Introduction

Brockway et al. (2019) pointed out that some studies have neglected that fossil fuels require more embedded energy, resulting in increased energy costs and decreased energy-return-on-investment (EROI) ratios. The values of oil, coal, and gas exceed 25:1 at the primary energy stage. However, after evaluating the final stage, they drop to about 6:1, such as exporting power to electricity and petrol [1].

In recent years, nations, particularly European countries, have shifted their focus to energy supply security, emphasizing the necessity and urgency of clean energy transition policies. However, the epidemic and the Russian-Ukrainian War have caused metal prices to rise, resulting in a surge in photovoltaic (PV) system costs. There is a growing concern that PV’s energy return (ER) is inferior to conventional energies, as much recent research indicates. This issue poses challenges for countries aiming to develop the solar industry. Unlike other renewable energy sources, PV technology presents distinct advantages over other renewable energy sources, including an extended system lifespan, low maintenance costs, no movement requirements, and low initial investment costs [2]. Additionally, experts have convincingly demonstrated the feasibility of installing floating PV (FPV) in water territories such as reservoirs and dams. When initiating such projects, it is crucial to understand the ER of PV deployments as it relates to funding gain.

The most common metrics for ER, energy payback time (EPBT), and EROI [3] represent essential aspects of renewable energy evaluation. EPBT indicates when a PV system can generate energy equivalent to its production, representing the time needed for PV systems to recoup the invested energy over their lifetime [4]. EROI quantifies the ratio of energy delivered from a specific energy source to the energy consumed to generate that output [5]. If a source’s EROI is equal to or less than one, it becomes an “energy sink” and is not sustainable. For energy to be considered viable, the EROI ratio between energy delivered and energy required for delivery must be at least 3:1[6]. Electricity carbon emission coefficient (ECEC) evaluates the impact of CO2 emission reduction, depicting the effect of CO2 emissions on the power production process [7]. Understanding these metrics is crucial for comprehending the sustainability and viability of renewable energy technologies.

Bhandari et al. (2015) systematically reviewed and meta-analyzed embedded energy, EPBT, and EROI indicators for crystalline Si and thin film PV technologies published from 2000 to 2013. They collected 232 references, selecting 11 and 23 for embedded energy and EPBT/EROI analysis, respectively. Furthermore, they standardized several comparative parameters using a system lifetime (30 years), performance ratio (0.75), insolation (1700 kWh/m2•year), and module efficiency (aSi: 6.3%; CdTe: 10.9%; CuInGaSe: 11.5%; poly-Si: 12.3%; mono-Si: 13.0%). The results indicate that the mean harmonized EPBT of all module types ranged from 1.0 to 4.1 years, ranking mono-crystalline silicon (mono-Si), poly-crystalline silicon (poly-Si), amorphous silicon (a: Si), copper indium gallium diselenide (CIGS), and cadmium telluride (CdTe) from highest to lowest. The mean harmonized EROI diverged from 8.7 to 34.2 [3].

Solar technologies, which have a lifetime range of 25–40 years, are experiencing annual growth as an alternative energy source. Kamal et al. (2022) introduced a model to help review and discuss articles on material compositions, manufacturing, and dismantling processes. Subsequently, they recommended a research roadmap to help future studies optimize PV’s overall sustainability [8]. Jackson and Jackson (2021) proposed a model (TranSim) to simulate the financial and economic significance of an energy technology transition involving a decrease in EROI. They aimed to clarify whether declining EROI could lead to rising energy prices and decreasing economic growth. They integrated the stock-flow consistent (SFC) approach with an input-output (I/O) model. The results indicate an initial increase in output due to increased investment but below-trend growth and subsequent recession due to higher prices and changes in the functional income distribution. Additionally, the capital intensity of green energy production positively correlates with a decrease in EROI [9].

Fukurozaki et al. (2013) used the lifecycle assessment (LCA) methodology to analyze the energy requirements for solar module production and system components’ balance to assess Brazil’s EPBT and CO2 emissions of a 1.2kWp PV rooftop system. They investigated and considered mass and energy flow over the manufacturing process of the mono-crystalline unit. Moreover, they calculated the seven assumed national energy yields, EPBT, and CO2 emissions rates from metallurgical silicon growth to power generation. The EPBT is 2.47–3.13 years, and the CO2 emissions rate is 14.54–18.68 gCO2-eq/kWh for current rooftop mountings [10]. Weißbach et al. (2013) compared the EROI of various typical energies based on their efficiency using a consistent mathematical and physical basis with a strict exergy concept. The results reveal that nuclear, hydro, coal, and natural gas power systems outperform PV and wind power [11].

