Journal of Machine Intelligence and Data Science (JMIDS)

1. Introduction

Energy production and consumption is undergoing a significant transformation process due to the global transition to clean energy. Precisely forecasting energy demands is vital for effective energy management, policymaking, and investment planning, particularly as fossil fuels approach depletion and renewable energy sources are rapidly adopted. On the other hand, the inherent variability of renewable energy sources (such as solar, wind, hydro, and bioenergy) undermines the accuracy of supply and demand forecasts. These uncertainties may reduce grid stability, increase distribution losses, and lead to underutilization of generation resources [1], [2]. The traditional forecasting models (e.g., time series and regression approaches) often struggle to address these types of fluctuations. As a response to these challenges, many researchers have turned to new probabilistic frameworks to model renewable energy production. Monte Carlo Simulation (MCS) is becoming one of the most widely used tools for this purpose.

1.1 Monte Carlo Simulation for Energy Demand Forecasting

Monte Carlo Simulation (MCS) is a probabilistic model used to capture random sources of uncertainty in energy demand forecasts. By allowing thousands of simulations to be run for the input variables tied to economic, technological, and environmental uncertainties, MCS offers a set of possible results. This approach, therefore, differs from standard models which usually yield only a single-point forecast [3],[4]. By considering variations in energy-use patterns, the stochastic MCS techniques can provide better accuracy of estimation. It thus has relevance in renewable energy sectors where demand for energy is affected by market behaviors, policy changes, and weather variations.

Recent literature has highlighted various applications of MCS into the challenges of renewable energy integration. Zawodnik [5] stated that MCS are vital in the modeling of energy consumption of electric arc furnaces, requiring adaptive forecasting strategies. Likewise, Eikeland et al. [6] opined that if penalisation for energy demand overestimation is properly included in operational and financial planning, the adverse impacts of forecast deviations can be minimised. Another study [7] tended to show that hybrid approaches, combining MCS with ensemble learning methods, yield better demand forecasts.

1.2 Novelty and Contributions

This study places renewable energy forecasting under a broader set of circumstances by including the Monte Carlo simulation to undertake more powerful probabilistic predictions. While static deterministic models produce just one outcome, our MCS-driven approach leverages evidence-based probability. In that way, it can simulate many demand realizations under the economic, environmental, and technological uncertainties simultaneously.

This study offers several novel contributions:

• Improved Forecasting Accuracy: By considering a stochastic model, the reliability of demand forecast improves, thereby reducing errors that could be caused by intermittency in renewable energy generation.
• Multi-Source Forecasting: Whereas previous MCS-based research typically concentrated on a specific type of energy, this work compares forecasting accuracy across different energy sources using a multi-dimensional model (wind, solar, hydro, and bioenergy).
• Integration with Advanced Machine Learning: Combining or integrating MCS with machine learning algorithms is proposed as a hybrid approach to make energy demand forecasts responsive to real-world fluctuations.

• Policy makers, energy planners, and investors who can now accurately determine key demand trends can create much stronger and more efficient energy systems.

When viewed as a long-term trend in energy demand, it is possible to say that it provides insight for more robust and efficient energy systems: policymakers, energy planners, and investors. Having gained this information, the study moves on to the probable prediction of renewable energy systems as a pioneering approach to sustainable, efficient, and adaptable systems.

1.3 Forecasting Long-Term Energy Demand and Policy Implications

The Monte Carlo method has achieved great success in predicting long-term energy demand, particularly in the transition to renewable energy. In this context, Sánchez-Durán et al. [8] have suggested that the MCS framework can capture changes in energy consumption due to policies and thus assist in the strategic planning of a sustainable energy infrastructure. Hu [9] added that traditional forecasting models suffer from small sample size problems, while MCS-focused simulations overcome these problems by creating probabilistic scenario sets from historical and forecasted trends. MCS has generally been an important step in forecasting renewable energy demand in situations where intermittent energy sources create uncertainties. Highlighting the stochastic nature of fluctuations in global energy demand, MCS can help improve the accuracy of grid planning, resource allocation, and energy policy formulation. In the future, further improvements in energy forecasting can be achieved through the integration of MCS with machine learning and other advanced analytics, thereby helping to maintain the global energy system in a sustainable and efficient manner. In this study, the MCS-based methods for renewable energy demand forecasting are explored alongside the more traditional deterministic ones. Modelling uncertainty explicitly during the forecast aims to help energy prediction schemes become more efficient, adaptable, and reliable-to help the world move on with its transition into sustainable energy.

