Evaluating different scenarios for Tradable Green Certificates by game theory approaches

Evaluating different scenarios for Tradable Green Certificates by game theory approaches Right now employment of polices and tools to decrease the carbon emission through electricity generation from renewable resources is one of the most important problem in energy policy. Tradable Green Certificate (TGC) is an economics mechanism to support green power generation. Any country has the challenge to choose an appropriate policy and mechanism for design and implementation of TGC. The purpose of this study is to help policy makers to design and choose the best scenario of TGC by evaluating six scenarios, based on game theory approach. This study will be useful for increasing the effectiveness of TGC system in interaction with electricity market. Particularly, the competition between thermal and renewable power plants is modeled by mathematical modeling tools such as cooperative games like Nash and Stackelberg. Each game is modeled by taking into account of the two following policies. The results of the six scenarios and the sensitivity analysis of some key parameters have been evaluated by numerical studies. Finally, in order to evaluate the scenarios we calculated the level of social welfare in the all scenarios. The results of all models demonstrate that when the green electricity share (minimum requirement) increases the TGC price decreases. Moreover, in all scenarios when the minimum requirement is 100% then the maximum level of social welfare is not met. Also when the minimum requirement is less than 50%, the scenarios with the market TGC price policy have more social welfare in comparison with the scenarios with fixed TGC price policy. Keywords Green electricity  Tradable Green Certificate  Game theory  Mathematical modeling Introduction develop renewable energy many countries have set road map, goals and mandatory targets to reduce greenhouse The policies of energy sector are one of the most effective gases emissions. The share of the renewable energy (RE) policies in development of countries. Climate change and should be increased from the current 17–30 or 75% or even energy security are the most important factors in the energy to 90% in some countries by 2050. Also, European Union policies, setting regulations and energy models of invest- (EU) has set a minimum target of 20% by 2020 in total ment (REN21 2012; Bazilian et al. 2011). It is necessary to energy consumption (GEA 2012; Zhou 2012). reduce the greenhouse gases emissions in order to control The significant outcome of using the RE will be the climate change (Buchner and Carraro 2005). Hence, to strengthening the economic growth by creating employ- ment, developing clean environment by reducing carbon emissions, enhancing technological innovation systems and curbing the volatility of fuel prices. On the other hand, RE can boost economic growth and it can mitigate pollutant & Ashkan Hafezalkotob emissions. Moreover, it can increase the supply adequacy a_hafez@azad.ac.ir; Hafezalkotob@iust.ac.ir and it might facilitate the access to electricity in order to Meysam Ghaffari promote the rural development and social welfare (Tiba st_m_ghaffari@azad.ac.ir; mghaffari7@yahoo.com et al. 2016; Azuela and Barroso 2011; Fargione et al. 2008). Industrial Engineering College, Islamic Azad University, South Tehran Branch, Entezari alley, Oskoui alley, Choobi Bridge, Tehran 1151863411, Iran 123 Journal of Industrial Engineering International One of the most important factors in reducing the carbon as supplier, transmitter, distributer, retailer and consumer emissions is electricity generation from renewable sources. of electricity (except the green electricity producers). This Currently, tendency of different countries to generate is obligated to purchase a certain share of the TGCs from electricity from renewable sources is increasing by using electricity producers based on the energy policies of every TGC systems and feed-in tariff (Tamas et al. 2010). country (Mitchell and Anderson 2000). Many researches have addressed feed-in tariffs. As a Certificates are usually issued by the government and in case in point, Oderinwale and van der Weijde (2016) used exchange for 1 MW/h or higher units or higher produced by an input–output table to analyze a next-generation energy the renewable power plant. Renewable power plant can be system to evaluate economic impacts of Japan’s renewable profitable by selling certificates and physical electricity. TGC energy sector and the feed-in tariff system. market as financial market is created by an interaction The previous researches indicate that the TGC system between the supplier of TGC (renewable power plant) and has better results in comparison with feed-in tariffs (Ciar- demandant of TGC (thermal power plant in this study). As a reta et al. 2014; Tama´s et al. 2010). case in point, Denmark has set obligation on customers The TGC system as an economic mechanism is intro- (Nielsen and Jeppesen 2003). In this policy, TGCs market duced to supply electricity from RE with the least cost for creates an interaction between the green electricity producers government. In this system, any entity of electricity supply and electricity consumers where the consumers are obliged to chain can require a certain share in the production or buy certificates or consume a certain proportion of the consumption of electricity from RE (Aune et al. 2010). renewable electricity based on minimum requirement. In this study, we will model the interaction between The countries may employ different mechanisms to thermal and renewable producers in the electricity and TGC organize the demand certificates by markets where the thermal producer is an obligation to supply 1. Setting a fixed price at certificates, a certain share of green electricity by buying TGC from 2. Creating an obligation at every entity of the electricity renewable producer. The models will be analyzed based on supply chain to purchase certificates within a certain imperfect competitive/cooperative situations like Nash and period, Stackelberg equilibriums. The impact of minimum require- 3. Establishing a mechanism to tender purchasing ment and the TGCs price on total electricity and electricity certificates, price will be investigated by a numerical study. 4. Using a voluntary demand mechanism for certificates The reminder of the paper is organized as follows: (Schaeffer et al. 2000). Literature review is presented in Sect. 2. Section 3 describes the prerequisites and assumptions. In Sect. 4, In TGC system content, there are a few formal resear- ches (Tama´s et al. 2010). By using economic analysis, profit function of the power plants in electricity and TGC markets is set up. Section 5 presents six scenarios based on Jensen and Skytte (2003) modeled the interaction of the the game theory models and TGC pricing policies. Sec- electricity market (with the assumption monopolistic tion 6 introduces the pricing system of electricity and TGC competition) and the TGC market (with the assumption of in six scenarios. Section 7 discusses the evaluation of a perfect competition). They showed that relationship policies by a numerical study and sensitivity analysis. between the TGC price and electricity price is linear. With Finally, Conclusion is provided in ‘‘Appendix’’ section. the same method, the polish scheme with regard to its economic functioning and its justification with reference to solve common obstacles for renewable technology deployment was analyzed by Heinzel and Winkler (2011). Literature review The results demonstrate that the scheme is not mandatory TGCs have been introduced as financial assets and they are to solve obstacles on the legal or institutional level. After allocated to the renewable power plants in exchange for the their liberalization, social acceptance might rather decrease amount of green electricity generated from renewable when power price for consumers goes up. sources. The outcome of this would be that the renewable By using the quality methods, Verhaegen et al. (2009) producers will benefit from sale of physical electricity in described and analyzed the details of the TGCs system in electricity market and sale green certificates in TGCs Belgium. With the same method, Verbruggen and Lauber market (Farinosi et al. 2012). (2012) evaluated the feed-in tariff and TGC system in three criteria of efficiency, equity and institutional feasibility. TGCs system is usually operates as a market and is based on demand and supply. The demand of TGCs is Some of the researchers analyzed the TGC system by using the system dynamic method. In recent researches, this determined by energy policies and the annual share of electricity production from renewable sources. Obligation method has been used for conceptualizing, analyzing, can be set on any point of the electricity supply chain such designing and evaluating issues in energy sectors such as 123 Journal of Industrial Engineering International energy policy, power pricing, strategies of electricity There is a little comprehensive research about modeling market, and interaction between electricity and TGC mar- of the TGC system. Most previous studies analyzed the kets (Ahmad and bin Mat Tahar 2014). Ford et al. (2007) electricity and TGC markets by economic, and a few predicted the price of certificates to aid green electricity dynamic system methods investigated the implementation from the wind resources. The results showed that after a of this policy in a specific country. To the best of our few years the wind power exceeds the requirements knowledge, almost TGC system has not been analyzed by a because in the early years when a market opens the price of game theoretical approach under pricing policies. How- TGC will be increased rapidly. Recently, Hasani-Marzooni ever, in this study six different scenarios are analyzed and Hosseini (2012) modeled the TGC system by based on two common pricing policies in the TGC system employing the system dynamics to identify the potential to enhance the knowledge of designers and policy makers investment in the wind energy. They showed that the sys- in designing and deploying the TGC system. tem dynamics can be used as an appropriate tool to The contributions of this paper are as follows: investigate TGC market and help the regulatory authorities 1. We analyzed game theory models to achieve appro- to choose the appropriate policies in the energy sector. priate mechanisms to design market structure for TGC To analyze the TGC system, a number of mathematical market. We showed some outcomes and impacts. models are used by some researchers. Marchenko (2008) 2. We modeled the market structure for electricity and through a simple mathematical model simulated the bal- TGC markets in case of imperfect competition Cournot ance of supply and demand in electricity and the TGC oligopoly and monopoly under fixed and variable TGC markets. He showed that the TGC system is not an price policy. appropriate policy to minimize the negative effects of 3. We used social welfare function for evaluating the energy production in the environment. Gu¨rkan and developed scenarios so policy makers and government Langestraat (2014) analyzed the renewable energy obliga- will be enable for choice the finest of energy policies. tions and technology banding in the UK by a nonlinear mathematical model. They studied three policies to apply the TGC and showed that the obligation target by UK banding policy cannot be achieved necessarily. Prerequisites and assumptions Recently Ghaffari et al. (2016) investigated a game theo- retical approach research to analyze the TGC system. In this We concentrate on the interaction of two producers for simplicity: renewable and thermal power plants. Electricity practice, the TGC price is assumed to be constant and will be determined by the government. They demonstrated that the producers compete in the electricity and TGC market under producer obligation. Thus, thermal power plant is obliged relation between the electricity price and the TGC price is reverse, whereas the relation between the electricity price and to buy a certain amount of TGCs based on minimum the minimum requirement is direct. Also in renewable power requirement. plant Stackelberg model, the production of total electricity The government sets the minimum requirement. We and the renewable electricity is at the maximum, while the consider two policies for the price of certificates. In the first price of electricity is at the minimum. policy, the price of certificates is fixed and is set by the Game theory is the one of the most important tools in government. In the second policy, the price of certificates is decision-making. Game theory focuses on the interaction determined by market conditions and supply and demand among the players in a game by assuming the conditions mechanisms. that each player chooses to rationalize their preferences (Myerson 1991; Jørgensen and Zaccour 2002). Notations According to game theory, all the players can use from pure or mixed strategies for their own interests. The