Techno-Economic Feasibility of Installing Wind Turbines in the Region of Eastern Thrace

Abstract

A cornerstone of climate action plans around the world, wind power is increasingly recognised as a primary source of clean, sustainable energy. Amidst the escalating challenges of global climate change, wind energy provides an essential balance, enabling environmental progress without compromising economic resilience. However, the significant investment costs associated with wind turbines require careful evaluation alongside the projected energy output to ensure both financial viability and operational efficiency. Given the localised nature of wind resources, it is essential that analysis and feasibility studies are carried out on a regional scale to take account of geographical and climatic variations, thereby maximising the effectiveness of wind energy deployment. This study presents a comprehensive analysis of wind turbine deployment in the Eastern Thrace region, using region-specific energy data and wind characteristics together with performance data from twenty comparable installations in the area. A Monte Carlo-based numerical simulation approach using probabilistic models was applied to provide valuable insights into the financial viability of wind energy investment in the region. The results show a strong potential for cost-effective wind power generation in Eastern Thrace, with an estimated 90% probability of achieving payback within five years. These results underline the economic and environmental benefits of wind energy, confirming its attractiveness to investors and its role as a key driver of sustainable development in the region.

1. Introduction

Energy production is a cornerstone of economic and social development, but it is increasingly recognised that existing energy production and consumption systems have significant environmental costs. These traditional energy systems, particularly those based on fossil fuels, contribute to air, water and soil pollution at local, regional and global scales. The environmental damage associated with the extraction, processing and consumption of fossil fuels, as well as their finite nature, has led to growing concern about the sustainability of these energy sources, particularly with regard to the energy needs of future generations.

In 2023, global wind power installations reached a record high, with 116,065 MW of new capacity added in just one year. This milestone brought global wind power capacity to a total of 1,047,288 MW by the end of the year, over 1 million MW (Figure 1). These figures are in line with the World Wind Energy Association’s (WWEA) forecasts for 2023. This achievement underlines the accelerating utilisation of wind energy worldwide, driven by the growing demand for renewable energy solutions. This growth reflects both technological improvements in turbine efficiency and the increasing economic competitiveness of wind energy compared to traditional fossil fuel-based power generation.

The development of wind energy is an area of active research and investment, with various studies focusing on different aspects of wind power, from wind speed estimation to the economic viability of wind farms.

The scientific literature on wind energy covers a wide range of topics. Many studies focus on wind speed estimation, as this is a key determinant of the energy production potential of wind turbines [2,3,4,5]. Some have investigated aerodynamic improvements in turbine design to improve energy capture [6,7,8], while others have examined the wind energy generation potential of different regions and countries [9,10,11]. Other research has focused on the financial and operational aspects of wind farm investments, particularly with regard to decision-making processes related to the feasibility and profitability of wind farms [12,13,14].

A significant body of literature also explores the use of simulation techniques to model the wind energy potential of specific areas and to estimate the cost of energy production. One widely used method is the Monte Carlo simulation technique, which is used to model the uncertainty and variability inherent in wind energy production [15,16,17]. This approach allows researchers and decision-makers to analyse the potential of wind energy by estimating parameters, such as wind speed and energy production, based on historical data or simulated distributions.

Building on this existing body of research, the present study takes a more comprehensive approach by incorporating both technical and economic considerations into an interdisciplinary framework for analysing wind energy investment in the Eastern Thrace region of Turkey. Unlike many studies that focus exclusively on one or the other (e.g., wind speed or economic feasibility), this study combines both aspects to provide a holistic view of the viability of wind farm investments.

In this study, real-world data were collected from 20 different turbines at several wind farms in the Eastern Thrace region. These data, collected over the course of a year, were analysed to assess the wind energy potential of the region and to simulate investment scenarios under different operational and economic conditions. The wind speed distribution was derived from actual measured data rather than estimated using theoretical models or meteorological station data, adding a level of accuracy and relevance to the analysis.

In addition, the study incorporates several key uncertainties that affect wind farm profitability, including wind speed variability, operations and maintenance (O&M) costs and financial variables such as capital investment and energy prices. Using Monte Carlo simulations and other advanced analytical techniques, the study estimates the potential profitability of wind energy investments in the region, providing insights into both the technical feasibility and economic returns of wind energy projects.