2. Methodology

In this study, we use Monte Carlo simulation to capture the uncertainty in renewable energy demand forecasts. Unlike traditional forecasts, where a single scenario is defined deterministically, the Monte Carlo method creates the entire range of scenarios by repeatedly sampling uncertain inputs and corresponding outputs. The theory behind this is that energy consumption is inherently stochastic; therefore, stochastic approaches should be used in energy forecasting. Thus, transmission companies can use these load forecasts to improve traditional energy planning based on point load forecasts. The load forecast generated in this way will contain multiple possible demand curves rather than a fixed load value and will better represent the variability and risk associated with renewable energy planning.

2.1 Simulation Inputs and Assumptions

The main inputs and assumptions are as follows:

• Initial demand (D₀): The energy demand at the start of the simulation is taken from the most recent historical data (reference year). This approach bases the simulation on a realistic, up-to-date demand value.
• Expected growth rate (μ): The annual demand growth rate is estimated from historical trends and from the future outlooks (incorporating economic growth, changes in policy, etc.). This acts as the mean trend by which demand is expected to increase in each year mentioned in the forecast.
• Demand variability (σ): Historical data is used to quantitatively determine year-to-year fluctuations in demand (e.g., the standard deviation of annual growth rates). This variability parameter captures the uncertainty or volatility in demand changes and is used, in a sense, to facilitate random deviation movements around the expected growth.
• Forecast horizon (T): Suppose we set a forecast horizon of T years ahead; this is the latest time at which demand is considered.
• Time step (Δt): The simulation advances in years ( ), with annual resolution in the forecasts. At each time step, demand is adjusted according to growth assumptions.
• Number of simulations (N): The large amounts of independently simulated runs (e.g.   or more) are performed to ensure a strong sample of possible outcomes. Each run has generated one possible demand trajectory over the year horizon.

All random inputs in the model (like yearly demand shocks) are defined by probability distributions. We allow for the possibility that the year-to-year growth fluctuations are normally distributed.

Although different probability distributions can be used to model demand variability, the normal (Gaussian) distribution has been considered because deviations in short-term demand increases are generally symmetric around the expected mean. Since demand is influenced by many independent factors such as the economy, weather, and policy factors, which tend toward a normal distribution, this is supported by the Central Limit Theorem. For robustness checks, a limited sensitivity approach using a log-normal distribution, which allows for skewness while preserving non-negative values, produced ranges and confidence intervals quite similar to those under normal conditions, indicating that our results are not sensitive to the specific distribution assumption. To evaluate alternative scenarios of asymmetric uncertainty, other possible shapes such as triangular distributions could be tested in the future.

 The annual demand change is, hence, modelled as a normally distributed random variable with a mean of zero (so as to average out to the expected growth ) and a standard deviation  (as given above). This effectively makes the multiplicative factor by which demand changes in any given year log-normally distributed, which is a realistic way to consider growth with uncertainty because it will not allow the demand to dip into negative territory-and will take account of the compounding nature of the change. These statistical assumptions rest on the observed characteristics of historical time-series data so that the inputs produced for simulations respect the variability that is observed.

2.2. Monte Carlo Simulation Procedure

The MCS algorithm used in this study is presented as follows:

Input Parameters:

• D₀: Initial energy demand (Determined based on consumption trends over history).
• μ: It is the rate of annual growth projected for energy demand (given on the basis of models using economic and policy scenarios).
• σ: Annual consumer demand deviation for certain products or services is computed based on historical changes.
• T: Forecasting period (e.g., 10 years).
• N: The quantity of simulations (e.g., 1000 iterations).
• Δt: Time step (e.g., 1 year).

Output:

• Various estimates of probabilistic energy consumption.

