1 Introduction

The maritime industry has been investigating effective solutions to reduce greenhouse gases (GHG) generated by ship freight transportation. Increasing green energy usage and enhancing energy efficiency have become significant concerns for both ports and ships in ensuring sustainable maritime transportation in compliance with the rules and regulations enforced by the International Maritime Organization (IMO) [1]. Large ships have been using their auxiliary machinery during port and anchorage operations, potentially leading to air pollution in urban areas. Diesel engines have been used as auxiliary machinery, contributing to the significant production of GHG [2]. The electricity to ports and marinas has been supplied from the grid electricity produced by liquefied natural gas (LNG) power plants that also cause CO2 emission [3]. Renewable energy sources (RES) are the primary contenders for mitigating air pollutants, and among RES technologies, the utilization of solar energy is a viable option for port and marina areas. A photovoltaic (PV) panel farm installed in a suitable location can fulfill the entire or a significant portion of the electricity demand for a marina or a small port, reducing reliance on fossil fuels and enhancing energy efficiency [4].

Several studies in the literature utilized PV panels integrated with renewable energy sources (RES) on shore facilities related to the marine industry and floating power plants. Zis [5] evaluated the possible utilization of cold ironing as an emission prevention and reduction methodology. This study established a quantitative framework for assessing the technology, taking various aspects into account. The perspectives of investors, ship operators, and port operators for various types of ships were assessed. The results highlighted that shore power sourced from renewable energy (RES) can serve as a viable emission-reduction alternative for the marine industry, especially when the adoption of cold ironing is promoted by regulations. Xu et al. [6] conducted a research that optimizes the wave-driven solar tracker utilized in floating PV (FPV). The proposed concept enables the construction of a floating PV plant at a lower overall cost with greater energy harvesting efficiency. The implementation of the proposed design was carried out in the following research conducted by Xu et al. [7]. On an actual body of water, the proposed solar tracker’s viability was examined. The outcomes demonstrate that the system can change 40° in two dimensions in approximately 28 s. Vahabzad et al. [8] analyzed the energy scheduling of a hybrid ship having PV panels, batteries, and diesel generators involving a cold-ironing energy supply. The usage of diesel generators was minimized by the utilization of PV and batteries, and cold-ironing in ports could increase the charging/discharging time by up to 3 h. The cost reduction was calculated more in cold-ironing utilization than in the unused scenarios. Caprara et al. [9] analyzed a system design to provide electricity to the ships berthed at the port of Civitavecchia which is one of the most visited cruise terminals around the world. Initially, the paper investigated the capacity of the grid power of the port, then a battery unit having an 8.73 MW power rating, and a capacity of 121.25 MWh to meet the load of the cruise vessels. The batteries were charged by RES, and the cruise ships were not required to work their generators with the utilization of the proposed system. Bakar et al. [10] provided the optimal design configuration and sizing of a hybrid (batteries, PV, and wind) energy system for a port facility in Aalborg Denmark. The performance of the determined combination was investigated regarding the economic value, reliability of energy, and environmental effects. The findings showed that RESs met 80% of the electrical demand, with only 14.7% of the energy supplied from the main grid. Claus and López [11] investigated the prominent issues for FPV systems in marine applications. The solar tracker options for the system have been evaluated. Xu et al. [12] designed a wave-driven solar tracker system for an FPV system. To restrict the movements of the two joints and track the solar position, a motion planning approach was also developed. The findings demonstrated that under the influence of restricted base movements with an amplitude smaller than 4°, the solar tracker was capable of adjusting the PV panels at a velocity of 8.89 deg/s. Back surface water cooling was also proposed by Gomaa et al. [13] to improve the efficiency of the PV modules by around 10%. It was found that the power output increment ratio can differ according to the different temperature ranges during the day, months, and seasons [14]. The economic feasibility of PV systems with back surface water cooling was also positively affected for shore facilities and marine vessels where the cooling water could be found abundantly [15].

