Introduction

Despite the ongoing geopolitical uncertainty, the topic of decarbonization is one of the key global trends and a significant driver of global investment. The Paris Agreement, adopted on December 12, 2015 and uniting more than 200 countries around the world, aims to keep the increase in global average temperature by moving to a low-carbon economy. This agreement stimulates the development of decarbonization and carbon footprint reduction programs around the world. For example, the countries of the European Union are implementing the European Green Deal program, which has a budget of about 1 trillion euros, with the aim of achieving carbon neutrality by 2050. The main driver of the decarbonization of the United States is the law on reducing inflation, which, among other things, provides for the development of renewable energy sources (RES), electric vehicles and reducing methane emissions. As part of China's national climate change goal "Dual Carbon", it is planned to achieve carbon neutrality by 2060.

One of the areas of implementation of decarbonization programs is the development of renewable energy sources. According to a statistical study [4] by the International Renewable Energy Agency (IRENA), from the beginning of 2020 to the beginning of 2025, the global renewable energy capacity increased by 75% from 2,538 GW to 4,443 GW, thereby reaching a comparable level with the global power generation capacity produced by thermal power plants (TPPs) at the beginning of 2025. – about 5,000 GW, powered by non-renewable energy sources. The International Energy Agency (IEA) predicts an increase in global renewable energy capacity by 4,600 GW over the 2025-2030 horizon. According to this forecast, by 2030, the installed capacity of renewable energy sources will exceed the installed capacity of alternative sources of energy generation, however, due to the low coefficient of renewable energy capacity utilization, it will still lag behind thermal power plants in terms of electricity generation.

Research Objective

With the increasing share of renewable energy generation in the structure of global energy production, it becomes necessary to take into account the variability of energy production due to the stochastic nature of obtaining resources for generation. The uncertain volume of electricity generation makes it difficult to predict the revenue of a generation facility when considering it as an investment project. Classical financial and economic models assume calculations based on deterministic cash flows, which is why the evaluation of investment projects related to renewable energy generation requires the development of an approach to accounting for the stochastic nature of renewable energy in financial models.

The assessment of investment projects using the cash flow discounting method is traditional in the practice of substantiating energy industry projects. This method assumes that the future cash flows of a project can be predicted with a high degree of accuracy based on the estimated revenue, operating and capital costs of the project. In this case, the degree of uncertainty and risk is taken into account through a discount rate or scenario analysis, while an assumption is made about the predictability of production volumes and the selling price of products. This assumption may be justified for generation facilities based on non-renewable energy sources, the generation volumes of which are controlled, however, this assumption is not applicable for renewable energy generation facilities.

The key feature of renewable energy generation facilities is the high volatility of energy supply to the generating unit due to natural factors. The variability of electricity generation is primarily characteristic of solar, hydro, and wind power.

Ignoring these specifics within the framework of classical DCF models can lead to a number of methodological limitations. Ignoring the variability of energy supply leads to a systematic overestimation of electricity generation. Overestimation of energy production distorts the projected cash flows of the generation facility in comparison with real flows, which is why the projected performance and financial stability indicators of the project may not objectively reflect reality. First of all, there is a risk of overestimating the investment attractiveness of the project. The indicators of net present value and internal rate of return, calculated without taking into account the volatility of energy supply, may show biased inflated values that do not reflect the actual level of viability of the project for investors. Failure to take into account the stochastic nature of natural factors affecting the project's cash flows may lead to an overestimation of the allowable debt burden, which reduces the project's resilience to adverse external conditions.

For an objective assessment of investment projects related to renewable energy, it is necessary to move from deterministic approaches to probabilistic assessment methods that will take into account the distribution of possible values of key indicators. These approaches include Monte Carlo simulation and the use of percentile characteristics (P50, P90) in making investment decisions.

Classical methods of investment analysis do not reflect the specifics of renewable energy projects and require significant adaptation of methodological tools to account for the stochastic nature of energy generation and the associated uncertainty of financial results.

The principles of electricity generation by renewable energy generation facilities differ significantly from the principles of operation of generation sources based on non-renewable energy sources. The main difference is the high level of volatility in the supply of a resource for generating electricity, which is caused by natural factors. The volatility of electricity generation is determined by a deterministic and random component.

