# Sustainability Assessment of Electricity Generation Development under the Implementation of Support Policies with Endogenous Financial Resources Using a Hybrid Decision Support Model

Authors: Fateme Dianat; Vahid Khodakarami; Hamed Shakouri Ganjavi; Seyed-Hossein Hosseini
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Sustainable electricity development is one of the requirements for achieving sustainable development in global communities. However, due to barriers, especially in less developed countries, there is little incentive to invest in the development of sustainable electricity technologies. Therefore, there should be a change in market mechanisms, and broad support policies have to be implemented for the sustainable development of electricity. In the long run, these policies must lead to the sustainable development of energy systems. To evaluate the efficiency and effects of the proposed support policies on the sustainability of electricity generation development, this study intends to analyze the multiple and complex dimensions of the problem using a hybrid decision support model. Moreover, by defining an indicator to assess the electricity generation expansion sustainability, this study assists policymakers in making logical decisions about sustainable support programs for the electricity development based on the characteristics of the electricity market of each country. Despite uncertainties in the electricity market, simulations show that the results of this hybrid model have approximately 88% conformance with historical data. Consequently, the model can evaluate the sustainability of the system under the implementation of the proposed support programs and compare them to select the most effective one. The results show that by assuming a competitive market and rational behavior and implementing support programs with endogenous financial resources, the installed renewable capacity can be improved by up to 70.4% compared with the direct subsidy policies. Regardless of the financial burden of policies (e.g., direct subsidies) and the possibility of facing a budget deficit, these programs can be up to 79.2% more effective in the sustainability of the energy system compared with the direct subsidy policy.


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## Body

## 1. Introduction

Sustainable development of electricity generation, which is a vital part of sustainable development, is achieved when its generation and consumption provide development in all economic, social, environmental, technical, and institutional aspects of human life in the long run [1, 2].The energy efficiency, required land, water and fuel consumption, Operation and Maintenance (O&M) costs, initial investment costs, number of jobs created, the amount of electricity generated, and the volume of greenhouse gases produced are some parameters in the evaluation of the sustainability of an electricity generation technology [2, 3].Numerous studies have shown that renewable electricity technologies are highly compliant with sustainability criteria and are deemed sustainable energy sources [4, 5].However, due to several reasons, especially in less developed countries, such as inadequate infrastructures, unreliable laws to support the development of renewable electricity generation, absence of pollution tariffs, high initial investment expenses for renewable power plants, and cheap fossil fuel (especially in countries rich in fossil resources), the construction of fossil power plants is still economically profitable [3]. Accordingly, there is low motivation in such countries to invest in developing renewable electricity technologies. As a result, governments need to pave the way for the development of renewable electricity by changing the market mechanisms or introducing support programs [6].Plans like tax cuts and technical subsidies for renewable energy development [7], feed-in tariffs (FIT) [7–10], fuel price reforming [10], tradable green certification (TGC) market [7, 11], and carbon emission tax [10, 12, 13] are instances of such support plans.In selecting appropriate support programs to achieve sustainable development, given the high initial investment costs of constructing a new renewable power plant capacity, it cannot be simply assumed that production is carried out at a constant rate [8]. In studies such as [14], the amount of funding needed for decision-makers to achieve specific goals under different scenarios is analyzed, while issues such as how they are funded, the effects of their scarcity, and the prediction of the financial crises are not considered. For long-term development, in addition to considering the system’s variables such as supply, demand, and pricing as endogenous, one should also think about financing new capacities and implementing these support programs [15]. If a decision-maker does not plan for covering these costs (e.g., as stated in [8]), the implementation of support plans (such as the FIT policy) with no feedback from the financial resources leads to the failure of the development plan despite the temporary satisfactory development effects. Plus, by causing a budget deficit for the government [16], they bring no profit except for short-term and unsustainable growth.Sustainability in energy systems has recently attracted the attention of researchers, and extensive literature exists on this topic. Table1 summarizes some key characteristics of recent studies on sustainable energy systems.Table 1
Recent studies on sustainable energy systems.
Aim of the studyYearMethodologyEnergy case studySupport programWith endogenous financial resourcesDimension of sustainabilityEnvironmentalEconomicSocialTechnicalInstitutionalEvaluation of the effect of subsidies for the construction of Home Solar Power Plants (HSPPs) on sustainable energy systems [14]2022System Dynamics (SD)HSPPsSubsidy∗∗∗∗∗A comparative study of FIT and Renewable Portfolio Standard (RPS) policy [17]2015OptimizationRenewable and nonrenewable electricityFIT and RPS∗∗∗∗∗Evaluation of renewable energy development [18]2013SDRenewable energy∗∗∗Evaluation of renewable energy policy [19]2015SDRenewable and nonrenewable electricity∗∗∗∗Creation of a model for the assessment of the sustainable development of energy systems [20]2017Multicriteria decision analysis (MCDA)Energy systems (all forms of energy)Subsidy∗∗∗Assessment of the dynamics of FIT policy [8]2020SDRenewable energyFIT∗∗∗∗∗Feasibility study of switching the electrical power supply [21]2017Engineering economicsSolar photovoltaic (PV) and nonrenewable electricityElectricity tariffs∗∗∗Sustainability analysis of PV/wind/diesel hybrid energy systems for decentralized energy generation [22]2020OptimizationPV/wind/diesel/battery (hybrid energy)∗∗∗∗∗Sustainable energy planning in Africa [23]2020Multicriteria decision analysis (MCDA)Renewable energy∗∗∗∗The role of geothermal resources in sustainable power system planning [24]2020SDGeothermal electricity∗∗∗The impact of the under enforcement of RPS in China [25]2019SDRenewable and nonrenewable electricityRPS∗∗∗Multicriteria optimization for the design and operation of distributed energy systems [26]2021OptimizationDistributed energy systems∗∗∗Reduction in carbon dioxide emissions [10]2022SDRenewable and nonrenewable electricityFIT, carbon cost, eliminating fossil fuel power plant’s subsidies∗∗∗∗∗Simulating the new British Electricity-Market Reform [27]2015SDRenewable and nonrenewable electricityFIT, carbon price, capacity mechanism∗∗∗∗Environmental and economic performance of China’s Emissions Trading Scheme (ETS) pilots [28]2021Scenario and regression analysisIndustrial sector (i.e., mining, manufacturing, producing and supplying electricity, heat, gas, and water)ETS∗∗∗Analysis of renewable energy subsidy in China under uncertainty [16]2021OptimizationRenewable and nonrenewable electricityFIT and RPS∗∗∗∗∗Confronting electricity challenges [29]2019SDRenewable and nonrenewable electricityEnergy efficiency measures, Electric Vehicle (EV) expansion, and renewables policies∗∗∗∗∗This study2022SD and Agent-Based Modeling (ABM) conceptsRenewable and nonrenewable electricityDirect subsidy and support programs with endogenous financial resource∗∗∗∗∗∗The present study attempts to evaluate support programs and their impacts on the development of electricity by identifying the dynamics and influential factors in renewable and conventional electricity development using a decision support model that matches the complexity of the problem. This article defines a comprehensive criterion using which the sustainability of electricity generation development can be properly measured and quantitatively compared under different support programs.A comprehensive and precise decision support model is proposed, which simulates the trend of system variables under different scenarios with decent accuracy. This model can be highly reliable for creating a macro perspective of the entire electricity generation system of a country since it takes into account the competition between players, the interaction between variables, and the uncertainties in the system. With the help of simulations executed on the hybrid model, decision-makers can observe the effects of the proposed support programs on the system before implementation and select the most sustainable support policies for the development of electricity generation with the least financial burden for the government.The remainder of this study is as follows. In Section2, the research method is stated. Section 3 presents a criterion for the sustainability of the support programs, the conceptual model of the problem, and the method of modeling the competition between renewable electricity technologies and conventional electricity generation technologies. In Section 4, the validity of the model is evaluated. In the next step, by assuming that these programs are implemented, their effects on the sustainability of the electricity generation development and the installed capacity of renewable power plants are measured in Section 5. Finally, Section 6 concludes the article.