The economic evaluation of PV systems has also been studied frequently in the literature. Ghafoor and Munir [16] performed a research paper that designs and economically assesses a PV system installation in households in Pakistan. Economic analyses were conducted by using life cycle cost (LCC) and annual life cycle cost (ALCC) metrics. Findings demonstrated that the electricity generation unit cost is much lower than the conventional system for households. Shukla et al. [17] ensured a rooftop PV system design and conducted an economic analysis by calculating the payback period (PBP), net present value, savings-to-investment ratio, and life-cycle costs. The system provided a total annual energy of 1927.7 kWh with a PBP of 8.2 years. Michael and Selvarasan [18] investigated the environmental effect and economic performance of a flat plate solar PV and thermal (PV/T) system placed on the roof of buildings. Findings indicated that the solar PV/T system has a greater advantage compared to the solar PV system. Also, it decreased the number of construction materials used and the PBP while making the greatest use of the home roof space available. Numbi and Malinga [19] optimized the economic performance of a solar PV system in South Africa. Economic costs and PBP were the main metrics of the analysis. Outcomes of the study showed that the energy cost savings were raised by 22.8% and the term was shortened to 14 years from 22 years by their approach. Irfan et al. [20] evaluated the economic feasibility of the PV system for rural energy supply in Pakistan. Results indicated that PV electricity production costs are much cheaper than the conventional systems for the specific area. Fuke et al. [21] performed a comparative study that evaluated the techno-economic performance of various solar PV systems regarding their tracking systems and module types. LCC, ALCC, PBP, cost of electricity (COE), and total lifetime earnings were evaluated within the scope of economic analysis. Using 1-axis tracking, the poly-c-Si and CdTe module systems had the best total lifetime earnings. Akinsipe et al. [22] carried out the design and economic performance evaluation of a PV system in Nigeria. LCC, ALCC, and COE were selected as performance metrics which are calculated at 10,110.85 $, 593.75 $, and 0.18 $/kWh, respectively. The modeling findings demonstrated the technical and financial viability of the off-grid PV system for generating electricity, serving as a template for the successful development and practical use of such systems. To evaluate the financial viability of a photovoltaic battery (PVB) system for various residential customer groups in Switzerland, it was clustered based on its annual electricity consumption, rooftop size, annual irradiation, and location. Han et al. [23] presented a techno-economic optimization model. They used levelized energy cost (LEC) and PBP as economic performance indicators. Ibrahim et al. [24] conducted an economic analysis of a novel power assessment design of a PV system. The findings indicated that the suggested power evaluation approach has a significant impact on minimizing overall cost since it reduces energy storage capacity and reduces PV generation based on the type of load pattern. The daily load pattern achieved the highest savings of 81.4%. Manoo et al. [25, 26] investigated the economic viability of various on-grid and off-grid renewable energy systems by using HOMER Pro simulation tool. Different case scenarios of using power systems solar panels, wind turbines, batteries and fuel cell were analyzed to compensate for all the power requirement of the facility. It was shown that solar system design is the cheapest option considering the installation costs and a challenging COE of 0.236 $/kWh is obtained. However, grid connected hybrid system had the lowest COE with 0.155 $/kWh.

In the literature, the studies mainly investigated the solar energy potentials for some countries and regions, the rooftop PV panel applications in urban areas, universities, floating RES plants, and green port applications to ensure shore electricity supply to the ships. The utilization of solar trackers was primarily investigated in floating RES plants since wave power can drive the tracker system. Economic analyses of PV systems were studied frequently by using various metrics such as COE, LEC, PBP, LCC, and ALCC. However, the investigation of the performance of a PV panel system with different installation configurations including fixed, horizontal, vertical, and two-axis in facilities with limited installation areas like marinas was found lacking in the literature. The objective of this study is to analyze the economic effects of the installation of high-efficiency solar panels in the limited marina area in the Çeşme district of İzmir to meet the energy requirement of the marina facility. To achieve this aim, ten different PV panel modules were assessed with the mentioned panel installation types and their economic performances were compared with novel comparative economic indicators. The comparative economic analysis is based on estimating the costs associated with purchasing electricity from the grid if a solar panel system that annually produces the most energy is not chosen. To conduct a comparative economic analysis for the provided solar panel sets, new economic indicators of Relative Levelized Energy Cost (RLEC) and Relative Payback Period (RPBP) were defined. A multiple-step comparative economic assessment was carried out, involving two specific steps in this case. These two metrics can provide crucial comparative solutions for solar PV system investors, especially for facilities that need to offset their remaining energy requirements from external sources, such as the grid and other renewable energy sources.

2 System Description

In this study, a yacht marina located in Izmir, Türkiye, was chosen as a case for the utilization of solar power to meet the energy demand of the establishment. The areas suitable for the installation of solar panels were identified through face-to-face interviews with marina officials. The jetty, open parking lots, and open spaces within the marina borderline were identified as suitable areas for panel installation. Figure 1 displays the designated areas for the installation of solar panels within the marina establishment.

