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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 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]