Deterministic factors include cyclical natural processes that repeat themselves with a certain frequency – diurnal, seasonal, and long-term fluctuations. These processes are implemented in accordance with a certain dependence and can be described using deterministic models.

Random factors are characterized by rare unpredictable natural processes that deviate significantly from the average values, such as abnormal weather conditions or extreme hydrological phenomena.

In this case, the random component is a source of risk of low power generation and determines the uncertainty of the cash flows of the investment project.

Solar, wind, and hydro generation account for 99% of the world's renewable energy capacity, while other renewable energy sources account for less than 1%. Solar energy accounts for 42% of the world's capacity, hydro generation - 32%, and wind generation – 25%. [5]

The following phenomena can be attributed to deterministic factors of solar energy:

· cycles of solar activity (increases and decreases due to the number of sunspots);

· seasonal cycle (caused by the rotation of the Earth around its axis: maximum in summer, minimum in winter);

· daytime cycle (due to the height of the Sun above the horizon: maximum at noon, minimum in the evening and morning).

To model these factors, the volumes of direct and scattered solar radiation, the angle of declination of the Sun, the latitude of the terrain, the angle of inclination to the horizon, the number of clear days and the average density of solar radiation flux on a clear day are used as initial data, which are used in the Angstrom regression model and the model of daily amounts of solar radiation for a cloudless sky [2]

A stochastic factor in solar energy is the presence of clouds, which reduces the amount of incoming solar radiation to the Earth's surface. The cloud factor is predicted using the beta distribution function or a model using the attenuating cloud coefficient, which requires data on the theoretical amounts of solar radiation in a cloudless sky and data on average daily insolation as input data.[2]

The following phenomena can be attributed to deterministic factors of hydropower:

· seasonal changes in river flow (due to the alternation of seasons: minimum in winter, maximum in summer);

· spring floods and summer-autumn rainfall (increased water inflows due to snowmelt and decrease due to freezing);

· tides (caused by cyclical lunar activity and winds);

· multi-year hydrological cycles

Modeling of these factors takes place using various forms of regression models for river flow, probabilistic models, as well as water balance equations, for which data on river flow volumes, average precipitation/probability distribution, duration of the ice cover period, and tide values are used as input data. [2]

Stochastic factors include various events that are atypical for the area under consideration, related to the discrepancy between the average precipitation from the norm, abnormally warm weather for winter, floods, droughts or winter floods, which are predicted using various distribution functions or the Monte Carlo method, which requires information about the average values of water consumption as input data. [2]

The following phenomena can be attributed to the deterministic factors of wind energy:

· circulation in the northern and southern hemispheres (warm air is directed to the poles, cold air is directed to the subtropics);

· monsoon winds (due to the temperature difference in summer, they are directed away from the ocean and away from land in winter);

· mountain valley winds (warm air from the slope is directed upward, cold air from the valley is directed downward);

· diurnal cycles (increasing speed during the day and decreasing at night)

To model these factors, the geographical coordinates of the project and the average wind speed in the project region are required, which is determined using the approximation of the Weibull–Goodrich velocity distribution function, which is widely used in foreign practice. [2]

The main stochastic factor in wind energy is wind lull or other extreme wind speeds. To make a forecast regarding extreme wind speeds, the most accurate method is to use data from long-term observations of wind characteristics in the study area in the context of monthly average, annual average wind speeds and their extreme values for the period under review.

To generate forecasts in regions where there is no data from long-term observations, specialized wind distribution functions are used, taking into account the terrain and the wind distribution function by gradation and height, which are less accurate than the basic method, but have wide application practice.[2]

The analysis demonstrates that the stochasticity of energy production by renewable energy generation facilities is due to the influence of natural factors characterized by both cyclic and random components. Therefore, it is necessary to consider electricity generation as a random variable described by a probability distribution. This condition is the basis for taking into account the randomness factor in energy generation and integrating uncertainty into financial models of investment projects in the renewable energy industry.

Traditional financial and economic models of investment projects are created based on the assumption of constant values of the parameters that generate cash flows. The values of output volume, selling prices, and expenses, as a rule, vary linearly without sharp fluctuations throughout the forecast period. The calculations based on deterministic values of key parameters result in point values of the investment project efficiency parameters.