Louwen et al. (2015) conducted a life-cycle assessment to identify the EPBT, cumulative energy demand of four silicon heterojunction (SHJ) cell designs, and greenhouse gas (GHG) footprint based on in-plane irradiation of 1700 kWh/m2•year. According to current designs, complete SHJ PV systems (with module efficiencies of 18.4%) could produce lifecycle GHG emissions of 32 gCO2-eq/kWh. In contrast, conventional mono-crystalline silicon systems (with a module efficiency of 16.1%) could produce 38 gCO2-eq/kWh. The EPBT of all SHJ designs stands at 1.5 years, compared with 1.8 years for the mono-crystalline PV system. Increasing cell efficiency can reduce the lifetime of GHG emissions for PV systems to 20 gCO2-eq/kWh for SHJ and 25 gCO2-eq/kWh for the mono-crystalline system. Additionally, EPBT could decrease to 0.9 and 1.2 years, respectively [12]. Some researchers analyzed the significant observed divergences to gain a better understanding and provided the optimal evaluations of the energy embedded for the primary energy of present-day CdTe thin-film and a-Si modules. The energy required ranges between 600 and 1500 MJ per m2 module area depending on cell and encapsulation type. The EPBT for a grid-connected module under 1700 kWh/(m2•year) irradiation is below two years. Achieving an EPBT below one year appears feasible shortly [13].

In 2020, Grant and colleagues analyzed the Energy payback time (EPBT) for all 50 states in the United States, evaluating changes by comparing how the PV system would be affected when solar intensity is taken into account to prioritize environmental returns, considering differences in PV potential, impact type, and electricity blend [14]. Murphy and Hall (2010) analyzed recent empirical findings on five topics, such as EROI for most major fuel types and how they evaluated EROI. They identified areas for improvement in EROI research [3]. Daniela-Abigail and colleagues (2022) conducted a study on PV waste disposal in environmentally vulnerable regions in Yucatan, Mexico, analyzing it from three dimensions: environment, economy, and society. They found that implementing sustainable regulations for photovoltaic waste can reduce the EPBT of PV systems, decrease waste toxicity by 78%, improve freshwater ecology, and lessen the Levelized cost of electricity (LCOE) by 2% through PV recycling compared to not recycling PV waste [15]. Some scholars developed a benefit-sharing model and utilized the internal rate of return (IRR) as a funding evaluation metric to evaluate the benefits of primary stakeholders in recycling PV module waste. The results revealed that the installer, waste disposal company, and PV module manufacturer had IRRs of 7.36%, 4.21%, and 18.62%, respectively, indicating an unequal distribution of benefits among stakeholders. As a result, the authors put forward three viable benefit-sharing schemes to alleviate the impact on IRR and promote investments [16].

Zhou and Carbajales-Dale (2018) evaluated previous PV system meta-analyses’ efficiency and energy inputs in EROI under high-cost and low-cost contexts by focusing on existing wafer, thin film, and organic technologies. Their findings reveal that highly efficient, low-cost thin-film technologies have yet to emerge, with the optimal ER advancement identified as the thin-film process [17]. In their study, Wang et al. (2021) investigated and analyzed various feedstock options, including first-generation sources like corn, second-generation sources like corn straw, and third-generation sources like algae, to assess the trade-off of the EROI of typical biomass conversion systems in China. They harmonized and compared the system boundaries of previous biomass footprint calculations and found that the highest EROI (8.06-24.13) is seen in solid fuel derived from raw biomass feedstock, followed by biomass power (2.07-16.48), biogas (1.24-11.05), and biodiesel (1.28-2.23) from first-generation sources [18].

Although much literature mentions the ER of fossil fuels and PV, researchers usually measured ratios at the primary energy stage. Consequently, they yield favorable results for EPBT and EROI due to not importing the LCA or Lifecycle energy analysis (LCEA) into ER estimates. Moreover, with the rapid development of PV technology in recent years, it is essential to investigate its impact on ER so that investors can use it as an investment decision-making factor. Research on EPBT and EROI of PV and FPV deployments helps policymakers, industry stakeholders, and researchers make informed decisions about promoting sustainable and efficient energy solutions. These metrics provide valuable insights into renewable energy systems’ performance, environmental impact, and long-term viability, conducive to a more sustainable energy future.

This paper uses time series forecasting, LCEA, and ER indicators to conduct a case study on the global most extensive investigation into whether solar technology innovation affects energy recovery. The approach proposed and the results should benefit investors’ decision-making for future offshore FPV (OFPV) or other PV projects.

Comparing ER from Fossil Fuels and Solar Energy

In research comparing EPBT and EROI, the focus is often on assessing the overall energy performance of different energy sources such as PV, wind turbines, hydropower, and biofuels (Breyer et al., 2022) [19]. These analyses consider the energy inputs and outputs across a technology’s entire lifecycle. It includes energy used in material extraction, processing, manufacturing, transportation, installation, operation, maintenance, and end-of-life disposal (Rossi et al., 2023) [20].

When considering fossil fuels’ EPBT and EROI, these metrics provide insights into the energy efficiency and environmental impacts of their extraction, processing, transportation, and consumption (da Silva Neves et al., 2023) [21]. Compared to renewable energy sources, fossil fuels typically exhibit different EPBT and EROI characteristics due to the nature of their extraction and utilization processes. Their EPBT is shorter than that of renewable energy sources. EPBT for oil and natural gas often involves the time it takes to extract, process, refine, transport, and consume the energy resource. These evolutions vary depending on the type of fossil fuel and extraction methods used (Slameršak et al., 2022) [22].