## 2. Methodology

Achieving sustainability goals in planning the development of power generation technologies requires a comprehensive analysis of the complexities of the electricity market. Therefore, this research begins by using qualitative methods such as interviewing experts in the electricity industry and studying previous research to identify the problem and its main influential factors. To assess the performance and make the right decision about the formulation of appropriate support programs that lead to the sustainable development of electricity generation, it is necessary to use a decision support model that addresses important aspects of the system, including the dynamics of problem variables, feedback relationships, and the interactions of players in a competitive market and an uncertain environment. In this research, the combination of the system dynamics (SD) simulation and the concepts of agent-based modeling (ABM) is used as a suitable decision support model for analysis. In this way, SD is used to model the complex structure of influential continuous variables, while ABM concepts are used to model the interaction between players, such as the competition between renewable power plants and other conventional ones.Liberalized electricity markets include several heterogeneous generators that compete based on their type of technology and risk-taking capacity. As a result, such markets deal with different agents (electricity generators) that form a multiagent (multiplayer) problem. However, due to the limited number of participants, the electricity market model is generally similar to an oligopoly (imperfect competition).To simplify modeling, the problem was solved for two players: (1) wind power generators (which represent renewable power plants because of their maturity and abundance [30]) and (2) combined-cycle gas turbines (CCGT, generators that represent conventional power plants since they offer high efficiency among fossil fuel generators and countries show more tendency toward their construction). By assuming a competitive market, the evolutionary game theory (EGT) method was used to find the equilibrium point of the game. Iran’s electricity market data [31] (as a sample to inspect the effects of the selected plans) were employed to perform this modeling for the period from 2010 to 2050. Moreover, the historical data from 2010 to 2019 were compared with the model behavior to validate the modeling. After ensuring the accuracy of the model, assuming the existence of a rational behavior between players and a competitive market, support programs with endogenous financial resources (that are assumed to be functional after 2022) were executed in the model so that they can be compared, and their effects on the system and their efficiency can be analyzed.