Fig. 1
figure 1

Specified areas suitable for solar panel installation inside the marina

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Zone 1, marked on the map, represents an area with a surface of 1,051.78 m2 on the jetty’s concrete surface. Zones 2 and 3 are open parking lots having surface areas of 881.15 m2 and 668.60 m2, respectively. The open-air space shown as Zone 4 is also considered for solar panel installation, which has a 191.13 m2 surface area. The total available solar panel installation area is calculated as 2792.66 m2 in the marina.

The average global solar irradiation values and daily sunshine durations of Çeşme district were obtained from the data published by the Republic of Türkiye Ministry of Energy and Natural Resources (GEPA) [27] to estimate the energy production potential from the selected areas for solar panel installation throughout the year. Figure 2 provides the monthly values of average global solar irradiation and daily sunshine duration for Çeşme.

Fig. 2
figure 2

Average global solar irradiation values and daily sunshine durations of Çeşme, Türkiye [27]

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3 Method

3.1 Energy Analysis of the Solar Power System for the Facility

This study utilized the PVGIS [28] online tool to simulate energy production from various solar panel systems and determined the optimal installation arrangement for specific areas. The methodology involves selecting the most suitable solar modules for the specified location and analyzing their energy output using the tool.

The study analyzed the placement of solar panels in the marina area by creating four different scenarios. The first scenario involved mounting solar panels at a fixed angle in suitable areas to maximize annual production. The remaining three scenarios incorporated vertical, horizontal, and two-axis solar tracking systems to enhance the efficiency of solar energy utilization within the system. To simulate these scenarios, commercially available solar panel models in the region were selected based on their efficiency and cost-effectiveness. A list of the solar panels analyzed within the scope of the study is presented in Table 1.

Table 1 The specifications of solar photovoltaic panels investigated in the study
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Table 1 presents the solar panels that were employed to carry out individual panel layouts and evaluations for each of the scenarios. When installing solar panels, one crucial factor to consider is the space between them. A larger gap between the panels is necessary to prevent overlapping shadows, but it also means that fewer panels can be installed in the area. To determine the appropriate spacing between rows and columns, this study utilized the sun’s elevation angles, which vary depending on the time of day and date, as well as the dimensions and orientation of the panels. The calculation formula provided in Eq. 1 was applied to determine the suitable distance between the panels to be placed in the designated area.

$$x=L(\mathit{or}\; B)\times \mathit{cot}\left(\alpha \right)\times \mathit{sin}(\theta ),$$
(1)

where \(L\) represents the length of the panel (m), \(B\) represents its width (m), \(\alpha\) is the minimum elevation angle of the sun, and \(\theta\) is either the maximum tilt angle allowed in scenarios where solar tracking systems are used or the fixed tilt angle in scenarios where the system is fixed.

The study calculated a single value for the angle \(\alpha\) for all scenarios since it depends on the position of the sun. To determine this value, the study considered factors such as the seasons when the marina is most heavily used, the varying sunrise and sunset times in the region, the sun’s height, and the angle of incidence on the panels at different times. Based on these factors, a fixed value was determined as the lowest angle at which the sun reaches the region between 08:30 and 16:30 from April 15 to September 15, when the marina’s energy demand and solar energy potential are highest. The aim of leaving a gap between the panels is to ensure that no shadow falls on the panels during the specified date range and hours. The minimum α angle was determined as 29.92°.

In Scenario 1 where a fixed system was used, the \(\theta\) was selected to optimize solar energy utilization throughout the year in the region. This value was obtained using the PVGIS database. As part of this study, the \(\theta\) angle for the fixed system scenario was determined to be a constant value of 29°, based on the conducted analyses.

The second scenario employed a system where solar panels track the sun on the vertical plane through solar tracking systems. The distance between two rows of solar panels during placement was determined through a trial-and-error method. The PVGIS tool was used to determine the maximum tilt angle allowed in the system. For each case, the \(\theta\) angle was regularly adjusted, and the distance between rows was calculated separately. The values that achieved the highest energy production from the panels placed in the area were used to determine the \(\theta\) angle for each panel separately. As a result, the spacing between the rows for each panel was determined individually.

