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Financial instruments that help provide revenue certainty are fundamental for project finance in liberalized electricity markets. Improved management of locational risk caused by network congestion is becoming increasingly important with a growing share of production from geographically remote renewable resources. Nodal markets have financial transmission rights (FTRs) to enable participants to manage locational risk, but there is no evidence that FTRs have been used to support project finance. Through a stochastic equilibrium model in which market participants invest in production assets and trade risk, we show that long-term FTRs promote surplus-maximizing generation investments and reduce the cost of capital. Investors pair them with energy price hedges and thus protect themselves against both types of risk. Our results suggest that altering the definition and allocation of FTRs to match the needs of project finance, e.g., by enabling new generators to procure a long-term right at the time of interconnection, could help ensure a complete risk market and encourage efficient investments. [ABSTRACT FROM AUTHOR]

We studied a supply chain consisting of multiple suppliers and multiple retailers. We use the Cournot–Stackelberg game, the Market–Stackelberg game, and the Market–Nash game to simulate the situation where the upstream seller's market dominance power gradually decreases while the downstream buyer's market power increases. The equilibrium decision and supply chain performance under the three models are compared and analyzed, as well as their responses to external market changes such as demand fluctuation and market competition intensity. The research shows that (1) in a seller-dominated supply chain, the increase in buyer power reduces market equilibrium production and wholesale price; (2) in the face of strong demand fluctuations, equivalent power between upstream and downstream can contribute to the stabilization of production and wholesale prices; (3) when market demand fluctuation is small, market power brings a higher profit level, and supply chain participants would like to actively compete for market power. However, when the demand fluctuates greatly, the profit advantage brought by market dominance is no longer significant, and there is no need to spend much to fight for market dominance; (4) the fierce competition of upstream suppliers will induce upstream to give up the competition for market dominance, and make the market power less attractive to downstream retailers. While the fierce horizontal competition downstream will stimulate both suppliers and retailers to actively compete for market power, (5) sufficient market competition will improve total supply chain profit, so encouraging competition is conducive to the overall economic development of society. [ABSTRACT FROM AUTHOR]

Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream supplier foregoes profitable strategic manipulation of water to the downstream supplier. To incorporate backward induction, we propose the Stackelberg social equilibrium concept. We prove the existence of Stackelberg social equilibrium in duopoly water markets with an upstream–downstream river structure and derive it in the example of a duopoly market. [ABSTRACT FROM AUTHOR]

Market power is a dominant feature of many modern electricity markets with an oligopolistic structure, resulting in increased consumer cost. This work investigates how consumers, through demand response (DR), can mitigate against market power. Within DR, our analysis particularly focusses on the impacts of load shifting and self-generation. A stochastic mixed complementarity problem is presented to model an electricity market characterised by an oligopoly with a competitive fringe. It incorporates both energy and capacity markets, multiple generating firms and different consumer types. The model is applied to a case study based on data for the Irish power system. The results demonstrate how DR can help consumers mitigate against the negative effects of market power and that load shifting and self-generation are competing technologies, whose effectiveness against market power is similar for most consumers. We also find that DR does not necessarily reduce emissions in the presence of market power. [ABSTRACT FROM AUTHOR]

This paper proposes a semi-analytical method to obtain the equilibrium bidding strategies for generation and demand units in a combined oligopoly and oligopsony wholesale electricity market. Such market structure is the outcome of the increasing deployment of demand response programs that facilitate active participation of demand-side players in the price-setting process. In this analysis, the concept of supply function equilibrium (SFE) is used to investigate the oligopolistic competition among generation units. The SFE model is extended and the demand function equilibrium (DFE) is obtained to study the oligopsonistic competition among demand units. The economic behavior of a market participant is formulated as a bi-level programming (BLP) problem. The imperfect competition among generation units, as well as among demand units, are modeled as a non-cooperative game. Next, a direct method is developed to calculate all candidate equilibriums of the market, and the locational marginal prices (LMPs) in terms of the bidding strategies of the market participants. The BLP problem is solved by obtaining the coordinated Pareto-dominant Nash equilibrium of the market participants’ non-cooperative games. Finally, the proposed analysis is examined in case studies. Accordingly, we report insightful observations with respect to the impact of the changes in the new market structure, at firm-level and market-level, such as in terms of mitigating market power of generation units, the market clearing prices and quantities, surplus for generation units and demand units, and potential impact on market efficiency. [ABSTRACT FROM AUTHOR]