reaction In this study, parameters and decision variables are as of an actor in a critical situation in a game can define a pure follows: strategy. Each combination of different player strategies will have a specific payoff for these players. The numbers of the Parameters desirability of possible outcomes show the payoffs in the game. These payoffs are dependent on the applied strategies a the minimum requirement of renewable electricity, of the players. There are two types of games such as coop- 0  a  1; erative and noncooperative games. In the first one, the players p the profit function of renewable producer; p the profit function of thermal producer; intend to cooperate with each other for higher economic and environmental benefits. In the second one, the system might p the total payoff of centralized producer, reach an equilibrium state (Lou et al 2004). (p ¼ p þ p ); R T 123 Journal of Industrial Engineering International Table 1 Scenarios of TGC Game theory models Market price of certificate Fixed price of certificate implementation Nash NM scenario NF scenario Stackelberg SM scenario SF scenario Cooperative CM scenario CF scenario TGC markets separately. The renewable producer cost C the cost function of thermal producer; C ðÞ q is a function of green electricity generated. The R R C the cost function of renewable producer; cost of the renewable power plant is only dependent on the U the consumer utility; green electricity generated q . Therefore, the renewable D the function of environmental damages. producer profit maximization problem will be as follows: Max p ¼ P q þð1  aÞP q  C ðÞ q R e R c R R R Decision variables S:t: ð1Þ P the end-user price of electricity ($/MWh), P [ 0; q  0 e e P the price of TGC ($/MWh), P [ 0; c c where P is the end user of each MW of generated elec- q the electricity generated from thermal energy (MW), tricity, a is the minimum requirement of green electricity q  0; and P is the price of certificate. This means that a q the generated from renewable energy (MW), q  0; R R renewable producer can receiveðÞ 1  a P for each unit in Q the total amount of electricity (MW), addition to the electricity price. Under the TGC system, a Q  0ðÞ Q ¼ q þ q . T R renewable producer would obtain per unit ‘‘subsidy’’ As shown in Table 1, we have modeled six scenarios to ðÞ 1  a P . implement the TGC system based on the game theory approach and government policies regarding the control Thermal producer price of certificates. Thermal producers can fulfill their obligation by either Assumptions production of the renewable electricity or buying the TGCs from renewable producer. The following assumptions have been considered in the Thermal producer cost C ðÞ q is a function of the T T proposed models: thermal electricity q . Therefore, the thermal producer profit maximization 1. There is no limitation for power plants in consumption problem will be as follows: of the resources. 2. There is no limitation on the demand and supply Max p ¼ P q  P aq  C ðq Þ T e T c T T T electricity and TGCs. S:t: ð2Þ 3. There is no excess demand and supply in the electricity q  0 and TGCs markets. 4. Parameters are deterministic and they are known in Thermal power plant can receive P for each unit of advance. electricity. The thermal producer is obliged to pay for 5. The demand function of TGC is similar to demand buying the TGC from the renewable producer in order to function of electricity. compensate the unfulfilled requirements. Therefore, the 6. In all models, the supply of certificate meets the thermal producer under the TGC system virtually pays a minimum requirementðÞ q  aQ . R per unit ‘‘tax’’ aP as in Eq. (2). In the developed model, there is just one thermal power plant that is obliged to hold a number of the TGCs equal to a times its production. Model formulation Renewable producer In this practice, we adopted profit functions for the power Amundsen and Nese (2009), discussed the relation of: P = wholesale plants by Tanaka and Chen (2013). Renewable power plant electricity price ? a P must be established in the competitive can sell the electricity and the TGCs on the electricity and equilibrium market with a large number of retailers. 123 Journal of Industrial Engineering International Cost functions Nash equilibrium is a vector of participation decisions so that no player has an incentive to deviate from his chosen strategy We adopt cost functions for the power plants by Jensen and after considering an opponent’s choice (Urpelainen 2014). All players have no motivation to exit the equilibrium, Skytte (2003) and for renewable and thermal power plants it can be described as follows: because the outcome of this will be reduction in profit of players. Krause et al. (2006) defined the Nash equilibrium as C ðq Þ¼ a q þ b q þ c ð3Þ R R R R R R follows: C ðÞ q ¼ a q þ b q þ c ð4Þ T T T T T T The strategy profile in a (n) players game of P ¼ P ; ...; P is a Nash equilibrium (NE) if for all i 2 1 n In Eqs. (1) and (2), it is assumed that a , b ; a ; b [ 0. R R T T fg 1; ...; n there is: Profit maximization problem for power plants U ¼ P ; ...; P  P ; ...; P ; P ; P ; ...P ð9Þ i i 1 n 1 i1 iþ1 n where U is the utility function of the ith player. Following Newbery (1998) and Tamas et al. (2010), we In this section, we consider a Cournot-NE game under a assume that the demand function for electricity is a linear TGC system. function, It can be seen that by solving NE , from Eqs. (7) and (8) P ¼ c  bQ ¼ c  bðÞ q þ q ; ð5Þ e R T q and q will be obtained. Now, with substitution of q T R T and q into p and p , the maximum profit of the pro- Meanwhile, Q ¼ðq þ q Þ is the total electricity. On R T R T the other hand, we assume that the price of electricity is a ducers (p and p ) will be reached. Propositions 1 and 2 R T decreasing function of amount of renewable electricity. present the optimum electricity production quantities in Moreover, based on sixth assumption the demand function Nash equilibrium under fixed TGC price and market TGC of TGC is similar to electricity assumed. The inverse price polices, respectively. Subscripts [NF] and [NM] demand function of TGC is as follows: denote the equilibrium points in the Nash game under fixed TGC price policy and the market TGC price policy, P ¼ h  uq ð6Þ c R respectively. With substitution of Eq. (5) into Eqs. (1) and (2), the Proposition 1 Under the fixed TGC price policy, the profit maximization problem can be formulated as follows. optimum amounts of production for the renewable and Renewable producer is given as below: thermal producers in the Nash model can be given as Max p ¼ðc  bðq þ q ÞÞq þ P q  a q  b q  c R R T R c R R R R R below: s:t: P ð2aa þ ab  2a  2bÞþ A c T T 1 q  0 q ¼ ð10Þ RN½ F 2D þ 3b ð7Þ PðÞ 2aa þ 2ba þ b þ A c R 2 q ¼ ð11Þ Thermal producer is given as below: TN½ F 2 2D þ 3b Max p ¼ðc  bðq þ q ÞÞq  P q  a q  b q  c T R T T c T T T T T where A ¼ 2b a  2a c þ 2bb  bb  bc; A ¼ 2b 1 R T T R T 2 T S:t: a 2a c þ 2bb  bb bc; D ¼ 2a a þ 2a b þ 2a b: R R T R R T R T q  0 All propositions have been proven in ‘‘Appendix’’. With ð8Þ substituting the optimal quantities and Cournot TGC price Note that with substitution of Eq. (6) into Eqs. (7) and into Eqs. (7) and (8), optimal profit of the power plants can (8), the problems of producers under market TGC price be calculated. policy will be obtained. Proposition 2 Under market TGC price policy, the opti- mal amounts of production for the renewable and thermal producers in the Nash solution can be given as below: Game theory models 2aa h þ abh þ F T 1 q ¼ ð12Þ RN½ M Noncooperative Nash game 4aa u þ 3abu þ F T 2 a hu  2aa h  ab u þ 2ab u  acu  ahu þ E R R T 1 q ¼ If no player has anything to gain by changing his strategy, TN½ M 4aa u þ 3abu þ F T 2 when the other players do not change their strategies, then the ð13Þ set of strategies for all the players and the corresponding payoffs constitute a Nash equilibrium (Lou et al 2004). The 123 Journal of Industrial Engineering International ð2aa h þ abh þ F Þðau  bÞ T 1 where F ¼ 2b a  2a c þ 2b h þ 2bb  bb  bc 1 R T T T R T q ¼ TS½ M 2 2ðb þ a Þð4aa u þ 2abu  b þ F Þ T T 2 2bh; F ¼ 4a a  4a b  4a b  4a u  3b  4b 2 R T R T T ah  b þ c u; E ¼2a b þ 2a c þ bb  2bb þ bc  bh  2b 1 R T R R T T  : ð17Þ 2ðb þ a Þ u þ 2cu. Cooperative game Noncooperative Stackelberg Games In this section, a cooperative relationship between thermal We investigated a noncooperative structure for interaction and renewable producers is investigated. In this model, between the thermal and renewable producers where the power plants collaborate together in electricity and TGCs initiative is the possession of one of the power plants, i.e., markets. We investigate this situation to increase our the leader. This can enforce its strategy on its rival, i.e., the knowledge about how to divide thermal producer capacity follower. The first move is made by leader to maximize its to generate in competition with the renewable producer. profit and then in return the follower reacts by choosing the Summation of Eqs. (7) and (8) gives cooperative model: best strategies. Max p ¼ðc  bðq þ q ÞÞq þ P q  a q  b q R T R c R R R R Since the objective of the TGC system is supporting the c þðc  bðq þ q ÞÞq R R T T increasing share of the electricity generated by RE pro- ducer, in this research we only examine renewable pro- P q  a q  b q  c c T T T T T ducer—Stackelberg model where the renewable producer S:t: is leader and the thermal power plant is the follower. In this q ; q  0 R T model, the renewable producer first sells its generated ð18Þ electricity in electricity market. Then the follower as thermal producer sells its generated electricity in electricity A Hessian matrix of p in Eq. (18) is: H ¼ market and buys certificates from renewable producer. 2b  2a 2b and the utility function p is a Propositions 3 and 4 present the optimum production of 2b 2b  2a electricity from renewable and thermal producers in concave function on (q ; q ) if and only if the Hessian R T Stackelberg equilibrium under fixed TGC price and market matrix H is negative definite. Propositions 5 and 6 present TGC price polices, respectively. Subscripts [SF] and [SM] the optimum production quantities of green and thermal refer to optimal values of Stackelberg models under the electricity of producers in cooperative game under fixed fixed TGC price and market TGC price, respectively TGC price and market TGC price polices, respectively. Subscripts [CF] and [CM] denote the optimum values in Proposition 3 Under fixed TGC price policy, the optimal the cooperative game model under fixed TGC price and amount of electricity generated from renewable and fossil market TGC price polices, respectively. sources in renewable producer—Stackelberg model—is: P ð2aa þ ab  2a  2bÞþ E c R R 2 Proposition 5 Since ð2b  2a Þð2b  2a Þ R T q ¼ ð14Þ R½SF K ð2bÞð2bÞ [ 0, the optimal amount of electricity gen- 2 2 erated from renewable and fossil sources in the coopera- P 2aa b þ ab  aE  2a b  2b þ bE þ Kðc  b Þ c R 2 R 2 T q ¼ T½SF tive game model under fixed TGC price policy will be: 2E ðb þ a Þ 2 R ð15Þ PðÞ aa  a  bþ B c T T 1 q ¼ ð19Þ R½CF where E ¼ 2a b  2a c þ 2bb  bb  bc; K ¼ 2 R R R R T 2 PðÞ aa þ bþ B c R 2 4a þ 8a b þ 2b . q ¼ ð20Þ T½CF Proposition 4 Under market TGC price policy, the opti- where B ¼ a b  a c þ bb  bb ; B ¼ a b  a c 1 T R T R T 2 R T R mal amount of electricity generated from renewable and bb þ bb : R T fossil sources in renewable producer—Stackelberg model—is: Substituting Eq. (4) into Eq. (18), the problem of profit centralized power plant under market TGC price policy 2aa h þ abh þ F T 1 q ¼ ð16Þ RS½ M 2 yields: 4aa u þ 2abu  b þ F T 2 123 Journal of Industrial Engineering International Table 2 Price of TGC in six Game models TGC price policy scenarios Market price Fixed price ð2aa hþabhþF Þu T 1 Nash P ¼ cte P ¼ h  cN½ F cN½ M 4aa uþ3abuþF T 2 ð2aa hþabhþF Þu T 1 Stackelberg P ¼ cte P ¼ h  cS½ F cS½ M 4aa uþ2abub þF T 2 ða uhþ2aa hþab hacuþG Þu Cooperative  T T 1 P ¼ cte P ¼ h  cC½ F 2 2 cC½ M a u þ4aa uþF þ3b T 2 ‘‘cte’’ represents a fixed value transaction level focuses on managing the implementation Max p ¼ðc  bðq þ q ÞÞq þðh  uq Þq R T R R R of discounts away from the reference or the price list which a q  b q  c þðc  bðq þ q ÞÞq R R R R R T T occur both on and off the invoice or receipt. ðh  uq Þq  a q  b q  c R T T T T T T In this section, the pricing at the electricity market level S:t: is considered in oligopoly and monopoly market structures. Oligopoly is a common form of market where a number of q ; q  0 R T firms are in competition with each other. Based on the ð21Þ game theory approach, the Cournot–Nash and Cournot– A Hessian matrix of the profit function in the TGC Stackelberg models are the oligopoly models. The oligo- market price policy is polies are in fact price setters rather than price takers (Perloff 2008). By substituting the optimal amounts of 2au  2a  2b  2uau  2b H ¼ and the utility green and black electricity production quantities in the 2b  2a 2b  2a T T payoff functions of the renewable and black power plants, function in the cooperative model is a concave function on the optimum prices of the electricity and TGC are achieved (q ; q ) if and only if the Hessian matrix H is negative R T in six scenarios. Tables 2 and 3 depict the electricity price definite. and TGC price in each scenario. Proposition 6 Since detðHÞ¼ð2au  2a  2b  2uÞ ð2b  2a Þðau  2bÞð2b  2a Þ [ 0, under market T T TGC price policy the optimal amount of electricity gener- Evaluation policies and sensitivity analysis ated from renewable and fossil sources in the cooperative game model are: Comparison price and production a hu þ 2aa h þ ab u  acu þ G T T 1 q ¼ ð22Þ R½CM 2 2 In this section, sensitivity analysis is performed by a u þ 4aa u þ 3b þ F T 2 numerical examples to illustrate performance differences a hu  2aa h  ab u þ 2ab u  acu  ahu þ G R R T 2 q ¼ between different models. T½CM 2 2 2 a u þ 4aa u þ 3b þ F T 2 We present numerical studies by assuming that the ð23Þ marginal costs and other parameters of the cost function in renewable power plant are higher than nonrenewable where G ¼þ2a b  2a c  2a u þ 2bb  2bb 1 T R T T R T power plant. 