3.4.1. Economic feasibility.

Cost-benefit analysis:

The cost-benefit analysis accounts for maintenance over the system’s lifetime, considering installation costs, annual energy savings, and maintenance costs. Let’s break it down:

1. Initial Solar Panel Installation Cost:
   • Cost per kW: $1,000
   • System Size: 1 MW (1,000 kW)
   • Total Installation Cost: $1,000,000
2. Annual Energy Production:
   • Average Daily Production: 4,320 kWh/day
   • Annual Production: 4,320 kWh/day ×  365 days =  1,576,800 kWh/year
3. Energy Cost Savings:
   • Electricity Cost: $0.10 per kWh
   • Annual Savings: 1,576,800 kWh/year ×  $0.10/kWh =  $157,680/year
4. Maintenance Costs:
   • Solar systems typically incur maintenance costs ranging from 1% to 2% of the installation cost
   • per year. Assuming an average of 1.5%:
   • Annual Maintenance Cost: 1.5% of $1,000,000 =  $15,000/year
5. Total Annual Benefit (Savings - Maintenance Costs):
   • Net Annual Savings: $157,680 - $15,000 =  $142,680/year
6. Payback Period (With Maintenance Costs Considered):
   • Payback Period:

The payback period is approximately 7.01 years, a reasonable investment timeframe for a large infrastructure project. Solar power integration would provide significant energy cost savings over the long term, contributing to reduced operational expenses after the payback period.

Lifetime maintenance costs (25 years):

• Total Maintenance Cost: $15,000/year × 25 years = $375,000

Lifetime net savings:

Over the system’s 25-year lifespan, the total net savings will be:

Factoring in the maintenance costs extends the payback period marginally to 7 years or so, with the system providing a net savings of about $3.57 million over 25 years of operation; that investment is financially viable over an extended period.

4.3.1 Assessment of grid integration system comparison.

The comparison of the grid integration system indicates significant differences between on-grid, off-grid, and hybrid systems. On-grid systems depend on a reliable, affordable grid. Off-grid systems offer total energy independence and are perfect for remote locations, but this comes with high initial investment and reliability limited by storage capacity. Hybrid systems, with mid-way grid dependency and energy autonomy, have moderate initial costs. They are dependable and ideal for backing up power in an urban landscape. Each system’s applicability depends on national conditions, economics, and the desired energy independence and reliability level.

5.2.1 Land use.

• Solar Panel Installation: Utility-scale solar farms need a lot of land, particularly when set up in street performance. For urban metro rail systems, the designs can be integrated with solar panel installation options on station rooftops or existing rail tracks, allowing for the minimization of land use.
• Land Efficiency: Using solar panels on unused empty urban space (rooftops or parking areas) ensures effective land use. This is especially important in dense urban environments, where available land is at a premium and expensive.
• Comparative Impact: Although solar installations may take up space, they use much less land than fossil fuel plants, whose fuels must extracted, transported, and stored, up to a thousand times less in some cases.

5.2.2 Water consumption.

• Solar Power versus Traditional Energy: Solar power dramatically reduces water consumption compared to coal or natural gas plants, which require a lot of water to cool and operate. Traditional thermal power plants consume about 500 to 1000 gallons of water for every megawatt-hour (MWh) of electricity produced, whereas solar panels, once installed, use minuscule amounts of water.
• Water Consumption in Solar Panel Cleaning: The main water usage for solar panels occurs when cleaning is required to keep them clean & efficient, which is more common in dusty or polluted environments. However, this water use is nothing compared to operational water use at fossil fuel plants.
• Water Savings: Using solar power to reduce electricity demand in urban transport can save considerable water, as electricity generation in water-poor regions must compete with agricultural and residential water demands.

5.2.3 Air quality.

• Reduction in Pollutants: Solar power generation reduces pollutants other than CO2, such as sulfur dioxide (SO2), nitrogen oxides (NOx), and particulate matter (PM). These pollutants can aggravate smog, air quality, and respiratory ailments in urban areas. Switching to solar power in metro rail systems reduces these emissions, improving air quality.
• Reducing Urban Heat Islands: Rooftop solar can help mitigate urban heat islands by absorbing solar radiation that would otherwise heat the city. This cools local air and limits the energy demand for air-conditioning buildings.

