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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]

We study a competitive partial equilibrium in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources. Both resources and the commodity can be stored for later consumption. Several examples of a multistage risked equilibrium are outlined, including aspects of battery and hydroelectric storage in electricity markets, distributed ownership of competing technologies relying on shared resources, and aspects of water control and pricing. The agents are assumed to have nested coherent risk measures based on one-step risk measures with polyhedral risk sets that have a nonempty intersection over agents. Agents can trade risk in a complete market of Arrow-Debreu securities. In this setting, we define a risk-trading competitive market equilibrium and establish two welfare theorems. Competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have strictly monotone one-step risk measures. Conversely, a social optimum with an appropriately chosen risk measure will yield a risk-trading competitive market equilibrium when all agents have strictly monotone risk measures. The paper also demonstrates versions of these theorems when risk measures are not strictly monotone. [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]

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]