The third scenario involved a solar panel system with solar tracking systems that follow the sun on the horizontal plane. During the placement of solar panels, the distance between two rows was determined using the fixed system distances because there is no horizontal change in this system. However, since panels can move horizontally in this system, the distance between columns as well as rows needed to be considered. To calculate this, the formula used \(B\) instead of \(L\) and azimuth angle instead of inclination angle. The maximum tilt angle allowed in the system was found by trial-and-error method. The \(\theta\) angle used was regularly adjusted, and panel intervals were calculated separately for each case. The \(\theta\) angle for each panel was determined based on the values that generated the highest energy production through the panels. Using this value, the spacing between columns of panels was determined, and the panel placement was calculated, considering both the distances that should be maintained between columns and rows.

The fourth scenario utilized solar tracking systems that allow the solar panels to follow the sun in both the horizontal and vertical planes. The distance between two rows during the placement of the solar panels was determined by considering that the vertical angle change in this system is equivalent to the horizontal angle change in the system with horizontal solar tracking. Therefore, the distance was set to be equal to the values calculated in the system where the panel angles change horizontally. Similarly, the distance between the columns was determined by using the values calculated for the distance between the columns in the scenario using a vertical-axis solar tracking system. Once the distances between columns and rows for each type of panel were calculated, technical drawing software was used to enable the optimal placement of the panels in the designated areas in the marina. However, it was acknowledged that various factors might deviate the calculation results from ideal conditions during the process. The study’s simulation included system losses, which are detailed in Table 2.

Table 2 System losses
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The efficiency of module placement in the marina area can serve as a performance indicator for the modules’ utilization in that area. To evaluate this, the occupancy ratio was calculated for each module used in each scenario. This ratio was determined by dividing the total area covered by the modules in the field by the total area of the field.

Finally, the annual energy demand for each scenario was evaluated based on the electricity consumption of previous years in the marina. The rate of solar energy generated to meet the electricity demand of the marina, which was described as the compensation rate, was also assessed for each scenario. The annual energy consumption of the marina is illustrated in Table 3. This data was obtained through face-to-face meetings with marina authorities.

Table 3 Monthly electrical energy consumption of the marina in a year
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3.2 Economic Analysis

The economic assessment of the system was conducted using recent retail market prices of system equipment obtained from PV module suppliers in March 2023. The cost data related to the PV modules is given in Table 4.

Table 4 Cost data of selected PV modules
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The analysis includes cabling/labor/project costs and the construction cost of the solar power system for calculating the investment cost, which were taken as 250 $/kW and 60 $/kW, respectively [29]. Operation and maintenance (O&M) costs of panel systems, inverters, and MPPTs were also considered for the lifetime of the solar power system. MPPTs and inverters are critical equipment in the system that cannot endure through the lifetime of the solar power system; thus replacement of these equipment was planned after 15 years of operation with a 33.4% reduced purchase cost of the initial cost [30]. The economic model of the solar PV system was established using the parameters given in Table 5.

Table 5 Parameters used in the economic model
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The key indicators of Levelized Energy Cost ($) \(\left(LEC\right)\), Relative Levelized Energy Cost ($) \(\left(RLEC\right)\), Payback Period (years) \((PBP)\), and Relative Payback Period (years) \((RPBP)\) were used to evaluate the economic feasibility of the systems. The investment costs ($) (\({C}_{invest}\)) were calculated based on panel costs ($) (\({C}_{PV}\)), cabling/labor/project costs ($) (\({C}_{CLP}\)), construction costs ($) (\({C}_{const}\)), inverter initial investment ($) (\({C}_{inv,init}\)), and replacement (\({C}_{inv,replace}\)) costs ($), as well as MPPT initial investment ($) (\({C}_{MPPT,init}\)) and replacement costs ($) (\({C}_{MPPT,replace}\)) by Eq. 2:

$$\begin{aligned}{C}_{invest}&={C}_{PV}+{C}_{CLP}+{C}_{const}+{C}_{inv,init}+{C}_{inv,replace}\\&+{C}_{MPPT,init}+ {C}_{MPPT,replace}.\end{aligned}$$
(2)

The Capital Recovery Factor (\(CRF\)) was used to obtain a coefficient that represents the present value of annuity over the lifetime (\(LT\)) of the system configurations. \(CRF\) was calculated using the following Eq. 3, where the interest rate (\(i\)) was assumed to be 6% and the \(LT\) was taken as 25 years:

$$CRF=i\times {(1+i)}^{LT}/[{\left(1+i\right)}^{LT}-1] .$$
(3)