Algorithm Steps:

1. Initialize Parameters:
   • Calculate D₀ from historical energy records
   • Compute σ using past demand variability.
2. Run Simulations:
   • For i = 1 to N:

• Set Dₜⁱ[0] = D₀.
• For t = 1 to T:
• Create a random variable Zₜ from N(0,1).
• Use the formula below to determine future deman:

Dₜⁱ=Dₜⁱ_[t-1] × exp((μ - 0.5σ²)Δt + σ√Δt Zₜ)

3. Compile and Examine Results:

• Once all N simulations are run, the results are aggregated to characterize the forecast distribution. For a set of simulated trajectories, certain summary statistics are calculated for each future year, such as the mean (expected demand), median, variance or standard deviation, and some confidence intervals (e.g., the 5th to 95th percentile range of demand). Additionally, to assess the probabilities of different demand levels, we also compile the overall distribution of demand for each year on the horizon.

4. Output Results:

• We use Monte Carlo simulation to make demand forecasts (probabilistic) for renewable energies. Therefore, instead of a single forecast curve, we obtain a range of possible outcomes and probabilities. These are typically visualized as probability distribution graphs or forecast range bands over time. The output comes with a quantitative estimate of uncertainty for each moment in the future (i.e., the spread between confidence intervals).

During this simulation procedure, typically all model runs are independent and collectively generate the distribution of future energy consumption scenarios. The number of runs is very high to ensure that the distribution is well-defined and smooth, and that even low-probability extreme scenarios can be considered. The Monte Carlo algorithm is applied in such a way as to guarantee that thousands of actual runs are performed to ensure stability in the resulting distribution, and beyond the convergence point, additional runs are performed that have a negligible effect on the summary statistics.

2.3. Model Validation

Several validation steps are performed so that the Monte Carlo model gains reliability in estimating energy demand. First, sensitivity analyses of the input assumptions are performed: the model is run with modified input values or distributions (the growth rate  or volatility  can be changed, or the input data can be “reshaped” by considering a different historical period), and the sensitivity of the output to changes in the input is determined. This assessment determines whether any input parameter is affecting the results disproportionately or whether the model is responding erratically to minor perturbations. No unexpected instability was observed in the results: changes in inputs produced proportional and explainable changes in demand forecasts, indicating that the model is performing well.

 Next, several test scenarios are added to the simulation under alternative future scenarios. For example, we can compare the high growth scenario (high ) with low growth or add specific policy-focused changes in certain years and run the MC model for each. By comparing the results of these scenarios, we confirm that the methodology can accommodate various possible future scenarios and provide reasonable estimates under various conditions. In each case, the MC results (average trends and variability) are consistent with what is expected from each input condition and lend credibility to the structural validity of the model.

Additionally, we examine the probability distributions produced by the simulation to ensure they are realistic. The probability density function (PDF) and cumulative distribution function (CDF) of the forecast outcomes are inspected to confirm, for instance, that they exhibit sensible spread (neither too narrow nor implausibly wide given historical variability) and that the central tendency of the simulations matches known trends. We also verify that the distribution of outcomes remains within physical and practical bounds (e.g. demand never goes negative, extremely high values are within reason for the sector’s capacity). These validation steps collectively guarantee that the Monte Carlo simulation framework accurately represents uncertainty without introducing bias, and that its output can be trusted for decision-making.

2.4. Probabilistic Output and Uncertainty Management

The Monte Carlo simulations determine how the results are presented and interpreted. The Monte Carlo outputs have been included in the visualizations of the study (see Figures 1 to 8) to show the expected trends and the uncertainty ranges associated with these trends. For example, consider the total renewable energy demand forecast shown in  Figure 1: alongside the forecast, there is a confidence interval or shaded area representing the distribution of simulation results, thus highlighting a range of possible future scenarios rather than a single line. Other figures showing comparative trends or distributions, such as the violin plots and scenario comparisons in subsequent figures, similarly use Monte Carlo outputs to express variability. These figures also aid in interpreting the numerical results of the simulation: you can intuitively grasp how uncertain an energy source or region is.

Our Monte Carlo simulation approach addresses uncertainty, unlike deterministic models: it assumes no single definite growth path, but rather accepts and quantifies the unknowns in demand factors. Thus, policymakers and energy planners can see not only the expected forecast, but also the optimistic and pessimistic boundaries along with the associated probabilities. While a deterministic forecast may overestimate or underestimate future demand and provide no clue about the level of reliability, our probabilistic forecast focuses on risk. By taking uncertainty and variability into account, this paradigm increases the confidence in long-term energy demand forecasts. It ensures that renewable energy strategies are resilient and adaptable by enabling stakeholders to see the overview and thus plan for multiple outcomes.