## 3. Model

To resolve concerns about the possibility of the termination of support programs due to financial pressures on governments [15] and budget deficiencies resulting from the implementation of programs such as FIT [8, 16], this study assumes that support programs with endogenous financial resources are sustainable, and evaluates their sustainability. Assuming a rational relationship between price changes and supply and demand, along with a competitive market, and inspired by a variety of support policies implemented in the world [7, 30], this study evaluates the sustainability of the three following support policies and offers solutions to provide implementation costs:(i)
Support policy 1 (SP1): taxing the emission of pollutants and allocating its revenue to wind power systems as subsidies(ii)
Support policy 2 (SP2): modifying the fuel price and allocating its revenue to wind power systems as subsidies(iii)
Support policy 3 (SP3): taxing electricity consumers and allocating the obtained revenue to wind power systems as subsidiesThese support plans increase profitability and appeal of investment in the development of their capacity by subsidizing the generation of renewable electricity per kilowatt-hour (kWh), which increases its generation. Figure1 shows the influence mechanisms of the mentioned support programs on the development of renewable electricity capacity.Figure 1
The effect of support programs on increasing the profitability of renewable electricity generation.Each support policy affects various aspects of the power generation system upon implementation, such as the amount of pollutant gas emissions or the development rate of renewable electricity generation. However, the effectiveness of implementing a support policy cannot be assessed solely based on the increase in the installed capacity of a power plant. In particular, implementing a policy may increase the price of electricity or the unemployment rate in other electricity generation technologies, which are not in line with the interests of consumers. Therefore, decision-makers should carefully evaluate the effects of support programs from various aspects. In this regard, a criterion should be defined that provides a quick macro view of the effects of implementing support programs on electricity generation development for better policy-making decisions.Several studies [32, 33] have assessed the sustainability of energy systems under the influence of different electricity generation technologies using various methods such as multiple-criteria decision-making (MCDM) [34]. Based on the focus of each study, performance indicators and various parameters have been proposed to evaluate the sustainability of an energy system, as listed in a review study [1]. In general, the sustainability of energy systems can be examined in five aspects: economic, social, environmental, technical, and institutional [2]. Using the parameters introduced in studies such as [1, 3], the present study proposes a criterion to determine the sustainability of the electricity generation expansion, called the electricity development sustainability index (EDSI), to provide a comprehensive view of the effectiveness of each support program. To achieve research objectives, after receiving comments from electricity industry experts, and taking into account model boundary and regardless of the implementation cost of support programs, the following factors are considered to affect EDSI:Competitiveness of renewable electricity and its market share [35, 36]Net job creation of the electricity industry [3, 36]Greenhouse gas emissions [36, 37]Consumer demand coverage [3, 23]Price affordability [1]As shown in Figure2, EDSI improves with the growth in the share of renewable electricity in electricity generation and its competitiveness in the market. This index also increases with the creation of jobs in the electricity industry (i.e., the total number of jobs created in the renewable and nonrenewable electricity industry) and the coverage of consumer demand. Finally, generating electricity at a reasonable and affordable price and reducing greenhouse gases are other influential factors.Figure 2
The relationship between the factors affecting EDSI.EDSI is normalized based on the first year of the study (2010), and as a result, its value for this year is one. This index is a relative quantity that can be used to understand the expansion trend of the electricity generation system toward sustainability or unsustainability, compare the proposed support programs, and provide policymakers with a better view, assisting their decisions.To simulate the EDSI and understand how it is affected by the implementation of support programs, it is necessary to simulate the involved factors. As shown in Figure1, one of the most significant factors affecting the tendency toward new investments in different generation technologies is the investor’s expected profitability ratio (IEPR), which depends on income and the levelized cost of energy (LCOE), as shown in the following equation:(1)IEPR=Income−LCOELCOE.The tendency toward new investment has been studied in the literature under titles such as Willingness For Investment (WFI) [9] or the attractiveness of constructing new power plants [10], which depends on its IEPR, and the IEPR of other power plants.It is evident that price, as the outcome of the interaction and balance between supply and demand in a competitive environment, plays a significant role in calculating IEPR and the tendency toward new investment.The price of electricity is partially related to the price elasticity of supply and demand. In other words, increasing the generation in power plants yields lower electricity prices, which means higher profit due to quantity and lower profit due to price. In contrast, if power plants generate less electricity, insufficient delivery of electricity increases the price, which means higher profit regarding price and lower profit regarding quantity.However, price is also affected by the competition mechanism of power plants in the electricity market. To elaborate, each power plant needs to adjust its behavior (price and generation capacity) based on the behavior of other power plants (i.e., they need to offer a competitive price for their electricity in accordance with the price of their competitors). Optimal bidding in the electricity market increases the profit of power plants. In order to have a more extensive view and accurate evaluation, we need to analyze factors that affect the market, including the dynamics of the development of renewable and nonrenewable power plants. Since the goal is to inspect the long-term trend of the system under support programs, and the long-term behavior of the market usually occurs in its stable equilibrium points, this study seeks to find the equilibrium bidding point in the electricity market.The relationships between price, supply, and demand in a competitive market are shown in Figure3. In this figure, endogenous funded support programs are marked with red arrows.Figure 3
The relationships between price, supply, and demand in support plans with endogenous financial resources.For competition analysis, game theory-based models are used as decision support tools, which are mainly used for the analysis of oligopoly competitions. According to the game theory, the ultimate price for market players occurs in the Nash equilibrium of market competition, where no player is willing to change its strategy to increase its profit.