2bh; G ¼2a b þ 2a c þ 2bb þ 2bb  2bb 2 R T R R R T Cost function of the renewable and nonrenewable pro- 2bh  2b u þ 2cu. ducers is assumed as below: Pricing is the most effective profit lever (Dolan and ðÞ Cq ¼ 0:06q þ 11q þ 100 and R R Simon 1996). This is a process for determining what a CqðÞ¼ 0:04q þ 8q þ 20: T T company will receive in exchange for its products or ser- T vices. Pricing can be considered in industry, market, and The price elasticity of the electricity supply and TGC transaction levels. At the industry level, the main focus is supply is assumed as below: b ¼ 0:4 and u ¼ 0:3. It is on the overall economics of the industry, including price assumed that c ¼ 150 and h ¼ 50: In fixed TGC price changes of the supply and demand changes of the cus- policies, the TGC price is set equal to average of the TGC tomer. On the other hand, in the market level the com- market prices per different amounts of the minimum quota. petitive situation of the price in comparison with the value Figure 1 illustrates the changes of total electricity sup- differential of the product to that of the comparative ply, green electricity supply and black electricity supply competing products will be considered. Pricing at the versus the minimum requirement of green electricity. 123 Journal of Industrial Engineering International Figure 2 shows the changes of electricity and TGC price versus the minimum requirement of green electricity. It can be seen from Fig. 1 that in every six scenarios of Table 1 when a increases Q decreases. However, supply of the green electricity increases in the market price policy and Nash model in the fixed price policy. Moreover, when a increases the black electricity decreases in every six scenarios. In the CM scenario, when a increases, supply of the total electricity in the first step decreases but then it starts to increase. But in the CF scenario when a increases, supply of total electricity consistently decreases. This means that contrary to the other five scenarios, in the CM scenario when minimum requirement of green electricity (aÞ is almost 60% the electricity generated is at minimum amount. The maximum amounts of the green electricity are generated in the CF scenario. The maximum amounts of the black electricity are generated in the NF scenario and the minimum amounts of the black electricity are supplied in CF scenario. Generally speaking, with changes of the minimum mandatory quota, supply of the total electricity in the SF scenario has the least changes in comparison with the other scenarios. Figure 1 demonstrates that supply of the total electricity in the SM scenario is greater than the SF scenario con- sistently. Moreover, the trend of electricity supply in both scenarios is descending with increase in the minimum quota. This result is supported by Jensen and Skytte (2003) and Tamas et al. (2010). Supply of the total electricity in the Nash model of both policies has a descending trend with increase in the minimum quota. Nevertheless, the total electricity generated in the NF scenario is greater than that of the NM scenario. About the cooperative model, it can be stated that the total electricity generated in the CF scenario with increase in the minimum quota has absolutely descending trend, whereas the CM scenario shows a convex shape. When the minimum requirement of green electricity is less than 60%, the total electricity generated in the CF scenario is greater than that of the CM scenario. Figure 2 shows that there is a reverse relation between the minimum requirement of green electricity and TGC price. However, the relation between the minimum requirement of green electricity and electricity price is direct. In other words, when a increases P increases and P decreases in all scenarios. This matter represents there is a reverse relation between price of TGC and electricity price. This result is supported by Jensen and Skytte (2003), Fristrup (2003), Tama´s et al. (2010) and Marchenko (2008). In the CM scenario, when a increases, there is a rapid reduction in the price of TGC in comparison with the other Table 3 Price of electricity in six scenarios Game TGC price policy Models Market price Fixed price ahðau2a 2a 2buÞþauðb þ2b cÞþE F P ð2aa þ2aa þ2ab2a bÞþA þA Nash  R T R T 1 1  c R T T 1 2 P ¼ c  b  P ¼ c  b eN½ M 4aa uþ3abuþF eN½ F T 2 2Dþ3b 0 1 2 2 2 2 ð2aa hþabhþF Þðauþbþ2a Þ Stackelberg  T 2 T cahb T P að4a þ 4a b þ b þ KÞ 2P ð2a þ 3a b þ b Þ P ¼ c  b þ c R c R R R eS½ M 2ðÞ bþa 2ð4aa uþ2abub þF ÞðÞ bþa T T 2 T B C þ E ð2a þ bÞþ Kðb þ cÞ B 2 R T C P ¼ c  bB C eS½ F 2KðÞ bþa @ A 2bðP aa þP bþB Þ að2a hþ2a hþb ub uþhuÞþG G  c R c 2 Cooperative  R T R T 1 2 P ¼ c þ P ¼ c  b 2 2 eC½ F D eC½ M a u þ4aa uþF þ3b T 2 Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 240 240 220 220 200 200 180 180 160 160 140 140 120 120 100 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 1 Changes of total, green and black electricity versus minimum quota scenarios. Among the game theory models, the Stackelberg Changes of payoffs of thermal, renewable and central- model in the fixed TGC price results in the minimum ized power plants are depicted in Fig. 3. The results of electricity price. However, the cooperative model has the numerical study show that by increasing a total payoff of maximum electricity price in both fixed TGC price and the centralized power plant decreases in all scenarios. Cen- market policy price. The price of electricity in the fixed tralized power plant payoff in cooperative model is higher TGC price policy is less than that of the same game theory than the other scenarios. By increasing a, the payoff of model in the market TGC price policy. green electricity producer decreases in all scenarios except CM scenario. Note that in Nash and Stackelberg models by Black electricity supply Green electricity supply Total electricity supply Total supply of electricity (Mwh) Supply of black electricity (Mwh) Supply of green electricity (Mwhr) Supply of black electricity (Mwh) Supply of green electricity (Mwh) Total supply of electricity Mwh) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 100 100 90 90 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 ( percentage) ( percentage) 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 2 Changes of TGC and electricity price versus minimum quota increasing a the payoff of green electricity producer relation to inverse demand function in Eq. (4), and it is decreases under market TGC price policy. Remarkably, by assumed to be equal to 100. Moreover, it is assumed that increasing a, the payoff of black electricity producer the cost function of the green and black power plants is 2 2 decreases in all scenarios, but in CM scenario, it decreases 5q þ 30q þ 100 and 3q þ 10q þ 20, respectively, R T R T faster than the other scenarios. It can be concluded that the where b ¼ 1:2 and u ¼ 1:2. It is assumed that: c ¼ use of CM scenario will lead to elimination of thermal 150; h ¼ 100 and k ¼ 0:4. Figure 4 depicts the results of power plants more quickly. this example in six scenarios. The evaluation of these polices reveals that in each six Social welfare scenarios by increasing the minimum quota, social welfare increases at first and decreases later. In other words, in all Social welfare is an appropriate criterion to evaluate any scenarios the maximum of social welfare does not happen policy or program (Tama´s et al. 2010). To evaluate the six when all the electricity supply is generated from the green proposed scenarios in this paper, we use the equation of sources (a ¼ 100%Þ. This result is in accordance with social welfare proposed by Currier (2013). In this case, the Currier (2013) and Currier and Sun (2014). In the fixed social welfare is equal to the total utility minus the all costs TGC price polices, in the first, by increasing of the mini- including the environmental damages and production costs. mum quota, the social welfare will increase with a fas- Here, U represents the consumer utility and D denotes the ter slope compared with the market TGC price polices. function of environmental damages. Generally, when the minimum requirement of renew- able energy sources in the electricity supply is less than SW ¼ UðQÞ Cðq Þ Cðq Þ Dðk; qÞð24Þ T R R almost 50%, the market TGC price polices lead to a higher Currier and Sun (2014) assumed that D ¼ q =2 and R level of welfare. The welfare in Stackelberg model with the ðÞ Q ¼ cQ  Q =2. Here c represents the parameter in Electricity price TGC price TGC price ($/Mwh) Electricity price ($/Mwh) Electricity price ($/Mwh) TGC price ($/Mwh) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 14000 14000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 12000 12000 10000 10000 8000 8000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 9000 9000 8000 8000 7000 7000 6000 6000 4000 4000 3000 3000 2000 2000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 3 Changes of power plants Payoff versus minimum quota market TGC price policy (SM scenario) is consistently TGC price policy (NM and SM scenarios) and 70–80% of greater than the fixed TGC price policy. But comparing the the electricity supply is generated from the RE sources. In two control price of certificates policies among other game contrast, the minimum welfare is obtained when that theory models (Nash and cooperative) shows that there is market structure follows the Nash or Stackelberg model not a constant trend in terms of welfare created. The with the fixed TGC price policy (i.e., NF and SF scenarios) maximum welfare is obtained when that market structure when minimum quota is zero (a = 0). When a =0, the follows the Nash or Stackelberg model with the market maximum welfare is obtained by CM scenario. Among six Black electricity producer payoff Green electricity producer payoff Total payoff of centralized power plant Payoff of renewable power plant ($) Total porofit of power plants($) Payoff of thermal power plant($) Payoff of thermal power plant($) Payoff of renewable power plant($) Total porofit of power plants($) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 350 350 300 300 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 4 Comparison of social welfare acquired in each scenario scenarios, SF scenario creates minimum welfare for all social welfare. In this policy, the use of NF scenario will be amounts of a. more beneficial in terms of social welfare and high power It seems that the results of this practice are useful for supply in comparison with three other scenarios. private and public investors, energy policy makers, gov- There are several directions for the future research. ernment and other active players in the electricity supply Firstly, this study considers the national trade in the elec- chain. It is an undeniable fact that pricing the TGC is a tricity market and the TGC system. Game theory formu- challenging problem for the government. Therefore, ana- lation of international TGC trade in the internal and lyzing these models with various scenarios can improve the external markets is interesting. Secondly, other approaches effectiveness of designing and implementing TGS system. of game theory to analyze the implementation of the TGC system can be considered. For example, modeling the TGC system in the incomplete information mode by Bayesian Conclusion models is both interesting and challenging. Thirdly, we only consider the producer’s obligation option in the TGC This study demonstrates that using market TGC price system, but other obligations in the TGC system can also policy is more beneficial when a country intends to deploy be considered. Finally, no time constraint was considered a system of credentials with a share of renewable energy to validate the certificates. Using the time variables in modeling of the TGC system seems to be useful. sources less than 50 percent because not only a higher social welfare in this sector is created but also by using this Open Access This article is distributed under the terms of the Creative policy the profit of thermal power plants will be decreased Commons Attribution 