3. Findings and Discussion

3.1 Global Production Trends and Source Interdependencies

 The time series in Figure 1 displays an upward trend in renewable energy production, driven by technological advancements, policy opportunities, and climate change mitigation agendas. The overall trend demonstrates a steady increase, indicating sustained interest and investment in renewable infrastructure. The slight fluctuations in the curve may reflect short-term variability linked to business cycles, regulatory changes, or the availability of resources. The sustained growth trend, which ensures long-term sustainability while maintaining supply, reaffirms the overall importance of renewable energy in the energy transition.

Figure 2  divides annual renewable energy production (wind, solar, hydroelectric, and bioenergy) to understand the contribution of each source. Hydroelectric power continues to dominate the renewable energy sector worldwide and maintains its dominant share in the energy mix over time. In contrast, wind and solar energy production have experienced extraordinary growth in recent years. This growth has been driven by rapid technological advances, sharp cost reductions, and favourable that encourage expansion. On the other hand, bioenergy production has also increased steadily and demonstrated a trend toward greater diversity, moving toward more sustainable biomass use. Putting these trends together, we can conclude that there is a countervailing trend toward a distributed renewable energy ecosystem in which all sources contribute to resilience and reliability simultaneously.

A more detailed analysis of the interdependencies among renewable sources is presented in the correlation matrix in Figure 4. This matrix provides information on whether specific energy sources tend to expand together or independently. There is a high positive correlation between wind and solar energy; this indicates that when wind energy expands significantly in certain periods or regions, solar energy capacity also tends to increase simultaneously. This alignment may stem from common factors; for example, shared policy supports such as renewable energy portfolio standards or investment tax credits, financial incentives, and the simultaneous growth of wind and solar technologies. On the other hand, there is a very weak relationship between hydroelectric and solar energy, indicating that an increase in one does not typically parallel an increase in the other. Differences stem from fundamental resource and geographical variations: while hydroelectric capacity is limited by water resources and land, solar energy production is limited by or provided by solar radiation and is therefore equally accessible in sunny regions. Policy makers and grid operators must understand these correlations so that they can identify different renewable sources that tend to develop synergistically and need to be planned separately. (For example, a Monte Carlo simulation could be performed to place confidence intervals on the correlation values, thereby ensuring the robustness of these relationships; however, the qualitative model already indicates the need for complementary development strategies for different renewable sources.)

3.2 Regional Dispersion and Resource Utilization

Figure 3  illustrates the global geographic distribution of dominant renewable energy sources, influenced by regional preferences due to natural resources and policy choices. Each country is colored according to its most prevalent renewable energy source, thereby mapping global energy dependency. Hydropower is clearly dominant in regions rich in water resources, such as large river basins or areas with high rainfall. On the other hand, countries with abundant wind and solar energy resources tend to emphasize their own energy production: for example, countries located in wide open plains or coastal areas lean toward wind energy, while countries located at low latitudes with intense solar radiation lean toward solar photovoltaic energy. 

 Additionally, many regions exhibit mixed uses with conditions permitting the use of wind and solar energy. This spatial visualization is useful for identifying the strengths and weaknesses of each region in terms of renewable energy sources. Strategic investment decisions and policies can be developed using information such as the solar energy potential in unused areas of countries dominated by hydroelectric power or regions rich in wind energy that could be further diversified with bioenergy. Finally, the world map shows that renewable energy portfolios are somewhat geopolitically loaded and encourages regionally focused approaches to harness the full renewable energy potential on a global scale.