### 3.1. Finding the Equilibrium Point of the Games

By reviewing the literature on game theory [38–43], it can be concluded that the methods for finding the Nash equilibrium points in competitive and noncooperative games can be divided into four categories based on the mathematical equations of the system and finiteness or infiniteness of the proposed pricing options, as shown in Figure 4.Figure 4
Categories of solutions for finding the equilibrium point of the games.In this figure, competition results of categories 1 and 3 are strongly influenced by the format of the objective function and relationships between variables [40]. However, in the real world, a different number of participants and decision variables can compete in the market with specific delays, sequential and feedback relationships, uncertainties, conditional relationships, and linear and nonlinear relationships with other participants. Moreover, different scenarios can be explored. As a result, objective functions become dependent on several factors, which makes the modeling of the problem as mathematical equations a time-consuming and challenging task. Furthermore, oligopoly market models, which rely only on the equation-based game theory, usually suffer from three shortcomings: disregarding feedback loops, disregarding time delays, and being limited to the definitive demand function [40]. This research studies the electricity market, which has high levels of intrinsic complexity and uncertainty sources with several feedback relations. Hence, solutions 1 and 3 are not appropriate for finding equilibrium points in this competition.Since the bidding price is a continuous variable, price options are infinite. Therefore, solution 2 is not accurate in finding an equilibrium price. Thus, to apply more realistic conditions and inspect the effects of different scenarios on electricity development sustainability in the uncertain and competitive environment of the electricity market, it is more appropriate to use the fourth category [42, 43]: the evolutionary strategy solution (i.e., the gradual finding of the answer).Studies comparing the results of game equilibrium using different methods [41] showed that if Nash equilibrium exists and the game assumptions are realistic, all solution methods converge to the same results [44, 45].Solutions provided in categories 1, 2, and 3 in Figure4 can only find the final equilibrium point, while they offer no information about the system’s path to the final solution. On the other hand, the evolutionary strategy solution, in addition to converging to the equilibrium point, gives the decision-maker information about how players dynamically decide in reaching the equilibrium point [42, 46].


### 3.2. Competition Modeling

The model assumes that the “pay as bid pricing” is the payment mechanism for market clearing price (MCP). To motivate investment in the construction of new power plants and the development of generation, each power plant should try to achieve more revenue and less cost (higher IEPR), compared to other competitors, according to the power generation and price bidding of the market. In this way, their tendency to invest in capacity expansion also increases.The adopted strategy and the profit of each player affect the profit of other competitors. Their decision to determine the price or quantity of their generated electricity results from an oligopoly game. At the equilibrium point, where all players consider each other’s strategies, their IEPRs are maximized. The model determines the acceptable quantity and price for the generation of power plants so that while they continue generation, the development of power plants can also be achieved simultaneously.In the evolutionary strategy solution, a probability of selecting or disregarding a strategy is assigned to each player. The value of this probability indicates the willingness of the player to select that strategy. The probability of choosing a behavior depends on its reward.In modeling the competition between two power plants,PWL is defined as the probability of offering a low price and PWH is the probability of offering a high price by the wind power plants. Similarly, PCL is the probability of offering a low price and PCH is the probability of offering a high price by CCGT. The relation between these parameters is shown in equations (2) and (3)(2)PWL=1−PWH,(3)PCL=1−PCH.As a result, four pricing conditions are formed. It is necessary to calculate the IEPR of each player in these four pricing conditions to find the equilibrium point and the best strategy for each player.WWLCL IEPR of the wind power plant when PWL and PCL occur, meaning that both the wind power plant and the CCGT power plant bid a low price.WWLCH is the IEPR of the wind power plant when PWL and PCH occur, meaning that the wind power plant bids a low price while the CCGT power plant bids a high price.WWHCL is the IEPR of the wind power plant when PWH and PCL occur, meaning that the wind power plant bids a high price, and the CCGT power plant bids a low price.WWHCH is the IEPR of the wind power plant when PWH and PCH occur, meaning that both the wind power plant and the CCGT power plant bid a high price.Moreover, CWLCL, CWLCH, CWHCL, and CWHCH are the corresponding IEPRs of CCGT power plants under similar bidding conditions.The IEPR in each bidding condition is determined according to the electricity price levels of the power plant, the electricity price levels of other power plants, and the effect of these prices on the power generation.The IEPRs of players dynamically and continuously change as the output of the SD model, and their results are continuously fed into the game model to decide on the equilibrium point (Figure5).Figure 5
Power market subsystems.To solve the game, the values of the variablesUPWL (utility of the wind power plant if PWL occurs, regardless of the CCGT’s bidding price), UPWH (utility of the wind power plant if PWH occurs, regardless of the CCGT’s bidding price), UPCL (utility of the CCGT power plant if PCL occurs, regardless of the wind power plant’s bidding price), UPCH (utility of the CCGT power plant if PCH occurs, regardless of the wind power plant’s bidding price), U¯W (the average utility of the wind power plant, under any bidding price condition), and U¯C (the average utility of the CCGT power plant, under any bidding price condition) are calculated according to equations (4) and (5).(4)UPWL=PCL×WWLCL+PCH×WWLCHUPWH=PCL×WWHCL+PCH×WWHCH⟶U¯W=PWL×UPWL+PWH×UPWH,(5)UPCL=PWL×CWLCL+PWH×CWHCLUPCH=PWL×CWLCH+PWH×CWHCH⟶U¯C=PCL×UPCL+PCH×UPCH.Equilibrium occurs when players are reluctant to change their strategy to gain more utility and maintain their bidding strategy in the market. In other words, according to equations (6) and (7), we have(6)dPWLdt=PWL×UPWL−U¯W=PWL×PWHPCL×WWLCL−WWHCL+PCH×WWLCH−WWHCH=0.(7)dPCLdt=PCL×UPCL−U¯C=PCL×PCHPWL×CWLCL−CWLCH+PWH×CWHCL−CWHCH=0.The points that simultaneously answer the above equations are equilibrium points. These points can be stable or unstable. In order to determine the stability of equilibrium points of the system’s replicate dynamic equations, the Friedman condition for the Jacobian matrix [47] or Lyapunov’s theory of stability must be satisfied [25, 42]. In our case, since the IEPRs of players continuously change, the unstable equilibrium answer cannot be maintained, and the system converges to the steady equilibrium state.When a strategy is successful in the evolutionary game, the movement toward it occurs gradually, and eventually, the answers to the evolutionary strategies converge to the Nash equilibrium point [42, 46]. The game equilibrium answer re-enters the SD and changes the model variables. As a result, a two-way relationship is observed between the SD and the game part, and the hybrid decision support model operates in a connected and integrated manner. The conceptual model of the problem ultimately takes the form of Figure 5.Figure5 illustrates the following: the relationship between demand and price in balancing loops B1 and B′1 [48], the effect of learning in reinforcing loops R1 and R′1 [8, 49, 50], the relationship between supply and price in balancing loops B2 and B′2 [48], dynamics of path dependence (the concept of the share of each player to the share of other players [40]) in the reinforcing loops R2 and R′2, and the effect of resource depletion in the balancing loops B3 and B′3 [49, 50]. This model can take into account the effects of social acceptance [8, 50], sensitivity analysis for possible uncertainties [51], and competition between electricity market players. By regarding a vast number of variables affecting the system and their interrelations [52], this model can evaluate the effects of several proposed support programs on the sustainability of power generation development and provide the decision-maker with a comprehensive view.