The \(LEC\) can be expressed as the ratio of the total lifetime cost of each system per year to the annual energy production (kWh) of the PV systems. \(LEC\) was determined using Eq. 4:

$$LEC=[(CRF\times {C}_{invest})+{C}_{O\&M,sys,annual}]/{W}_{PV,annual},$$
(4)

where \({C}_{O\&M,sys,annual}\) is defined as the annual O&M cost ($) of the systems, which is the sum of the annual O&M costs of the PV system ($) (\({C}_{O\&M,PV,annual}\)), inverter ($) (\({C}_{O\&M,inv,annual}\)), and MPPT ($) (\({C}_{O\&M,MPPT,annual}\)) as given in Eq. 5:

$${C}_{O\&M,sys,annual}={C}_{O\&M,PV,annual}+{C}_{O\&M,inv,annual}+{C}_{O\&M,MPPT,annual} .$$
(5)

The Payback Period (\(PBP\)) of each system is calculated by Eq. 6:

$$PBP={C}_{invest}/[({C}_{ele}\times {W}_{PV,annual})-{C}_{O\&M,sys,annual}],$$
(6)

where \({C}_{ele}\) is the electricity purchase cost ($/kWh) of the marina from the grid, assumed to be 0.153 $/kWh [31].

The comparative economic assessment is based on including the power purchase costs from the grid for not selecting the solar panel system yielding the maximum annual energy production. For this reason, new economic indicators of Relative Levelized Energy Cost \(\left(RLEC\right)\) and Relative Payback Period (\(RPBP\)) were defined to carry out a comparative economic analysis for the given solar panel sets. These two indicators are essential parameters for facilities that have to compensate for the remaining energy requirement from external sources, e.g., the grid, and other renewable energy sources. \(RLEC\) for each solar panel system was calculated using Eq. 7, where \(\mathit{max}\left({W}_{PV,annual}\right)\) is the best annual energy production capacity (kWh) value obtained among the span of selected PV panel sets.

$$RLEC=\left[\left(CRF\times {C}_{invest}\right)+{C}_{O\&M,sys,annual}+ \left(\left(\mathit{max}\left({W}_{PV,annual}\right){- W}_{PV,annual}\right)\times {C}_{ele}\right)\right]/ {W}_{PV,annual}.$$
(7)

The Relative Payback Period (\(RPBP\)) is also a key economic indicator to assess which solar system will return the investment more quickly relative to the other solar panel systems by considering the annual energy production difference that will be compensated from the grid. The \(RPBP\) calculations for each solar system were made using Eq. 8.

$$\begin{aligned}RPBP&={C}_{invest}/[({C}_{ele}\times {W}_{PV,annual})-{C}_{O\&M,sys,annual} \\&-(\left(\mathit{max}\left({W}_{PV,annual}\right)-{W}_{PV,annual}\right)\times {C}_{ele})].\end{aligned}$$
(8)

4 Results and Discussion

4.1 Energy Analysis Results

The study explored four different scenarios to determine the amount of energy produced by solar panels. These scenarios involved either mounting the panels at a fixed angle or using different types of solar tracking systems that could move horizontally, vertically, or in both directions. Table 6 indicates the maximum number of modules that can be installed in the specified area for each scenario.

Table 6 Number of modules that can be installed in the area for all scenarios
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Table 6 clearly illustrates that the number of modules that can be installed in a given area varies depending on the scenario. This variation is due to the need to maintain appropriate distances between rows and columns, given that solar modules can move both horizontally and vertically in this system. As the modules move horizontally, the distance between rows is adjusted to allow for the maximum allowed vertical tilt angle. This results in an increase in the distance between rows, unlike in a fixed-angle system. Similarly, as the modules move vertically, the distance between columns is adjusted to provide for the maximum allowed horizontal tilt angle. This leads to an increase in the distance between columns, which is not the case in a fixed-angle system where the distance is zero. Finally, when the modules can move in both axes, the distance between both rows and columns increases. Ultimately, an increase in the distance between rows and/or columns leads to a reduction in the number of modules that can be installed in the area.

Figure 3 displays the amount of annual energy that can be produced for all scenarios when the maximum number of installable modules, as provided in Table 6, is installed in the area.

Fig. 3
figure 3

Annual energy production of solar modules

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Based on the values presented in Fig. 3 and Table 6, it is evident that the maximum annual energy production can be achieved as 415,233 kWh by utilizing 693 units of module 5 among fixed system configurations. However, it is important to note that the order of the annual production values per module depicted in the figure does not correspond to the order of efficiency values of the modules listed in Table 1. This indicates that the efficiency values of the modules are not the sole determinant of the annual energy production when optimally placed in the region. Furthermore, the sizes of the panels play a crucial role in determining the number of modules that can be accommodated in limited spaces. While smaller modules may seem advantageous, it is observed that modules 8 and 10, which are smaller than module 5 and have higher efficiency, produce marginally lower annual energy when examined in totality. This finding highlights the importance of considering various configurations when designing a solar array system, particularly in areas with limited space, where a significant number of modules are arranged in different configurations as in this study.