The bidding behaviors of the energy storage systems (ESS) are complicated due to time coupling and market coupling limited by their capacity states. The existing research is mainly based on optimization models and reinforcement learning (RL) models, which are idealized with analytical objective functions, rational decisions, and virtual historical data. This leads to mismatches between theoretical results and actual bidding behaviors, and the obtained results cannot be generalized to a real-world market. In recent years, the disclosure of market data has enabled data-driven analysis, while the complexity of actual data makes the analysis process challenging and calls for more suitable methods. On the basis of our investigation of ESS bidding behaviors and market data, we propose a novel inverse RL (IRL)-based framework to identify the bidding decision objective function of ESS in coupled multi-market through their historical bidding records and operation status. The identification results can be used as the model parameters to help RL-based simulation models available for a real-world market. Based on the proposed framework, we conduct an empirical analysis on the real-world data of a battery ESS in the Australian electricity market. The results show how the ESS balances its objective among different markets and maintains its state of charge (SOC) to gain more profits. This framework can help us model ESS behaviors by relying on historical data to better understand the ESS bidding decision-making mechanism, which will facilitate market equilibrium analysis and mechanism design. [ABSTRACT FROM AUTHOR]

The conventional model of the day-ahead electricity markets employs an energy-based approach to manage the competition among the players. Under this format, it is assumed that everything (including the demand and output power of the generating units) is constant during each hour. This assumption greatly simplifies the market, and it is widely incorporated over the globe. However, it leads to mismatches in the real-time operation. With the increase in the share of intermittent sources, such mismatches get higher amplitude and become more threatening for market performance and system security. Powerbased modelling of the electricity market (PbM), which has been introduced as a remedy to eliminate mismatches in real-time operation, has been scrutinized. The previous comparisons between the conventional model and PbM generally deploy a rigid approach based on the existence of perfect competition. They assume that all the generation companies offer their maximum capacity and marginal cost into the market. Moreover, they model a single-side auction in which only the supply side is actively involved in the market. In order to develop the previous studies on PbM, an equilibrium environment to model the players' interactions within a competitive market has been employed. Employment of an equilibrium model brings the benefits of modelling a double-side market and can simulate the strategic behaviour of the market players on both sides within a partially competitive electricity market. The equilibrium model provides empirical insight on how changing the market structure to PbM affects players' behaviour and shifts the market equilibrium and provided some unreported attributes of PbM. The study is based on a real-world network of the Gilan province in northern Iran. [ABSTRACT FROM AUTHOR]

Transitioning from fossil fuel dominated power systems to high penetrations of intermittent renewable generation is affecting classical electricity market designs. Here, a method is proposed to model and assess the absence of co-optimization of energy and reserve that prevails in the European system. Co-optimization is formulated through an optimization problem (COM), and its absence as an equilibrium problem (EQM) built on Karush-Kuhn-Tucker conditions of agents’ optimization and market clearing equations. EQM cannot be reformulated as a single optimization problem. Market distortions are identified by comparing the complementarity conditions of both models. These are then discussed on system with Feed in Premium to wind generation. Parameters in the models allow to represent different market configurations regarding: available wind generation, Feed in Premium to wind, generators’ risk aversion, and required reserve from wind generation. [ABSTRACT FROM AUTHOR]

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]

A supply-function equilibrium model fits well current electricity market practice, but entails the solution of an equilibrium problem composed of bi-level problems, which is computationally very demanding. To ease such computational burden, we propose a computationally efficient single-level equilibrium model that identifies equilibria similar to those obtained by equilibrium models of bi-level problem. In our model, producers/consumers offer/bid both energy and prices. We use a simple example and a case study to illustrate and characterize the performance of the proposed single-level equilibrium model. [ABSTRACT FROM AUTHOR]

The increasing integration of uncertain and volatile renewable power generation poses challenges to the operation of the interdependent electricity and gas markets. In this paper, a robust operational equilibrium solution method for the interactive markets of power and gas systems is proposed, where the bidirectional interactions include both firm energy and reserve contracting, and the impacts of the uncertainties of wind generation outputs on the two markets are characterized. The line pack as well as bidirectional flow characteristics of gas pipelines are depicted in the gas system model so as to improve its operational flexibility. To guarantee the robustness of market equilibrium against uncertainties, the power and gas market clearing models become two-stage robust ones. Column-and-constraint generation (C&CG) based and the best response algorithms are devised to clear the two markets as well as to coordinate them, respectively. Simulation results validate the effectiveness of the proposed robust operational equilibrium model and the performance of the devised solution methodology. [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]

