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China has integrated tradable green certificates and carbon markets with its electricity sector to promote renewable energy and reduce carbon emissions. However, the impact mechanism of decision-making behaviors of involved entities in these integrated markets on the market equilibrium is still unclear, hence limiting the further development of renewable energy industries and carbon reduction progress to some extent. Therefore, conducting in-depth research to inform policy makers about the impacts of entities' decision-making behaviors on market equilibrium within the context of integrated multiple markets is crucial. This study aims to analyze the characteristics of entities' decision-making behaviors and equilibrium states within the collaborative dynamics of carbon, electricity, and green certificate markets. Specifically, an optimal decision-making model for entities given the multi-market coupling was developed by employing mathematical programming methods to analyze market equilibriums across various market combinations and policy parameters. The conclusions underscore equilibrium price shifts and decision-making characteristics among entities across multiple markets. The result shows that the carbon market could increase power prices and decrease green certificate prices. To ensure sustainable energy development, policymakers should consider the decision-making behavior of entities under multi-market coupling, which can promote the low-carbon transformation of the Chinese energy industry. • Equilibrium price formation mechanisms under multi-market coupling are analyzed. • Simulates micro individual behavior, revealing macro energy structure shifts. • Reveals relationships among markets, aiding in differentiated policy formulation. • Carbon market could increase power prices and decrease green certificate prices. • Carbon market reduce more emission shortly than renewable energy deployment. [ABSTRACT FROM AUTHOR]

Equilibrium capacity expansion is an effective tool to help regulators predict the generation evolution of power systems by analyzing the decision-making of generation companies (Gencos). With the development of carbon markets (CMs) and electricity markets (EMs), Gencos' decisions in these two markets (encompassing investment and bidding decisions related to carbon emission allowances and electricity) are deeply intertwined through market clearing results. However, existing studies mainly focus on equilibrium capacity expansion with fixed carbon prices and usually ignore the realistic clearing process of CMs, which cannot simulate Gencos' coupled decision-making and accurately predict generation evolution under the CMs and EMs. This paper proposes a two-level equilibrium capacity expansion model for power systems which considers the coupled decisions of Gencos between CMs and EMs. At the upper level, multiple Gencos' coupled decision models are proposed based on their interaction with market clearing results. At the lower levels, CMs and EMs are respectively cleared to determine the varying carbon and electricity prices. Furthermore, the developed equilibrium capacity expansion model is reformulated as an equilibrium problem with equilibrium constraints (EPEC), which is solved by a diagonalization-based solution procedure. Finally, a provincial power system of southeast China is used to validate the performance of the proposed framework. The results illustrate that under CMs and EMs, non-fossil energy would account for 81.3% of total capacity and 73.88% of total generation in 2050. Compared to the existing model using fixed carbon prices, the consideration of realistic carbon market clearing will promote the installation of renewable energies and improve social welfare. The proposed model can provide beneficial references for regulators to perceive the evolution of power systems in CMs and EMs. • A two-level equilibrium capacity expansion model for power systems is proposed. • A novel coupled decision model for Gencos in CMs and EMs is developed. • The proposed model is solved by a diagonalization based solution procedure. • The results can guide the transition of power systems under the CMs and EMs. [ABSTRACT FROM AUTHOR]