Furthermore, fossil fuels have traditionally exhibited high EROI values due to their high energy density and relative ease of extraction and processing. Although higher EROI figures for them indicate they can provide society with a more extensive net energy surplus than the energy invested in their extraction, processing, and distribution, their reserves have declined over time, particularly as extraction becomes more energy-intensive or shifts to unconventional sources (Stern, 2019) [23]. The ecological impacts associated with fossil fuel extraction and combustion, such as GHG emissions and air pollution, also play a critical role in assessing the sustainability and desirability of continued fuel use [24]. The long-term sustainability, environmental impact, and shifting energy landscape of renewable energy sources, such as wind and solar, generally have lower EPBT and EROI values than conventional fossil fuel sources, underscoring the prominence of transitioning towards more sustainable energy alternatives [25]. For example, PV systems typically have reduced EPBT and increased EROI due to advancements in technology and manufacturing processes [26].

Examining solar energy’s EPBT and EROI provides valuable insights into PV stations’ efficiency, sustainability, and environmental impact. EPBT for solar energy represents the time needed for a solar PV system to generate energy equivalent to what was used in its production, installation, and decommissioning [27]. Factors influencing the EPBT of solar energy include

  1. (1).

    the energy intensity of materials used in PV panel production,

  2. (2).

    the efficiency of solar panels,

  3. (3).

    the location of the installation (insolation availability), and

  4. (4).

    the energy used in system installation and maintenance [28].

Contrarily, solar deployments typically exhibit high EROI values. EROI for solar energy measures the ratio of energy output (electricity generated) to energy input (production, installation, maintenance) over the system’s lifetime. Their values for PV systems have increased as technology improves, resulting in higher energy yields and more efficient energy conversion [29]. Factors affecting the EROI of solar energy include solar panel efficiency, operational lifespan, maintenance requirements, system design, and geographic location [30].

OFPV Deployment, PV System Type, and Single Diode Model (SDM)

Deployment of OFPV

Deploying OFPV involves installing solar modules on a structure that floats in offshore waters [31]. The functionality, circumstances, and surroundings of OFPV actively drive its expansion [32]. Regions with limited land but extensive sea territories increasingly recognize the importance of actively embracing this approach to align with the global low-carbon energy trend. To counter the effects of climate and tides, OFPV necessitates a floating stage, typically made of plastic and galvanized steel or entirely of plastic units [33], supporting construction, anchoring structure, and underwater cable [34]. Figure 1 shows an OFPV configuration.

Fig. 1
figure 1

OFPV deployment [34]

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The Bureau of Energy of Taiwan introduced the “Photovoltaic Two-year Promotion Plan” in 2016 to urge industries to promote clean energy and accelerate the shift from traditional carbon-based energy to green energy [35]. The sector can proceed with OFPV deployment once it has showcased significant achievements on reservoirs and detention ponds in recent years. The 181 MWp OFPV at Changhua Coastal Industrial Park is the largest in the world and became the first successfully deployed offshore plan. It benefits FPV development.

PV System Type

Sahu, Yadav, and Sudhakar (2016) classified PV stations into ground-mounted, roof-top, canal-top, floating, and offshore. The canal-top and floating types commonly use abandoned mines, ponds, reservoirs, and lakes to deploy water-based PV systems (Fig. 2) [36]. Choi declared that the FPV power generation efficiency is 11% higher than standard ground-based PV because of alleviative module temperature [32]. It enhances its power yield and helps CO2 emission [37].

Fig. 2
figure 2

PV System Type [36]

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Single Diode Model (SDM)

Figure 3 displays the PV cell’s equivalent circuit. This SDM model consists of a current source connected to the load, a diode, a shunt, and a series resistor [38]. Equation 1 describes the load current (IL) for the SDM as a constant function under its operating conditions [39, 40].

$${\mathrm{I}}_{\mathrm{L}}={\mathrm{I}}_{\textbf{pc}}-{\mathrm{I}}_{\textbf{rsc}}\left[\exp\ \left(\frac{{\mathrm{V}}_0+{\mathrm{I}}_{\mathrm{L}}{\mathrm{R}}_{\mathrm{s}}}{\mathrm{n}{\mathrm{V}}_{\mathrm{jv}}}\right)-1\right]-\frac{{\mathrm{V}}_0+{\mathrm{I}}_{\mathrm{L}}{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{s}\mathrm{h}}}$$
(1)
Fig. 3
figure 3

Equivalent Circuit of the PV Cell (i.e., SDM) [38]

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In eq. 1, Ipc indicates the photoelectric current, Irsc to the reverse saturation current, Vo to the cell output voltage, Rs to the series resistance, n to the diode ideality factor, Vjv to the junction voltage, and Rsr to the shunt resistance. IL represents the load current, Rs represents the series resistance, n signifies the diode ideality factor, and Rsh represents the shunt resistance. Manufacturers must utilize Standard test conditions (STC), which entail an irradiance of 1000 W/m2 (AM1.5) and a temperature of 25 °C, to conduct tests and assess the module’s electrical parameters. Installing the modules on the sea (water) surface in tropical conditions keeps the average temperature of the cell P-N junction below 12 °C, resulting in an 11% increase in module efficiency [32].