5.2.4 Waste and end-of-life considerations.

• Solar Panel Lifespan: The average lifespan of solar panels is 25-30 years. These generate e-waste that requires management at the end of its life. Recycling and disposal of these two strategies are necessary to minimize these systems’ long-term environmental effects.
• Comparative Analysis: The risk of pollution from solar panel waste is lower than the long-term pollution associated with fossil fuel power plants. Pollution is generated during operation, and waste products, such as ash and mining waste, are wasted.

5.2.5 Biodiversity.

• Minimal Impact on Natural Habitats: Solar panel development has a far lower impact on natural habitats and biodiversity than many traditional energy projects, like hydroelectric dams or fossil fuel extraction, making panel installation on existing town infrastructure especially low-impact.
• Ecosystem Considerations for Ground-mounted Solar: Implementing sustainable land practices, such as agro-voltaic, which involve co-locating agriculture with solar farming, can minimize adverse effects on ecosystems while maximizing land use.

The discussion often focused only on the CO₂ emissions factor, then the solar-powered metro rail system has better environmental implications and would save on land and water, improve air quality, and minimize biodiversity impact. However, these benefits must be carefully planned, including maximizing space productivity, sustainable water use, and, at end-of-life, recycling solar panels to maximize these benefits. In summary, solar power integration into urban transportation systems contributes to achieving sustainability goals and tackling multiple environmental challenges currently facing cities.

5.4.1 Social benefits overview.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

5.4.2 Quantified social impacts.

• Job creation: 10 MW installation of large-scale solar system, for example, in metro rail, generates 150-200 jobs per ten MW; this will add to the economy.
• Air Quality: Decreased reliance on fossil fuels can lead to lower levels of particulate matter (PM2. 5) and NO_x emissions from 10% to 15%, leading to a cleaner urban environment.
• Mitigation of urban heat: solar panels can help reduce the urban heat island effect, lowering surface temperatures by around 5-10% in dense metro areas.

6.1.1 Maximize solar power generation.

The objective is to maximize the amount of solar power produced during the evaluation period [0, T]:

(14)

Equation (14) describes the problem of maximizing solar power generation for an evaluation period of [0, T]. The goal is to maximize the integral of Esolar(t), the solar power generated at time t. This goal is crucial in maximizing energy generation at solar systems.

6.1.2 Minimize unmet energy demand.

The optimization minimizes the difference between energy demand and the total supply from both solar power and energy storage:

(15)

Equation (15) aims to minimize the difference between the energy demand D (t) of the metro rail system and the total energy supplied from solar Power P solar (t) and energy storage P ess (t) over the period [0, T]. By minimizing this integral, the optimization ensures that the energy supply closely matches the demand, reducing unmet demand and improving system reliability. This objective helps balance energy generation and storage to meet the metro rail system’s operational needs efficiently.

6.1.3 Minimize grid dependency.

The optimization also aims to decrease dependence on the external power grid, reducing the amount of energy imported from the grid:

(16)

Equation (16) aims to minimize the total energy exchanged with the external power grid in the interval [0, T]. Here, G (t) represents the power flow between the metro rail system and the grid at time t, where positive values indicate energy drawn from the grid and negative values indicate energy supplied back to the grid. By minimizing , the optimization reduces the system’s dependency on the grid, promoting greater energy self-sufficiency through solar power and storage.

6.1.4 Ensure reliability during low-sunlight periods.

To maintain system reliability under conditions of reduced sunlight for long periods (winter or overcast days) that form a constraint in keeping a backup to the grid and storage reserves in sufficient volume:

(17)

Equation (17) ensures that even in low solar hours, where solar power generation may not be enough to meet the system’s demand, the charge and grid combined energy supply will be able to satisfy the system’s peak demand. This equation for low sunlight hours defines Dpeak(t) as the peak energy demand at time t, Pess(t) as the energy supply from storage, and G(t) as the grid power consumed at time t. This equation ensures that the metro rail will have sufficient power to maximize its energy needs during important hours when solar generation will be less.

6.2.1 Energy storage capacity constraints.

The energy storage system is constrained by its maximum capacity C j:

(18)

The constraints on the state of charge of the energy storage system described are in equation (18). The state of charge over time t must be between 0 and the maximum capacity of the battery’s maximum capacity C j. This allows us to never deplete a storage system j too much to the point where it can no longer store or discharge energy. This limits storage space, preventing the system from filling up or running out entirely, and keeps the operation within realistic constraints.

