomes, highlighting the various combinations of PV module types and FC sizes. The calculated values of the COE range from 0.498 USD/kWh to 0.738 USD/kWh, while the NPC values range from USD 703,194 to 1,040,000, depending on the FC size and PV module type. The analysis indicates that the most favorable FC size is 30 kW. Figure 4 illustrates the variation in COE with different FC sizes and PV module types. The lowest COE of 0.498 USD/kWh is achieved with Trina solar and a 30 kW FC, followed by Jinko and Powerwave using the same FC size. Tindo demonstrates the highest COE of 0.738 USD/kWh. Overall, the results highlight the optimal configuration as a 30 kW FC combined with Trina solar panels, resulting in the most cost-effective energy generation.

Based on the calculation presented in Table 2, the optimal size for the case study consists of 201 kW of PV, 30 kW of FC, 60 kg of electrolyzer, 180 kg of H₂ tank, and 29.3 kW of converter. The total capital cost for this system is USD 286,423. The details of the NPC for different components of the PV/PEMFC system can be found in

Table 3. Evaluation of NPC for PV/PEMFC system components with 30 kW fuel cell.

	Jinko Solar-JKM415M-54HL4	Powerwave-PW-390-BMD-HV	Tindo Karra-330P	Trina Solar TSM-430NEG9R.28
Electrolyzer	USD 43,024.93	USD 50,195.75	USD 50,195.75	USD 50,195.75
Fuel Cell	USD 401,442.63	USD 405,270.82	USD 405,054.34	USD 405,270.82
Hydrogen Tank	USD 63,000.00	USD 70,000.00	USD 70,000.00	USD 70,000.00
Converter	USD 12,617.51	USD 206,004.51	USD 205,143.70	USD 11,424.62
Trina 430 Watt	USD 183,108.63	USD 12,441.30	USD 12,441.30	USD 234,205.96
Total	USD 703,193.69	USD 743,912.38	USD 742,835.09	USD 771,097.15

and Figure 5. For instance, in the case of Trina Solar TSM-430NEG9R.28, the total NPC is calculated to be USD 771,097.15. Among all the components, the FC NPC accounts for the highest portion at approximately 52.55%, amounting to USD 405,270.82. This is followed by the NPC of the PV at USD 50,195.75, while the NPC of the converter represents the lowest share at 1.48%.

The energy production and consumption data for a hybrid PV/PEMFC system with a 30 kW fuel cell are provided in

Table 4. Technical details of energy production and consumption in a hybrid PV/PEMFC system with a 30 kW fuel cell.

	Jinko Solar-JKM415M-54HL4	Powerwave-PW-390-BMD-HV	Tindo Karra-330P	Trina Solar TSM-430NEG9R.28
Electrical production
PV power, kWh/yr	233,300 (83.2%)	233,070 (83.2%)	232,910 (83.2%)	258,948 (84.7%)
FC power, kWh/yr	47,087 (16.8%)	47,084 (16.8%)	47,060 (16.8%)	46,680 (15.3%)
Total power, kWh/yr	280,387 (100%)	280,153 (100%)	279,970(100%)	305,628 (100%)
Electrical consumption
AC load, kWh/yr	89,714 (40.6%)	89,711 (40.6 %)	89,689 (40.6)	89,678 (40.8%)
Electrolyzer, kWh/yr	131,120 (59.37%)	131,100 (59.37%)	131,071 (59.37%)	129,973 (59.2%)
Total, kWh/yr	220,834 (100%)	220,810 (100%)	220,761(100%)	219,651 (100%)
PV array
Mean output, kW	26.6	26.6	26.6	29.6
Mean Output, kWh/d	639	639	638	709
Capacity Factor	14.6%	14.5%	14.5%	14.7 %
Maximum output, kW	142	142	142	159
PV Penetration	256%	255%	255%	284%
Hours of operation, h/yr	4277	4277	4277	4277
Levelized cost, $/kWh	0.0561	0.0559	0.0638	0.0449
Fuel cell
Hours of operation, h/yr	5189	5186	5189	5136
Number of starts, starts/yr	376	375	375	375
Operational life, yr	7.71	7.71	7.71	7.79
Capacity factor	17.9%	17.9	17.9	17.8%
Mean electrical output, kW	9.07	9.08	9.07	9.09
Maximum output, kW	30.0	30.0	28.0	30.0
Electrolyzer
Mean input, kW	15.0	15.0	15.0	14.8
Maximum input, kW	70.0	70.0	70.0	60
Capacity factor	21.4%	21.4	21.4	24.7 %
Total production, kg/yr	2826	2825	2824	2801
Specific consumption, kWh/kg	46.4	46.4	46.4	46.4
Hydrogen tank
Levelized COH, $/kg	16.7	16.7	17.3	15.9
Energy storage capacity, kWh	6667	6667	6667	6000
Tank autonomy, h	640	640	640	576