Time Series Analysis, LCA, and LCEA

Time Series Analysis

Time series analysis is a random process theory that uses mathematical statistics to predict future values based on historical data. In most problems, random data is sequenced according to time, which includes statistical inspection, like autocorrelation analysis [41].

A deterministic trend of time series is one where realizations of the time series process are a fixed function of time, like a high-order polynomial (eq. 2).

$${\mathrm{y}}_{\textbf{t}}={\upbeta}_{\textbf{0}}+{\upbeta}_{\textbf{1}}\mathrm{t}+{\upbeta}_{\textbf{2}}{\mathrm{t}}^{\textbf{2}}+{\upbeta}_{\textbf{3}}{\mathrm{t}}^{\textbf{3}}$$
(2)

In this case, yt depends on t. If adding a stationary component to the trend, we can achieve eq. 3.

$${\mathrm{y}}_{\textbf{t}}={\upbeta}_{\textbf{0}}+{\upbeta}_{{\textbf{1}}^{\mathrm{t}}}+{\upbeta}_{\textbf{2}}{\textbf{t}^2}+{\upbeta}_{\textbf{3}}{\textbf{t}^3}+\upvarepsilon \mathrm{t}$$
(3)

The process is said to be trend-stationary. Long-run forecasts will converge to the trend. In the simplest case, we have yt = β0 + β1t, a linear trend described as eq. 4.

$$\Delta {\mathrm{y}}_{\mathrm{t}}={\upbeta}_0,\mathrm{or}\Delta {\mathrm{y}}_{\mathrm{t}}={\upbeta}_0+\upvarepsilon \mathrm{t}\left(\mathrm{with}\ \mathrm{noise}\right)$$
(4)

Lifecycle Analysis (LCA) and Lifecycle Energy Analysis (LCEA)

When constructing an OFPV system, power is a must throughout the manufacturing, creation, and disposal phases. Considering the total energy usage throughout the project’s lifespan, LCA can mitigate and devise strategies for energy consumption. It involves evaluating whether all stages (from cradle to grave) of a project, product, or service will impact the environment (Fig. 4) [42]. A comprehensive, multi-impact conventional LCA is necessary as the primary environmental impacts stem from energy consumption. Hence, a simplified version of LCA, known as LCEA, can be a viable alternative. Nonetheless, it is advantageous to implement LCEA alongside a thorough investigation of LCA.

Fig. 4
figure 4

LCA’s Conceptual Illustration [42]

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When evaluating the environmental consequences of finished products, the process involves extracting and processing raw materials (cradle), followed by product manufacturing, distribution, and use, and finally, recycling or disposing of used products (grave) [43].

Klöpffer and Grahl highlighted that the scope of LCA assessment encompasses material extraction, FPV system construction, and the entire power production process, including system operation and post-service processing measures [44]. Klöpffer further outlines an LCA implementation process, which includes defining goals and scope, conducting inventory analysis, assessing impacts, and interpreting results [45], following ISO 14040 and 14044 standards [46]. Klöpffer conducted a cradle-to-grave lifecycle evaluation of the entire FPV system, ecologically and financially simulating and comparing it with conventional solar plants [45]. Cromratie Clemons et al. (2021) performed an LCA for a 30-year 150 MWp FPV plant lifespan in Thailand, revealing significant impacts of approximately 110 m3 of water and 73 kgs of GHG [46]. However, this research directly correlates energy use with associated GHG emissions.

LCEA, following the original four-step LCA methodology, focuses solely on energy and accompanying carbon emissions as measures of environmental impact [47]. As an extension, LCEA is a benchmark for assessing a project’s energy-saving and environmental benefits. However, Fay et al. (2000) argued that LCEA cannot replace conventional LCA [48]. Instead, it provides a more detailed energy analysis for products and services where energy consumption is a primary environmental concern [49]. Additionally, LCEA calculates the total energy required to produce a product, with the comprehensive system boundary in the manufacturing process extending from material importation to module disposal after system dismantling [50]. The Environmental Protection Agency’s (EPA) National Risk Management Research Laboratory further illustrates LCEA as a technique to evaluate the ecological aspects and potential impacts associated with a product, process, or service (Fig. 5) [51].

Fig. 5
figure 5

LCA’s Conceptual Stage Diagram [51]

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ER Analysis- A Case Study

Study Area

The Changhua Coastal Industrial Park is the most remarkable industrial zone in the district, an outlying island-type industrial area developed from newly reclaimed land in the northwest corner of Changhua County. It overlooks the western Taiwan Strait and hosts various industrial activities, research, development, recreational facilities, and sightseeing spots. The investor utilized 176 ha of sea surface to install over 570,000 solar modules (181MWp) and established one of the world’s most extensive OFPV station at the park (Fig. 6). Since February 2021, the grid-connected system has been capable of supplying electricity to approximately 41,000 households [52].

