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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]

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 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]

• 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]