2. Modelling Method

In this study, a selection of 20 wind turbines with similar specifications and power ratings were selected from different wind farms located in the Eastern Thrace region of Turkey. The Eastern Thrace region, located in the northwestern part of Turkey, covers over 6000 km² and is known for its diverse topography and wind conditions. The region’s terrain is characterised by elevations ranging from 100 to 500 m above sea level, which can influence local wind patterns and turbine performance. The predominant wind directions in the region are from the north and northeast, influenced by the proximity to the Black Sea and the Aegean Sea. Seasonal variations indicate higher wind speeds during winter and spring, contributing to stable energy generation throughout the year. When compared with other wind-rich regions in Turkey, such as the Aegean and Marmara coastal areas, Eastern Thrace demonstrates a competitive wind potential. While the Aegean region benefits from higher wind speeds in some locations, Eastern Thrace offers a more balanced wind distribution with fewer extreme gusts, which can be advantageous for turbine longevity and maintenance. Additionally, the region’s relatively lower population density and available land provide an opportunity for large-scale wind farm development without significant environmental or social constraints.

The selected wind turbines have a rated capacity of 3.2 MW each, an average overall height of 110 m and rotor blade lengths of approximately 55 m. These turbines were selected for their comparable technical characteristics to ensure consistency in the study’s analysis. The wind farms from which the turbines were selected are strategically located throughout the region, and their exact locations are shown in Figure 2. Figure 3 and Figure 4 show the wind map and wind roses for the region.

For this study, real-time operational data were collected over the course of a full year, with hourly measurements of wind turbine performance recorded by the turbines’ monitoring systems. The data include a wide range of variables, including wind speed, turbine power and other environmental factors that affect wind energy production. This comprehensive dataset provides insight into the performance and efficiency of the turbines under varying regional conditions over an extended period of time.

Based on the data collected, a forecasting model was developed to predict the profitability of wind energy investments in the region, focusing on a 20-year simulation period. Figure 5 illustrates the flowchart of the methodology used in the study. As shown, the research was organised into three distinct phases: definition, establishment and execution.

In the defining phase, the primary goal was to ensure the identification of the key parameters influencing the profitability of wind turbine investments. This was achieved through an extensive literature review and consultation with industry experts. These steps enabled the critical factors—such as wind resource potential, turbine efficiency, capital costs, operation and maintenance costs and electricity market conditions—to be identified as key components of the simulation model. By synthesising information from both academic research and industry insight, a well-rounded understanding of the variables affecting the profitability of wind energy investments was established.

The second phase involved the development of the forecasting model. Several main steps were followed:

1. Determination of key parameters: The most influential variables identified in the definition phase were clearly defined and quantified.

2. Data collection: Relevant data for each of these key parameters were collected from a variety of sources, including historical records, industry reports and proprietary datasets.

3. Data preparation: The collected data were processed, cleaned and organised to ensure consistency and suitability for simulation. This step involved addressing gaps or inconsistencies in the data, normalising the data where necessary and preparing it for input into the simulation model.

The final stage was to run the simulation model. Using the prepared data and defined parameters, the model was run to generate forecasts of the profitability of the wind energy investment over a 20-year horizon. Various uncertainties were taken into account, such as fluctuations in energy prices, changes in wind patterns and potential technological advances in wind turbine efficiency. The output of the simulation provided a comprehensive view of the expected financial performance, which could then be analysed to assess the potential risks and rewards of the investment.

Through these three phases—definition, establishment and execution—a robust forecasting model was created, providing valuable insights into the long-term viability of wind energy investments in the region.

3. Development of the Simulation Model

3.1. Key Input Parameters

For the analysis of turbine performance and economic viability, input variables have been categorised into two main groups: productivity parameters and cash flow parameters. Productivity parameters are defined by technical, financial and geographical factors that influence turbine performance, while cash flow parameters are used to assess the financial feasibility of wind power investments. In order to identify these parameters and facilitate investment decisions for wind farms, data were collected from both operating wind farms and authorised institutions. These data provided a comprehensive basis for assessing the potential of the turbine in terms of both efficiency and profitability. Productivity parameters include various conditions and factors that affect turbine efficiency and energy output. These include technical specifications, maintenance requirements, financial costs associated with turbine operation and geographical factors such as wind conditions and site characteristics, which are known to have a significant impact on energy production.

The cash flow parameters, on the other hand, are essential for carrying out feasibility analyses to assess the financial soundness of the investment. These parameters include the real interest rate for its impact on financing costs, the inflation rate for its impact on long-term cost projections and the unit price of electricity as a critical determinant of revenue. Annual operating costs are included to reflect the recurring costs associated with the wind farm, and the initial investment cost of the turbine is included as it plays a key role in determining capital requirements. By analysing efficiency and cash flow parameters together, a detailed and data-driven feasibility assessment was made.