The reliability option (RO) ensures generation capacity adequacy, drawing inspiration from financial product options. However, most recent RO studies overlook the gaming strategies employed by power producers. This paper proposes a bi-level model based on an equilibrium analysis of the power market under RO. The upper-level model aims to maximize the power producers' profit, whereas the lower-level model focuses on market clearing. Profit calculation considers factors like electricity sales income, option fees income, fuel cost, expansion investment cost, refund cost, and penalties. The bi-level model is reformulated into a mathematical problem with equilibrium constraints (MPEC) for each producer using Karush–Kuhn–Tucker conditions of the lower-level model. We then apply a series of linearization methods. The market equilibrium is obtained through the dynamic game framework for all MPECs. We also provide a comprehensive purchase cost calculation and demonstrate its equivalence to user side surplus. We examine cases from various spot market construction maturities in a provincial area of China. Our results indicate that implementing the RO mechanism and aligning parameters with the proposed optimal RO parameter curve, one can reduce the comprehensive purchase cost. • Various strategies of all power producers are considered. • The MPEC under RO mechanism is precisely linearized to MILP. • Dynamic game framework is used to solve market equilibrium to be more practical. • RO mechanism can increase the user side surplus according to the equilibrium. • The optimal RO parameter curve is obtained as the parameter setting suggestion. [ABSTRACT FROM AUTHOR]

Clean energy dominant and electricity centric is the inevitable trend of the future energy development. Electric power industry has entered into an increasingly competitive era in recent years due to the deregulation of power systems. However, power market should not be fully competitive and need to be regulated strictly to satisfy the safe and reliable operation of power systems. Base on the market equilibrium principle in microeconomics, a novel power market clearing model with limited competition was put forward, in which the limited competition power satisfies the power flow adjustment and the network losses distribution. Further, the free transaction ratio which can be regarded as the measurement of the degree of power market deregulation was analyzed according to the formulated market clearing model. Finally, three case studies were made on the IEEE-30 test system to verify the practicality and efficiency of the method. The results show that different transaction ratio has significant influence on the operation of power systems and the optimal transaction ratio can be determined. [ABSTRACT FROM AUTHOR]

• Modeling GenCos' CW in market equilibrium problem considering SCGMS. • Obtaining oligopolistic generation and maintenance schedules, consumption of loads, and nodal prices based on KKT conditions. • Capacity withholding analysis of GenCos using two novel indices WTI and RWLI. • Considering wealth transfer from loads to GenCos to model GenCos' CW impacts on electricity markets. • Introducing RWLI to model GenCos' CW by measuring loss of social welfare. The analysis of capacity withholding (CW) plays an important role in monitoring of the market power. One way of CW in oligopoly electricity markets is the strategic maintenance of generation companies. In this paper, a security-constrained generation maintenance scheduling is proposed using two sets of comparison indices to analyze the CW from the nodal and global points of view. The relative welfare loss index measures the market inefficiency in the form of social welfare loss relative to efficient markets, while the wealth transfer index enables the analysis of wealth transfer from customers to GenCos due to the CW. It is revealed that these indices identify the additional strategic leeway of GenCos due to the maintenance scheduling. Consequently, they can be used by the regulators and independent system operators for the evaluation of CW in the presence of GenCos' strategic maintenance. Focusing on changes in generation, nodal prices, and social welfare, the modified versions of IEEE 30 and 118-bus test systems are provided to demonstrate the robustness and effectiveness of the proposed indices. It is revealed that the price and welfare based measures detect the CW in the context of maintenance scheduling whereas the mere analysis of quantities is not sufficient. [ABSTRACT FROM AUTHOR]

Energy storage can provide a range of revenue streams for investors in electricity markets. However, as their deployments continue to rise, storage will no longer be a player on the sidelines and remain a price-taker, rather, these assets will start to impact prices. In this study, accounting for energy storage as a price-maker and using data from CAISO, we investigate strategic market behavior among competing investors using a non-cooperative game. We establish a centralized optimization problem to compute the market equilibrium. In the game, each investor initially decides on how much to invest and then how to operate their asset over a time horizon. Investors are allowed to deploy different energy storage technologies. Analytically, we show that an increasing number of investors will increase the market competition thereby reducing profits while increasing the total capacity of storage deployed. Numerically, our key findings include: (a) the difference in optimal investments under price-taker and price-maker assumptions, (b) as wind and solar assets expand under different resource-mix scenarios, there is a corresponding non-monotonic variation in arbitrage potential for energy storage, (c) when competition is intense and investors are allowed to invest in different technologies, a slight increase in storage technology performance can significantly improve an investor's profit share, (d) when the arbitrage opportunity increases with renewables, longer duration storage technologies may gain an advantage, (e) Li-ion batteries dominate the market under low-moderate renewable energy penetration or with steep energy-capacity cost reductions in the future. • We develop a game-theoretical framework for strategic investments in energy storage. • The framework derives a centralized optimization problem to compute the Nash equilibrium. • The impact of energy storage on market price is characterized using CAISO data. • We present insights on arbitrage potential and market competition for energy storage investors. • We quantify the effects of the number of investors, renewable energy levels, and technology heterogeneity. [ABSTRACT FROM AUTHOR]