### 3.3. Data and Mathematical Equations

In this study, Iran’s electricity market data (energy balance), published by the Power Ministry of Iran [31], was used for modeling. Additional data were also extracted from statistics published by CCGT and wind power plants and articles that studied Iran’s electricity generation [10], including the historical data of wind farms and CCGT capacities, the fuel cost of CCGT power plants, discount rates, fixed and variable O&M costs, and the annual number of jobs created per gigawatt-hour electricity generation using wind power and CCGT. General parameters such as natural gas heat rate and the capacity factor (CF) of CCGT and wind power plants (mentioned in articles such as [53]) were also utilized.After extracting the necessary data, the mathematical equations of the model and the relationship between model variables were determined using the studies on electricity generation in Iran (e.g., [8, 10, 54]) and interviewing experts in the energy field and employees of the Power Ministry. The data and mathematical equations were developed in the form of stock-flow diagrams in Vensim software using the conceptual model depicted in Figure 5.It was assumed that, according to Table2, a tax would be levied on CCGT power plants in proportion to the pollutant emissions to implement the SP1, which changes the LCOE of CCGT power plants.Table 2
Emission cost and emission factor.
PollutionNOXSO2COPMCO2CH4Emission cost ($/g)0.001072780.003262890.0003352220.007687890.00001788890.000374222Emission factor (g/MMBtu)2002519600001.5It was also assumed that implementing SP2 would increase the fuel cost for Iran’s CCGT power plants from $0.3 to $0.9 per MMBtu, consequently changing the LCOE of CCGT power plants similar to SP1. In addition, it was assumed that consumers should pay an additional $0.003 per kWh electricity consumption as tax to implement the SP3. The modeling also simulates the direct subsidy relative to underdevelopment (DSRU) program.The DSRU program is an instance of the FIT policy for renewable electricity. DSRU has also been mentioned in some articles as a policy of closeness to the goal [8], a policy in which renewable electricity power plants receive less support as renewable energy share increases. The DSRU simulation assumed that wind farms would receive $0.35 per kWh generated electricity until they reach 1% of the market share and $0.21 per kWh generated electricity until they reach 5% of the market share.


## 3.1. Finding the Equilibrium Point of the Games

By reviewing the literature on game theory [38–43], it can be concluded that the methods for finding the Nash equilibrium points in competitive and noncooperative games can be divided into four categories based on the mathematical equations of the system and finiteness or infiniteness of the proposed pricing options, as shown in Figure 4.Figure 4
Categories of solutions for finding the equilibrium point of the games.In this figure, competition results of categories 1 and 3 are strongly influenced by the format of the objective function and relationships between variables [40]. However, in the real world, a different number of participants and decision variables can compete in the market with specific delays, sequential and feedback relationships, uncertainties, conditional relationships, and linear and nonlinear relationships with other participants. Moreover, different scenarios can be explored. As a result, objective functions become dependent on several factors, which makes the modeling of the problem as mathematical equations a time-consuming and challenging task. Furthermore, oligopoly market models, which rely only on the equation-based game theory, usually suffer from three shortcomings: disregarding feedback loops, disregarding time delays, and being limited to the definitive demand function [40]. This research studies the electricity market, which has high levels of intrinsic complexity and uncertainty sources with several feedback relations. Hence, solutions 1 and 3 are not appropriate for finding equilibrium points in this competition.Since the bidding price is a continuous variable, price options are infinite. Therefore, solution 2 is not accurate in finding an equilibrium price. Thus, to apply more realistic conditions and inspect the effects of different scenarios on electricity development sustainability in the uncertain and competitive environment of the electricity market, it is more appropriate to use the fourth category [42, 43]: the evolutionary strategy solution (i.e., the gradual finding of the answer).Studies comparing the results of game equilibrium using different methods [41] showed that if Nash equilibrium exists and the game assumptions are realistic, all solution methods converge to the same results [44, 45].Solutions provided in categories 1, 2, and 3 in Figure4 can only find the final equilibrium point, while they offer no information about the system’s path to the final solution. On the other hand, the evolutionary strategy solution, in addition to converging to the equilibrium point, gives the decision-maker information about how players dynamically decide in reaching the equilibrium point [42, 46].