To ensure that the Monte Carlo simulation accurately represented the variability in the data collected, statistical models were first identified that best approximated the underlying data distribution. This was achieved by performing a curve fitting analysis using EasyFit V.6.0 software. EasyFit automatically evaluates several theoretical distributions and compares them to the empirical data, allowing the selection of distribution types that best fit the observed data patterns. For each variable in the dataset, the software identifies the best-fitting probability distribution model (e.g., normal, log-normal, Weibull or exponential), taking into account measures of fit such as the Kolmogorov–Smirnov, Anderson–Darling and chi-square tests. The software primarily focuses on distribution fitting and nonlinear curve fitting. It includes over 60 predefined probability distributions, such as normal, log-normal, exponential, Weibull, and Gamma, allowing users to fit these models to data. The software uses statistical methods like maximum likelihood estimation to estimate model parameters and provides goodness-of-fit tests, including the chi-squared, Kolmogorov–Smirnov and Anderson–Darling tests, to assess the model’s accuracy.

Additionally, EasyFit supports nonlinear curve fitting, enabling users to fit custom mathematical models, such as exponential or logarithmic functions, using optimization algorithms like least squares. The software also features Monte Carlo simulations for estimating uncertainty in fitted parameters. Overall, EasyFit offers a versatile set of tools for fitting distributions and custom curves to data while ensuring statistical validation.

Once the optimal distribution for each parameter was determined, the associated parameters—such as mean, standard deviation, shape and scale parameters—were extracted. These parameters served as inputs to the Monte Carlo simulation model, ensuring that the simulated scenarios reflected the true statistical properties of the observed data, thereby increasing the reliability and accuracy of the simulation results. To determine the appropriate sample size for a Monte Carlo power analysis, it is essential to first define the key parameters of the study, including the expected effect size, the type of statistical test, the significance level (typically set at 0.05) and the desired power (commonly set at 0.80). An initial sample size estimate is then selected, often informed by prior research or domain-specific guidelines. Following this, a series of simulations are conducted, typically involving thousands of iterations, with data generated based on the predefined parameters. The statistical test of interest is applied to each simulated dataset, and the outcome is recorded to determine whether the null hypothesis is rejected (i.e., whether a statistically significant result is obtained). Once the simulations are completed, empirical power is calculated as the proportion of simulations in which the null hypothesis was rejected. If the resulting power is lower than the target, the sample size is increased, and the process is repeated. Conversely, if the power exceeds the desired threshold, the sample size is reduced. This iterative procedure continues until the sample size produces the desired statistical power, ensuring that the study is adequately powered to detect the specified effect size.

The number of simulations to run in a Monte Carlo analysis is contingent upon the desired accuracy and precision of the power estimate. A common recommendation is to conduct a minimum of 1000 to 5000 simulations to obtain a reliable estimate of statistical power. However, for more complex models or when detecting smaller effect sizes, a larger number of simulations, such as 10,000 or more, may be necessary to ensure greater stability and reduce variability in the results. Increasing the number of simulations generally enhances the accuracy of the power estimate by minimizing random fluctuations across runs. Nevertheless, this improvement in precision comes at the cost of greater computational resources. Thus, a balance must be found between the computational feasibility and the required level of precision for the analysis. In most cases, 5000 to 10,000 simulations provide an adequate level of accuracy, although convergence of the power estimate can be monitored as additional simulations are conducted to ensure reliable results.

Monte Carlo simulation can be effectively applied to multi-criteria decision-making (MCDM) by incorporating uncertainty and variability into the decision-making process, thereby enhancing the robustness and reliability of decisions in complex and uncertain environments. MCDM involves the evaluation and comparison of multiple alternatives based on several conflicting criteria, yet real-world decision problems often involve various forms of uncertainty, such as imprecise data, ambiguous preferences or unpredictable outcomes. Monte Carlo simulation addresses these uncertainties by generating a range of possible outcomes based on probabilistic inputs.

In the context of MCDM, the process typically unfolds in several key stages. First, decision alternatives and evaluation criteria must be identified, with each alternative assessed across multiple criteria that may be assigned different weights to reflect their relative importance. Second, the uncertainty associated with each criterion is modelled. This involves assigning probability distributions (e.g., normal, triangular or uniform) to reflect variability in the parameters such as costs, risks or performance outcomes for each alternative.

Next, Monte Carlo simulation involves running a large number of simulations, typically thousands or more, in which the uncertain parameters for each criterion are randomly sampled from their specified probability distributions. For each simulation run, a decision matrix is constructed, and the alternatives are evaluated based on the weighted criteria. The results of these simulations are then aggregated to provide a distribution of possible outcomes for each alternative, allowing for the calculation of expected values, variances and probabilities of achieving favourable results.