To take into account the stochastic nature of the volume of electricity generation by renewable energy facilities and the rational description of this logic in the financial and economic model, it is recommended to use random variables limited by a rational upper and lower range to avoid absurd values as key parameters affecting the cash flows of the project. Thus, the initial parameters, namely wind speed, level of insolation or water consumption, which affect the installed capacity utilization rate and the selling price of electricity, are set in the form of probability distributions. Within the framework of the proposed estimation method, the volume of electricity generation is formed as a random variable, revenue and cash flows acquire a probabilistic character, indicators of the effectiveness of the financial stability of the project are interpreted as distributions, which allows for consistency between the physical nature of generation and the economic assessment of the project.

To model the stochastic logic of generating cash flows of renewable energy generation facilities in the practice of investment valuation, the Monte Carlo method is used in conjunction with the percentile approach.

The Monte Carlo method is a classic tool for modeling random outcomes. This method involves calculating thousands of iterations of a project using random values of the source data, which are generated through a probability distribution. As a result of the iteration, random values of the initial data are generated, after which electricity generation, revenue, EBITDA, cash flows and performance indicators are calculated sequentially.

Within the framework of this method, a sample of project performance indicators is formed, which allows evaluating project results not as point values, but as probability distributions.

In addition, to account for risk and determine the probability of favorable and unfavorable outcomes simultaneously with the Monte Carlo method, it is recommended to use a percentile approach, which is widely used in project financing and allows analyzing the data obtained through the prism of the median value or baseline scenario (P50) and considering a conservative estimate of performance parameters (P90).

Thanks to the combination of these methods, it is possible to evaluate the following parameters, which will allow taking into account the risks not only of the baseline scenario, but also to consider the most extreme outcomes of the project:

· average NPV;

· median NPV;

· NPV < 0 probability;

· NPV range P10–P90;

· the likelihood of violating the DSCR covenant;

· P90 of the generation volume.

As a result, investment decisions are made taking into account the probabilistic profile of the project, not just its average profitability.

Technically, this analysis can be implemented using standard MS Excel tools. The most popular functions that will allow you to generate random parameter values ("RAND (СЛЧИС)") and calculate the probabilistic results of the obtained iterations are the following functions: «RANDBETWEEN (СЛУЧМЕЖДУ)», «NORM.INV(НОРМ.ОБР)», «AVERAGE (СРЗНАЧ)», «STDEV.S(СТАНДОТКЛОН.В)», «PERCENTILE.INC(ПЕРСЕНТИЛЬ.ВКЛ)», «COUNTIF(СЧЁТЕСЛИ)».

The simplest way to generate thousands of possible values of the initial project data is to add a "Data Table", which allows you to generate a set of random values based on the input parameter.

A more professional option for generating random source data is to write a macro using the programming language built into MS Excel applications, designed to automate routine tasks, which will allow you to generate a list of random values.

The stochastic nature of the generation of electricity generation facilities using renewable energy requires a transition from deterministic financial and economic models to probabilistic approaches. Using the Monte Carlo method in conjunction with a percentile assessment allows you to take into account the uncertainty of electricity generation and make a more objective assessment of the effectiveness and risks of the project.

Conclusion

This study has shown that renewable energy generation facilities cannot be objectively evaluated using classical methods of evaluating investment projects due to the stochastic nature of obtaining resources for energy generation due to cyclical and random natural factors. Evaluating such projects using models based on assumptions about deterministic cash flows that do not take into account the nature of renewable energy generation projects will reflect a distorted result and mitigate the main project risks.

In connection with these prerequisites, the need to switch to probabilistic methods of analysis was justified, which allows taking into account the stochastic nature of electricity generation. The Monte Carlo simulation method, combined with the use of a percentile approach, provides the formation of distributions of financial indicators based on repeated modeling of scenarios of the initial project data.

The integration of stochastic parameters into the financial model makes it possible to move from point estimates to the analysis of distributions of performance indicators, which makes it possible to assess not only the expected profitability in the baseline scenario, but also the likelihood of adverse outcomes.

Thus, taking into account the stochastic nature of renewable energy generation and the use of probabilistic modeling methods make it possible to increase the validity of investment assessment and more objectively take into account the possible risks of investment projects in the renewable energy industry.