## 3.2. Competition Modeling

The model assumes that the “pay as bid pricing” is the payment mechanism for market clearing price (MCP). To motivate investment in the construction of new power plants and the development of generation, each power plant should try to achieve more revenue and less cost (higher IEPR), compared to other competitors, according to the power generation and price bidding of the market. In this way, their tendency to invest in capacity expansion also increases.The adopted strategy and the profit of each player affect the profit of other competitors. Their decision to determine the price or quantity of their generated electricity results from an oligopoly game. At the equilibrium point, where all players consider each other’s strategies, their IEPRs are maximized. The model determines the acceptable quantity and price for the generation of power plants so that while they continue generation, the development of power plants can also be achieved simultaneously.In the evolutionary strategy solution, a probability of selecting or disregarding a strategy is assigned to each player. The value of this probability indicates the willingness of the player to select that strategy. The probability of choosing a behavior depends on its reward.In modeling the competition between two power plants,PWL is defined as the probability of offering a low price and PWH is the probability of offering a high price by the wind power plants. Similarly, PCL is the probability of offering a low price and PCH is the probability of offering a high price by CCGT. The relation between these parameters is shown in equations (2) and (3)(2)PWL=1−PWH,(3)PCL=1−PCH.As a result, four pricing conditions are formed. It is necessary to calculate the IEPR of each player in these four pricing conditions to find the equilibrium point and the best strategy for each player.WWLCL IEPR of the wind power plant when PWL and PCL occur, meaning that both the wind power plant and the CCGT power plant bid a low price.WWLCH is the IEPR of the wind power plant when PWL and PCH occur, meaning that the wind power plant bids a low price while the CCGT power plant bids a high price.WWHCL is the IEPR of the wind power plant when PWH and PCL occur, meaning that the wind power plant bids a high price, and the CCGT power plant bids a low price.WWHCH is the IEPR of the wind power plant when PWH and PCH occur, meaning that both the wind power plant and the CCGT power plant bid a high price.Moreover, CWLCL, CWLCH, CWHCL, and CWHCH are the corresponding IEPRs of CCGT power plants under similar bidding conditions.The IEPR in each bidding condition is determined according to the electricity price levels of the power plant, the electricity price levels of other power plants, and the effect of these prices on the power generation.The IEPRs of players dynamically and continuously change as the output of the SD model, and their results are continuously fed into the game model to decide on the equilibrium point (Figure5).Figure 5
Power market subsystems.To solve the game, the values of the variablesUPWL (utility of the wind power plant if PWL occurs, regardless of the CCGT’s bidding price), UPWH (utility of the wind power plant if PWH occurs, regardless of the CCGT’s bidding price), UPCL (utility of the CCGT power plant if PCL occurs, regardless of the wind power plant’s bidding price), UPCH (utility of the CCGT power plant if PCH occurs, regardless of the wind power plant’s bidding price), U¯W (the average utility of the wind power plant, under any bidding price condition), and U¯C (the average utility of the CCGT power plant, under any bidding price condition) are calculated according to equations (4) and (5).(4)UPWL=PCL×WWLCL+PCH×WWLCHUPWH=PCL×WWHCL+PCH×WWHCH⟶U¯W=PWL×UPWL+PWH×UPWH,(5)UPCL=PWL×CWLCL+PWH×CWHCLUPCH=PWL×CWLCH+PWH×CWHCH⟶U¯C=PCL×UPCL+PCH×UPCH.Equilibrium occurs when players are reluctant to change their strategy to gain more utility and maintain their bidding strategy in the market. In other words, according to equations (6) and (7), we have(6)dPWLdt=PWL×UPWL−U¯W=PWL×PWHPCL×WWLCL−WWHCL+PCH×WWLCH−WWHCH=0.(7)dPCLdt=PCL×UPCL−U¯C=PCL×PCHPWL×CWLCL−CWLCH+PWH×CWHCL−CWHCH=0.The points that simultaneously answer the above equations are equilibrium points. These points can be stable or unstable. In order to determine the stability of equilibrium points of the system’s replicate dynamic equations, the Friedman condition for the Jacobian matrix [47] or Lyapunov’s theory of stability must be satisfied [25, 42]. In our case, since the IEPRs of players continuously change, the unstable equilibrium answer cannot be maintained, and the system converges to the steady equilibrium state.When a strategy is successful in the evolutionary game, the movement toward it occurs gradually, and eventually, the answers to the evolutionary strategies converge to the Nash equilibrium point [42, 46]. The game equilibrium answer re-enters the SD and changes the model variables. As a result, a two-way relationship is observed between the SD and the game part, and the hybrid decision support model operates in a connected and integrated manner. The conceptual model of the problem ultimately takes the form of Figure 5.Figure5 illustrates the following: the relationship between demand and price in balancing loops B1 and B′1 [48], the effect of learning in reinforcing loops R1 and R′1 [8, 49, 50], the relationship between supply and price in balancing loops B2 and B′2 [48], dynamics of path dependence (the concept of the share of each player to the share of other players [40]) in the reinforcing loops R2 and R′2, and the effect of resource depletion in the balancing loops B3 and B′3 [49, 50]. This model can take into account the effects of social acceptance [8, 50], sensitivity analysis for possible uncertainties [51], and competition between electricity market players. By regarding a vast number of variables affecting the system and their interrelations [52], this model can evaluate the effects of several proposed support programs on the sustainability of power generation development and provide the decision-maker with a comprehensive view.