Fig. 6
figure 6

Changhua Coastal Industrial Park’s OFPV [52]

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Solar Module Fabrication Process and Specifications

The module’s manufacturing process is as follows:

  1. (1).

    Cell string arrangement: Lay solar cells into cell strings with ribbons.

  2. (2).

    Welding: After laying the cell strings neatly, weld them after connecting them in parallel with the bus bar welding tape.

  3. (3).

    Lamination: Cross-link the encapsulation material by vacuum and high temperature, which can closely bond the glass and protect the cell.

  4. (4).

    Encapsulated aluminum frame: Protect the module frame and strengthen the prevention of moisture infiltration.

  5. (5).

    Mount the junction box: Export the electricity generated by the solar module through the junction box.

  6. (6).

    Classification: Rank the modules according to the power level.

  7. (7).

    Packing: Pack the modules to ensure shipment and transportation quality.

The TAIWAN Plus PV technical specification requires installers to use high-efficiency solar modules with a 25-year output warranty for projects recruited by the government in 2019. The specifications in Table 1 and Fig. 7 detail that they comply with the National Standard of the Republic of China CNS 15114 and 15115 [55].

Table 1 Electrical Specifications [53]
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Fig. 7
figure 7

Current-Voltage(I-V Curve) [53]

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Research Design

This paper uses time series and LCEA analyses to conduct the ER assessment of the target OFPV in a 30-year lifespan to examine its EPBT and EROI. Figure 8 shows the research flowchart of the ER assessment.

Fig. 8
figure 8

Flowchart of ER Assessment for Changhua Coastal Industrial Park’s OFPV

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Goal Definition and Scope, Inventory Analysis, and Boundary Setting

Goal Definition and Scope

Before data collection begins, the goal and scope of the assessment need to be clearly defined. It involves identifying the purpose of the assessment and the system boundaries (Omrany et al., 2021) [56].

Inventory Analysis

This stage involves data collection on all inputs (e.g., energy, materials) and outputs (e.g., waste, emissions) associated with each stage of the product’s lifespan, from raw material extraction to disposal (Barni et al., 2022) [57]. Data collection in LCEA is systematic processes that comprehensively understand a product or process’s environmental implications throughout its lifecycle (Safari & AzariJafari, 2021) [58]. They require careful planning, data gathering, and analysis to ensure the accuracy and reliability of the assessment results (Selicati & Cardinale, 2023) [59]. Here is a general overview of the process:

  1. a.

    Primary data: We directly collect the data from the assessed processes.

  2. b.

    Secondary data: We obtain this from existing databases, literature, and industry reports. Additionally, to ensure the reliability and accuracy of the collected data, the investigators thoroughly check it for inconsistencies and errors.

Boundary Setting

The boundary setting determines the extent of the lifecycle to be analyzed. It encompasses the entire lifecycle of the OFPV system under investigation. It involves all stages, from raw material extraction and processing, component manufacturing, system installation, operation, and maintenance to end-of-life disposal or recycling [60]. The investigators adopt a gate-to-gate boundary setting in this study to analyze LCEA from the factory gate to the installation site.

Considering the energy inputs and outputs at each stage of the OFPV system’s lifecycle, the LCEA boundary ensures a comprehensive ER assessment, enabling the calculation of EPBT and EROI to evaluate the system’s long-term energy production efficiency and sustainability. Specifically, the boundary encompasses:

  1. (1)

    Raw Material Extraction and Processing: This involves the energy inputs embedded to obtain raw phase materials such as silicon, metals, and other components required for PV panel manufacturing.

  2. (2)

    Component Manufacturing: This stage considers energy inputs related to the manufacturing processes of PV panels, support structures, electrical components, and other system components.

  3. (3)

    System Installation: Energy consumed during the transportation, construction, and installation of the OFPV system, including the energy embodied in infrastructure and transportation activities, is included.

  4. (4)

    Operation and Maintenance: Energy used for operating and maintaining the OFPV system throughout its operational lifespan, including regular maintenance, cleaning, and any energy required for system monitoring and management.

  5. (5)

    End-of-Life: We account for the energy inputs related to decommissioning, dismantling, recycling, or disposal of the OFPV system components and any energy recovered through recycling processes.

Results and Discussion

Establishment of Goal Definition and Scope

  1. a.

    Establishment of Goal Definition

The goal of this study is to assess the ER of the OFPV system over a 30-year lifespan using time series analysis and LCEA. Specifically, the study aims to investigate the EPBT and EROI of OFPV systems to understand their long-term energy production efficiency. It aims to be conducive to informed decision-making by investors, policymakers, industry stakeholders, and researchers regarding promoting and adopting sustainable and efficient energy solutions, ultimately advancing towards a more sustainable energy future.

  1. b.

    The scope of the study

It includes:

  1. (1).

    Conducting time series analysis to forecast the energy production of OFPV systems over 30 years.

  2. (2).

    A comprehensive LCEA will be performed to account for the energy inputs and outputs throughout the lifecycle of OFPV systems.

  3. (3).

    Evaluating EPBT and EROI as critical indicators of energy recovery efficiency, considering the entire lifecycle of OFPV systems.