6.2.2 Environmental constraints on solar panel efficiency.

The efficiency of solar panel as a function of temperature T(t) and solar irradiance I(t):

(19)

A solar panel system’s output energy, E solar (t), is simulated in equation (19), considering the temperature change and irradiance for efficiency. The energy produced at the time, t, is given by the panel’s efficiency surface area Ai, and the function fi (T(t), I(t)) that accounts for environmental factors, such as temperature T(t) and solar irradiance I(t). This equation illustrates the extent to which real-world conditions impact the power capacity of the panel.

6.2.3 Cost Constraints.

The optimization is subject to total cost constraints for installing solar panels and storage systems, including upfront capital and maintenance costs. The total cost of installation is as follows:

(20)

The total cost (C_total)of installing and maintaining the solar panel and storage system, including savings from solar power (20). The cost includes the installation cost (C_install) and the annual cost of maintenance (C_maint), which then subtracts the energy savings(S_energy) produced by the system over time. This equation ensures that the economic benefits from solar power offset part of the installation and maintenance costs, optimizing the project’s financial feasibility.

6.2.4 Reliability constraints.

As the metro rail system must be able to handle peak energy requirements, the system must consistently satisfy all peak energy needs, which may include all generating units and stored energy that can meet unit load.

(21)

Equation (21) ensures that the total energy from solar power (P solar (t)) and energy storage (P ess (t)) meets the peak energy requirement (D peak (t)) of the system. This constraint also ensures that the system can consistently provide sufficient energy during periods of high demand, allowing for reliable operation throughout peak load periods.

6.2.5 Seasonal solar power generation constraint.

Solar power generation is based on solar irradiance, which is season-dependent. To model this variability, use I(t) as a time-varying function describing solar irradiance, accounting for intervals of less sunlight:

(22)

Equation (22) calculates the solar power generated at time t, Esolar (t), based on various factors affecting solar panel performance. Where η is the efficiency of the solar panels, A is the total surface area of the panels, and I(t) represents the solar irradiance at time t. The function f(T(t), I(t)) adjusts for environmental influences, such as temperature T(t), to account for how these factors impact panel performance. This equation provides a detailed way to model the solar power output under varying conditions.

7.1.1 Effective combination of solar panels and storage systems.

The advanced model-based analysis is required to achieve the optimum balance between solar panels’ energy generation capacity and energy storage systems efficiency, based on all energized agents’ cost efficacy, and encourage a feedback loop for the overall system optimization.

Comparison of solar panel technology: Analyze simulation and real-world testing of monocrystalline, polycrystalline, and thin-film panels regarding efficiency, cost-effectiveness, and the urban environment. It evaluates the following metric(s):

• Efficiency under Urban Conditions: High temperatures and shading impact panel sorts differently. Monocrystalline panels also perform better in urban conditions due to their higher efficiency, whereas thin-film panels are more shade-tolerant but produce less energy per area.

Comparison of storage system: Energy storage is the key to solar intermittent moderation. Lithium-ion batteries, flow batteries, and super capacitors are compared based on charge/discharge efficiency, energy density, cost, and degradation rates. The comparison looks at:

• Charge/Discharge Cycles: Lithium-ion batteries are more responsive and have a higher efficiency than flow batteries but have a lower cycle life, making them more suited for shorter storage capabilities.

Fig 13 compares solar panel and energy storage technologies based on their efficiency, cost, energy density, degradation rate, and suitability for metro rail systems. Monocrystalline panels, with 18% efficiency, cost $0.60/kWh, and a degradation rate of 1.5% per year, are highly suitable for metro rail systems due to their high performance. Polycrystalline panels have moderate suitability at 15% efficiency and $0.50/kWh, while thin-film panels have only 10% efficiency and higher degradation, particularly in shaded areas. Among storage systems, lithium-ion batteries offer high efficiency (95%) and energy density (250 Wh/kg), making them well-suited for metro rail applications despite a 2% yearly degradation. Flow batteries, with lower efficiency (85%) but longer-duration storage potential, are also suitable, especially for extended energy needs. Super capacitors, with nearly 99% efficiency, are best for short bursts of energy but have a lower energy density, making them ideal for short-duration storage in metro systems. Each technology’s performance, cost, and degradation play key roles in optimizing energy solutions for metro rail.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 13. Comparison between solar panel and storage systems.

https://doi.org/10.1371/journal.pone.0320016.g013

7.1.2 Optimal grid integration and off-grid operation.

The analysis evaluates the best configuration for grid integration, hybrid systems, or complete off-grid operation. The goal is to maximize self-sufficiency while minimizing grid dependency and operational costs.