## 3.3. Data and Mathematical Equations

In this study, Iran’s electricity market data (energy balance), published by the Power Ministry of Iran [31], was used for modeling. Additional data were also extracted from statistics published by CCGT and wind power plants and articles that studied Iran’s electricity generation [10], including the historical data of wind farms and CCGT capacities, the fuel cost of CCGT power plants, discount rates, fixed and variable O&M costs, and the annual number of jobs created per gigawatt-hour electricity generation using wind power and CCGT. General parameters such as natural gas heat rate and the capacity factor (CF) of CCGT and wind power plants (mentioned in articles such as [53]) were also utilized.After extracting the necessary data, the mathematical equations of the model and the relationship between model variables were determined using the studies on electricity generation in Iran (e.g., [8, 10, 54]) and interviewing experts in the energy field and employees of the Power Ministry. The data and mathematical equations were developed in the form of stock-flow diagrams in Vensim software using the conceptual model depicted in Figure 5.It was assumed that, according to Table2, a tax would be levied on CCGT power plants in proportion to the pollutant emissions to implement the SP1, which changes the LCOE of CCGT power plants.Table 2
Emission cost and emission factor.
PollutionNOXSO2COPMCO2CH4Emission cost ($/g)0.001072780.003262890.0003352220.007687890.00001788890.000374222Emission factor (g/MMBtu)2002519600001.5It was also assumed that implementing SP2 would increase the fuel cost for Iran’s CCGT power plants from $0.3 to $0.9 per MMBtu, consequently changing the LCOE of CCGT power plants similar to SP1. In addition, it was assumed that consumers should pay an additional $0.003 per kWh electricity consumption as tax to implement the SP3. The modeling also simulates the direct subsidy relative to underdevelopment (DSRU) program.The DSRU program is an instance of the FIT policy for renewable electricity. DSRU has also been mentioned in some articles as a policy of closeness to the goal [8], a policy in which renewable electricity power plants receive less support as renewable energy share increases. The DSRU simulation assumed that wind farms would receive $0.35 per kWh generated electricity until they reach 1% of the market share and $0.21 per kWh generated electricity until they reach 5% of the market share.


## 4. Verification and Validation

Before using the model to analyze support programs, its validity was investigated using several tests to ensure the accuracy of the results. Specifically, to verify the framework (boundary adequacy and structure assessment), the reasonableness of the dynamics of renewable and nonrenewable electricity development trends, balancing and reinforcing loops, and cause-and-effect relationships between the problem variables (Figure5) were evaluated and approved by renewable electricity experts.As shown in Figure6, in 2019, the sustainability of power generation development using the index defined in this study (EDSI) is 2.5 times the historical data from the initial year (2010), indicating that Iran’s electricity industry is moving toward sustainable development.Figure 6
The simulated and historical data for EDSI.The mean absolute percentage error (MAPE) value was used to evaluate the conformance of the simulated values with the historical data. This rate is 12.1% for EDSI, 0.8% for the demand, 14.6% for wind power capacity, and 3.7% for CCGT power capacity. The Pearson correlation coefficient (a coefficient between 1 and −1) was employed to calculate the correlation between the simulated values and historical data. The obtained values for this coefficient were 0.956 for EDSI, 0.996 for demand, 0.959 for wind power capacity, and 0.976 for CCGT power capacity. Competitive modeling validity and Nash equilibrium were also assessed using the sample data.