4.0 International License (http://creative with a modest slope and it will not lead to an abrupt commons.org/licenses/by/4.0/), which permits unrestricted use, dis- withdrawal from the market and lack of power supply. tribution, and reproduction in any medium, provided you give Moreover, if the goal is accelerating the removal of these appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were power plants with abrupt withdrawal, then using the CM made. scenario is beneficial where the profit of fossil fuels is reduced more steeply. This scenario also will have the lowest power supply among the six scenarios, and it will Appendix have the lowest levels of social welfare for a values above 50%. Proof of Proposition 1 If the second-order derivative for If a country is so much developed that can provide more Eq. (7) is negative, the profit function of the green pro- than 50% of its electricity from renewable sources, then ducer will be concave. The first-order derivative for Eq. (7) using fixed TGC price policy can be beneficial too because is: at this point it acts like market TGC price policy in creating Social Welfare Social Welfare Journal of Industrial Engineering International Therefore, the profit function of the green producer is op ¼ðP þ cÞðbq þ 2bq þ 2a q þ b Þ¼ 0: c T R R R R concave. Similarly, the first-order derivative for Eq. (8)is oq as follows: ð25Þ op ¼ q ð2b  2a Þþ q ðb þ uaÞþ c  ah  b ¼ 0: The second-order derivative for Eq. (7) is as follows: T T R T oq o p ð31Þ ¼ ðþ2bþ2a Þ: ð26Þ o q The second-order derivative is as follows: Since the amounts of b and a are positive, the second- o p o p R ¼2a  2b ¼ 0: ð32Þ order derivative is negative \0 : 2 o q R o q Therefore, the profit function of the green producer is Since it is assumed that b; a [ 0, the second-order concave. Similarly, the first-order derivative for Eq. (8)is o p derivative is negative \0 . as follows: 2 o q Therefore, the profit function of the green producer is op ¼ c ð2bq þ bq þ Pca þ 2a q þ b Þ¼ 0: ð27Þ T R T T T concave. oq Solving Eqs. (29) and (31), it follows that the optimal The second-order derivative for Eq. (8) yields: production of power plants is: o p T 2aa h þ abh þ F T 1 ¼ð2bþ2a Þ: ð28Þ q ¼ ; T RN½ M 4aa u þ 3abu þ F T 2 o q a hu  2aa h  ab u þ 2ab u  acu  ahu þ E R R T 1 q ¼ : TN½ M Since the amounts of b and a are positive, the second- T 4aa u þ 3abu þ F T 2 o p order derivative is negative \0 : 2 h o q Hence, the profit function of the thermal producer will Proof of Proposition 3 To solve the model, q is first be concave. Solving Eqs. (25) and (27), it follows that the obtained as a function of q and then the first-order optimal production of power plants is: derivative is first examined for a profit function of the P ð2aa þ ab  2a  2bÞþ A c T T 1 thermal power plant of Eq. (8). The best response strategy q ¼ ; RN½ F 2D þ 3b for a thermal power plant is computed as follows: PðÞ 2aa þ 2ba þ bþ A c R 2 q ¼ : aP þ q b þ b  c TN½ F 2 c R T 2D þ 3b q ¼ : ð33Þ 2ðb þ a Þ Substituting Eq. (33) into Eq. (7) gives: aP þ bq þ b  c c R T p ¼ P q þ c  b þ q q R c R R R 2ðb þ a Þ Proof of Proposition 2 If the second-order derivative of a q  b q  c : R R R R Eq. (7) under market TGC price policy is negative, the ð34Þ profit function of the green producer will be concave. The first-order derivative for Eq. (7) is: The first-order derivative for Eq. (34) yields: op op b ¼ q ð2u  2b þ au þ ua  2a Þ R R R ¼ P  b  þ 1 q þ c oq c R oq 2ðb þ a Þ R T þ h þ c  bq  ah  b ¼ 0: ð29Þ T R aP þ bq þ b  c c R T b  þ q  2a q  b ¼ 0: R R R R 2ðb þ a Þ The second-order derivative for Eq. (7) under market TGC price policy is as follows: ð35Þ o p The profit function of the renewable power plant is ¼ 2au  2a  2b  2u ¼ 0: ð30Þ o q R concave if the second-order derivative for Eq. (34)is negative. The second-order derivative for the renewable Since it is assumed that u; b; a [ 0, and 0  a  1. We power plant gives: know (au\a þ b þ uÞ, then the second-order derivative 2 2 o p o p 2a a þ 2a b þ b R R T R is negative \0 : ¼ : ð36Þ o q b þ a o q T 123 Journal of Industrial Engineering International 2aa h þ abh þ F T 1 Regarding the assumptions and parameter values, q ¼ : RS½ M 4aa u þ 2abu  b þ F Eq. (36) is negative. Therefore, the profit function of the T 2 renewable power plant is found to be concave. From Substituting q into Eq. (37), the optimal black RS½ M Eq. (35), it follows that the optimal green electricity electricity production is: production is: T½SM P ð2aa þ ab  2a  2bÞþ E c R R 2 2 2 P 2aa b þ ab  aE  2a b  2b þ bE  b E þ E c c R 2 R 1 T 2 2 q ¼ : R½SF ¼ : 2E ðb þ a Þ 2 R Substituting q into Eq. (33), the optimal black RS½ F electricity production is: ð2aa h þ abh þ F Þðau  bÞ T 1 q ¼ TS½ F 2ðb þ a Þð4aa u þ 2abu  b þ F Þ T T 2 Proof of Proposition 5 The first-order derivative for the ah  b þ c profit function of the power plants in Eq. (25) yields (in the 2ðb þ a Þ fixed TGC price policy): op ¼ P þ c  2bðq þ q Þ 2a q  b ¼ 0; ð41Þ c T R R R R oq Proof of Proposition 4 To solve the model, q is first obtained as a function of q and then the first-order R op ¼ c  2bðq þ q Þ aP  2a q  b ¼ 0: ð42Þ T R c R T T derivative is examined for a profit function of the thermal oq power plant of Eq. (8) under market TGC price policy; the Solving Eqs. (41) and (42), they give: best response strategy of the thermal power plant is com- puted as follows: PðÞ aa  a  bþ B c T T 1 q ¼ : R½CF q au  q b  ah  b þ c R R T q ¼ : ð37Þ PðÞ aa þ bþ B 2ðb þ a Þ c R 2 q ¼ : T½CF Substituting Eq. (37) into Eq. (7) gives: p ¼ðq u þ hÞq R R R q au  bq  ah  b þ c R R T Proof of Proposition 6 The first-order derivative for the þ c  b  þ q q R R 2ðb þ a Þ profit function of the power plants in Eq. (26) yields (in the ðq u þ hÞaq  a q  b q  c : R R R R R R market TGC price policy): ð38Þ op ¼ q ð2au  2a  2b  2uÞþ q ðau  2bÞ R R T oq The first-order derivative for Eq. (38) yields: ah  b þ c þ h ¼ 0; ð43Þ op au  b ¼ h  b  þ 1 q op oq 2ðb þ a Þ R T ¼ q ð2au  2bÞþ q ð2a  2bÞ R T T oq q au  bq  ah  b þ c T R R T : þ c  b  þ q 2ðb þ a Þ  ah  b þ c ¼ 0; ð45Þ T T þ q ð2u þ au þ ua  2a Þ b ¼ 0 R R R Since Hessian matrix for this function is negative ð39Þ definite, the profit function is concave. Thus, Solving Eqs. (43) and (44) yields: The profit function of the renewable power plant is a hu þ 2aa h þ ab u  acu þ G T T 1 concave if the second-order derivative for Eq. (38)is q ¼ ; R½CM 2 2 2 a u þ 4aa u þ 3b þ F negative. The second-order derivative for the renewable T 2 power plant gives: a hu  2aa h  ab u þ 2ab u  acu  ahu þ G R R T 2 q ¼ : T½CM 2 2 2 a u þ 4aa u þ 3b þ F T 2 o p au  b ¼2u  2b þ 1 þ 2au  2a : ð40Þ 2ðb þ a Þ o q T Regarding the assumptions and parameter values, Eq. (40) will be negative. From Eq. (39), it follows that the optimal green electricity production is: 123 Journal of Industrial Engineering International Heinzel C, Winkler T (2011) Economic functioning and politically References pragmatic justification of tradable green certificates in Poland. Environ Econ Policy Stud 13:157–175 Ahmad S, bin Mat Tahar R, (2014) Using system dynamics to Jensen S, Skytte K (2003) Interactions between the power and green evaluate renewable electricity development in Malaysia. Kyber- certificate markets. Energy Policy 30:425–435 netes 43(1):24–39 Jørgensen S, Zaccour G (2002) Time consistency in cooperative Amundsen E, Nese G (2009) Integration of tradable green certificate differential games. In: Zaccour G (ed) Decision & Control in markets: what can be expected? J Policy Model 31:903–922 Management Science Advances in Computational Management Aune F, Dalen H, Hagem C (2010) Implementing the EU renewable Science, vol 4. Springer. Boston, MA, pp 349–366 target through green certificate markets. Energy Econ Krause T, Beck E, Cherkaoui R, Germond A, Andersson G, Ernst D 34:992–1000 (2006) A comparison of Nash equilibria analysis and agent based Azuela G, Barroso L (2011) Design and performance of policy modelling for power markets. Electr Power Energy Syst instruments to promote the development of renewable energy: 28:599–607 emerging experience in selected developing countries. Energy Lou HH, Kulkarni MA, Singh A, Huang YL (2004) A game theory and mining sector board discussion paper no. 2. The World based approach for emergy analysis of industrial ecosystem Bank, Washington, DC under uncertainty. Clean Technol Environ Policy 6(3):156–161 Bazilian M, Hobbs B, Blyth W, MacGill I, Howells M (2011) Marchenko O (2008) Modeling of a green certificate market. Renew Interactions between energy security and climate change: a focus Energy 33:1953–1958 on developing countries. Energy Policy 39:3750–3756 Mitchell C, Anderson T (2000) The implication of tradable green Buchner B, Carraro C (2005) Modelling climate policy perspectives certificate for UK. Int J Ambient Energy 21(3):161–168 on future negotiations. J Policy Model 27:711–732 Myerson R (1991) Game theory: analysis of conflict. Harvard Ciarreta A, Espinosa MP, Pizarro-Irizar C (2014) Switching from University Press, Cambridge, Chicago feed-in tariffs to a Tradable Green Certificate market. Interrelat Newbery D (1998) Competition, contracts, and entry in the electricity Between Financ Energy 54:261–280 spot market. Rand J Econ 29:726–749 Currier KM (2013) A regulatory adjustment process for the determi- Nielsen L, Jeppesen T (2003) Tradable Green Certificates in selected nation of the optimal percentage requirement in an electricity European countries—overview and assessment. Energy Policy market with Tradable Green Certificates. Energy Policy 31:3–14 62:1053–1057 Oderinwale T, van der Weijde AH (2017) Carbon taxation and feed-in Currier K, Sun Y (2014) Market power and welfare in electricity tariffs: evaluating the effect of network and market properties on markets employing Tradable Green Certificate systems. Int Adv policy effectiveness. Energy Systems 8(3):623–642 Econ Res 20(2):129–138 Perloff J (2008) Microeconomics theory and applications with Dolan R, Simon H (1996) Power pricing. Free Press, New York calculus. Pearson, Boston Fargione J, Hill J, Tilman D, Polasky S, Hawthorne P (2008) Land REN21 (2012) Renewables 2012 global status report. REN21 clearing and the biofuel carbon deb. Science 319:1235–1238 Secretariat, Paris Farinosi F, Carrera L, Mysiak J, Breil M, Testella F (2012) Tradable Schaeffer GJ (2000) Options for design of tradable green certificate certificates for renewable energy: the Italian experience with systems. Report/Energy Research Centre of the Netherlands hydropower. In: 9th International conference on the European (Netherlands) energy market (EEM 2012). IEEE, Florence, pp 1–7 Tama´s M, Shrestha S, Zhou H (2010) Feed-in tariff and tradable Ford A, Vogstad K, Flynn H (2007) Simulating price patterns for green certificate in oligopoly. Energy Policy 38:4040–4047 tradable green certificates to promote electricity generation from Tanaka M, Chen Y (2013) Market power in renewable portfolio wind. Energy Policy 35:91–111 standards. Energy Econ 39:187–196 Fristrup P (2003) Some challenges related to introducing tradable Tiba S, Anis O, Mohamed F (2016) The four-way linkages between green certificates. Energy Policy 31(1):15–19 renewable energy, environmental quality, trade and economic GEA (2012) Global energy assessment: toward a sustainable future. growth: a comparative analysis between high and middle-income Cambridge University Press, Cambridge countries. Energy Syst 7:103–144 Ghaffari M, Hafezalkotob A, Makui A (2016) Analysis of imple- Urpelainen J (2014) Grid and off-grid electrification: an integrated mentation of Tradable Green Certificates system in a competitive model with applications to India. Energy Sustain Dev 19:66–71 electricity market: a game theory approach. J Ind Eng Int Verbruggen A, Lauber V (2012) Assessing the performance of 12(2):185–197 renewable electricity support instruments. Energy Policy Gu¨rkan G, Langestraat R (2014) Modeling and analysis of renewable 45:635–644 energy obligations and technology bandings in the UK electricity Verhaegen K, Meeus L, Belmans R (2009) Towards an international market. Energy Policy 70:85–95 tradable green certificate system—the challenging example of Hasani-Marzooni M, Hosseini S (2012) Dynamic interactions of TGC Belgium. Renew Sustain Energy Rev 13:208–215 and electricity markets to promote wind capacity investment. Zhou H (2012) Impacts of renewables obligation with recycling of the IEEE Syst J 6:46–57 buy-out fund. Energy Policy 46:284–291 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Industrial Engineering International Springer Journals

Evaluating different scenarios for Tradable Green Certificates by game theory approaches

Free
15 pages
Loading next page...
 
/lp/springer_journal/evaluating-different-scenarios-for-tradable-green-certificates-by-game-H8nRoAeVkZ
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by The Author(s)
Subject
Engineering; Industrial and Production Engineering; Quality Control, Reliability, Safety and Risk; Facility Management; Engineering Economics, Organization, Logistics, Marketing; Mathematical and Computational Engineering
ISSN
1735-5702
eISSN
2251-712X
D.O.I.
