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This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.

• The utilization of game theory in an EPEC format to obtain the strategic bidding equilibrium of the MG. This novel application of game theory enhances the understanding of the competitive dynamics within the MG context. • The adoption of a tri-level MPEC approach, where each strategic producer, including the MG and other strategic and non-strategic rivals, aims to maximize their profits. This comprehensive approach captures the complex interactions and decision-making processes of the market participants. • The development of tri-level model formulations tailored specifically for MGs, considering the inherent fluctuations in wind unit power within the third level, which corresponds to the balancing market. This inclusion allows for a more realistic representation of the MG's behavior and dynamics in the context of power system operations. This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state. [ABSTRACT FROM AUTHOR]

[Display omitted] • Flexibility provision based on the priorities of TSO and DSO. • Using market mechanisms to prioritize the provision of flexibility. • A definition and presentation of the flexibility that DSO can provide to enhance the degree of freedom for TSO. • Providing flexibility in corresponding networks by modeling the price bargaining method between TSO and DSO. The effective use of the flexibility sources of transmission and distribution networks necessitates smooth coordination between transmission and distribution system operators (TSO–DSO) as well as proper interfacing between the energy and flexibility markets. In this paper, mathematical centralized/decentralized optimization frameworks of flexibility market structures is proposed for four market mechanisms of a transmission-level centralized market, a local distribution- and centralized transmission-level market, a TSO priority market, and a TSO–DSO price equilibrium market. Further, prioritization mechanisms are developed by allocating ramp flexibilities in multi-interval day-ahead market clearing procedures for the wholesale (transmission level) and local markets (distribution level) to reduce the prediction error and improve the performance of the real-time flexibility market, which is a single-interval optimization market. Accordingly, the concurrent provision of the energy and flexibility requirements of the transmission and distribution networks is explored in a joint energy and flexibility day-ahead market. As a base case, the centralized market model does not prioritize TSO–DSO flexibility. The second market model gives the DSO priority in terms of providing flexibility. The DSO starts by using the resources of the distribution network. It then makes the upstream market an offer for the flexibility capacities of the remaining unused resources. In the third proposed market, the TSO receives priority in providing flexibility. The optimization frameworks proposed for the third market mechanisms are formulated as mixed-integer linear programming models (MILP). In addition, to ensure a higher resilience, a lower complexity of algorithms, and the possibility to better adapt to the efficient flexibility allocation in the TSO/DSO collaboration, an approach of the decentralized alternating direction method of multipliers (ADMM) in the decentralized optimization framework is performed to clear the proposed wholesale market while taking into account the local markets at the distribution level. Finally, to evaluate the proposed multi-level centralized/decentralized optimization frameworks, simulation results are performed on a modified IEEE 30-bus/118-bus transmission network with three/five IEEE 33-node distribution networks connected. In the case studies, various market clearing and prioritization mechanisms are implemented and evaluated through numerical simulations. [ABSTRACT FROM AUTHOR]

• Introducing a Nash equilibrium model for futures and day-ahead electricity markets. • Proposing a model for optimal gaming of speculators in futures electricity market. • The model can follow real-world rules, hence, is suitable for power system analysis. • Confirming the role of speculators in increasing market liquidity and reducing prices. • Highlighting the role of futures market in dealing with power grid uncertainties. Uncertainties in different parameters such as the output power of renewable energy sources, available capacity of generators, or the condition of grid lines in the future, face market players with financial risks in the power system. Futures contracts are used in parallel with the day-ahead electricity markets to protect market players against financial risks of undesirable price fluctuations. Supplying a demand by both futures and day-ahead markets leads to mutual impacts between these two markets. In this paper, a Nash equilibrium approach is introduced to model the interactions between the futures and day-ahead markets. The proposed model includes producers, retailers, and speculators as market players, the uncertainty in the output power of wind farms (WFs), the possibility of the financial settlement of contracts, market players' risk preferences, and transmission system limitations. Using this approach, the optimal strategy of market players in futures and day-ahead markets, the effects of transmission system congestion on the Nash equilibrium of the system, and the role of the financial settlement of contracts in dealing with the uncertainty of WFs' output power and transmission lines capacity are discussed. Eventually, the behavior of speculators and their impacts on the gaming of other market players are evaluated. Simulation results highlight the role of the financial delivery feature in the effective utilization of futures contracts and the behavior of market players. [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]

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]