Finally, the decision-maker can analyse these aggregated results to assess the likelihood of each alternative’s success across a range of possible scenarios. Sensitivity analysis can also be performed to examine how changes in uncertain parameters influence the decision outcomes, helping to identify alternatives that are more robust under varying conditions. The primary advantage of applying Monte Carlo simulation in MCDM is its ability to provide a comprehensive view of potential outcomes, as opposed to relying on single-point estimates. This approach enables decision-makers to better understand the risks and uncertainties inherent in each alternative, facilitating more informed and resilient decision-making.

Integrating Monte Carlo simulations and grid computing in finance for corporate performance management (CPM) offers significant benefits but also entails various costs. Monte Carlo simulations enhance risk analysis by modelling uncertainty, enabling better decision-making in areas like investment strategy and portfolio management. Grid computing improves the accuracy and efficiency of these simulations by distributing computational tasks across multiple systems, allowing for faster processing and more reliable results. This combination supports real-time analysis and scenario planning, helping organisations adapt to market changes and optimise long-term strategic planning.

However, the implementation of these technologies comes with high initial costs, including investment in hardware, software and networking infrastructure, especially when not leveraging cloud-based systems. Operational complexity also arises from managing distributed computing tasks, which requires specialised expertise. Ongoing maintenance and the need for high-quality data further increase costs. Additionally, grid computing can lead to substantial energy consumption, which may offset some of the efficiency gains. Ultimately, while the integration of Monte Carlo simulations and grid computing offers valuable enhancements to CPM, organisations must carefully weigh the associated costs against the long-term benefits to ensure a positive return on investment.

3.1.1. Real Interest Rate ($i_r)$

The real interest rate is the interest rate without inflation. It is the form of the nominal interest rate adjusted for inflation. For this purpose, the nominal interest rate and inflation rate have been taken in Turkey for 20 years, and the collected data are given in Equation (1).

$$\left(1+i_r\right)={\displaystyle \frac{(1+i_n)}{(1+r)}}$$

(1)

i_r = real interest rate

i_n = nominal interest rate

r = inflation rate

Nominal Interest Rate (i_n)

The nominal interest rate can be defined as the interest rate used in the market. The nominal interest is used by banks when applying for loans and deposits, and it is not adjusted for the effect of inflation. In this study, the nominal interest rates for the last 20 years were collected, and a logistic curve was fitted as shown in Figure 6. Statistical information such as the mean, minimum and maximum values of these parameters are shown in Table 1. The parameters and coefficients of these curves are given in Table 2. The equation used for the logistic distribution model is

$$f\left(x\right)={\displaystyle \frac{\alpha {\frac{(x-\gamma )}{\beta }}^{\alpha -1}}{\beta {(1+{\frac{(x-\gamma )}{\beta }}^{\alpha })}^2}}$$

(2)

where

γ: continuous location parameter

β: continuous scale parameter β > 0

α: continuous shape parameter α > 0

Figure 6. Fitted curve for nominal interest rate data.

Figure 6. Fitted curve for nominal interest rate data.

Table 1. Statistical information on the nominal interest rate data collected.

Cash Flow Parameter (%)	Values	Minimum	Mean	Maximum	Standard Deviation
in	237	0.11	2.55	24.97	2.47

Table 1. Statistical information on the nominal interest rate data collected.

Cash Flow Parameter (%)	Values	Minimum	Mean	Maximum	Standard Deviation
in	237	0.11	2.55	24.97	2.47

Table 2. Characteristics of the fitted curve for nominal interest rate data.

Cash Flow Parameter (%)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
in	LogLogistic	2.87	2.16	−0.16	-	-	-	-	-

Table 2. Characteristics of the fitted curve for nominal interest rate data.

Cash Flow Parameter (%)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
in	LogLogistic	2.87	2.16	−0.16	-	-	-	-	-

3.1.2. Inflation Rate (r)

Inflation is a rise in the prices of goods and services. However, the prices of goods and services can rise or fall over time. Inflation is not just an increase in the price of a particular good or service but a continuous increase in the general price level. In this study, the inflation rates for the last 21 years were collected, and an InvGauss curve was fitted, as shown in Figure 7. Statistical information such as the mean, minimum and maximum values of these parameters are shown in Table 3. The parameters and coefficients of these curves are given in Table 4. The equation used for the InvGauss distribution model is

$$f\left(x\right)=\sqrt{{\displaystyle \frac{\lambda }{2\pi x^3}}}{e}^{-\left[{\displaystyle \frac{\lambda {\left(x-\mu \right)}^2}{2{\mu }^{2}x}}\right]}$$

(3)

where

μ: continuous parameter μ > 0

λ: continuous parameter λ > 0

Figure 7. Fitted curve for inflation rate data.