10.1007/s40092-018-0272-8
Publisher site
See Article on Publisher Site

Abstract

Right now employment of polices and tools to decrease the carbon emission through electricity generation from renewable resources is one of the most important problem in energy policy. Tradable Green Certificate (TGC) is an economics mechanism to support green power generation. Any country has the challenge to choose an appropriate policy and mechanism for design and implementation of TGC. The purpose of this study is to help policy makers to design and choose the best scenario of TGC by evaluating six scenarios, based on game theory approach. This study will be useful for increasing the effectiveness of TGC system in interaction with electricity market. Particularly, the competition between thermal and renewable power plants is modeled by mathematical modeling tools such as cooperative games like Nash and Stackelberg. Each game is modeled by taking into account of the two following policies. The results of the six scenarios and the sensitivity analysis of some key parameters have been evaluated by numerical studies. Finally, in order to evaluate the scenarios we calculated the level of social welfare in the all scenarios. The results of all models demonstrate that when the green electricity share (minimum requirement) increases the TGC price decreases. Moreover, in all scenarios when the minimum requirement is 100% then the maximum level of social welfare is not met. Also when the minimum requirement is less than 50%, the scenarios with the market TGC price policy have more social welfare in comparison with the scenarios with fixed TGC price policy. Keywords Green electricity  Tradable Green Certificate  Game theory  Mathematical modeling Introduction develop renewable energy many countries have set road map, goals and mandatory targets to reduce greenhouse The policies of energy sector are one of the most effective gases emissions. The share of the renewable energy (RE) policies in development of countries. Climate change and should be increased from the current 17–30 or 75% or even energy security are the most important factors in the energy to 90% in some countries by 2050. Also, European Union policies, setting regulations and energy models of invest- (EU) has set a minimum target of 20% by 2020 in total ment (REN21 2012; Bazilian et al. 2011). It is necessary to energy consumption (GEA 2012; Zhou 2012). reduce the greenhouse gases emissions in order to control The significant outcome of using the RE will be the climate change (Buchner and Carraro 2005). Hence, to strengthening the economic growth by creating employ- ment, developing clean environment by reducing carbon emissions, enhancing technological innovation systems and curbing the volatility of fuel prices. On the other hand, RE can boost economic growth and it can mitigate pollutant & Ashkan Hafezalkotob emissions. Moreover, it can increase the supply adequacy a_hafez@azad.ac.ir; Hafezalkotob@iust.ac.ir and it might facilitate the access to electricity in order to Meysam Ghaffari promote the rural development and social welfare (Tiba st_m_ghaffari@azad.ac.ir; mghaffari7@yahoo.com et al. 2016; Azuela and Barroso 2011; Fargione et al. 2008). Industrial Engineering College, Islamic Azad University, South Tehran Branch, Entezari alley, Oskoui alley, Choobi Bridge, Tehran 1151863411, Iran 123 Journal of Industrial Engineering International One of the most important factors in reducing the carbon as supplier, transmitter, distributer, retailer and consumer emissions is electricity generation from renewable sources. of electricity (except the green electricity producers). This Currently, tendency of different countries to generate is obligated to purchase a certain share of the TGCs from electricity from renewable sources is increasing by using electricity producers based on the energy policies of every TGC systems and feed-in tariff (Tamas et al. 2010). country (Mitchell and Anderson 2000). Many researches have addressed feed-in tariffs. As a Certificates are usually issued by the government and in case in point, Oderinwale and van der Weijde (2016) used exchange for 1 MW/h or higher units or higher produced by an input–output table to analyze a next-generation energy the renewable power plant. Renewable power plant can be system to evaluate economic impacts of Japan’s renewable profitable by selling certificates and physical electricity. TGC energy sector and the feed-in tariff system. market as financial market is created by an interaction The previous researches indicate that the TGC system between the supplier of TGC (renewable power plant) and has better results in comparison with feed-in tariffs (Ciar- demandant of TGC (thermal power plant in this study). As a reta et al. 2014; Tama´s et al. 2010). case in point, Denmark has set obligation on customers The TGC system as an economic mechanism is intro- (Nielsen and Jeppesen 2003). In this policy, TGCs market duced to supply electricity from RE with the least cost for creates an interaction between the green electricity producers government. In this system, any entity of electricity supply and electricity consumers where the consumers are obliged to chain can require a certain share in the production or buy certificates or consume a certain proportion of the consumption of electricity from RE (Aune et al. 2010). renewable electricity based on minimum requirement. In this study, we will model the interaction between The countries may employ different mechanisms to thermal and renewable producers in the electricity and TGC organize the demand certificates by markets where the thermal producer is an obligation to supply 1. Setting a fixed price at certificates, a certain share of green electricity by buying TGC from 2. Creating an obligation at every entity of the electricity renewable producer. The models will be analyzed based on supply chain to purchase certificates within a certain imperfect competitive/cooperative situations like Nash and period, Stackelberg equilibriums. The impact of minimum require- 3. Establishing a mechanism to tender purchasing ment and the TGCs price on total electricity and electricity certificates, price will be investigated by a numerical study. 4. Using a voluntary demand mechanism for certificates The reminder of the paper is organized as follows: (Schaeffer et al. 2000). Literature review is presented in Sect. 2. Section 3 describes the prerequisites and assumptions. In Sect. 4, In TGC system content, there are a few formal resear- ches (Tama´s et al. 2010). By using economic analysis, profit function of the power plants in electricity and TGC markets is set up. Section 5 presents six scenarios based on Jensen and Skytte (2003) modeled the interaction of the the game theory models and TGC pricing policies. Sec- electricity market (with the assumption monopolistic tion 6 introduces the pricing system of electricity and TGC competition) and the TGC market (with the assumption of in six scenarios. Section 7 discusses the evaluation of a perfect competition). They showed that relationship policies by a numerical study and sensitivity analysis. between the TGC price and electricity price is linear. With Finally, Conclusion is provided in ‘‘Appendix’’ section. the same method, the polish scheme with regard to its economic functioning and its justification with reference to solve common obstacles for renewable technology deployment was analyzed by Heinzel and Winkler (2011). Literature review The results demonstrate that the scheme is not mandatory TGCs have been introduced as financial assets and they are to solve obstacles on the legal or institutional level. After allocated to the renewable power plants in exchange for the their liberalization, social acceptance might rather decrease amount of green electricity generated from renewable when power price for consumers goes up. sources. The outcome of this would be that the renewable By using the quality methods, Verhaegen et al. (2009) producers will benefit from sale of physical electricity in described and analyzed the details of the TGCs system in electricity market and sale green certificates in TGCs Belgium. With the same method, Verbruggen and Lauber market (Farinosi et al. 2012). (2012) evaluated the feed-in tariff and TGC system in three criteria of efficiency, equity and institutional feasibility. TGCs system is usually operates as a market and is based on demand and supply. The demand of TGCs is Some of the researchers analyzed the TGC system by using the system dynamic method. In recent researches, this determined by energy policies and the annual share of electricity production from renewable sources. Obligation method has been used for conceptualizing, analyzing, can be set on any point of the electricity supply chain such designing and evaluating issues in energy sectors such as 123 Journal of Industrial Engineering International energy policy, power pricing, strategies of electricity There is a little comprehensive research about modeling market, and interaction between electricity and TGC mar- of the TGC system. Most previous studies analyzed the kets (Ahmad and bin Mat Tahar 2014). Ford et al. (2007) electricity and TGC markets by economic, and a few predicted the price of certificates to aid green electricity dynamic system methods investigated the implementation from the wind resources. The results showed that after a of this policy in a specific country. To the best of our few years the wind power exceeds the requirements knowledge, almost TGC system has not been analyzed by a because in the early years when a market opens the price of game theoretical approach under pricing policies. How- TGC will be increased rapidly. Recently, Hasani-Marzooni ever, in this study six different scenarios are analyzed and Hosseini (2012) modeled the TGC system by based on two common pricing policies in the TGC system employing the system dynamics to identify the potential to enhance the knowledge of designers and policy makers investment in the wind energy. They showed that the sys- in designing and deploying the TGC system. tem dynamics can be used as an appropriate tool to The contributions of this paper are as follows: investigate TGC market and help the regulatory authorities 1. We analyzed game theory models to achieve appro- to choose the appropriate policies in the energy sector. priate mechanisms to design market structure for TGC To analyze the TGC system, a number of mathematical market. We showed some outcomes and impacts. models are used by some researchers. Marchenko (2008) 2. We modeled the market structure for electricity and through a simple mathematical model simulated the bal- TGC markets in case of imperfect competition Cournot ance of supply and demand in electricity and the TGC oligopoly and monopoly under fixed and variable TGC markets. He showed that the TGC system is not an price policy. appropriate policy to minimize the negative effects of 3. We used social welfare function for evaluating the energy production in the environment. Gu¨rkan and developed scenarios so policy makers and government Langestraat (2014) analyzed the renewable energy obliga- will be enable for choice the finest of energy policies. tions and technology banding in the UK by a nonlinear mathematical model. They studied three policies to apply the TGC and showed that the obligation target by UK banding policy cannot be achieved necessarily. Prerequisites and assumptions Recently Ghaffari et al. (2016) investigated a game theo- retical approach research to analyze the TGC system. In this We concentrate on the interaction of two producers for simplicity: renewable and thermal power plants. Electricity practice, the TGC price is assumed to be constant and will be determined by the government. They demonstrated that the producers compete in the electricity and TGC market under producer obligation. Thus, thermal power plant is obliged relation between the electricity price and the TGC price is reverse, whereas the relation between the electricity price and to buy a certain amount of TGCs based on minimum the minimum requirement is direct. Also in renewable power requirement. plant Stackelberg model, the production of total electricity The government sets the minimum requirement. We and the renewable electricity is at the maximum, while the consider two policies for the price of certificates. In the first price of electricity is at the minimum. policy, the price of certificates is fixed and is set by the Game theory is the one of the most important tools in government. In the second policy, the price of certificates is decision-making. Game theory focuses on the interaction determined by market conditions and supply and demand among the players in a game by assuming the conditions mechanisms. that each player chooses to rationalize their preferences (Myerson 1991; Jørgensen and Zaccour 2002). Notations According to game theory, all the players can use from pure or mixed strategies for their own