  4. (4).

    Comparing the results with existing literature on ER of fossil fuels and conventional PV systems highlights the importance of incorporating LCA or LCEA into ER assessments.

  5. (5).

    Investigating the impact of recent PV technology advancements on EPBT and EROI to provide insights for investors and policymakers.

  6. (6).

    Providing recommendations and insights for investors and policymakers regarding the feasibility and sustainability of OFPV projects and other PV deployments.

Findings of the Inventory Analysis

In this step, the authors extracted the recent 180-month meteorological data, the technical specifications for high-efficiency solar modules [35], and the organization’s primary standard and secondary activities.

Study Boundary Setting

By defining the following boundaries, the study can effectively address the outlined objectives and provide valuable insights into the energy production potential and sustainability of the OFPV system, contributing to informed decision-making by stakeholders in the renewable energy sector. We can outline the boundary setting for the OFPV as follows:

  1. (1).

    Research Objective: The study aims to comprehensively evaluate the energy production potential and sustainability of OFPV systems over 30 years.

  2. (2).

    Scope of the Study:

  1. a.

    Time Series Analysis: We are conducting a time series analysis to forecast energy production patterns of OFPV systems over 30 years.

  1. b.

    LCEA: This study conducts a comprehensive LCEA to assess the energy inputs and outputs throughout the entire OFPV system’s lifecycle.

  2. c.

    Critical Indicators Evaluation: We are evaluating EPBT and EROI as critical indicators of energy recovery efficiency, considering the complete lifecycle of OFPV systems.

  3. d.

    Comparison with Existing Literature: The study results are compared with existing literature on the ER of fossil fuels and conventional PV systems, emphasizing the necessity of incorporating LCEA in ER assessments.

  4. e.

    Technological Impact Assessment: We are investigating the influence of recent advancements in PV technology on EPBT and EROI to offer valuable insights for investors and policymakers.

  5. f.

    Recommendations and Insights: We provide actionable recommendations and insights for investors and policymakers regarding the feasibility and sustainability of OFPV projects and other PV deployments.

  6. g.

    Study Limitations: The study will focus specifically on OFPV systems, which may not directly apply to other types of solar technologies. Assumptions and uncertainties in data inputs and modeling techniques may affect the accuracy of the forecasts and assessments. External factors such as policy changes, market dynamics, and technological advancements may influence the validity and relevance of the study results over time.

Time-Series Trend and Auto Correlation Function (ACF)

Figure 9 presents the trend graph of 180 monthly time series, comprising five thousand four hundred seventy-nine data points on insolation, sunshine hours, and radiation amount. When considering a significance level of α = 5%, the trend sign value (T) derived from the Mann[61]-Kendall [62] trend test is 2, slightly exceeding 1.96. It suggests that the trend aligns with the null hypothesis, indicating a consistent upward trend in the tested time series [63].

Fig. 9
figure 9

Monthly Time Series Trend Graph

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Researchers can generate an auto-correlogram graph by converting the data value and computing the correlation between the original and lagged values. This process helps determine whether the data will converge. Figure 10 displays the autocorrelation for the 180 sample data presented in Fig. 9. It illustrates that the autocorrelation gradually converges and approaches zero after 130 lags through data transformation and fitting. The results of the Mann-Kendall and autocorrelation tests align, confirming the correlation between the original and lagged data [64].

Fig. 10
figure 10

Auto-Correlogram

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LCEA Analysis

Although power generation depends on management and climatic factors, including typhoons and earthquakes, equation 5 yielded a total energy production of 5435 GWh of electricity over the span of 30 years [65].

$${\mathrm{P}}_{\mathrm{p}}\equiv {\mathrm{C}}_{\textbf{inc}}\left(\mathrm{kWp}\right)\ \mathrm{x}\ {\mathrm{G}}_{\textbf{ph}}\ \left(\mathrm{h}/\mathrm{day}\right)\ \mathrm{x}\ \left(1+\mathrm{n}\right)\ \mathrm{x}365.25\ \left(\mathrm{day}/\mathrm{year}\right)\ \mathrm{x}\ 30\mathrm{years}\ \mathrm{x}\ {\mathrm{S}}_{\textbf{se}}\ \mathrm{x}\ \left(1-{\mathrm{D}}_{\textbf{dr}}\right)\ \mathrm{x}\ \left(1-{\mathrm{M}}_{\textbf{sdt}}\right)$$
(5)

Pp: 30 years of power production.

n: diode ideality factor (based on 11% [32].)

Cinc: the solar module installation capacity(kWp).

Gph: practical daily electricity generation hours.

Sse: system efficiency (based on 75%, considering power loss of components like inverters, transformers, and wiring [3]).

Ddr: decay rate of solar modules (decrease by about 1% annually in 30 years [66].)

Msdt: system downtime (Based on 5% [67]).

