Abstract
In Walrasian markets, an auctioneer proposes a price to the market participants, who react by revealing the quantities they are willing to buy or sell at this price. The auctioneer then proposes new prices to improve the demand and supply match until the equilibrium is reached. This market, common for stock exchanges, has also been proposed for electricity markets like power electricity exchanges, where iterations among auctioneer and market participants take place before the interval settlement period (ISP) until supply and demand match and a stable price is reached. We propose a Walrasian design for local electricity markets where the iterations between auctioneer and market participants happen in real time, so previous imbalances are used to correct the proposed price for the next ISP. The designs are simulated to test convergence and their capability of achieving efficient dynamic prices.

Abstract
When the price of the energy shared within an energy community is based on a local energy market, it is the responsibility of each participant to bid adequately so that participating provides a larger benefit than not participating. Alternatively, centralized energy community bill minimization may be an option, but a mechanism to share the collective benefits among the members is needed. This mechanism should be fair and easy to explain, no members should be harmed with respect to their individual optimal behavior and should provide the right economic signal. This paper analyses and compares some common pricing mechanisms for the internal compensation for the energy shared among the members of an energy community centrally managed. Simple case examples are used to identify those pricing mechanisms that are fairer and provide the righter economic signals to the participants.

Abstract
Prosumers can organize themselves in CSCstructures and REC to share energy they produce locally. In addition, through their contracted BRP, i.e.,RET and AGR, they could become flexibility providers for system services to solve, for example, local grid constraints. Since CSC and REC structures are progressively being regulated in many countries, LEM and LFM to be developed with these structures should find the way to comply with existing CSC rules to settle energy transactions and flexibility activation, both, locally and with the WS market settlement, or the existing barriers and regulatory improvements identified to allow future implementations. Indeed, the integration of local and WS electricity markets is still a matter of development, demanding innovative solutions, one of the main issues being, for example, the impact of the flexibility activation by one BRP into another BRP's expected delivery commitment in the WS market. This work proposes innovative designs for LEM and LFM based on common CSC rules of existing regulations, and a conceptual approach to integrate them together and with the WS market balancing responsibilities of the BRPs involved, identifying existing regulatory barriers. While many LEMs in the literature operate as WS markets, with future markets and delivery commitments for prosumers, we propose the use of a post-delivery LEM that can be cleared even after the delivery of energy, which strongly simplifies prosumers participation avoiding the need of these a priori unrealistic commitments. The business model, the main roles involved, and the contractual framework to connect the BRPs while allowing prosumers to freely contract the BRP of their choice for both energy supply and flexibility provision are described, and can serve as a guide for future regulatory improvement of the common regulatory frameworks. © 2023 Elsevier Ltd