interests. The reaction In this study, parameters and decision variables are as of an actor in a critical situation in a game can define a pure follows: strategy. Each combination of different player strategies will have a specific payoff for these players. The numbers of the Parameters desirability of possible outcomes show the payoffs in the game. These payoffs are dependent on the applied strategies a the minimum requirement of renewable electricity, of the players. There are two types of games such as coop- 0  a  1; erative and noncooperative games. In the first one, the players p the profit function of renewable producer; p the profit function of thermal producer; intend to cooperate with each other for higher economic and environmental benefits. In the second one, the system might p the total payoff of centralized producer, reach an equilibrium state (Lou et al 2004). (p ¼ p þ p ); R T 123 Journal of Industrial Engineering International Table 1 Scenarios of TGC Game theory models Market price of certificate Fixed price of certificate implementation Nash NM scenario NF scenario Stackelberg SM scenario SF scenario Cooperative CM scenario CF scenario TGC markets separately. The renewable producer cost C the cost function of thermal producer; C ðÞ q is a function of green electricity generated. The R R C the cost function of renewable producer; cost of the renewable power plant is only dependent on the U the consumer utility; green electricity generated q . Therefore, the renewable D the function of environmental damages. producer profit maximization problem will be as follows: Max p ¼ P q þð1  aÞP q  C ðÞ q R e R c R R R Decision variables S:t: ð1Þ P the end-user price of electricity ($/MWh), P [ 0; q  0 e e P the price of TGC ($/MWh), P [ 0; c c where P is the end user of each MW of generated elec- q the electricity generated from thermal energy (MW), tricity, a is the minimum requirement of green electricity q  0; and P is the price of certificate. This means that a q the generated from renewable energy (MW), q  0; R R renewable producer can receiveðÞ 1  a P for each unit in Q the total amount of electricity (MW), addition to the electricity price. Under the TGC system, a Q  0ðÞ Q ¼ q þ q . T R renewable producer would obtain per unit ‘‘subsidy’’ As shown in Table 1, we have modeled six scenarios to ðÞ 1  a P . implement the TGC system based on the game theory approach and government policies regarding the control Thermal producer price of certificates. Thermal producers can fulfill their obligation by either Assumptions production of the renewable electricity or buying the TGCs from renewable producer. The following assumptions have been considered in the Thermal producer cost C ðÞ q is a function of the T T proposed models: thermal electricity q . Therefore, the thermal producer profit maximization 1. There is no limitation for power plants in consumption problem will be as follows: of the resources. 2. There is no limitation on the demand and supply Max p ¼ P q  P aq  C ðq Þ T e T c T T T electricity and TGCs. S:t: ð2Þ 3. There is no excess demand and supply in the electricity q  0 and TGCs markets. 4. Parameters are deterministic and they are known in Thermal power plant can receive P for each unit of advance. electricity. The thermal producer is obliged to pay for 5. The demand function of TGC is similar to demand buying the TGC from the renewable producer in order to function of electricity. compensate the unfulfilled requirements. Therefore, the 6. In all models, the supply of certificate meets the thermal producer under the TGC system virtually pays a minimum requirementðÞ q  aQ . R per unit ‘‘tax’’ aP as in Eq. (2). In the developed model, there is just one thermal power plant that is obliged to hold a number of the TGCs equal to a times its production. Model formulation Renewable producer In this practice, we adopted profit functions for the power Amundsen and Nese (2009), discussed the relation of: P = wholesale plants by Tanaka and Chen (2013). Renewable power plant electricity price ? a P must be established in the competitive can sell the electricity and the TGCs on the electricity and equilibrium market with a large number of retailers. 123 Journal of Industrial Engineering International Cost functions Nash equilibrium is a vector of participation decisions so that no player has an incentive to deviate from his chosen strategy We adopt cost functions for the power plants by Jensen and after considering an opponent’s choice (Urpelainen 2014). All players have no motivation to exit the equilibrium, Skytte (2003) and for renewable and thermal power plants it can be described as follows: because the outcome of this will be reduction in profit of players. Krause et al. (2006) defined the Nash equilibrium as C ðq Þ¼ a q þ b q þ c ð3Þ R R R R R R follows: C ðÞ q ¼ a q þ b q þ c ð4Þ T T T T T T The strategy profile in a (n) players game of P ¼ P ; ...; P is a Nash equilibrium (NE) if for all i 2 1 n In Eqs. (1) and (2), it is assumed that a , b ; a ; b [ 0. R R T T fg 1; ...; n there is: Profit maximization problem for power plants U ¼ P ; ...; P  P ; ...; P ; P ; P ; ...P ð9Þ i i 1 n 1 i1 iþ1 n where U is the utility function of the ith player. Following Newbery (1998) and Tamas et al. (2010), we In this section, we consider a Cournot-NE game under a assume that the demand function for electricity is a linear TGC system. function, It can be seen that by solving NE , from Eqs. (7) and (8) P ¼ c  bQ ¼ c  bðÞ q þ q ; ð5Þ e R T q and q will be obtained. Now, with substitution of q T R T and q into p and p , the maximum profit of the pro- Meanwhile, Q ¼ðq þ q Þ is the total electricity. On R T R T the other hand, we assume that the price of electricity is a ducers (p and p ) will be reached. Propositions 1 and 2 R T decreasing function of amount of renewable electricity. present the optimum electricity production quantities in Moreover, based on sixth assumption the demand function Nash equilibrium under fixed TGC price and market TGC of TGC is similar to electricity assumed. The inverse price polices, respectively. Subscripts [NF] and [NM] demand function of TGC is as follows: denote the equilibrium points in the Nash game under fixed TGC price policy and the market TGC price policy, P ¼ h  uq ð6Þ c R respectively. With substitution of Eq. (5) into Eqs. (1) and (2), the Proposition 1 Under the fixed TGC price policy, the profit maximization problem can be formulated as follows. optimum amounts of production for the renewable and Renewable producer is given as below: thermal producers in the Nash model can be given as Max p ¼ðc  bðq þ q ÞÞq þ P q  a q  b q  c R R T R c R R R R R below: s:t: P ð2aa þ ab  2a  2bÞþ A c T T 1 q  0 q ¼ ð10Þ RN½ F 2D þ 3b ð7Þ PðÞ 2aa þ 2ba þ b þ A c R 2 q ¼ ð11Þ Thermal producer is given as below: TN½ F 2 2D þ 3b Max p ¼ðc  bðq þ q ÞÞq  P q  a q  b q  c T R T T c T T T T T where A ¼ 2b a  2a c þ 2bb  bb  bc; A ¼ 2b 1 R T T R T 2 T S:t: a 2a c þ 2bb  bb bc; D ¼ 2a a þ 2a b þ 2a b: R R T R R T R T q  0 All propositions have been proven in ‘‘Appendix’’. With ð8Þ substituting the optimal quantities and Cournot TGC price Note that with substitution of Eq. (6) into Eqs. (7) and into Eqs. (7) and (8), optimal profit of the power plants can (8), the problems of producers under market TGC price be calculated. policy will be obtained. Proposition 2 Under market TGC price policy, the opti- mal amounts of production for the renewable and thermal producers in the Nash solution can be given as below: Game theory models 2aa h þ abh þ F T 1 q ¼ ð12Þ RN½ M Noncooperative Nash game 4aa u þ 3abu þ F T 2 a hu  2aa h  ab u þ 2ab u  acu  ahu þ E R R T 1 q ¼ If no player has anything to gain by changing his strategy, TN½ M 4aa u þ 3abu þ F T 2 when the other players do not change their strategies, then the ð13Þ set of strategies for all the players and the corresponding payoffs constitute a Nash equilibrium (Lou et al 2004). The 123 Journal of Industrial Engineering International ð2aa h þ abh þ F Þðau  bÞ T 1 where F ¼ 2b a  2a c þ 2b h þ 2bb  bb  bc 1 R T T T R T q ¼ TS½ M 2 2ðb þ a Þð4aa u þ 2abu  b þ F Þ T T 2 2bh; F ¼ 4a a  4a b  4a b  4a u  3b  4b 2 R T R T T ah  b þ c u; E ¼2a b þ 2a c þ bb  2bb þ bc  bh  2b 1 R T R R T T  : ð17Þ 2ðb þ a Þ u þ 2cu. Cooperative game Noncooperative Stackelberg Games In this section, a cooperative relationship between thermal We investigated a noncooperative structure for interaction and renewable producers is investigated. In this model, between the thermal and renewable producers where the power plants collaborate together in electricity and TGCs initiative is the possession of one of the power plants, i.e., markets. We investigate this situation to increase our the leader. This can enforce its strategy on its rival, i.e., the knowledge about how to divide thermal producer capacity follower. The first move is made by leader to maximize its to generate in competition with the renewable producer. profit and then in return the follower reacts by choosing the Summation of Eqs. (7) and (8) gives cooperative model: best strategies. Max p ¼ðc  bðq þ q ÞÞq þ P q  a q  b q R T R c R R R R Since the objective of the TGC system is supporting the c þðc  bðq þ q ÞÞq R R T T increasing share of the electricity generated by RE pro- ducer, in this research we only examine renewable pro- P q  a q  b q  c c T T T T T ducer—Stackelberg model where the renewable producer S:t: is leader and the thermal power plant is the follower. In this q ; q  0 R T model, the renewable producer first sells its generated ð18Þ electricity in electricity market. Then the follower as thermal producer sells its generated electricity in electricity A Hessian matrix of p in Eq. (18) is: H ¼ market and buys certificates from renewable producer. 2b  2a 2b and the utility function p is a Propositions 3 and 4 present the optimum production of 2b 2b  2a electricity from renewable and thermal producers in concave function on (q ; q ) if and only if the Hessian R T Stackelberg equilibrium under fixed TGC price and market matrix H is negative definite. Propositions 5 and 6 present TGC price polices, respectively. Subscripts [SF] and [SM] the optimum production quantities of green and thermal refer to optimal values of Stackelberg models under the electricity of producers in cooperative game under fixed fixed TGC price and market TGC price, respectively TGC price and market TGC price polices, respectively. Subscripts [CF] and [CM] denote the optimum values in Proposition 3 Under fixed TGC price policy, the optimal the cooperative game model under fixed TGC price and amount of electricity generated from renewable and fossil market TGC price polices, respectively. sources in renewable producer—Stackelberg model—is: P ð2aa þ ab  2a  2bÞþ E c R R 2 Proposition 5 Since ð2b  2a Þð2b  2a Þ R T q ¼ ð14Þ R½SF K ð2bÞð2bÞ [ 0, the optimal amount of electricity gen- 2 2 erated from renewable and fossil sources in the coopera- P 2aa b þ ab  aE  2a b  2b þ bE þ Kðc  b Þ c R 2 R 2 T q ¼ T½SF tive game model under fixed TGC price policy will be: 2E ðb þ a Þ 2 R ð15Þ PðÞ aa  a  bþ B c T T 1 q ¼ ð19Þ R½CF where E ¼ 2a b  2a c þ 2bb  bb  bc; K ¼ 2 R R R R T 2 PðÞ aa þ bþ B c R 2 4a þ 8a b þ 2b . q ¼ ð20Þ T½CF Proposition 4 Under market TGC price policy, the opti- where B ¼ a b  a c þ bb  bb ; B ¼ a b  a c 1 T R T R T 2 R T R mal amount of electricity generated from renewable and bb þ bb : R T fossil sources in renewable producer—Stackelberg model—is: Substituting Eq. (4) into Eq. (18), the problem of profit centralized power plant under market TGC price policy 2aa h þ abh þ F T 1 q ¼ ð16Þ RS½ M 2 yields: 4aa u þ 2abu  b þ F T 2 123 Journal of Industrial Engineering International Table 2 Price of TGC in six Game models TGC price policy scenarios Market price Fixed price ð2aa hþabhþF Þu T 1 Nash P ¼ cte P ¼ h  cN½ F cN½ M 4aa uþ3abuþF T 2 ð2aa hþabhþF Þu T 1 Stackelberg P ¼ cte P ¼ h  cS½ F cS½ M 4aa uþ2abub þF T 2 ða uhþ2aa hþab hacuþG Þu Cooperative  T T 1 P ¼ cte P ¼ h  cC½ F 2 2 cC½ M a u þ4aa uþF þ3b T 2 ‘‘cte’’ represents a fixed value transaction level focuses on managing the implementation Max p ¼ðc  bðq þ q ÞÞq þðh  uq Þq R T R R R of discounts away from the reference or the price list which a q  b q  c þðc  bðq þ q ÞÞq R R R R R T T occur both on and off the invoice or receipt. ðh  uq Þq  a q  b q  c R T T T T T T In this section, the pricing at the electricity market level S:t: is considered in oligopoly and monopoly market structures. Oligopoly is a common form of market where a number of q ; q  0 R T firms are in competition with each other. Based on the ð21Þ game theory approach, the Cournot–Nash and Cournot– A Hessian matrix of the profit function in the TGC Stackelberg models are the oligopoly models. The oligo- market price policy is polies are in fact price setters rather than price takers (Perloff 2008). By substituting the optimal amounts of 2au  2a  2b  2uau  2b H ¼ and the utility green and black electricity production quantities in the 2b  2a 2b  2a T T payoff functions of the renewable and black power plants, function in the cooperative model is a concave function on the optimum prices of the electricity and TGC are achieved (q ; q ) if and only if the Hessian matrix H is negative R T in six scenarios. Tables 2 and 3 depict the electricity price definite. and TGC price in each scenario. Proposition 6 Since detðHÞ¼ð2au  2a  2b  2uÞ ð2b  2a Þðau  2bÞð2b  2a Þ [ 0, under market T T TGC price policy the optimal amount of electricity gener- Evaluation policies and sensitivity analysis ated from renewable and fossil sources in the cooperative game model are: Comparison price and production a hu þ 2aa h þ ab u  acu þ G T T 1 q ¼ ð22Þ R½CM 2 2 In this section, sensitivity analysis is performed by a u þ 4aa u þ 3b þ F T 2 numerical examples to illustrate performance differences a hu  2aa h  ab u þ 2ab u  acu  ahu þ G R R T 2 q ¼ between different models. T½CM 2 2 2 a u þ 4aa u þ 3b þ F T 2 We present numerical studies by assuming that the ð23Þ marginal costs and other parameters of the cost function in renewable power plant are higher than nonrenewable where G ¼þ2a b  2a c  2a u þ 2bb  2bb 1 T R T T R T power plant. 