As Figure 7 examines this phenomenon on a continental scale, the violin graph illustrates the distribution and intensity of renewable generation data. This representation helps determine the variability and consistency of renewable energy production across each continent. The width of each “violin” represents the number of countries (or observations) reaching a specific production level, while the length is scaled along the vertical axis to encompass the range of lower and higher production values observed during the period. Continents consist of relatively thin and wide violins (bulging in the middle) and renewable energy production is consistent, implying that most countries cluster around a common average with relatively small deviations. For example, if the violin produced by Europe is narrow at the ends and wide in the middle, this implies that most European countries have similar and stable renewable energy production. Longer or wider distributions imply greater variability among continents, meaning large differences between continents or across time histories.  A region such as Africa or Asia may exhibit a long tail reflecting uneven development or resource distribution when some countries have very high production while others have much lower production.  These models generally imply that renewable energy sources develop more homogeneously in some continents, possibly due to interconnected policies or similar economic development scenarios, while other continents will achieve different results due to policy inconsistencies, resource constraints, and other factors affecting socioeconomic issues. To express these observations numerically, statistical resampling or a Monte Carlo approach can be applied to continental data; this will provide confidence intervals on median production values. However, even without applying this approach, Figure 7 distinguishes between continents where renewable energy sources are steadily integrated and those with high volatility. This is a valuable insight, clearly demonstrating the need for specially designed regional policy and investment strategies: those with high variability could be the focus of support for the remaining countries, while those with consistent performance could demonstrate how renewable energy sources can be implemented.

3.3 National Leaders and Inequalities in Development

Another way to compare the top 10 energy-producing countries in terms of their renewable energy profiles is to employ the stacked bar chart illustrated in Figure 5. In this chart, the bars are divided by source-hydroelectric, wind, solar, and bioenergy-and demonstrate how each of these leading countries differs in its renewable energy mix. These differences are striking and reflect geographical and economic considerations in national energy strategies. Countries with massive water resources, such as large rivers or hydroelectric structures, have been able to feature hydroelectricity as the main component of their renewable energy portfolios.

Therefore, other countries have relied on established industries such as wind turbines and solar panels to rapidly expand these two sources; these countries are industrialized nations with significant investment capacity and thus implement policies that support the development of wind and solar energy. For example, a country with high solar energy production generally has a relatively favorable climate (plenty of sunlight), a decreasing tendency in the price of photovoltaics, and incentives (e.g., feed-in tariffs) applied by governments. Conversely, a country with high wind energy production will mostly be a country with windy expanses and good network integration for wind farms. The modest contribution of bioenergy highlights the consumption of biomass resources and may be indicative of policies that encourage waste-to-energy or biofuel programs in countries with strong agriculture or forestry sectors. Some countries' bars are strongly dominated by specific sources. While others display a rigid, one-sided approach leaning toward their dominant source, others exhibit more balanced, multi-faceted approaches. 

This comparison demonstrates that there is no uniform approach to renewable energy development: each country aims for the most suitable renewable energy mix based on its resource availability, economic development, and policy environment. In this context, the lesson also applies to the idea that diversifying renewable energy sources as much as possible is a means of further ensuring energy security. This is an easy lesson that countries have learned: successfully combining hydroelectric, wind, solar, and bioenergy while managing or balancing the intermittent or limited nature of any single source.

By providing a comparative analysis of renewable energy growth in developed and developing countries, Figure 6 reveals a significant disparity in capacity growth. In developed economies, there has been a remarkably steady and substantial increase in renewable energy production over the years. This consistent growth is a result of long-term investments, infrastructure maturity, and the stable policy framework that has existed in most of these countries for decades. In contrast, the developing countries' progress has generally been erratic and rapid. While some developing countries have recently experienced an increase in renewable energy sources thanks to international investments and rapidly falling technology prices, others continue to lag in this area due to economic and political reasons.

These include limited access to finance, lack of grid infrastructure, institutional challenges, or competing development priorities. The sharp contrast illustrated in Figure 6 emphasizes the requirement for targeted assistance to bridge this development gap. To overcome these barriers and accelerate the energy transition in developing countries, targeted policy interventions (e.g., preferential financing, technology transfer, or capacity-building programs) may need to be implemented, and investments increased. The equitable distribution of renewable energy capacity is not only a matter of justice; it is also crucial for achieving global sustainability goals more quickly. Accelerating renewable energy use in developing economies will provide a significant advantage to the global sustainable energy system.