Figure 7. Fitted curve for inflation rate data.

Table 3. Statistical information on the inflation data collected.

Cash Flow Parameter (%)	Values	Minimum	Mean	Maximum	Standard Deviation
r	21	6.16	15.19	68.53	14.73

Table 3. Statistical information on the inflation data collected.

Cash Flow Parameter (%)	Values	Minimum	Mean	Maximum	Standard Deviation
r	21	6.16	15.19	68.53	14.73

Table 4. Characteristics of the fitted curve for inflation data.

Cash Flow Parameter (%)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
r	InvGauss	-	-	-	9.59	3.48	-	-	5.60

Table 4. Characteristics of the fitted curve for inflation data.

Cash Flow Parameter (%)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
r	InvGauss	-	-	-	9.59	3.48	-	-	5.60

3.1.3. Annual Income (AI)

The annual income (AI) refers to the annual income of a wind turbine. It is obtained by multiplying the unit price of electricity (UPE) by the energy produced (PE).

Unit Price of Electricity $\left(UPE\right)$

The unit price of electricity (UPE) is the unit selling price of electricity generated by wind farms. Data were collected for the last 22 years, and an ExtValue curve was fitted as shown in Figure 8. Statistical information such as mean, minimum and maximum values of these parameters is shown in Table 5. The parameters and coefficients of these curves are given in Table 6. The equation used for the ExtValue distribution model is

$$f\left(x\right)={\displaystyle \frac{1}{b}}\left({\displaystyle \frac{1}{e^{\frac{x-a}{b}+\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{a-x}{b}\right)}}}\right)$$

(4)

where

a(alpha): continuous location parameter

b(beta): continuous scale parameter, beta > 0

Figure 8. Fitted curve for UPE data.

Figure 8. Fitted curve for UPE data.

Table 5. Statistical information on the unit price of UPE collected.

Cash Flow Parameter ($/kWh)	Values	Minimum	Mean	Maximum	Standard Deviation
UPE	22	0.07	0.10	0.13	0.01

Table 5. Statistical information on the unit price of UPE collected.

Cash Flow Parameter ($/kWh)	Values	Minimum	Mean	Maximum	Standard Deviation
UPE	22	0.07	0.10	0.13	0.01

Table 6. Characteristics of the fitted curve for the UPE.

Cash Flow Parameter ($/kWh)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
UPE	ExtValue	-	-	-	-	-	0.09	0.01	-

Table 6. Characteristics of the fitted curve for the UPE.

Cash Flow Parameter ($/kWh)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
UPE	ExtValue	-	-	-	-	-	0.09	0.01	-

Produced Energy (PE)

Produced energy (PE) is the energy produced by wind turbines. The wind power available per unit area swept by the turbine blades is given by the following equation:

$$P={\displaystyle \frac{1}{2}}\rho C_p\sum \left(V_i^3{t}_i\right)$$

(5)

where $\rho$ is the air density, $V_i$ is the mean wind speed for the $i_{th}$ time interval, $t_i$ is the number of hours corresponding to the time interval divided by the total number of hours and $C_p$ is a power coefficient. As the turbines are all selected in the same region and with the same characteristics, all parameters except the wind speed are neglected. Thus, in Figure 9, a linear correlation has been established between the monthly mean wind speed data and the energy obtained for each turbine.

Wind Speed (WS)

Wind speed is the most effective parameter on the energy produced. In this study, one year of wind speed data was collected from 20 turbines with similar characteristics in the Eastern Thrace region, and the data distribution of monthly mean values for each turbine is presented in Figure 10. Although the wind speed distribution often encountered in literature and practice is Weibull [18], the curve that best fit the data collected in this study was ExtValue. Statistical information such as mean, minimum and maximum values of these parameters is given in Table 7. The parameters and coefficients of these curves are presented in Table 8. The equation used for the ExtValue distribution model is

$$f\left(x\right)={\displaystyle \frac{1}{b}}\left({\displaystyle \frac{1}{e^{\frac{x-a}{b}+\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{a-x}{b}\right)}}}\right)$$

(6)

where

a(alpha): continuous location parameter

b(beta): continuous scale parameter, beta > 0

Figure 10. Fitted curve for WS data.

Figure 10. Fitted curve for WS data.