2bh; G ¼2a b þ 2a c þ 2bb þ 2bb  2bb 2 R T R R R T Cost function of the renewable and nonrenewable pro- 2bh  2b u þ 2cu. ducers is assumed as below: Pricing is the most effective profit lever (Dolan and ðÞ Cq ¼ 0:06q þ 11q þ 100 and R R Simon 1996). This is a process for determining what a CqðÞ¼ 0:04q þ 8q þ 20: T T company will receive in exchange for its products or ser- T vices. Pricing can be considered in industry, market, and The price elasticity of the electricity supply and TGC transaction levels. At the industry level, the main focus is supply is assumed as below: b ¼ 0:4 and u ¼ 0:3. It is on the overall economics of the industry, including price assumed that c ¼ 150 and h ¼ 50: In fixed TGC price changes of the supply and demand changes of the cus- policies, the TGC price is set equal to average of the TGC tomer. On the other hand, in the market level the com- market prices per different amounts of the minimum quota. petitive situation of the price in comparison with the value Figure 1 illustrates the changes of total electricity sup- differential of the product to that of the comparative ply, green electricity supply and black electricity supply competing products will be considered. Pricing at the versus the minimum requirement of green electricity. 123 Journal of Industrial Engineering International Figure 2 shows the changes of electricity and TGC price versus the minimum requirement of green electricity. It can be seen from Fig. 1 that in every six scenarios of Table 1 when a increases Q decreases. However, supply of the green electricity increases in the market price policy and Nash model in the fixed price policy. Moreover, when a increases the black electricity decreases in every six scenarios. In the CM scenario, when a increases, supply of the total electricity in the first step decreases but then it starts to increase. But in the CF scenario when a increases, supply of total electricity consistently decreases. This means that contrary to the other five scenarios, in the CM scenario when minimum requirement of green electricity (aÞ is almost 60% the electricity generated is at minimum amount. The maximum amounts of the green electricity are generated in the CF scenario. The maximum amounts of the black electricity are generated in the NF scenario and the minimum amounts of the black electricity are supplied in CF scenario. Generally speaking, with changes of the minimum mandatory quota, supply of the total electricity in the SF scenario has the least changes in comparison with the other scenarios. Figure 1 demonstrates that supply of the total electricity in the SM scenario is greater than the SF scenario con- sistently. Moreover, the trend of electricity supply in both scenarios is descending with increase in the minimum quota. This result is supported by Jensen and Skytte (2003) and Tamas et al. (2010). Supply of the total electricity in the Nash model of both policies has a descending trend with increase in the minimum quota. Nevertheless, the total electricity generated in the NF scenario is greater than that of the NM scenario. About the cooperative model, it can be stated that the total electricity generated in the CF scenario with increase in the minimum quota has absolutely descending trend, whereas the CM scenario shows a convex shape. When the minimum requirement of green electricity is less than 60%, the total electricity generated in the CF scenario is greater than that of the CM scenario. Figure 2 shows that there is a reverse relation between the minimum requirement of green electricity and TGC price. However, the relation between the minimum requirement of green electricity and electricity price is direct. In other words, when a increases P increases and P decreases in all scenarios. This matter represents there is a reverse relation between price of TGC and electricity price. This result is supported by Jensen and Skytte (2003), Fristrup (2003), Tama´s et al. (2010) and Marchenko (2008). In the CM scenario, when a increases, there is a rapid reduction in the price of TGC in comparison with the other Table 3 Price of electricity in six scenarios Game TGC price policy Models Market price Fixed price ahðau2a 2a 2buÞþauðb þ2b cÞþE F P ð2aa þ2aa þ2ab2a bÞþA þA Nash  R T R T 1 1  c R T T 1 2 P ¼ c  b  P ¼ c  b eN½ M 4aa uþ3abuþF eN½ F T 2 2Dþ3b 0 1 2 2 2 2 ð2aa hþabhþF Þðauþbþ2a Þ Stackelberg  T 2 T cahb T P að4a þ 4a b þ b þ KÞ 2P ð2a þ 3a b þ b Þ P ¼ c  b þ c R c R R R eS½ M 2ðÞ bþa 2ð4aa uþ2abub þF ÞðÞ bþa T T 2 T B C þ E ð2a þ bÞþ Kðb þ cÞ B 2 R T C P ¼ c  bB C eS½ F 2KðÞ bþa @ A 2bðP aa þP bþB Þ að2a hþ2a hþb ub uþhuÞþG G  c R c 2 Cooperative  R T R T 1 2 P ¼ c þ P ¼ c  b 2 2 eC½ F D eC½ M a u þ4aa uþF þ3b T 2 Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 240 240 220 220 200 200 180 180 160 160 140 140 120 120 100 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 1 Changes of total, green and black electricity versus minimum quota scenarios. Among the game theory models, the Stackelberg Changes of payoffs of thermal, renewable and central- model in the fixed TGC price results in the minimum ized power plants are depicted in Fig. 3. The results of electricity price. However, the cooperative model has the numerical study show that by increasing a total payoff of maximum electricity price in both fixed TGC price and the centralized power plant decreases in all scenarios. Cen- market policy price. The price of electricity in the fixed tralized power plant payoff in cooperative model is higher TGC price policy is less than that of the same game theory than the other scenarios. By increasing a, the payoff of model in the market TGC price policy. green electricity producer decreases in all scenarios except CM scenario. Note that in Nash and Stackelberg models by Black electricity supply Green electricity supply Total electricity supply Total supply of electricity (Mwh) Supply of black electricity (Mwh) Supply of green electricity (Mwhr) Supply of black electricity (Mwh) Supply of green electricity (Mwh) Total supply of electricity Mwh) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 100 100 90 90 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 ( percentage) ( percentage) 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 0 0.1 0. 2 0.3 0. 4 0.5 0. 6 0.7 0. 8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 2 Changes of TGC and electricity price versus minimum quota increasing a the payoff of green electricity producer relation to inverse demand function in Eq. (4), and it is decreases under market TGC price policy. Remarkably, by assumed to be equal to 100. Moreover, it is assumed that increasing a, the payoff of black electricity producer the cost function of the green and black power plants is 2 2 decreases in all scenarios, but in CM scenario, it decreases 5q þ 30q þ 100 and 3q þ 10q þ 20, respectively, R T R T faster than the other scenarios. It can be concluded that the where b ¼ 1:2 and u ¼ 1:2. It is assumed that: c ¼ use of CM scenario will lead to elimination of thermal 150; h ¼ 100 and k ¼ 0:4. Figure 4 depicts the results of power plants more quickly. this example in six scenarios. The evaluation of these polices reveals that in each six Social welfare scenarios by increasing the minimum quota, social welfare increases at first and decreases later. In other words, in all Social welfare is an appropriate criterion to evaluate any scenarios the maximum of social welfare does not happen policy or program (Tama´s et al. 2010). To evaluate the six when all the electricity supply is generated from the green proposed scenarios in this paper, we use the equation of sources (a ¼ 100%Þ. This result is in accordance with social welfare proposed by Currier (2013). In this case, the Currier (2013) and Currier and Sun (2014). In the fixed social welfare is equal to the total utility minus the all costs TGC price polices, in the first, by increasing of the mini- including the environmental damages and production costs. mum quota, the social welfare will increase with a fas- Here, U represents the consumer utility and D denotes the ter slope compared with the market TGC price polices. function of environmental damages. Generally, when the minimum requirement of renew- able energy sources in the electricity supply is less than SW ¼ UðQÞ Cðq Þ Cðq Þ Dðk; qÞð24Þ T R R almost 50%, the market TGC price polices lead to a higher Currier and Sun (2014) assumed that D ¼ q =2 and R level of welfare. The welfare in Stackelberg model with the ðÞ Q ¼ cQ  Q =2. Here c represents the parameter in Electricity price TGC price TGC price ($/Mwh) Electricity price ($/Mwh) Electricity price ($/Mwh) TGC price ($/Mwh) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 14000 14000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 12000 12000 10000 10000 8000 8000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) 9000 9000 8000 8000 7000 7000 6000 6000 4000 4000 3000 3000 2000 2000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 3 Changes of power plants Payoff versus minimum quota market TGC price policy (SM scenario) is consistently TGC price policy (NM and SM scenarios) and 70–80% of greater than the fixed TGC price policy. But comparing the the electricity supply is generated from the RE sources. In two control price of certificates policies among other game contrast, the minimum welfare is obtained when that theory models (Nash and cooperative) shows that there is market structure follows the Nash or Stackelberg model not a constant trend in terms of welfare created. The with the fixed TGC price policy (i.e., NF and SF scenarios) maximum welfare is obtained when that market structure when minimum quota is zero (a = 0). When a =0, the follows the Nash or Stackelberg model with the market maximum welfare is obtained by CM scenario. Among six Black electricity producer payoff Green electricity producer payoff Total payoff of centralized power plant Payoff of renewable power plant ($) Total porofit of power plants($) Payoff of thermal power plant($) Payoff of thermal power plant($) Payoff of renewable power plant($) Total porofit of power plants($) Journal of Industrial Engineering International Market TGC price policy Fixed TGC price policy 350 350 300 300 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ( percentage) ( percentage) Nash Stackelberg Cooperave Fig. 4 Comparison of social welfare acquired in each scenario scenarios, SF scenario creates minimum welfare for all social welfare. In this policy, the use of NF scenario will be amounts of a. more beneficial in terms of social welfare and high power It seems that the results of this practice are useful for supply in comparison with three other scenarios. private and public investors, energy policy makers, gov- There are several directions for the future research. ernment and other active players in the electricity supply Firstly, this study considers the national trade in the elec- chain. It is an undeniable fact that pricing the TGC is a tricity market and the TGC system. Game theory formu- challenging problem for the government. Therefore, ana- lation of international TGC trade in the internal and lyzing these models with various scenarios can improve the external markets is interesting. Secondly, other approaches effectiveness of designing and implementing TGS system. of game theory to analyze the implementation of the TGC system can be considered. For example, modeling the TGC system in the incomplete information mode by Bayesian Conclusion models is both interesting and challenging. Thirdly, we only consider the producer’s obligation option in the TGC This study demonstrates that using market TGC price system, but other obligations in the TGC system can also policy is more beneficial when a country intends to deploy be considered. Finally, no time constraint was considered a system of