On-Grid, Off-Grid, and Hybrid configurations:

• On-Grid: The system can draw energy from the grid during peak demand periods and sell excess solar power back to the grid. This configuration is highly dependent on grid availability and tariffs.
• Off-Grid: Relies entirely on solar power and storage systems. It offers complete independence but requires larger storage systems to handle energy demand during non-sunny periods.
• Hybrid: A combination of on-grid and off-grid configurations, where solar power and storage handle the base load, the grid is used as a backup during energy deficits. A solar-grid hybrid configuration takes several key steps toward maintaining grid stability:

1. Energy Storage: Batteries can store surplus energy produced by solar systems and release that energy when solar is low (balancing demand and supply).
2. Real-Time Monitoring: Modern energy management systems monitor solar output and grid demand in real-time to facilitate seamless transitions.
3. Grid Synchronization: Inverters minimize the disruption risk by synchronizing solar power with grid voltage and frequency.
4. Demand Response: Non-elastic loads can turn down with solar fluctuations, which aids the grid.
5. Hybrid Inverter Control: Inverters regulate power flows among solar, storage, and electric grids while providing a smooth transition between sources.

These measures help maintain grid stability during transitions between solar and grid power.

Fig 14 compares performance metrics for grid integration in on-grid, off-grid, and hybrid systems for metro rail applications. On-grid systems show 25% grid dependency and have the lowest capital cost at $1.0 million, but they offer only 75% energy self-sufficiency and face an unmet demand of 5,000 kWh/year. Though fully self-sufficient (100%), off-grid systems have the highest capital cost of $1.8 million and the most significant unmet demand (20,000 kWh/year) due to the challenges of entirely relying on solar and storage. Hybrid systems strike a balance, with 10% grid dependency, 90% self-sufficiency, and a moderate capital cost of $1.5 million. The lower unmet demand of 10,000 kWh/year has become reliable and cost-efficient for displacing grid energy and providing a stable and continuous energy flow.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 14. Performance metrics for grid integration.

https://doi.org/10.1371/journal.pone.0320016.g014

The optimal hybrid setup is the one that maximizes energy self-sufficiency at 90% and limits dependency on the grid for utility top-ups while minimizing unmet demand for these services and aggressive capital costs. The utility of off-grid systems is less attractive for metro rail because off-grid storage is costlier, and demand tends to be higher and unmet for longer durations during extended cloudy periods.

7.2.1 Carbon emission reductions.

The solar power launches versus the carbon emissions of average grid electricity.

Fig 15 compares carbon emission differences in on-grid, off-grid, and hybrid solar-integrated metro rail systems. 25% share of solar power in an on-grid case, 750,000 MWh of solar power is generated, which avoids 375,000 tons CO₂ emissions with an emissions factor of 0.5 kg CO₂/kWh. With an off-grid system exclusively powered by solar, the factory produces 3 million MWh, eliminating 1.5 million tons of CO₂. Using such a hybrid system with a 90% solar share gives 2,700,000 MWh of generation and avoids 1,350,000 tons of emissions. As the output analysis shows, off-grid systems have the most significant carbon emissions offset if managed national emission limit compliant. In contrast, hybrid systems achieve a good trade-off in grid independence and environmental benefits.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 15. Carbon emission reduction.

https://doi.org/10.1371/journal.pone.0320016.g015

7.2.2 Energy savings.

Cost savings due to energy are assessed based on the capacity of solar produced and the cost of displaced power from the grid.

Fig 16 compares electricity cost savings estimates under varying scenarios of solar power utilization for metro-related railways. Under the on-grid scenario, with 25% of the total energy coming from solar, 750,000 MWh of solar power is generated, resulting in $90 million in savings, with the electricity costing $0.12/kWh. In the off-grid case of 100% solar power, 3,000,000 MWh are generated with savings of $360 million. For another hybrid case with a solar power share of 90%, 2,700,000 MWh is produced with annual savings of $324 million. However, this analysis also shows that scaling up solar integration helps significantly reduce energy costs, especially for off-grid and hybrid systems.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 16. Energy Cost Savings.

https://doi.org/10.1371/journal.pone.0320016.g016

7.3.1 Sensitivity analysis.

Sensitivity analysis can help to identify the most influential variables on system performance (e.g., solar irradiance, storage efficiency, grid interaction, etc.). The most sensitive variables are those with the highest impacts on energy generation, storage, and costs.

