Risk-return analysis of clean energy grid project investment based on integrated ISM and Monte Carlo model

To solve the problem of complex and difficult to quantify factors affecting investment returns and risks in clean energy power grids, this study comprehensively applies the interpretive structural model and Monte Carlo model to the analysis of investment risk-returns in clean energy power grid projects. The interpretive structural model is utilized to analyze project investment returns, while the Monte Carlo model is used to analyze project investment risks. The project investment risk is based on the factor analysis of project investment returns, and key risk factors are identified through 1000 simulations, and the impact of these risks on project returns is quantified. By combining the two, the investability of the project is analyzed. The results showed that grid electricity prices, kilowatt hour subsidies, technology learning rates, total annual sunshine hours, and system power generation efficiency were key factors driving investment returns. The average expected value of investment return was about 20%, and the probability of investment return below 6% was close to 0. The overall project is worth investing in. From this, it can be seen that the research designed investment risk-return analysis methods for clean energy grid projects can effectively distinguish the main factors affecting investment returns and risks, and pre simulate the risk situation of returns. This study can provide reference for investor decision-making.


Introduction
As the increasing severity of global climate change and the increasing scarcity of fossil fuels, clean energy has gradually gained attention due to its advantages of pollution-free and widespread resource distribution.The power grid project (PGP) is the core of the clean energy utilization system, and the focus of the PGP is on stability.
However, the supply of clean energy will also change with changes in the external environment, leading to fluctuations in the level of energy supply, which in turn affects the stability of the power grid, and has an impact on investment returns and risk [1][2][3].The research mainly uses two models, Interpretive Structural Modeling (ISM) and Monte Carlo model, to analyze the investment risk and return of clean energy grid projects.The ISM model can identify the relationships between various elements in a system, thereby helping decision-makers understand the structure of complex systems and the dynamic relationships between elements [4][5][6].The Monte Carlo model can evaluate the S. Li et al.
2 performance of the system under uncertain conditions and quantify the risk of the system through a large number of random simulations.By combining the two, it is possible to systematically and comprehensively evaluate the investment risks and benefits of clean energy grid projects under uncertain conditions [7][8][9].Therefore, this study combines

Literature Review
In recent years, the investment problem of power grid has attracted widespread attention.Gruber et al. analyzed the expected profit of winter investment based on the cost of power system winterization, combined with electricity demand estimation and power plant shutdown prediction.
The results showed that the profit expectation of winter investment in the power system was positive, but due to the high investment risk and the uncertainty of power generation failure in low-temperature environments, the cost of winter investment was relatively high, which is higher than the cost of social power shortage [10].

DeMenno et al. analyzed the resilience and sustainability of
the US power grid system, using financial sector stress testing methods to test the power sector and analyze its investment situation.The results showed that multi sector coordinated investment projects were often more resilient [11].Bera et al. analyzed the economic benefits of energy storage system projects in the market and proposed a comprehensive investment evaluation and solidification framework.This framework evaluated the income situation throughout the project lifecycle after considering the impact of income estimation after degradation costs on investment returns.The results showed that the method was effective and could provide decision-makers with decision-making basis [12].
In the application of the ISM model, the Kumar R team applied the ISM model to bibliometric and visual analysis, and applied VOSviewer and Biblioshiny software for literature analysis.The results showed that after 2000, the number of annual publications using ISM technology showed a rapid growth trend.In addition, through visual analysis, the most influential authors, sources, articles, countries, and organizations could be identified, providing reference for future research [13].Zayed

Methodology
When conducting risk-return analysis on investment in clean energy grid projects, two models, ISM model and Monte Carlo model, are studied and established.The ISM model is used for investment return analysis of clean energy grid projects, while the Monte Carlo model is used for investment risk analysis of clean energy grid projects, which is based on investment return analysis.

Investment risk-return analysis of clean energy grid projects using ISM model
The ISM model is an effective method that can classify the hierarchical elements and levels of many influencing factors on investment returns of clean PGPs [17] In formula (3), L R represents the technical learning rate.R(t) represents the cumulative installed capacity, calculated using formula (4).
In formula (4), R α represents the newly added installed capacity.The financial cost is reflected in the annual loan interest, which is determined by the loan ratio and interest rate level.The calculation method is as shown in formula (5).
In formula (5), θ represents the loan ratio and δ represents the interest rate level.The cost of power generation is based on financial costs, initial investment, and operation and maintenance costs.The calculation method is as shown in formula (6).(6) In formula (6), β represents the proportion of operation