Electricity production is a key sector in global decarbonization efforts, and variable renewable energy (VRE) technologies are a primary way to produce carbon- free electricity. We study an electricity market where generation is 100% VRE, while storage and elastic demand resolve temporal supply-demand imbalances. We model hourly market equilibrium to analyze price formation and imperfect, Cournot-type competition with varying levels of ownership concentration. Market power is exerted either with storage-only or with both VRE and storage. In such a system, prices are determined dynamically by demand and intertemporal storage decisions, breaking the static logic of "merit order" with dispatchable generation. The numerical results indicate that market power with storage has a relatively moderate effect on prices and market efficiency. However, market power exerted with VRE has far larger welfare impacts, resulting from curtailed generation. However, such actions could be more readily observed by a regulator via monitoring. [ABSTRACT FROM AUTHOR]

Summary: Water and energy are two scarce and concerning resources interconnected in the closed‐loop water‐energy nexus, exemplifying the co‐dependence of water and energy production. In this article, we investigate the interaction between the industries of these two resources and model it as a simultaneous game. We consider a supply chain that consists of water suppliers (WSs), power suppliers (PSs), and consumers of these commodities. In the supply chain, WSs purchase power from the power market, and PSs purchase water from the water market. Other consumers can also buy these resources at the water and power markets. The prices of these commodities depend on their quantities supplied to the markets. Each firm tries to maximize its own profit, in doing so the suppliers of water and power decide their production quantities. In this research, the Nash equilibria of the firms are determined and a comparative statics is performed on various economic measures. When there are multiple equilibria, the analysis finds the Pareto optimal equilibrium. We find that when there is sufficient supply to meet the demand of both industries and consumers, improvement of production technology improves social welfare and other economic measures of the supply chain. We also find that higher competition in either industry improves all economic measures. However, when either water or power supply is solely consumed by the firms in the cross industry, improvement of technology and higher competition can have a negative effect on some measures. [ABSTRACT FROM AUTHOR]

We study the value of adding flexibility to Transmission Expansion Planning (TEP) projects from the perspective of a social planner using real options. Due to the deregulation of electricity markets, TEP projects currently face multiple uncertainties. These uncertainties often cause traditional project valuation methods to recommend sub-optimal investment decisions. Additionally, to incorporate the effects of uncertainties on the valuation of TEP projects, current literature rely on some critical simplifications that do not fit well with the real operations of a power market. This paper models the power market in a realistic way by combining an equilibrium model, to assess the power market equilibrium that the TEP project will generate, with a valuation model based on real options, to incorporate the value of flexibility. The methodology is applied to determine the value of adding capacity expansion flexibility to a portion of the rigid TEP project that connects the main two interconnected systems in Chile since 2018. Our results show that, in this case, adding flexibility increases the net expected social welfare by $14.03 million. Several sensitivity analyses confirm that this flexibility has more value when uncertainty is higher and/or investment costs are lower. [ABSTRACT FROM AUTHOR]

The envisaged decarbonisation of electricity systems has attracted significant interest around the role and value of energy storage systems (ESSs). In the deregulated electricity market, there is a need to investigate the complex impacts of ESSs, considering the potential exercise of market power by strategic players. This study aims at comprehensively analysing the impacts of both price-taking and price-making storage behaviours on energy market efficiency, corresponding to potential settings with small and large storage players, respectively. In order to achieve this and in contrast to previous papers, this work develops a multi-period equilibrium programming market model to determine market equilibrium stemming from the interactions of independent strategic producers and ESSs, while capturing the time-coupling operational constraints of ESSs as well as network constraints. The results of case studies on a test market capturing the general conditions of the GB electricity system demonstrate that the introduction of ESSs mitigates market power exercise and improves market efficiency, with this beneficial impact being higher when ESSs act as price takers. When the electricity network is congested, the location of ESSs also affects the market outcome, with their beneficial impact on market efficiency being higher when they are located in higher-priced areas. [ABSTRACT FROM AUTHOR]

