Abstract
Distributed energy resources (DERs) offer untapped potential to meet the flexibility needs of power systems with a high share of non-dispatchable renewable generation, and local flexibility markets (LFMs) can be effective mechanisms for procuring it. In LFMs, energy communities (ECs) can aggregate and offer flexibility from their members' DERs to other parties. However, since flexibility prices are only known after markets clear, flexibility bidding curves can be used to deal with this price uncertainty. Building on previous work by the authors, this paper employs a two-stage methodology to calculate flexibility bids for an EC participating in an LFM, including not only batteries and photovoltaic panels, but also cross-sector (CS) flexible assets like thermal loads and electric vehicles (EVs) to assess their impact. In Stage 1, the EC manager minimizes the energy bill without flexibility to define its baseline. In Stage 2, it computes the optimal flexibility to be offered for each flexibility price to build the flexibility bidding curve. Case examples allow to assess the impact of CS flexible assets on the final flexibility offered.

Abstract
Planning Energy communities (ECs) requires engaging members, designing business models and governance rules, and sizing distributed energy resources (DERs) for a costeffective investment. Meanwhile, the growing share of nondispatchable renewable generation demands more flexible energy systems. Local flexibility markets (LFMs) are emerging as effective mechanisms to procure this flexibility, granting ECs a new revenue stream. Since sizing with flexibility becomes a highly complex problem, we propose a 2 -stage methodology for estimating DERs size in an EC with collective self-consumption, flexibility provision and cross-sector (CS) assets such as thermal loads and electric vehicles (EVs). The first stage computes the optimal DER capacities to be installed for each member without flexibility provision. The second stage departs from the first stage capacities to assess how to modify the initial capacities to profit from providing flexibility. The impact of data clustering and flexibility provision are assessed through a case study.

Abstract
As energy systems evolve, protecting and empowering consumers is vital, enabling participation in decentralized electricity markets and maximizing benefits from energy resources. The integration of Distributed Energy Resources (DER) and Renewable Energy Sources (RES) fosters new energy communities, shifting from centralized systems to distributed structures. Consumers can sell excess production to neighbors, increasing income, reducing bills, and advancing energy transition goals. This paper proposes a community-based peer-topeer (P2P) energy market model that reduces costs while respecting network constraints. Using the Alternating Direction Method of Multipliers (ADMM), ensures privacy enhancement, decentralization, and scalability. The Relaxed Branch Flow Model (RBFM) manages constraints, and Electric Vehicles (EVs) reduce imports and costs through strategic discharging. Tested on a 33-bus distribution network, the ADMM-based approach aligns closely with a centralized benchmark, showing minor discrepancies while maintaining system reliability. This model underscores the potential of decentralized markets for consumercentric, flexible, and efficient energy trading.

Abstract
The increasing integration of renewable energy sources and decentralized generation requires demand-side flexibility to improve grid stability and balance local energy flows. Local Flexibility Markets (LFMs) provide a framework for optimizing flexibility transactions within energy communities. This paper presents a model for quantifying and pricing residential resources flexibility, enabling prosumers to submit bids in an LFM managed by the Community Manager. The methodology relies on a linear optimization problem, where a Home Energy Management System first determines optimal consumption baselines. Then an iterative sensitivity analysis estimates upward, and downward flexibility bands and sets offer prices per resource. The market operates as two asymmetric voluntary pools, clearing flexibility offers and requests. Results show that Battery Energy Storage Systems and Electric Vehicles provide the most effective flexibility, significantly reducing energy costs. Future research should improve pricing mechanisms and scalability to support LFM adoption in different residential settings.

Abstract
Renewable energy resources are crucial for addressing global economic and environmental challenges. Energy communities, which unite consumers to pursue shared energy goals, present a promising solution for reducing energy costs and enhancing sustainability. This study analyzes the optimal sizing and operation of energy community resources, formulating the problem as mixed-integer linear programming (MILP) models. Two tools are employed: one for daily operation, calculating energy setpoints for community assets such as battery energy storage systems (BESS) and electric vehicles (EVs), and another for sizing photovoltaic (PV) panels and BESS capacities to minimize costs while optimizing local energy trades. Due to the high computational demands of MILP, three optimization methods are compared: deterministic, hybrid particle swarm optimization (PSO), and evolutionary PSO (EPSO). The hybrid PSO method handles binary and continuous variables efficiently, while EPSO introduces diversity to improve solution quality in complex scenarios. These metaheuristic approaches address the trade-off between solution accuracy and computational effort, providing reliable tools for decision-makers in energy communities.