Search

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]

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]

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]

This paper proposes a model to compute nodal prices in oligopolistic markets. The model generalizes a previous model aimed at solving the single-bus problem by applying an optimization procedure. Both models can be classified as conjectured supply function models. The conjectured supply functions are assumed to be linear with constant slopes. The conjectured price responses (price sensitivity as seen for each generating unit), however, are assumed to be dependent on the system line's status (congested or not congested). The consideration of such a dependence is one of the main contributions of this paper. Market equilibrium is defined in this framework. A procedure based on solving an optimization problem is proposed. It only requires convexity of cost functions. Existence of equilibrium, however, is not guaranteed in this multi-nodal situation and an iterative search is required to find it if it exists. A two-area multi-period case study is analysed. The model reaches equilibrium for some cases, mainly depending on the number of periods considered and on the value of conjectured supply function slopes. Some oscillation patterns are observed that can be interpreted as quasi-equilibria. This methodology can be applied to the study of the future Iberian electricity market. [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]

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]