. Specifically, when utilizing the Trina solar TSM-430NEG9R.28 module, the total annual energy production amounts to 305,628 kWh. The PV array accounts for 84.7% of the total energy production, while the FC contributes the remaining 15.3%. The PV array exhibits an average output of 29.6 kW and a daily output of 709 kWh. It operates for 4277 h annually, resulting in a capacity factor of 14.7%. Figure 6 displays the monthly average power output when utilizing the Trina solar TSM-430NEG9R.28 module. Notably, compared to the Tindo Karra-330P solar PV module, the levelized COE is reduced by 29.6%, declining from USD 0.0638/kWh to USD 0.0449/kWh. Figure 7 illustrates the monthly electric production from both the PV array and PEMFC.

As depicted in Figure 8, the range of Levelized Cost of Hydrogen (COH) values is between USD 23.4/kg and USD 15.9/kg. There is a significant 32% cost reduction when utilizing a Trina solar panel with 30 kW compared to a Tindo PV module with 50 kW. The average monthly storage of hydrogen, as illustrated in Figure 9, is higher when employing a Trina solar TSM-430NEG9R.28 with a 30 kW FC. The months of May, June, July, August, September, and October exhibit peak levels of stored hydrogen. Detailed hourly data for May and September are displayed in Figure 10a,b, respectively.

7. Conclusions

This study investigated the viability and economic efficiency of utilizing solar photovoltaic/PEM fuel cell systems to power a specific load in NEOM city. The optimal system size was determined by evaluating three different PEMFC sizes and four distinct solar panel types, considering the cost of energy (COE) and net present cost (NPC) as key factors. The outcomes revealed that the most favorable configuration consisted of a 30 kW PEMFC combined with a 201 kW Trina solar TSM-430NEG9R.28 system. This configuration yielded a COE of USD 0.498/kWh and an NPC of USD 703,194, making it the optimal choice in terms of economic feasibility. Additionally, using Trina solar panels with 30 kW was found to be 32% less expensive than using Tindo PV modules with 50 kW. Furthermore, the study assessed the Levelized Cost of Hydrogen, which ranged from USD 15.9/kg to USD 23.4/kg. This analysis demonstrates the economic feasibility of hydrogen as an energy storage medium within the studied system. Overall, the results of this study highlight the viability and economic advantages of utilizing solar photovoltaic/PEM fuel cell systems in NEOM city. The optimal system configuration identified in this research provides valuable insights for the implementation of renewable energy solutions, emphasizing the importance of selecting the appropriate components and system sizes to achieve cost-effective and sustainable energy generation.

In future studies, the following topics will be investigated:

• Integration of multiple energy storage technologies, such as batteries and supercapacitors, in parallel with hydrogen storage within the PV/PEMFC system.
• Conduct a long-term performance analysis of the optimized PV/PEMFC system to evaluate its reliability and durability over an extended period.
• Perform a comprehensive life cycle assessment of the PV/PEMFC system to evaluate its environmental impacts, including carbon footprint, water usage, and materials used.