The penetration of renewables on the demand side has recently attracted a large amount of attention. Its dual identity has an important impact on the competition between power producers and market dispatching. This study analyzed the participation of prosumers in the Nash–Cournot model for power market clearing. On this basis, we considered the uncertainty of renewable energy production, under which we used the distributionally robust optimization (DRO) model to produce a market equilibrium. Moreover, the Column-and-Constraint Generation algorithm was employed to solve the model. As a result, the impact of prosumers penetration and their production uncertainty on market equilibria was quantified and analyzed. Numerical simulations on an IEEE-30 bus system investigated the impact of the uncertainty of renewable energy output, the penetration level of wind power, and the demand level on the market equilibria. Test results demonstrate that the social welfare obtained from the proposed DRO model is 6.89% higher than that obtained from traditional robust optimization models. [ABSTRACT FROM AUTHOR]

In the energy transition towards a carbon-free society, the continuous changes that energy systems are experiencing, the increasing penetration of renewable generation, and the incorporation of short-term storage technologies such as batteries have increased the effort to model and predict its development and operation. In this context, power system models play a relevant role. However, to be suitable for the decision-making process, these tools should not require a massive computational effort. To overcome this challenge, this paper proposes a new methodology that reduces the temporal dimension of the problem while maintaining accurate results. This methodology is specially designed for medium-term operation of real-size power systems with a significant presence of renewable generation and storage systems. By means of a two-stage clustering algorithm, the proposed approach transforms the temporal structure of the model's input parameters into different levels of time aggregation. This arrangement makes the problem manageable and computationally tractable. In addition, together with the newly incorporated model formulation, this methodology allows capturing at the same time the short- and medium-term variability present in power systems. • Representation of short-term variability in long-term power system planning models. • Short-term storage constraints are formulated in a market equilibrium model. • A two-stage clustering algorithm reduces the temporal dimension of the model. • The methodology makes the problem tractable while maintaining accuracy in the results. • The performance of this approach is assessed in a real-size case of the MIBEL market. [ABSTRACT FROM AUTHOR]

• Identify Nash equilibrium by stochastic complementarity problem embedded with DEA. • Consider two scenarios of market powers between manufacturers and wholesalers. • Apply stochastic programming and robust optimization to address price uncertainty. • Show price uncertainty in the upstream significantly affecting the profits of the whole market. • Suggest the wholesalers should be leaders and the manufacturers negotiate the profit-sharing contracts. This study investigates how the exercise of market power affects the economic efficiency and revenue sharing in a bi-level market, which integrates upstream contract market and downstream wholesale market. We consider price volatility and identify Nash equilibrium restricted by the data envelopment analysis (DEA)-estimated capacity constraint. This study develops stochastic mixed complementarity problems (MiCP) models embedded with stochastic programming (SP) and robust optimization (RO) to address price uncertainty in a bi-level market. We investigate the exercise of market power: (1) wholesalers as leaders or (2) bilateral market power between manufacturers and wholesalers. A numerical study of the power generation market is conducted to validate the proposed stochastic MiCP models. The results show that price uncertainties in the upstream contract market have a significant effect in a bi-level market, and thus controlling price volatility in the upstream contract market will improve productivity and support policies. In addition, we suggest the wholesalers should be market leaders and the manufacturers should negotiate profit-sharing contracts with the wholesalers in a deregulated system. [ABSTRACT FROM AUTHOR]