G = R × H × φ(7)
In formula (7), H represents annual sunshine time, R represents cumulative installed capacity, and φ represents power generation efficiency.The system's operating revenue is based on the annual power generation, as shown in formula (8).
In formula (8),   represents the grid electricity price.
Clean energy grids do not generate greenhouse gas emissions during the profitable process, and are a lowcarbon technology that can generate a portion of carbon emissions trading revenue through carbon emissions trading.Because of the lack of a carbon emission trading mechanism in China, the trading price of the EU's carbon emission system is used, as shown in formula (9).
In formula (9),  represents carbon emissions, and   represents carbon emission trading prices.Then the total income is as shown in formula (10).
=   +   (10) Due to the clean energy grid replacing fossil energy generation, it has significant environmental benefits, as shown in formula (11).
In formula (11), E G represents the unit environmental cost.In addition, in order to encourage the development of clean energy, China has a certain subsidy policy for clean energy power generation, as shown in formula (12).
() =   ( − 1) −   (12) In formula (12),   represents the reduction in electricity subsidies.According to the logical relationship between two factors, the correlation between different factors is shown in Table 3.

Table 3. Table of influencing factors
According to Table 3, the adjacency matrix A for all factors can be derived, and the matrix elements are defined as formula (13).
In formula (14), I represents an identity matrix of the same order as the adjacency matrix, with diagonal elements of 1 and non-diagonal elements of 0, representing the maximum number of transfers.The reachable matrix can divide various elements in the system into three hierarchical sets: the antecedent set, the reachable set, and the highest level element set.The antecedent set represents the set of elements corresponding to all rows with element 1 in a certain element column.The reachable set represents the set of elements corresponding to all columns with 1 element in a certain element row.The set of superlative elements represents a set of elements whose reachable set and antecedent set are the same, which can be expressed as formula (15).

R′(Si) ∩ A(Si) = R(Si)(15)
In formula (15), R(Si) represents the reachable set, A(Si) represents the antecedent set, and R′(Si) represents the set of highest level features.By using formula (15), the nodes at this level can be obtained, which in turn determines the hierarchy of factors affecting the investment returns of the power grid.

Monte Carlo model investment risk-return analysis of clean energy grid projects
The clean energy grid investment risk-return model constructed based on the ISM model is deterministic, meaning that the variables in the model are fixed and unchanged.However, in real production and operation situations, there are often certain risks, and all influencing factors may not be deterministic, but are influenced by various uncertain factors, which can lead to investment risks.Therefore, in order to analyze the investment risks of clean energy grid projects, a Monte Carlo model was used to evaluate the system under uncertain conditions.In the Monte Carlo model, the net present value model is used as the core mathematical model, as shown in formula (16).
In formula (16), NPV represents net present value, C t represents net cash flow, t represents year, T represents project period, and r represents discount rate.The Monte Carlo model is a simulation method that uses random sampling.Its basic principle is to treat the input variable as a random variable and calculate the probability distribution of the system output through extensive simulation.Monte Carlo simulation can help analyze the impact of different variables on system output, identify key risk factors, and quantify the impact of these risks on project returns.Due to the fact that the investment risks of clean energy grid projects mainly come from five main aspects: market risk, technical risk, policy risk, financial risk, and operational risk, based on the experience of investment return analysis, it is determined that the risks mainly come from five uncertain factors: grid electricity price, kilowatt hour subsidies, technical learning rate, total annual sunshine hours, and system power generation efficiency.On this basis, define the model input variables as indicated in Table 4.

Results
In the results analysis section, investment returns and risks were analyzed separately.In both sections, important influencing factors and simulation results were analyzed.
Risk simulation analysis was based on the analysis of returns.For example, the intersection of S1, S6, S26 and S1, S2, and S12 was S1, indicating that S1 is directly influenced by S6, S26, S2, and S12.From the element relationship, S26 was the first level node.Removing this part of the elements will result in the second level node.By continuously removing elements, the 6th node is finally obtained, as shown in Table 6.

Simulation analysis results of investment returns
Table 6.The 6th level node set table From Table 6, S1, S6, S7, S13, and S16 were the factors that occupy the core position and had the highest independence in the project, respectively.These factors include grid electricity prices, kilowatt hour subsidies, technology learning rates, total annual sunshine hours, and system power generation efficiency.These factors had an

Results of investment risk simulation analysis
When conducting investment risk simulation analysis, the probability and sensitivity of investment return were analyzed from two perspectives.Sensitivity analysis was mainly used to analyze the impact of key factors on investment risk, as shown in Figure 4.  Through extensive simulations, the average expected value of investment return was about 20%, with a peak of around 37% and a valley of around 5%.However, the overall probability of a valley occurring was relatively low.
The probability of an investment return between 13% and 25% was close to 50%, while the probability of an investment return below 6% was close to 0. From this, the overall investment risk of the project was low and the returns were good.In addition, from the perspective of influencing factors, the impact of annual sunshine hours on investment returns reached 0.37, with the greatest impact.
Next was the system power generation efficiency, with an impact value of 0.24.The impact of grid electricity prices on investment returns was 0.19.The impact of electricity subsidies on investment returns was 0.14.The impact of technology learning rate on investment returns was minimal, only 0.03.In the process of paying attention to project investment returns, the first thing to focus on was the annual sunshine hours, followed by the system power generation efficiency, while the influence of technology learning rate was not sufficient to a certain extent.