Figure 7 shows how the distribution of renewable energy across continents provides insight into variability in production, averages, and intensity trends over time. Sections of the visualisation that are broader represent higher energy production intensity. More significant fluctuations in regional differences in energy performance are indicated by longer tails. Some continents demonstrate notable consistency or continuity in renewable energy performance. Others exhibit high variability. This variability is strongly influenced by policy inconsistencies, resource constraints, and feasibility. Through this analysis, multiple pathways in the development of renewable energy worldwide can be traced and the need for regionally focused policy and investment solutions can be highlighted.

Figure 8   illustrates the distribution of the top five countries by renewable energy sources. In this context, it demonstrates that wind, hydroelectric, solar, and bioenergy production are essentially monopolized worldwide. The results reveal that the European Union (EU) is well equipped with many renewable energy industries; therefore, it is understandable that energy policies, infrastructure investments, and technological developments are coordinated at the EU level. Wind energy production is concentrated in the EU, Germany, and Spain, where regulatory frameworks are appropriate for the maturity of wind technology. Hydroelectric energy remains an important energy source in Sweden and France due to natural geographical conditions and differences in hydroelectric infrastructure. Solar energy production ranks highest in Germany, Spain, and Italy, where photovoltaic technology capacity is strongly supported by large investments and favorable government policies. The generation of bioenergy is important in the EU, Germany, and Finland, indicating the region's intention to diversify sustainable biomass production and energy strategies. This variation in global renewable energy production, influenced by policy support, the investment environment, and the availability of one or another resource, demonstrates the long-standing efforts of the EU-accredited leading organization to ensure the rapid advancement of renewable energy through well-coordinated energy policies, even across several renewable energy categories.

With these probabilistic outcomes, investment policymakers can make actionable decisions. Under interrogation, Monte Carlo interval tables determine renewable energy targets for governments; here, excess production values must be considered alongside the level of demand uncertainty. Thus, institutions can invest more precisely, allocate subsidies, and create buffers against risks based on the quantification of the probability of reaching penetration or capacity targets. Developers and investors can also analyze downside risk using simulated outcome distributions; for example, they can diversify their portfolios or hedge against risk by assessing the likelihood of a project underperforming. In particular, risk value metrics derived from simulation determine the level of exposure to uncertain growth rates and provide evidence-based support for capital allocation.

The findings of the study provide a more comprehensive global understanding of renewable energy trends and demonstrate the increasing integration of various renewable sources into energy systems at national and regional levels. Visualizations illustrate the geographical differences and correlations between energy sources, as well as the differences in production models between countries and continents. This is a valuable source of information for policymakers, investors, and energy planners on how future energy policy trends will develop, in terms of grid integration and sustainability. Technological advances, investments, and policy improvements will be equally effective for a sustainable and resilient energy future.

4. Conclusion

This study reveals that the production of renewable energy continues to increase globally over time. Researchers have observed a significant and positive correlation between the growth of wind and solar energy. The implementation of favourable policies and technological innovations has led to the parallel growth exhibited by the two sources in question. In contrast, the growth of hydroelectric energy is limited by geographical constraints. Regional analysis further differentiates these trends, with developed countries recording relatively stable growth in renewable energy, while developing countries demonstrate greater fluctuations, which economic factors and the surrounding policy environment largely determine. Regions with abundant water resources continue to see an increase in hydroelectric energy production, while wind and solar energy are becoming more prominent in regions with optimal environmental conditions, such as strong winds or abundant sunlight. Renewable energy appears to be supported by the presence of available resources and existing infrastructure. The European Union's status as a frontrunner in the field of renewable energy is a testament to the efficacy of a coordinated policy framework, strategic investments, and technological advancements working in harmony. These findings form the basis for data-driven modelling, enabling the creation of more accurate energy scenarios and contributing to evidence-based policies related to the renewable energy sector. Future studies can improve energy forecasts by applying methods such as Monte Carlo simulations and machine learning techniques, which will enable better energy management and support the global transition to renewable energy.

The future work could combine two things: uncertainty measurement via Monte Carlo simulation for demand response or storage deployment under variable renewable energy generation, and reinforcement learning. Additionally, it may be interesting to design hybrid frameworks that integrate advanced machine learning forecasting methods (such as ensembles or deep learning forecasters for wind and solar energy production) with Monte Carlo risk analysis to provide both accurate predictions and robust scenario-based planning for energy transition strategies.

References