Table 7. Statistical information of the WS.

Parameter (m/s)	Values	Minimum	Mean	Maximum	Standard Deviation
WS	240	4.33	6.61	10.19	1.36

Table 7. Statistical information of the WS.

Parameter (m/s)	Values	Minimum	Mean	Maximum	Standard Deviation
WS	240	4.33	6.61	10.19	1.36

Table 8. Properties of the fitted curve for the WS.

Parameter (m/s)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
WS	ExtValue	-	-	-	-	-	5.98	1.08	-

Table 8. Properties of the fitted curve for the WS.

Parameter (m/s)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
WS	ExtValue	-	-	-	-	-	5.98	1.08	-

3.1.4. Annual Expenses (AE)

The annual cost of a wind turbine consists of variable costs such as maintenance per turbine and fixed costs such as personnel, security and insurance. The historical annual cost data (60 values) for each turbine were obtained from the relevant wind turbine databases. The data obtained and the InvGauss curve fitted to these data are shown in Figure 11. Statistical information such as mean, minimum and maximum values of these parameters can be seen in Table 9. The parameters and coefficients of these curves are given in Table 10. The equation used for the InvGauss distribution model is

$$f\left(x\right)=\sqrt{{\displaystyle \frac{\lambda }{2\pi x^3}}}{e}^{-\left[{\displaystyle \frac{\lambda {\left(x-\mu \right)}^2}{2{\mu }^{2}x}}\right]}$$

(7)

where

$\mu$: continuous parameter, $\mu$> 0

$\lambda$: continuous parameter, $\lambda$> 0

Figure 11. Fitted curve for AE data.

Figure 11. Fitted curve for AE data.

Table 9. Statistical information on AE.

Cash Flow Parameter ($)	Values	Minimum	Mean	Maximum	Standard Deviation
AE	60	−128,426.00	−109,943.18	−85,288.00	11,393.83

Table 9. Statistical information on AE.

Cash Flow Parameter ($)	Values	Minimum	Mean	Maximum	Standard Deviation
AE	60	−128,426.00	−109,943.18	−85,288.00	11,393.83

Table 10. Characteristics of the fitted curve for AE.

Cash Flow Parameter ($)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
AE	InvGauss	-	-	-	62,014	1,810,110	-	-	−171,957

Table 10. Characteristics of the fitted curve for AE.

Cash Flow Parameter ($)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
AE	InvGauss	-	-	-	62,014	1,810,110	-	-	−171,957

3.1.5. Investment Cost of a Wind Turbine (ICWT)

The investment cost of a wind turbine consists of the land cost and the installation cost. The investment cost values of 20 turbines considered in this study were obtained from the relevant wind turbine database. The obtained data and the corresponding Weibull curve are shown in Figure 12. Statistical information such as mean, minimum and maximum values of these parameters is shown in Table 11. The parameters and coefficients of these curves are given in Table 12. The equation used for the Weibull distribution model is

$$f\left(x\right)={\displaystyle \frac{\alpha x^{\alpha -1}}{{\beta }^{\alpha }}}{e}^{-{\left(x/\beta \right)}^{\alpha }}$$

(8)

where

$\alpha$: continuous shape parameter ($\alpha$> 0)

$\beta$: continuous scale parameter ($\beta$ > 0)

$\gamma$: continuous location parameter ($\gamma$= 0 for the two-parameter Weibull distribution)

Figure 12. Fitted curve for ICWT data.

Figure 12. Fitted curve for ICWT data.

Table 11. Statistical information from the ICWT.

Cash Flow Parameter ($)	Values	Minimum	Mean	Maximum	Standard Deviation
ICWT	20	−3,494,451.00	−3,143,038.55	−2,506,463.00	274,387.96

Table 11. Statistical information from the ICWT.

Cash Flow Parameter ($)	Values	Minimum	Mean	Maximum	Standard Deviation
ICWT	20	−3,494,451.00	−3,143,038.55	−2,506,463.00	274,387.96

Table 12. Characteristics of the fitted curve for the ICWT.

Cash Flow Parameter ($)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
ICWT	Weibull	2.83	793,701						−3,848,563

Table 12. Characteristics of the fitted curve for the ICWT.