It becomes apparent that a higher amount of annual energy can be generated with fewer modules compared to the fixed system by using vertical-axis solar tracking systems for all module groups upon analyzing the simulation results presented in Fig. 3 and Table 6. The increase in energy production per module is attributed to the higher utilization of solar energy in the vertical-axis solar tracking system. From another perspective, it is important to note that the ranking of modules in terms of energy production changes when compared to the fixed system, even though the same module groups are used in the same region and season. This is due to variations in the distance between rows and columns in each scenario, the limited area of the application region, and the possibility of using different numbers of each module in each scenario.

For the use of a horizontal-axis solar tracking system, it can be interpreted from Fig. 3 that a similar pattern emerges to the scenario where a vertical-axis solar tracking system was investigated, whereby fewer modules can produce more energy annually compared to the fixed system, for all module groups. The reason for this is due to the need to create gaps between the columns in this scenario, as the modules can move horizontally. The reason for an increase in energy production per module is due to higher solar energy utilization resulting from the use of horizontal solar tracking.

The maximum annual energy production among all module groups was achieved by module 8 with two-axis configurations with a capacity of 453,619 kWh. Implementing a two-axis solar tracking system can result in higher annual energy generation with a reduced number of modules for all module groups, in contrast to using fixed-angle systems or single-axis solar tracking systems. The reason for this reduction in the number of modules that can be placed in the area is due to the need to maintain appropriate distances between rows and columns, as the solar modules can move both horizontally and vertically in this system. Despite this reduction, the two-axis tracking system enabled higher solar energy utilization compared to single-axis solar tracking systems or fixed systems, thanks to its tracking capabilities in both axes.

The occupancy ratio of solar arrays in the designated areas of the marina can be an indicator of effective area usage. Table 7 shows the occupancy ratios for each module group for all four scenarios.

Table 7 Occupancy ratios for each solar module group in the area for all four scenarios
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According to Table 7, the occupancy rates of solar modules varied significantly depending on the module type and scenario. Overall, the fixed system scenario was found to be the most effective for area utilization. This is because in this scenario, the modules do not move horizontally, eliminating the need for gaps between columns, and the distance that needs to be left between rows is relatively lower since the modules do not move vertically. On the other hand, the two-axis solar tracking system was found to have the lowest efficiency in terms of area usage. This is because, in this scenario, the modules can move in both axes, requiring gaps to be left between the columns and more space to be left between the rows. Additionally, different modules had varying occupancy ratios within the same scenarios, which is due to factors such as limited area, module dimensions, and required distances between rows and columns.

Figure 4 shows the monthly energy compensation rates of the investigated solar modules. The energy compensation rate is a dimensionless coefficient that is multiplied by the energy demand of the corresponding month. The best average energy compensation ratio could be achieved by module 8 as 14.44% from the two-axis configuration. The ranks of module 8 with vertical and horizontal-axis solar tracker configurations were also found to be the best in terms of average energy compensation rates. However, module 5 yielded the best average energy compensation ratio among fixed configurations with a value of 13.22%.

Fig. 4
figure 4

Monthly compensation rates of solar modules for the marina’s electric energy requirement

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The monthly compensation rates of solar modules, indicating a coefficient of the marina’s energy needs that can be fulfilled by solar modules throughout the year, were based on factors like solar radiation, module efficiency, module angles, and seasonal changes in energy demand. The compensation rates were observed to decrease in winter and summer, while increasing in spring and autumn, mainly due to higher energy demand during summer months and lower energy production in winter months. Using a vertical-axis solar tracking system led to higher compensation rates in spring and summer (an average of 16.56% energy compensation ratio for module 8) but lower rates in autumn (14.60% for module 8) and winter (10.89% for module 8). The findings of Alanazi et al. [32] support this outcome and demonstrate that the solar-tracker specifications and design parameters are affected by local or seasonal variables. Therefore, they should be decided specific to the application by conducting a comprehensive analysis. The seasonal variation of the energy compensation ratio could be because more solar panels can be installed in specific areas of the marina with vertical-axis tracking systems as two-axis tracking systems require leaving a distance between the two columns to avoid shading, resulting in a decreased number of solar panels. However, considering the average compensation rate over a year, two-axis solar tracking systems were found to increase solar energy utilization rates with a smaller number of modules.