Fig 17 shows the Sensitivity analysis effect on energy generation and cost savings for solar metro rail systems. Solar irradiance was the most significant factor, contributing the highest proportion of variance for energy generation (60%) and cost savings (50%), suggesting the availability of sunlight is a significant determinant of system performance. Panel efficiency is also a key component and accounts for a 25% increase in energy generation and a 30% increase in cost savings, showcasing the importance of efficient solar technology. The impact of storage efficiency is medium, with a 10% effect on energy generation and 15% on cost savings--furthering the argument for reliable storage systems to optimize energy generation outputs. Grid tariff rates play the least role, influencing energy generation and cost savings by 5%, indicating that while tariffs matter, they are not as important as more technical elements such as irradiance and efficiency. Optimizing solar panels and storage efficiency and maximizing solar exposure can significantly increase energy output and provide financial benefits.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 17. Sensitivity analysis.

https://doi.org/10.1371/journal.pone.0320016.g017

According to the analysis, monocrystalline panels and lithium-ion batteries are the most effective technologies for harnessing solar power and storage in metro rail systems. Hybrid grid install approaches are optimized for energy independence versus cost, achieving a 90% reduction in grid reliance. Especially in a hybrid and off-grid setup, a massive decrease in CO₂ emissions is possible, and in a hybrid system alone, up to 1.35 million tons of CO₂ can be avoided each year. Solar irradiance and panel efficiency emerge as the two most influential factors from sensitivity analysis. These findings further endorse the impact of tech soup on sustainability, operational cost reduction, and the implementation of environmental goals with solar-powered metro rail systems.

7.3.2 Statistical validation.

Sensitivity analysis calculates confidence intervals (CIs) for the percentage impacts across different parameters. Sensitivity analysis shows the effect of various parameters on energy generation and cost savings of solar-powered metro rail systems. Confidence intervals (CIs) typically assess sensitivity result reliability through statistical validation. Confidence intervals provide a range in which the true impact of each parameter is allowed to evaluate the robustness of the results. Analysis of statistical validation explanation:

• Solar Irradiance: The estimated effect on energy generation is 60%, with a 95% confidence interval of [55%, 65%]. This means 95% confidence the true impact lies between these values. The 50% estimate is associated with a CI of 45% to 55%, which is relatively tight and reliable for cost savings. The CI for energy production and cost savings is a reasonably tight range. It indicates a high degree of confidence in solar irradiance as a highly influential factor. The range suggests limited uncertainty, so the results are robust across varying scenarios of solar exposure.
• Panel Efficiency: The impact on energy generation is 25%, with a CI of [20%, 30%], suggesting moderate confidence in this range. The effect on cost savings is 30%, with a CI of [25%, 35%], showing that increasing panel efficiency significantly affects both energy output and financial savings. The CI for panel efficiency is moderately broad, reflecting some uncertainty, particularly for energy generation. However, the CIs indicate that improvements in panel efficiency would result in consistent benefits to both energy generation and cost savings.
• Storage Efficiency: The CI for storage efficiency’s 10% impact on energy generation is [8%, 12%], with a similar precision for the 15% cost savings estimate at [12%, 18%]. The CIs for storage efficiency suggest that the estimated impacts are reliable. The higher sensitivity to cost savings highlights the importance of efficient energy storage in reducing overall costs.
• Grid Tariff Rates: The impact is relatively low at 5%, but the CIs are quite narrow at [4%, 6%], indicating consistent outcomes across different scenarios. The impact of grid tariff rates is minor and well-contained within a tight range, confirming that while grid rates affect cost savings, their role is less significant compared to factors like solar irradiance and panel efficiency.

This analysis highlights the points of optimizing solar irradiance utilization and improving the efficiencies of the panels and storage systems to maximize the performance of the solar-powered metro rail systems. The confidence intervals from this sensitivity analysis provide a statistical measure of confidence, or precision, of the impact estimates. The primary role of solar irradiance and plate efficiency as the key components to energy generation and cost savings is validated. Panel and storage technology advancements will keep improving the overall system efficiency. Generally, the results from the analysis substantiated the findings with significant confidence in the sensitivity percentages.