The envisaged decarbonisation of electricity systems has attracted significant interest around the role and value of energy storage systems (ESSs). In the deregulated electricity market, there is a need to investigate the complex impacts of ESSs, considering the potential exercise of market power by strategic players. This study aims at comprehensively analysing the impacts of both price‐taking and price‐making storage behaviours on energy market efficiency, corresponding to potential settings with small and large storage players, respectively. In order to achieve this and in contrast to previous papers, this work develops a multi‐period equilibrium programming market model to determine market equilibrium stemming from the interactions of independent strategic producers and ESSs, while capturing the time‐coupling operational constraints of ESSs as well as network constraints. The results of case studies on a test market capturing the general conditions of the GB electricity system demonstrate that the introduction of ESSs mitigates market power exercise and improves market efficiency, with this beneficial impact being higher when ESSs act as price takers. When the electricity network is congested, the location of ESSs also affects the market outcome, with their beneficial impact on market efficiency being higher when they are located in higher‐priced areas. [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]

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]

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]

This paper analyzes the operation of water resources of hydro-electric plants in competitive generation power markets. With that purpose, the traditional definition of water value used in centralized systems is updated and extended in order to adapt it to electricity markets, where generation companies face the hydrothermal coordination under a competitive environment. Two different water values are defined, as well as their applications: profit-based value and cost-based value. The paper proves that for the short-term operation of hydro units, the correct long-term signal is the cost-based water value, even in oligopoly markets. The proposed methodology to compute both water values is presented by means of an illustrative example, which is used to derive the mathematical formulation. Finally, the model is applied to a study case, where the obtained results show clearly the practical implications of the concepts discussed previously. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a framework for the design and simulation of electrical distribution systems and short term electricity markets specific to the UK. The modelling comprises packages relating to the technical and economic features of the electrical grid. The first package models the medium/low distribution networks with elements such as transformers, voltage regulators, distributed generators, composite loads, distribution lines and cables. This model forms the basis for elementary analysis such as load flow and short circuit calculations and also enables the investigation of effects of integrating distributed resources, voltage regulation, resource scheduling and the like. The second part of the modelling exercise relates to the UK short term electricity market with specific features such as balancing mechanism and bid-offer strategies. The framework is used for investigating methods of voltage regulation using multiple control technologies, to demonstrate the effects of high penetration of wind power on balancing prices and finally use these prices towards achieving demand response through aggregated prosumers. [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]

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]

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]

Nash equilibrium is usually used as the solution of generator's strategic bidding in electricity markets. The available literature has shown by simulation that multiple market equilibria or no pure equilibrium may be induced after the inclusion of net- work constraints (transmission constraints). This paper presents a systematical analysis for the impacts of network constraints on the market equilibrium in oligopolistic electricity markets. In our modeling, the independent system operator (ISO) dispatches generation and determines nodal prices via solving an optimal power flow (OPF); and the individual generator optimizes its submitted supply function with Nash-supply function equilibrium (SFE) strategy, after taking into account ISO's decision-making process on dispatched generations and nodal prices. The conditions for the existence of equilibrium are given, and it is shown that there may be multiple equilibria or no pure Nash equilibrium. The equilibrium, if it exists, will be at a point where generators pay no congestion charge. [ABSTRACT FROM AUTHOR]

In electricity wholesale markets, generators often sign long term contracts with purchasers of power in order to hedge risks. In this paper, we consider a market where demand is uncertain, but can be represented as a function of price together with a random shock. Each generator offers a smooth supply function into the market and wishes to maximize his expected profit, allowing for his contract position. We investigate supply function equilibria in this setting, using a model introduced by Anderson and Philpott. We study first the existence of a unique monotonically increasing supply curve that maximizes the objective function under the constraint of limited generation capacity and a price cap, and discuss the influence of the generator's contract on the optimal supply curve. We then investigate the existence of a symmetric Nash supply function equilibrium, where we do not have to assume that the demand is a concave function of price. Finally, we identify the Nash supply function equilibrium which gives rise to the generators' maximal expected profit. [ABSTRACT FROM AUTHOR]

The meaning and significance of medium-term marginal costs for a generation company in a competitive power market in analysed. A methodology to compute and decompose medium-term generation marginal costs in a competitive environment is proposed. The methodology is based on a market equilibrium model. The aim is to provide a useful tool for generation companies so that they can manage their resources in an optimal way, helping them with their operation, decision-making processes, asset valuations or contract assessments. [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]