Cash Flow Parameter ($)	Distribution Model	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$	$\mathit{\mu }$	$\mathit{\lambda }$	a	b	Shift
ICWT	Weibull	2.83	793,701						−3,848,563

3.2. NPV Analysis

There are many economic performance measures used by investment professionals. Of these, NPV and PP are the most popular. NPV is generally used to make investment decisions and is a financial analysis method used to determine overall profitability. NPV can be described as the sum of discounted cash receipts and cash payments. The parameters for NPV are annual incomes, annual outcomes (expenses) and ICWT. Among these, the parameters that constitute annual incomes are produced energy and wind speed unit price of energy, while the annual outcomes are the annual costs of a wind turbine. Figure 13 shows an example of an NPV calculation diagram. The mathematical representation of the NPV method used in this study is shown in Equation (9) below.

$${NPV}_n=[{\sum }_{n=1}^{10}{\displaystyle \frac{{AI}_n}{{(1+i_r)}^n}}-{\sum }_{n=1}^{10}{\displaystyle \frac{{AO}_n}{{(1+i_r)}^n}}]-ICWT$$

(9)

where

${NPV}_n$: NPV in nth year

$ICWT$: investment cost of a wind turbine

${AI}_n$: annual income in nth year

${AO}_n$: annual outcome in nth year

Figure 13. Net present value graph for n years.

Figure 13. Net present value graph for n years.

3.3. Conducting Simulation

To assess the financial outcomes of the project, a simulation model was built by first performing curve fitting on key input parameters. Historical and forecast data were analysed to accurately represent the behaviour of each input and to capture a realistic range of potential outcomes. These inputs were then incorporated into a net present value (NPV) equation, which was set as the primary metric for assessing the long-term viability of the project over a 20-year period.

The simulation model was run using @RISK software (version 5.5) with 5000 iterations. In each iteration, a unique NPV result was generated by randomly sampling from the fitted distributions of the input parameters. This stochastic approach allowed for uncertainty and variability in key parameters, resulting in a robust distribution of potential NPV outcomes. @RISK uses Monte Carlo simulation as its core algorithm, performing simulations by generating random values for uncertain input variables based on assigned probability distributions. It runs multiple trials to model possible outcomes, helping users estimate the likelihood of different results. The software employs various sampling methods, including Latin hypercube sampling, random sampling and quasi-random sampling, to improve the accuracy and efficiency of the simulations.

Additionally, @RISK offers sensitivity analysis to determine how changes in input variables impact the outcome, using tools like tornado diagrams and sensitivity charts. It also incorporates optimisation algorithms, such as genetic and evolutionary algorithms, to identify optimal solutions under uncertainty. Analytical methods and regression tools are available for specific problems, allowing for efficient modelling in cases where closed-form solutions are applicable. Overall, @RISK combines Monte Carlo simulation with advanced techniques for risk analysis and decision-making.

On completion of the simulation, a sensitivity analysis was performed on the NPV results to identify the parameters with the greatest impact on project profitability. By identifying the most influential factors, greater insight was gained into the inputs that drive variability in NPV, providing valuable information on areas of risk and opportunity. These insights are critical for guiding future decisions and adjusting project strategies to improve profitability under uncertain conditions.

4. Results and Discussion

As a result of simulation studies, we obtained the probability of a positive net present value (NPV) for a wind turbine investment over a 20-year period in the region. The results include probabilities over specific 5-year intervals, as shown in Figure 14, and the annual probabilities of a positive NPV are summarised in

Table 13. The probability that the net present value (NPV) is greater than zero over the years.

Years	Probability of NPV > 0 (%) by Years (%)
1	0.5
2	12.3
3	55.3
4	91.8
5	99.4

. Figure 14 is added to visualise the financial outcomes of a project under uncertainty by running Monte Carlo simulations. It shows the distribution of possible NPV values based on varying inputs such as wind speed, electricity prices, capital and operational costs and the discount rate. The X-axis of the diagram represents the range of NPV values, with negative NPVs on the left and positive NPVs on the right. The Y-axis represents the probability density or likelihood of each NPV value occurring. The probability distribution curve, which is generated from the simulations, can be normal, log-normal or triangular depending on the data.

The diagram helps identify the range of possible NPVs and the associated risks by showing percentiles, such as the 10th, 50th and 90th percentiles, indicating the probability of the NPV being below or above certain thresholds. Key insights from the diagram include understanding the expected NPV, assessing the spread of outcomes and evaluating the level of risk. The diagram also helps answer questions like the likelihood of a positive NPV or the probability of achieving specific financial targets.

Table 13 shows the probability of the NPV being greater than zero for each year within the first 5 years. It shows that the probabilities of NPV being greater than zero in 5 years are 0.5%, 12.3%, 55.3%, 91.8% and 99.4% respectively. This pattern indicates a strong trend towards profitability in the early years. Specifically, by the end of the third year, the investment has a 50% chance of being profitable. By the fifth year, profitability is almost certain, with a 99.4% probability that the net present value will be positive. Thus, while the initial returns may be low, the probability of a successful investment in the wind turbine project increases significantly over time, particularly after the third year.