Conclusions
The the ISM model with the Monte Carlo model to provide scientific basis for investment in clean energy grid projects and strong support for decision-making.The research can be divided into four main parts.The first part introduces the theme of investment risk and return analysis for clean energy grid projects.The second part proposes evaluation methods for investment risk and return of clean energy grid projects, namely ISM model return analysis and Monte Carlo model risk analysis.The third part conducts simulation analysis to test and analyze the factors affecting investment risk and return.The fourth part draws research conclusions.
and maintenance costs.Due to the influence of external environment, the power generation of new energy generation often varies in different regions and systems, and the power generation efficiency also varies in different time periods.The annual power generation is shown in formula EAI Endorsed Transactions on Energy Web | Volume 11 | 2024 | (7).
impact on the overall project without being disturbed by other factors, namely critical nodes.When considering investment priorities, it is necessary to focus on monitoring and optimizing these independently influential factors, which are the key factors driving the growth of investment returns.The initial investment and power generation simulation are shown in Figure 2. EAI Endorsed Transactions on Energy Web | Volume 11 | 2024 | S. Li et al.

Figure 2 .Figure 3 .
Figure 2. Initial investment and power generation simulation results

Figure 4 .
Figure 4. Investment risk simulation results investment return and risk assessment of clean energy grid projects are key issues that investors should pay attention to before investing.Research used the ISM model to the hierarchical analysis of investment returns in clean energy grid projects, and used the Monte Carlo model to the simulation evaluation of investment risks in clean energy grid projects.The findings indicated that in the investment return analysis of clean energy grid projects, the simulated data line of the system showed a trend of first increasing and then decreasing with the actual data line, reaching a peak of around 0.6 in 2016, and the two lines were relatively close.In addition, the model deduced that the key factors driving investment returns were grid electricity prices, kilowatt hour subsidies, technology learning rates, total annual sunshine hours, and system power generation efficiency.From the simulation results of the Monte Carlo model, the investment return rate was between 5% and 37%, with an average expected value of 20%.The probability of a return rate between 13% and 25% was close to 50%, while the probability of an investment return rate below 6% was close to 0. This project has certain investment value.From this, the risk return analysis method for PGP investment designed in the research can effectively screen important factors and accurately estimate the project's returns and risks.Although the research designed methods are relatively effective, they only focus on clean EAI Endorsed Transactions on Energy Web | Volume 11 | 2024 | EO et al. used the ISM model to analyze the obstacles to sustainable supply chain management in Egyptian industry.The study collected [15]lopment of Egyptian industry based on this[14].In the application of Monte Carlo modeling, Christensen A P et al. applied Monte Carlo simulation to psychological measurement and analyzed the number of correctly identified factors in multivariate data.The study analyzed the efficacy of different community psychological detection algorithms under different community data conditions through Monte Carlo simulation.The outcomes denoted thatFast-greedy, Louvain, and Walktrap algorithms had relatively better accuracy[15].Soleimani H et al. used

Table 1 .
Table of impact factors environmental cost, carbon emission coefficient of electricity production, and operation and maintenance rate.The other variables are auxiliary variables, and the specific variable system is shown in Table2.
An ISM model variable system is constructed based on the influencing factor table, which takes unit investment return as the core variable and constant variables such as technology learning rate, total annual sunshine hours, unit EAI Endorsed Transactions on Energy Web | Volume 11 | 2024 |

Table 2 .
Variable system table (2)  ( − 1) −   (2)In formula(2),   represents the amount of cost reduction.The amount of cost reduction is shown in formula

Table 4 .
Model input variable table to extract sample values from the pre-defined probability distribution of the input variables.In this step, a single value needs to be selected from the distribution interval of each element to generate a random sample, which is repeatedly repeated and operated based on mathematical logic and core mathematical models.To fully evaluate the uncertainty of the project, the Monte Carlo model will conduct a large number of repeated simulations.This study conducted 10000 simulations, each time generating a different set of random samples and calculating the corresponding output results.Afterwards, all simulation results are collected for statistical analysis.

Table 5 .Table 5 .
When conducting investment return simulation analysis, the first step was to analyze the various elements of investment returns, identify the main factors driving the growth of investment returns, and based on this, conduct simulation.The first level node set table is shown in The first level node set table EAI Endorsed Transactions on Energy Web | Volume 11 | 2024 |