Activities related to product production and various departments primarily contribute to power consumption, encompassing energy utilization across different areas and the percentage of occupancy energy attributed to facilities, which includes production and air conditioning power consumption. Energy distribution and emissions from materials adhere to the computational procedures outlined in the Product category rules (PCRs). The analysis reveals that the production power for 12,345 modules amounts to 2.5GWh. In contrast, we record air conditioning power consumption at 71.1MWh (0.071GWh), totaling approximately 2.6GWh (Table 2). Consequently, the power requirement for producing 574,603 modules (181MWp) amounts to about 119.7GWh based on the specified proportions. When factoring in the additional 50.3GWh (1 MJ/Wp) essential for creating the exact wattages of solar cells [11], a total of 170GWh is needed to manufacture 181MWp solar modules. Considering a 25% power loss from system components during the operational lifespan of 30 years, this sum equates to approximately 1358.8 GWh.

Table 2 Table of Solar Module Electricity Consumption [68]
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ER Indicators Calculations

When examining the feasibility of a new PV project, investors should calculate the project’s EPBT and EROI. EPBT explains the time in a power station’s electricity generation equivalent to its production. Researchers typically use years as the unit for EPBT measurement. A shorter payback period indicates better energy recovery. Equation 6 shows how to find the energy payback time (Ppb).

$${\mathrm{P}}_{\mathrm{pb}}={E}_{ir}\ \mathrm{x}\ \left({\mathrm{E}}_{\textbf{yout}}-{\mathrm{E}}_{\textbf{ylc}}\right)^{-1}$$
(6)

Eir represents the energy required to provide that energy, Eyout represents the yearly energy production during the FPV’s lifecycle and Eylc represents the yearly energy consumed during the FPV’s lifecycle.

Equation 6 allows us to achieve the Ppb (including solar cells [11]), which is about 1.25 years. The park’s insolation is 1278.4 kWh/ m2• year; after adjusting the insolation factor, its EPBT is 0.94 years under 1700 kWh/ m2• year, prevailing Bhandari et al. (2015) [69].

EROI is a practical investment assessment index in energy economics and ecological energetics. It expresses the ratio between energy produced by equipment (Eout) and power consumed to create that output (Eir). Equation 7 shows the balance between the available energy resources and the specific number of energy sources provided.

$${\mathrm{E}}_{\textbf{roi}}=\left({\mathrm{E}}_{\mathrm{out}}-{\mathrm{E}}_{\mathrm{lc}}\right)\ \mathrm{x}\ {{\mathrm{E}}_{\textbf{ir}}}^{-\textbf{1}}$$
(7)

When EROI>1, the total energy output (Eout-Elc) is greater than the input energy (Eir), indicating that the energy is efficient. The higher the EROI value, the higher the efficiency of energy output. The difference between the total energy output and energy input energy must be more dominant than one since net energy is equivalent to EROI-1. Equation 7 shows that EROI is about 31.9, after considering the insolation factor, which aligns with the part of the cap of the previous research [3].

The ECEC indicates GHG emission management status. Taiwan has set goals to control ECEC in stages since 2005. Taiwan’s figure was 0.509 kg CO2e/kWh in 2021 [65], slightly increasing by 1.4% compared to 2020. It combines the number into sales according to direct supply, public electricity transfer, or clean energy, showing a downward trend since 2017 (Fig. 11) [70].

Fig. 11
figure 11

Graph of carbon emission coefficient of electricity over the years [70]

Full size image

Equation 8 estimates the CO2 emitted volume per kilowatt hour (kWh) by dividing the fuel depleted by Taipower, synergy industries, and private power plants by the total power yield based on the Electricity Industry Law on ECEC description [71].

$$\mathrm{ECEC}=\left({\mathrm{CO}}_{\textbf{2}\textbf{tpc}}-{\mathrm{CO}}_{\textbf{2}\textbf{el}}\right)\mathrm{x}\ {\mathrm{CO}}_{\textbf{2}{\textbf{t}}}{^{-\textbf{1}}}$$
(8)

CO2tpc represents the power generation industry, and self-use energy producers sell electricity carbon emissions to public electricity sales, CO2el to the electricity carbon emissions borne by the loss, and CO2t to the total electricity sales of public electricity sales.

According to Taiwan’s ECEC (0.509 CO2e/kWh) in 2021, the CO2 emission reduction effect over a 30-year lifespan achieved approximately 2766.4 kt. This paper uses US$19 per ton, the same as Switzerland’s [72], so the carbon credit benefits about US$52.6 million.

Discussion

Brockway et al. (2019) delivered that fossil fuels’ EROI may be much closer to that of renewable energies than previously expected. On the other hand, In their study, Bhandari et al. concluded that the mean harmonized EROI and EPBT varied (2015) from 8.7 to 34.2 and 1.0 to 4.1 years, respectively, for the various PV technologies. However, with the advancement of PV technology, recent research has not addressed its updated ER, which has increased public concerns about renewable energy ER. It is not conducive to the PV business. Therefore, it is essential to re-investigate it to provide PV-involved stakeholders with decision-making.

Indeed, discrepancies exist based on the findings of previous studies on EBPT and EROI. Many factors affect the study results, like system installation scale, module and system efficiencies, installation location, system lifespan, and low-light effects. It is the authors’ motive in conducting this study. It proposes clarifying the ER indicators after PV technology innovation has significantly improved.