4.2 Economic Analysis Results

The economic performance of the ten different PV panel configurations including the auxiliary components of the system for four different installation scenarios were evaluated. The performance metrics used for this analysis include LEC, RLEC, PBP, and RPBP. The cost data of the system constituents are demonstrated in Table 4, and the parameters used in the economic model are illustrated in Table 5. Although \(LEC\) and \(PBP\) show the exact economic indicators for a single installation project, they fail to recognize the additional energy costs due to the yearly energy production difference among different solar PV panel configurations, and consequently, the economic benefits of using a higher power-yielding PV panel set are ignored. In this study, \(RLEC\) and \(RPBP\) are indicated as relative economic performance metrics for a specified set of ten solar modules to conduct a comparative economic assessment. These relative indicators should be utilized in economic analyses where there are options that can produce more energy for a system, to obtain comparable results by considering the additional energy costs due to the requirement for a facility to compensate for the remaining energy required from external sources. Commonly, higher power-yielding solar PV panel systems cost more than PV systems with lower energy production capacities. This method enables a comparative economic analysis among different solar PV systems to determine the most economical choice. A two-step comparative economic assessment was applied for this case by first considering the \(\mathit{max}\left({W}_{PV,annual}\right)\) value of two-axis configurations. Then, the \(\mathit{max}\left({W}_{PV,annual}\right)\) value of vertical-axis configurations was taken by eliminating the two-axis configurations from the span because they did not yield the best relative economic performance in the comparative assessment.

In Fig. 5, the \(LEC\), \(RLEC\),\(PBP\), and \(RPBP\) results of the economic analysis for each configuration regarding the installation method are illustrated, where \(\mathit{max}\left({W}_{PV,annual}\right)\) is referenced to the module 8 panel set with the two-axis solar tracker system having a 453,619 kWh annual energy production capacity, as indicated in the energy analysis results of the systems presented in Fig. 3.

Fig. 5
figure 5

The \(LEC\) and \(RLEC\) results obtained for a fixed, b horizontal, c vertical, d two-axis solar panel configurations and the \(PBP\) and \(RPBP\) results obtained for e fixed, f horizontal, g vertical, h two-axis solar panel configurations (\(\mathit{max}\left({W}_{PV,annual}\right)\) is taken for module 8 panel set with the two-axis solar tracker system)

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Figure 5 reveals that all the economic performance metrics of the two-axis solar panel configurations of each module are higher than those of their fixed, horizontal, and vertical alternatives. It can be said that these results are foreseeable due to the higher investment costs of two-axis tracking systems and the lower number of modules that can be placed in the limited marina area, given the large gap requirement of two-axis systems between each module. In this case, the significant energy production capacity differences obtained from two-axis PV configurations could not compensate for the investment and O&M costs over the systems’ lifetime as rapidly as their alternative configurations, as evident from the \(PBP\) and \(RPBP\) values in Fig. 5e–h. The best \(RPBP\) value was 7.681 years for the two-axis PV system, while the fixed module 5 configuration yielded the lowest \(RPBP\) at 7.131 years, primarily due to the lower investment costs of fixed configurations. The LEC values exhibited a similar trend to the PBP graphs, indicating better economic performance for fixed configurations, although RLEC values for fixed configurations are nearly as high as those for two-axis configurations.

The second step of the comparative economic assessment involved the elimination of the two-axis module configurations from consideration due to their suboptimal relative economic performance. A new comparative assessment was conducted by selecting the maximum annual energy production capacity value \(\mathit{max}\left({W}_{PV,annual}\right)\) from the new span, which was obtained from the vertical-axis configurations of module 8, with an annual energy production capacity of 447,234 kWh. This assessment step is necessary because the change in the maximum energy production capacity yielding PV module set occurs when the two-axis configurations are excluded from the span, thus reducing the practical economic benefits of not purchasing energy from the grid. The economic analysis results derived from this comparative assessment are presented in Fig. 6.