Abstract: Many of the models used for the representation of the generation companies’ behavior in oligopolistic electricity markets are based on conjectural variation equilibria, which are a generalization of the classic Cournot approach. However, one of the main drawbacks of these approaches is the complexity of assigning adequate values to the conjectures, which can dramatically affect the results obtained from these models. This paper reviews and analyses the main formulations of conjectural equilibria applied to electricity markets. The paper shows how these different formulations are equivalent, and presents the relationships among the conjectures they use. Finally, it presents a brief overview on the main methods to estimate or compute the conjectures of these types of models. [ABSTRACT FROM AUTHOR]

Abstract: Electricity spot markets generally operate on an hourly basis; under this condition GENCOs can closely observe their competitors’ market behavior. For this purposes, a detailed dynamic model is one of the tools used by GENCOs to understand the behavioral variations of competitors over time. The required abilities to rapidly adjust one''s own decision-making create a need for new learning procedures and models. Conjectural variations (CV) have been proposed as a learning approach. In this paper a model based on forward expectations (FE) is proposed as a learning approach, and through illustrative examples it is shown that the market equilibria found by the CV model are also obtained by the FE model. [Copyright &y& Elsevier]

Abstract: The game-theory based methods are widely applied to analyze the market equilibrium and to study the strategic behavior in the oligopolistic electricity markets. Recently, the conjecture variation approach, one of well-studied methods in game theory, is reported to model the strategic behavior in deregulated electricity markets. Unfortunately, the conjecture variation models have been criticized for the drawback of logical inconsistence and possibility of abundant equilibria. Aiming for this, this paper investigates the existence and uniqueness of consistent conjectural variation equilibrium in electricity markets. With several good characteristics of the electricity market and with an infinite horizon optimization model, it is shown that the consistent conjecture variation will satisfy a set of coupled nonlinear equations and there will be only one equilibrium. This result can provide the fundamentals for further applications of the conjecture variation approach. [Copyright &y& Elsevier]

The global share of renewable energy sources (RES) in total generation capacity reached 34.7% in 2019 and has been continuously increasing. Power system flexibility addressing the uncertainty and variability of RES has become a major concern in energy transition. This paper proposes to apply mobile energy storage (MES) from independent MES owners as a flexibility-enhancement ancillary service in the day-ahead electricity market. First, we have proposed a market-based methodology to incent MES owners to provide flexibility service in power systems by simultaneously releasing Locational Marginal price (LMP) and Uncertainty Marginal Price (UMP). The LMP and UMP were obtained by solving robust unit commitment and security-constrained economic dispatch, representing the need for flexibility resources. Second, the optimal operational strategy of MESs was established to respond to LMP and UMP and maximize their profits by providing energy and reserve flexibility subjects to the reserve and traffic constraints. Third, a game-theoretic model was developed to determine market equilibrium by minimizing the operational costs of the power system and maximizing the profits of MES owners. To avoid homogenous behaviors of MESs in solving this model, a sequential dispatching algorithm was developed such that each MES of one MES owner has a unique price signal. An objective function update strategy was accordingly developed to take the interaction among MESs into consideration and ensure a maximum total profit for MES owners. Finally, case studies with IEEE 6-bus system, IEEE 118-bus system, and MATPOWER 300-bus system were provided to validate the proposed methods, demonstrating that MESs increase power system flexibility and their own profits while decreasing the energy and reserve payment of consumers. • Mobile energy storage has temporal, spatial, and power/energy flexibility. • We provide a market-based methodology to incent mobile energy storage to provide flexibility. • Efficient algorithm is developed to obtain the market equilibrium. • Flexibility provided by mobile energy storages reduces the operational cost of power systems. • Mobile energy storage owners obtain revenue by providing flexibility service. [ABSTRACT FROM AUTHOR]