## 5. Results and Discussion

The designed model can determine EDSI over time and under the influence of different support programs. Assuming that there exists a competitive market and that rational behavior prevails, the results of the EDSI under the three support programs (i.e., SP1, SP2, and SP3) are illustrated in diagrams 1, 2, and 3 in Figure7, respectively. Moreover, the EDSI for the DSRU program is illustrated in diagram 4. Finally, EDSI in the absence of support programs (while it is assumed that the market is competitive and logical behavior prevails) is presented in diagram 5 in Figure 7.Figure 7
EDSI under different scenarios.Figure7 shows that SP1, SP2, and SP3 positively impact the sustainability of power generation development. Although diagram 4 is simulated regardless of the DSRU program implementation cost, the efficiency of the DSRU policy in the sustainability of the energy generation development is still less than the other three mentioned programs that are financed endogenously.Compared with the absence of support programs, the sustainability of energy generation development was improved by 85.8%, 31.4%, and 13.5% for SP1, SP2, and SP3, respectively. However, the DSRU program could only increase the sustainability of electricity generation development by 3.7% compared with the state of having no support plans.The capacity development results for CCGT power plants and wind farms are illustrated in Figures8(a) and 8(b), in respective order, under different scenarios.Figure 8
The installed capacity of CCGT (a) and wind (b) power plants.
(a)(b)As shown by the red arrows in Figure3, corrections in fuel prices or emission taxes increase the cost of generating conventional electricity, resulting in a lower profit and incentive to invest in the sector. By spending the mentioned revenues on subsidizing renewable electricity generation, the income and profitability of renewable power plants will increase, yielding the development of renewable electricity (Diagrams 1 and 2 of Figure 8). It is evident that these effects intensify as the revenues increase [12].It is worth mentioning that implementing the tradable green certificate (TGC) market can be considered the opposite of the emission trading system (ETS). While emission trading imposes a cost on nonrenewable electricity generation, TGC generates additional revenue for renewable electricity and ensures that a certain percentage of the electricity generation comes from renewable sources [11]. Therefore, it seems that the implementation of the TGC market, such as taxing the emission of pollutants and allocating its revenue as a subsidy (SP1) or modifying the fuel price and allocating its revenue as a subsidy to wind power systems (SP2), can lead to further development of wind power systems.Nevertheless, upon the implementation of TGC, a market is created to purchase and sell these certificates, and it seems that the bureaucracy for implementing this program is higher than the two other programs (SP1 and SP2). Due to this bureaucracy, its implementation seems unlikely in countries with a weaker information flow system. This lack of extensiveness may be one of the reasons why TGC markets are utilized mostly in European countries and some US states.In contrast to SP1 and SP2, which imposed financial pressure on the electricity generated through fossil fuels, SP3 increases the tax paid by consumers for electricity. In the early years of its implementation, consumers may be less willingly involved with this program. As a result, electricity demand in the consumer sector will decrease. However, sensitivity analysis shows that this drop in demand is relatively small and negligible. With the total demand remaining approximately constant, the taxes collected from consumers can be allocated to multiple objectives, including subsidizing per kWh of renewable electricity (diagram 3, Figure8), offering discounts for initial investments in the construction of wind power plants, or increasing the guaranteed purchase price of the wind power generators. In all cases, positive effects can be seen on the development of renewable electricity capacity and the sustainability of electricity generation development.In policies that impose financial pressure on the electricity generated from fossil fuels (SP1 and SP2), revenues are proportional to the electricity generation by CCGT power plants. From another perspective, the incomes obtained from conventional power plants are divided by the capacity of wind power generation to obtain a subsidy per kWh for wind power generation (Figure1). However, as the generation of wind farms has an upward trend, the amount of subsidy given per kWh of wind power generation decreases (as shown in Figure 9). Simulation results show that although the per kWh subsidies are initially higher than DSRU, they decrease significantly over time. Even though DSRU will be greater than subsidies of SP1, SP2, and SP3 in later years (even if the financial resources of the country are large enough that the budget deficit caused by the DSRU program does not prevent it from continuing), the efficiency of this policy (and the development of wind power as its result) is less than the rate of development caused by the support policies with endogenous financial resources.Figure 9
Subsidy per kWh of electricity generated from the wind under different scenarios.According to Figure8(b), implementing tax programs on emissions and providing subsidies for wind power (SP1), reforming fuel prices and providing subsidies for wind power (SP2), and taxing consumption and providing subsidies to wind power (SP3) yield an increase of 70.4%, 24.9%, and 8.5% on the installed capacity of wind farms compared with the DSRU program, respectively.Figure9, and its correlation to Figure 8(b), shows that appropriate timing for the utilization of incentives, their intensity, and the manner through which these support policies are initiated determine further development of renewable electricity. Midttun and Gautesen [6] also share a similar view.The increased growth rate of any technology reduces its production costs in later stages, which yields further development of power plant capacity and sustainability improvement.As shown in diagrams 1 and 3 of Figure9, if it is assumed that the subsidy allocated to wind power, which results from the implementation of taxing programs on emissions (SP1) or consumers (SP3) are equal, SP1 will impose financial pressures on the electricity generated from fossil fuels, reducing the share of this sector in the market (diagrams 1 and 3 of Figure 8(a)). Consequently, by implementing SP1, the capacity of wind farms and EDSI will be 57.1% and 63.6% more than those obtained from implementing SP3, as shown in diagrams 1 and 3 of Figure 8(b) and diagrams 1 and 3 of Figure 7, respectively.In diagrams 2 and 3 of Figure9, even though the subsidy given to wind power plants from the fuel price modification program (SP2) is less than that obtained from taxing electricity consumers (SP3) per kWh of wind power generation, the financial pressure on fossil fuel electricity and its effect on reducing the share of this sector in the market (diagrams 2 and 3 Figure 8(a)) increase the capacity of wind farms (diagrams 2 and 3 Figure 8(b)) by 15.1%, and causes EDSI to grow by 15.8% (diagrams 2 and 3 of Figure 7) compared with SP3.Therefore, implementing financial support programs that impose pressures on fossil fuel electricity (SP1 and SP2) will cause less development in this sector compared with the development caused by subsidies through taxing consumers (SP3) and the DSRU mode (Figure8(a)). Consequently, if the decision-makers aim to achieve sustainability in the energy generation system, reduce the share of fossil fuel electricity, increase the share of renewable electricity, and reduce emissions, financing policies through pressure on fossil fuel electricity are suggested to be more efficient.On the other hand, if decision-makers solely aim to increase the total generation capacity of their country’s power plants to cover consumer demand, it seems appropriate to tax the total electricity consumption (SP3) as it would not change demand remarkably and would not impose high social costs on governments. However, this practice will not massively influence fossil fuel power plants. In this case, SP3 is suitable for developing both renewable and nonrenewable electricity. Nevertheless, as this scenario generates less clean electricity and more emissions than SP1 and SP2, it has less effect on the sustainability of the energy system.


## 6. Conclusions

In this study, a hybrid model was used to investigate the effects of support programs on the sustainability of an energy system and the capacity development of renewable power plants. The goal was to provide simultaneous analysis of the main aspects of the problem, including dynamics between factors, feedback relationships, competitiveness, and the uncertain environment of the electricity market. The model was executed using Iran’s electricity industry data.The results show that programs funded from within the system (such as the three programs mentioned in this article) can be considered sustainable support programs for the development of renewable electricity. These programs improve the installed capacity of the wind farms by 8.5% to 70.4% more than direct subsidy policies and do not impose additional costs and financial burdens on the government, while at the same time, they have 9.5% to 79.2% greater development sustainability compared with direct subsidy.This research has some limitations which can be improved in the future. For example, the demand in the electricity industry can be increased or decreased by imports and exports, depending on the conditions of each country. In this study, the effect of the electricity import and export subsystem has been omitted in the model since Iran’s net import and export is negligible in relation to the country’s total electricity demand. In future studies, this subsystem can be implemented in the model, particularly for countries with higher electricity imports and exports.In future research, the sustainability of electricity generation development can also be assessed by implementing other programs (or a combination of programs) that support the development of clean electricity using the proposed model.



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*Source: 7436749-2022-05-18.xml*