Fig. 6
figure 6

The \(LEC\) and \(RLEC\) results obtained for a fixed, b horizontal, c vertical solar panel configurations and the \(PBP\) and \(RPBP\) results obtained for d fixed, e horizontal, f vertical solar panel configurations (\(\mathit{max}\left({W}_{PV,annual}\right)\) is taken for module 8 panel set with vertical-axis solar tracker system)

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The validity of the economic calculations can be assured by comparing the PBPs with similar applications. Although each application involves local factors such as sunshine hours or electricity price, the PBP benchmarking can depict a general consistency of analysis. Shukla et al. [17] computed 8.2 years of \(PBP\) for a rooftop system, and Han et al. [23] stated the \(PBP\) s of different configurations between 6.2 and 14.9 years. The \(PBP\)s of the modules varied between 7.013 and 7.648 years and \(RPBP\)s were between 7.167 and 7.744 years. In the article of Tushar et al. [33], the \(PBP\) metric was calculated lowest at 6.49 years and it increased up to 21.27 years regarding the service years and panel specifications. These outcomes demonstrate that the economic model shows conformity to the literature. In addition, the determined configurations provided a satisfactory performance compared to similar studies.

The most economically favorable option, as determined by \(LEC\) and \(PBP\), is the fixed configuration of module 7, with costs of 0.0885 $/kWh and a payback period of 7.013 years, as shown in Figs. 5 and 6. However, an examination of Fig. 6a–c revealed that the \(RLEC\) of PV modules with vertical-axis solar trackers is relatively lower compared to their counterparts with horizontal-axis and fixed PV configurations. Notably, module 5 and module 10 exhibited the most favorable relative economic performance in terms of \(RLEC\), with costs of 0.090 $/kWh. Analyzing the \(RPBP\) values presented in Fig. 6d–f indicated that fixed PV modules recoup their investment more rapidly than PV modules with horizontal-axis solar trackers, although there is only a slight difference between fixed and vertical-axis PV configurations. While the best PBP was associated with the fixed module 7, the best \(RPBP\) was attributed to the fixed module 5, with a payback period of 7.113 years. The rationale behind achieving the best \(PBP\) and \(RPBP\) from the fixed PV systems can be attributed to their lower investment costs. Nevertheless, the most critical economic indicators in this context are \(RLEC\) and \(LEC\), as they lead to higher cumulative net profits over the lifetime of the systems. Consequently, the solar module that demonstrates the most robust economic performance is module 5 with a vertical-axis solar tracker configuration, characterized by the lowest \(RLEC\) and \(RPBP\) as they lead to higher cumulative net profits over the lifetime of the systems, while the lowest \(LEC\)s and \(RLEC\)s of solar PV systems are approximately 41% cheaper than the cost of purchasing electricity.

5 Conclusion

The study meticulously compared various solar module configurations and solar tracking alternatives, focusing on their energy production and economic performance. Relative economic indicators, \(RLEC\) and \(RPBP\), provide a more nuanced economic analysis, recognizing that traditional metrics like \(LEC\) and \(PBP\) often overlook significant energy cost variations among different solar PV panel configurations.

According to the study, the following key findings are presented:

  • Module Placement Efficiency: Fixed solar modules allow for more arrays in a given area, but single-axis and two-axis tracking systems, despite having fewer arrays, yield higher energy output.

  • Influencing Factors on Energy Production: The efficiency of solar modules is not the sole determinant of energy production. Factors like module and area dimensions, geographical location, and seasonal conditions play significant roles.

  • Optimal Energy Compensation: The two-axis configuration, particularly with module 8, demonstrated the highest average energy compensation ratios.

  • Economic Analysis: Fixed module configurations, particularly module 5 and module 7, exhibited superior economic performance in terms of \(PBP\) and \(LEC\). However, the introduction of \(RLEC\) and \(RPBP\) alters the economic assessment, underscoring the importance of these relative metrics. When there are multiple system options that can generate higher energy output, it is important to use these relative indicators in economic analyses to obtain comparable results. It is found necessary to account for the additional energy costs associated with compensating for any remaining energy needs from external sources.

Future investigations should delve deeper into assessing operational and maintenance costs over these systems’ extended lifetimes and explore optimizing solar panel placement in diverse environmental conditions. Analyzing Life Cycle Cost (LCCA) would provide comprehensive economic evaluations across the lifespan of solar panels, aiding in precise cost predictions and economic decisions. Additionally, examining market trends, policy influences, and the integration of energy storage solutions would enhance insights into economic implications, thereby supporting informed decision-making in solar energy technology adoption and sustainability strategies. This study offers valuable insights for solar panel system designers and decision-makers, highlighting the need for nuanced economic metrics in an evolving renewable energy landscape.