credentials with a share of renewable energy to validate the certificates. Using the time variables in modeling of the TGC system seems to be useful. sources less than 50 percent because not only a higher social welfare in this sector is created but also by using this Open Access This article is distributed under the terms of the Creative policy the profit of thermal power plants will be decreased Commons Attribution 4.0 International License (http://creative with a modest slope and it will not lead to an abrupt commons.org/licenses/by/4.0/), which permits unrestricted use, dis- withdrawal from the market and lack of power supply. tribution, and reproduction in any medium, provided you give Moreover, if the goal is accelerating the removal of these appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were power plants with abrupt withdrawal, then using the CM made. scenario is beneficial where the profit of fossil fuels is reduced more steeply. This scenario also will have the lowest power supply among the six scenarios, and it will Appendix have the lowest levels of social welfare for a values above 50%. Proof of Proposition 1 If the second-order derivative for If a country is so much developed that can provide more Eq. (7) is negative, the profit function of the green pro- than 50% of its electricity from renewable sources, then ducer will be concave. The first-order derivative for Eq. (7) using fixed TGC price policy can be beneficial too because is: at this point it acts like market TGC price policy in creating Social Welfare Social Welfare Journal of Industrial Engineering International Therefore, the profit function of the green producer is op ¼ðP þ cÞðbq þ 2bq þ 2a q þ b Þ¼ 0: c T R R R R concave. Similarly, the first-order derivative for Eq. (8)is oq as follows: ð25Þ op ¼ q ð2b  2a Þþ q ðb þ uaÞþ c  ah  b ¼ 0: The second-order derivative for Eq. (7) is as follows: T T R T oq o p ð31Þ ¼ ðþ2bþ2a Þ: ð26Þ o q The second-order derivative is as follows: Since the amounts of b and a are positive, the second- o p o p R ¼2a  2b ¼ 0: ð32Þ order derivative is negative \0 : 2 o q R o q Therefore, the profit function of the green producer is Since it is assumed that b; a [ 0, the second-order concave. Similarly, the first-order derivative for Eq. (8)is o p derivative is negative \0 . as follows: 2 o q Therefore, the profit function of the green producer is op ¼ c ð2bq þ bq þ Pca þ 2a q þ b Þ¼ 0: ð27Þ T R T T T concave. oq Solving Eqs. (29) and (31), it follows that the optimal The second-order derivative for Eq. (8) yields: production of power plants is: o p T 2aa h þ abh þ F T 1 ¼ð2bþ2a Þ: ð28Þ q ¼ ; T RN½ M 4aa u þ 3abu þ F T 2 o q a hu  2aa h  ab u þ 2ab u  acu  ahu þ E R R T 1 q ¼ : TN½ M Since the amounts of b and a are positive, the second- T 4aa u þ 3abu þ F T 2 o p order derivative is negative \0 : 2 h o q Hence, the profit function of the thermal producer will Proof of Proposition 3 To solve the model, q is first be concave. Solving Eqs. (25) and (27), it follows that the obtained as a function of q and then the first-order optimal production of power plants is: derivative is first examined for a profit function of the P ð2aa þ ab  2a  2bÞþ A c T T 1 thermal power plant of Eq. (8). The best response strategy q ¼ ; RN½ F 2D þ 3b for a thermal power plant is computed as follows: PðÞ 2aa þ 2ba þ bþ A c R 2 q ¼ : aP þ q b þ b  c TN½ F 2 c R T 2D þ 3b q ¼ : ð33Þ 2ðb þ a Þ Substituting Eq. (33) into Eq. (7) gives: aP þ bq þ b  c c R T p ¼ P q þ c  b þ q q R c R R R 2ðb þ a Þ Proof of Proposition 2 If the second-order derivative of a q  b q  c : R R R R Eq. (7) under market TGC price policy is negative, the ð34Þ profit function of the green producer will be concave. The first-order derivative for Eq. (7) is: The first-order derivative for Eq. (34) yields: op op b ¼ q ð2u  2b þ au þ ua  2a Þ R R R ¼ P  b  þ 1 q þ c oq c R oq 2ðb þ a Þ R T þ h þ c  bq  ah  b ¼ 0: ð29Þ T R aP þ bq þ b  c c R T b  þ q  2a q  b ¼ 0: R R R R 2ðb þ a Þ The second-order derivative for Eq. (7) under market TGC price policy is as follows: ð35Þ o p The profit function of the renewable power plant is ¼ 2au  2a  2b  2u ¼ 0: ð30Þ o q R concave if the second-order derivative for Eq. (34)is negative. The second-order derivative for the renewable Since it is assumed that u; b; a [ 0, and 0  a  1. We power plant gives: know (au\a þ b þ uÞ, then the second-order derivative 2 2 o p o p 2a a þ 2a b þ b R R T R is negative \0 : ¼ : ð36Þ o q b þ a o q T 123 Journal of Industrial Engineering International 2aa h þ abh þ F T 1 Regarding the assumptions and parameter values, q ¼ : RS½ M 4aa u þ 2abu  b þ F Eq. (36) is negative. Therefore, the profit function of the T 2 renewable power plant is found to be concave. From Substituting q into Eq. (37), the optimal black RS½ M Eq. (35), it follows that the optimal green electricity electricity production is: production is: T½SM P ð2aa þ ab  2a  2bÞþ E c R R 2 2 2 P 2aa b þ ab  aE  2a b  2b þ bE  b E þ E c c R 2 R 1 T 2 2 q ¼ : R½SF ¼ : 2E ðb þ a Þ 2 R Substituting q into Eq. (33), the optimal black RS½ F electricity production is: ð2aa h þ abh þ F Þðau  bÞ T 1 q ¼ TS½ F 2ðb þ a Þð4aa u þ 2abu  b þ F Þ T T 2 Proof of Proposition 5 The first-order derivative for the ah  b þ c profit function of the power plants in Eq. (25) yields (in the 2ðb þ a Þ fixed TGC price policy): op ¼ P þ c  2bðq þ q Þ 2a q  b ¼ 0; ð41Þ c T R R R R oq Proof of Proposition 4 To solve the model, q is first obtained as a function of q and then the first-order R op ¼ c  2bðq þ q Þ aP  2a q  b ¼ 0: ð42Þ T R c R T T derivative is examined for a profit function of the thermal oq power plant of Eq. (8) under market TGC price policy; the Solving Eqs. (41) and (42), they give: best response strategy of the thermal power plant is com- puted as follows: PðÞ aa  a  bþ B c T T 1 q ¼ : R½CF q au  q b  ah  b þ c R R T q ¼ : ð37Þ PðÞ aa þ bþ B 2ðb þ a Þ c R 2 q ¼ : T½CF Substituting Eq. (37) into Eq. (7) gives: p ¼ðq u þ hÞq R R R q au  bq  ah  b þ c R R T Proof of Proposition 6 The first-order derivative for the þ c  b  þ q q R R 2ðb þ a Þ profit function of the power plants in Eq. (26) yields (in the ðq u þ hÞaq  a q  b q  c : R R R R R R market TGC price policy): ð38Þ op ¼ q ð2au  2a  2b  2uÞþ q ðau  2bÞ R R T oq The first-order derivative for Eq. (38) yields: ah  b þ c þ h ¼ 0; ð43Þ op au  b ¼ h  b  þ 1 q op oq 2ðb þ a Þ R T ¼ q ð2au  2bÞþ q ð2a  2bÞ R T T oq q au  bq  ah  b þ c T R R T : þ c  b  þ q 2ðb þ a Þ  ah  b þ c ¼ 0; ð45Þ T T þ q ð2u þ au þ ua  2a Þ b ¼ 0 R R R Since Hessian matrix for this function is negative ð39Þ definite, the profit function is concave. Thus, Solving Eqs. (43) and (44) yields: The profit function of the renewable power plant is a hu þ 2aa h þ ab u  acu þ G T T 1 concave if the second-order derivative for Eq. (38)is q ¼ ; R½CM 2 2 2 a u þ 4aa u þ 3b þ F negative. The second-order derivative for the renewable T 2 power plant gives: a hu  2aa h  ab u þ 2ab u  acu  ahu þ G R R T 2 q ¼ : T½CM 2 2 2 a u þ 4aa u þ 3b þ F T 2 o p au  b ¼2u  2b þ 1 þ 2au  2a : ð40Þ 2ðb þ a Þ o q T Regarding the assumptions and parameter values, Eq. (40) will be negative. From Eq. (39), it follows that the optimal green electricity production is: 123 Journal of Industrial Engineering International Heinzel C, Winkler T (2011) Economic functioning and politically References pragmatic justification of tradable green certificates in Poland. Environ Econ Policy Stud 13:157–175 Ahmad S, bin Mat Tahar R, (2014) Using system dynamics to Jensen S, Skytte K (2003) Interactions between the power and green evaluate renewable electricity development in Malaysia. Kyber- certificate markets. Energy Policy 30:425–435 netes 43(1):24–39 Jørgensen S, Zaccour G (2002) Time consistency in cooperative Amundsen E, Nese G (2009) Integration of tradable green certificate differential games. In: Zaccour G (ed) Decision & Control in markets: what can be expected? J Policy Model 31:903–922 Management Science Advances in Computational Management Aune F, Dalen H, Hagem C (2010) Implementing the EU renewable Science, vol 4. Springer. Boston, MA, pp 349–366 target through green certificate markets. Energy Econ Krause T, Beck E, Cherkaoui R, Germond A, Andersson G, Ernst D 34:992–1000 (2006) A comparison of Nash equilibria analysis and agent based Azuela G, Barroso L (2011) Design and performance of policy modelling for power markets. Electr Power Energy Syst instruments to promote the development of renewable energy: 28:599–607 emerging experience in selected developing countries. Energy Lou HH, Kulkarni MA, Singh A, Huang YL (2004) A game theory and mining sector board discussion paper no. 2. The World based approach for emergy analysis of industrial ecosystem Bank, Washington, DC under uncertainty. Clean Technol Environ Policy 6(3):156–161 Bazilian M, Hobbs B, Blyth W, MacGill I, Howells M (2011) Marchenko O (2008) Modeling of a green certificate market. Renew Interactions between energy security and climate change: a focus Energy 33:1953–1958 on developing countries. Energy Policy 39:3750–3756 Mitchell C, Anderson T (2000) The implication of tradable green Buchner B, Carraro C (2005) Modelling climate policy perspectives certificate for UK. Int J Ambient Energy 21(3):161–168 on future negotiations. J Policy Model 27:711–732 Myerson R (1991) Game theory: analysis of conflict. Harvard Ciarreta A, Espinosa MP, Pizarro-Irizar C (2014) Switching from University Press, Cambridge, Chicago feed-in tariffs to a Tradable Green Certificate market. Interrelat Newbery D (1998) Competition, contracts, and entry in the electricity Between Financ Energy 54:261–280 spot market. Rand J Econ 29:726–749 Currier KM (2013) A regulatory adjustment process for the determi- Nielsen L, Jeppesen T (2003) Tradable Green Certificates in selected nation of the optimal percentage requirement in an electricity European countries—overview and assessment. Energy Policy market with Tradable Green Certificates. Energy Policy 31:3–14 62:1053–1057 Oderinwale T, van der Weijde AH (2017) Carbon taxation and feed-in Currier K, Sun Y (2014) Market power and welfare in electricity tariffs: evaluating the effect of network and market properties on markets employing Tradable Green Certificate systems. Int Adv policy effectiveness. Energy Systems 8(3):623–642 Econ Res 20(2):129–138 Perloff J (2008) Microeconomics theory and applications with Dolan R, Simon H (1996) Power pricing. Free Press, New York calculus. Pearson, Boston Fargione J, Hill J, Tilman D, Polasky S, Hawthorne P (2008) Land REN21 (2012) Renewables 2012 global status report. REN21 clearing and the biofuel carbon deb. Science 319:1235–1238 Secretariat, Paris Farinosi F, Carrera L, Mysiak J, Breil M, Testella F (2012) Tradable Schaeffer GJ (2000) Options for design of tradable green certificate certificates for renewable energy: the Italian experience with systems. Report/Energy Research Centre of the Netherlands hydropower. In: 9th International conference on the European (Netherlands) energy market (EEM 2012). IEEE, Florence, pp 1–7 Tama´s M, Shrestha S, Zhou H (2010) Feed-in tariff and tradable Ford A, Vogstad K, Flynn H (2007) Simulating price patterns for green certificate in oligopoly. Energy Policy 38:4040–4047 tradable green certificates to promote electricity generation from Tanaka M, Chen Y (2013) Market power in renewable portfolio wind. Energy Policy 35:91–111 standards. Energy Econ 39:187–196 Fristrup P (2003) Some challenges related to introducing tradable Tiba S, Anis O, Mohamed F (2016) The four-way linkages between green certificates. Energy Policy 31(1):15–19 renewable energy, environmental quality, trade and economic GEA (2012) Global energy assessment: toward a sustainable future. growth: a comparative analysis between high and middle-income Cambridge University Press, Cambridge countries. Energy Syst 7:103–144 Ghaffari M, Hafezalkotob A, Makui A (2016) Analysis of imple- Urpelainen J (2014) Grid and off-grid electrification: an integrated mentation of Tradable Green Certificates system in a competitive model with applications to India. Energy Sustain Dev 19:66–71 electricity market: a game theory approach. J Ind Eng Int Verbruggen A, Lauber V (2012) Assessing the performance of 12(2):185–197 renewable electricity support instruments. Energy Policy Gu¨rkan G, Langestraat R (2014) Modeling and analysis of renewable 45:635–644 energy obligations and technology bandings in the UK electricity Verhaegen K, Meeus L, Belmans R (2009) Towards an international market. Energy Policy 70:85–95 tradable green certificate system—the challenging example of Hasani-Marzooni M, Hosseini S (2012) Dynamic interactions of TGC Belgium. Renew Sustain Energy Rev 13:208–215 and electricity markets to promote wind capacity investment. Zhou H (2012) Impacts of renewables obligation with recycling of the IEEE Syst J 6:46–57 buy-out fund. Energy Policy 46:284–291

Journal

Journal of Industrial Engineering InternationalSpringer Journals

Published: Jun 1, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off