Mann-Kendall and autocorrelation test results show the detected trend in data at the confidence interval, implying that we cannot reject the estimated time series results. The PV embedded and lifecycle energies conducted by the LCEA process reveal that compared with conventional fuels, PV ER indicators are more significant. It is imperative to clarify this to the public. Alternatively, it will not be conducive to develo** the PV industry.

From a sustainability perspective, solar energy outperforms fossil fuels due to its lower environmental impact, excellent social benefits, and improved economic viability [73]. Governments must incentivize the transition to renewable energy sources like solar to mitigate climate change, improve public health, and create a more resilient and sustainable energy system. To analyze the sustainability of fossil fuels and solar energy, the investigators mainly focus on their environmental, social, and economic impacts:

(1) Fossil Fuels:

  1. a.

    Environmental Impact: Fossil fuels remarkably contribute to GHG emissions and air pollution, leading to climate change and health issues. In addition, their extraction and burning also cause habitat destruction, water contamination, and ecosystem disruption [74].

  2. b.

    Social Impact: Dependence on fossil fuels can lead to geopolitical conflicts due to resource competition, as seen in many parts of the world. Additionally, communities near fossil fuel operations often suffer from health problems due to air and water pollution [75].

  3. c.

    Economic Impact: Fossil fuel prices can be volatile due to supply disruptions, geopolitical events, and market speculation. Transitioning away from them may require considerable investments in retraining workers and transforming energy infrastructure [76].

(2) Solar Energy:

  1. a.

    Environmental Impact: Although solar panels have an environmental footprint during production and disposal, their operation has minimal environmental impact. Since solar energy is renewable and generates electricity without emitting GHGs, it is crucial in combating climate change [77].

  2. b.

    Social Impact: Solar power decentralization empowers individuals and communities to produce energy, reducing reliance on centralized utilities. Increased adoption of solar energy can create local jobs in installation, maintenance, and manufacturing [78].

  3. c.

    Economic Impact: Solar energy costs have decreased steadily, making it increasingly competitive with fossil fuels in many regions. Investments in solar energy can stimulate economic growth, attract new industries, and improve energy security [79].

Grid flexibility is a crucial aspect of smart grid integration, allowing for dynamic adjustments to match energy production with demand fluctuations. This flexibility is essential for accommodating variable renewable energy sources like solar and wind and managing changes in demand patterns throughout the day [80]. Load management strategies like demand response programs, energy storage systems, and smart appliances can help balance supply and demand on the grid, strengthening overall efficiency and reducing the reliance on traditional fossil fuel generation. Integrating the intelligent grid incorporates advanced technologies and strategies into the traditional power grid infrastructure. It optimizes energy production, distribution, and consumption. Leveraging digital communication and automation technologies helps improve the grid’s efficiency, reliability, sustainability, and flexibility [81].

Fossil fuels, despite their environmental concerns, continue to play a significant role in power generation due to their reliability and affordability. In the context of smart grid integration, fossil fuel power plants can provide baseload power to meet constant demand. Simultaneously, sustainable energy sources such as solar and wind can complement them by supplying variable or intermittent power. These power sources can be integrated into an intelligent grid through advanced monitoring, control, and management systems that enable optimal utilization of resources based on real-time demand and supply conditions [82].

FPV systems represent a novel approach to solar energy generation. They install solar panels on water bodies such as lakes, reservoirs, or oceans. These developments offer several advantages, including increased efficiency due to water cooling, conservation of land space, and potential synergy with hydropower facilities. They can contribute to grid flexibility in an intelligent grid context by providing additional renewable energy capacity that can be quickly deployed and scaled [83].

Synthesizing fossil fuels and floating PV systems into a sustainable and efficient energy system requires a holistic approach considering environmental impact, economic viability, and technological innovation. By combining diverse energy sources and leveraging advanced grid management techniques, intelligent grid integration can help transit towards a more sustainable and robust energy infrastructure while meeting the evolving needs of modern society [84].

Conclusions

This paper utilized time series and LCEA analyses to conduct a case study, exploring PV ER indicators and examining whether PV technology creation involves ER indicators. The authors conclude that setting boundaries in LCEA and PV technology creation impacts EPBT and EROI. Concerning OFPV deployment, researchers will discover better PV ER than fuel energies when defining LCEA boundaries, more specifically, echoing the conclusion of Brockway et al. (2019).

Due to the LCEA’s scope of the study, the authors do not consider the final disposal phase of the system. Nevertheless, the power depletion in the removal stage is insignificant (less than 1% of the LCEA cut-off rule) compared to the system’s lifespan. The solar cell’s fabrication is in the manufacturer’s overseas factory, so the investigation range is limited to modules. However, to present the LCEA consequences more accurately, the investigators added previous findings in the study [11]. In future work, they suggests implementing the ER investigation of the whole production chain in vertical segments to increase the integrity of LCEA assessments and the validity of PV’s ER. The approach presented in this paper and the study results may facilitate the related studies of the ER more practically and help investors’ decision-making when funding future OFPV or other PV projects.