This work investigates the interaction between power producers with conventional and wind generation portfolios participating in a network-constrained pool-based market. A stochastic bi-level problem is introduced to model the strategic behavior of each single producer. The upper-level problem maximizes the producers' expected profits and the lower-level problem optimizes the jointly cleared energy and balancing market under economic dispatch. Market participants' offers are modeled using linear stepwise curves, and the stochastic wind power generation is realized through a set of plausible wind scenarios. The bi-level problem is recast into a single-level mathematical problem with equilibrium constraints with primal-dual formulation using the Karush-Kuhn-Tacker first order optimality conditions and the strong duality theorem. The joint solution of all strategic producers' problems constitutes an equilibrium problem with equilibrium constraints. The latter is reduced into an equivalent mixed integer linear program by using disjunctive constraints. Different objective functions are applied to the final program to define the range of market equilibria, and a single-iterate diagonalization process is used to justify those equilibria that are meaningful. The model addresses several cases considering different types of market competition, transmission line congestions, and different levels of wind power penetration and volatility. • A primal-dual MPEC formulation is used as basis for the EPEC model. • Different EPEC objective functions determine the characteristics of the derived Nash equilibria. • The higher the collusion between producers the higher the market clearing prices. • Wind power increment causes the reserve flexible units to recover part of their expected profit losses. • Continuous increase of wind generation volatility leads gradually in costlier equilibria. [ABSTRACT FROM AUTHOR]

• We design a methodology to find specific Nash equilibrium in electricity markets. • We devise an efficient column-and-constraint generation method to solve the EPEC. • We benchmark the proposed solution method with the state-of-the-art methodology. • The proposed algorithm is 20 times faster than current state-of-the-art on average. Equilibrium analysis is crucial in electricity market designs, with Nash equilibrium recognized as the most powerful one. Its most prominent hindrance, however, is an efficient methodology to compute an equilibrium point in large-scale systems. In this work, a Column-and-Constraint Generation (CCG) algorithm is proposed to tackle this challenge. More precisely, the master problem finds a candidate for Nash equilibrium and the oracle identifies whether this candidate point is indeed an equilibrium. A set of numerical experiments was conducted, comparing its computational performance with the solution of an Equilibrium Problem with Equilibrium Constraint (EPEC). We identify that the proposed algorithm overcomes the benchmark in the magnitude of 20 times on average and more than 30 times in the most demanding instances. Furthermore, the scalability of the EPEC formulation is challenged even for medium-scale instances, whilst the proposed algorithm was able to handle all tested instances in a reasonable computational time. [ABSTRACT FROM AUTHOR]

With increasing penetration of renewable energy, multi-energy systems constitute an effective mechanism to optimize energy distribution and improve social welfare. However, a centralized operation of the multi-energy system might not be appropriate under the existing energy markets. Therefore, this paper proposes an equilibrium model for improving the operation of the electricity, gas and district heating subsystems of a district or urban area. The proposed model allows each energy subsystem to pursue its own objective (i.e., maximum social welfare), while considering the interconnection with other subsystems. More specifically, this model represents the behavior of each subsystem and reflects the interactions of the multi-energy system in a practical way. This equilibrium problem is formulated as a nonlinear complementarity problem. An illustrative case study is analyzed to show the relevance of the proposed approach. • A multi-energy market model is proposed for the joint operation of the electricity, gas and district heating systems. • An equilibrium problem is developed to simulate the gaming process of subsystem operators in the multi-energy market. • The proposed equilibrium model is also compared with a centralized optimization model. • Real-time market prices are solved to further explore the interactions among the different energy subsystems. • The effect of different wind power levels on the market behavior and energy exchange is discussed. [ABSTRACT FROM AUTHOR]