In addition, a convergence test was conducted, and it was found that all of the outputs (or probability of NPV > 0 (%) by years (%)) converged with a 95% confidence level and 3% convergence tolerance.

According to these values, the probability that the time-dependent NPV value is greater than zero is shown in Figure 15. Figure 15 showing the probability of NPV being greater than zero by years visualises how the likelihood of a positive NPV changes over the life of a project, accounting for uncertainties like cash flows, discount rates and operational factors. The X-axis represents time, typically from the start to the end of the project’s expected lifespan, while the Y-axis shows the probability of a positive NPV at each point in time. Early years often have a low probability of a positive NPV, as projects usually incur high initial costs with little revenue. As the project moves into its operational phase, the probability of a positive NPV increases, especially if the project generates revenue and recovers initial investments. Over the long term, the probability continues to rise, often reaching higher probabilities of a positive NPV as steady revenues come in and risks decrease. The probability curve depends on factors such as initial investment, market conditions, operational costs and subsidies. The diagram helps stakeholders assess when a project is likely to become profitable and the risks involved, assisting in decision-making about whether to proceed with the investment. Thus, in the equation of the curve (y = −5.0083 × 3 + 44.011 × 2 − 84.081x + 45.36), if the planned payback period of the investment is set to x value, the probability of NPV being greater than zero for this year will be found.

The parameters that most affect the NPV value calculated in Figure 16 are shown in the tornado graph as a sensitivity analysis tool. The three most influential parameters are wind speed, investment cost and unit price of electricity. Monte Carlo simulations are widely used to assess the probability of a positive NPV for wind turbine projects, considering variables such as wind speed, electricity prices, capital and operational costs. Studies show that the probability of a positive NPV after 5 years can be low due to high initial investment and startup inefficiencies. For instance, research by [19] found a 30–40% chance of positive NPV in offshore projects under low to moderate wind conditions, but it rose to over 80% with favourable wind and energy prices.

Wind resource availability is crucial; turbines in high-wind areas tend to have a higher probability of achieving positive NPV. For example, ref. [20] observed that the probability in the UK and Germany for offshore wind projects could range from 50–60% in high-wind regions to lower percentages in moderate areas. Similarly, Jung et al. (2016) found a 40–55% probability in U.S. onshore wind projects.

Initial capital and financing costs also play a significant role. Ref. [21] noted that projects in Spain showed only a 10–25% chance of positive NPV after 5 years, but with favourable financing, this increased to 60–70% over time. Ref. [22] similarly found a low probability of positive NPV (20–40%) for offshore projects in Denmark in the first 5 years due to high upfront costs, but the probability improved over a 10-year period.

Electricity prices have a strong influence on financial outcomes. Ref. [23] found that fluctuating electricity prices could reduce the 5-year probability of positive NPV to 15–50%, but under high carbon prices and strong energy prices, the probability could rise to 70%. Ref. [24] observed a similar trend for European onshore wind projects, with probabilities ranging from 30–50% in volatile markets to 80–90% with long-term contracts.

Government policies, such as tax credits and subsidies, have a large impact. Ref. [25] showed that U.S. wind projects with the Production Tax Credit (PTC) had a 70% chance of positive NPV after 5 years, compared to 30% without subsidies. For offshore projects, incentives led to a sharp increase in long-term probabilities, with chances of positive NPV reaching 85%.

5. Conclusions

The power generation potential of wind turbines is highly dependent on regional characteristics of wind speeds, geographical location and local climate. Regions with high and consistent wind potential can achieve lower costs per MWh through increased output and efficiency, making wind energy a cost-effective renewable option. However, installation and operating costs vary widely from region to region, influenced by factors such as geography, distance from grid infrastructure and the specific challenges of onshore and offshore wind.

In this study, a simulation-based 20-year forecasting model is developed specifically for the Eastern Thrace region, a location characterised by high wind potential. The simulation results, obtained using energy production data collected from wind turbines in the region, show a favourable financial outlook for wind turbine investments in Eastern Thrace, with a 90% probability of achieving a payback period of between three and five years.

The methodological approach used in this study provides valuable insights into the economic viability of wind energy in different regions and offers a versatile framework that can be adapted for analysis in different geographical locations with different wind potentials. Future research will extend this approach to areas with different wind characteristics, providing a more comprehensive understanding of wind energy potential and encouraging a targeted expansion of renewable energy investment in other high potential locations.