Abstract
Fuzzy modelling of power systems is proposed, to take in account the qualitative aspects and vagueness or uncertainty that have not, in fact, a random nature and therefore cannot be modelled by a probabilistic approach. An operative procedure to derive fuzzy load diagrams associated with different types of energy consumption is presented. The feasibility of the development of fuzzy linear programming models for power system planning is demonstrated. A DC and an AC fuzzy load flow formulations are developed and the quality and usefulness of the results obtained with them is made evident with the help of an example.

Abstract
Most optimization and decision problems in power systems include integer or binary variables, leading to combinatorial problems. In this paper, several approaches using metaheuristics and genetic algorithms are presented that deal with real problems of the power industry Most of these methodologies are now implemented in distribution management systems (DMS) used by several utilities.

Abstract
This text describes a real-world DMS environment in which intelligent tools and techniques such as neural networks, fuzzy sets and meta-heuristics (like evolutionary computing and simulated annealing) have given a strong positive contribution.

Abstract
The energy sector transition to more decentralized and renewable structures requires greater participation by local consumers, which may be enabled by innovative models such as the setup of renewable energy communities (RECs). To maximize the self-consumption of local renewable energy generated by assets normally connected to the low voltage distribution grid, these RECs typically involve jointly owned assets such as collective photovoltaic solar panels (CPVs) and collective energy storage systems (CESS). This work proposes a novel mathematical model for a REC, accounting for three distinct economic approaches to the redistribution of collective benefits among community members. The main objective of this study is to understand how the participation of community members in collective assets (CAs) can help increase the fairness and equity of RECs. An illustrative REC case comprising members with individual and collective ownership of the assets is used to assess the proposed economic approaches. Extracting several answers, among them that the most advantageous configuration comes from agents with quotas in the CESS and CPV. An important conclusion is that depending on the selected economic approach, the social welfare and agent's revenue vary significantly. In any case, CESSs increase equity among REC members.

Abstract
As prosumers and energy communities gain prominence in power systems, energy trading between prosumers in local P2P markets is paramount. Within this novel market design, peers can directly exchange energy with each other, leading to economic advantages while supporting the decarboniza-tion of the sector. To ensure that voltage and congestion issues are properly addressed, a thorough coordination between the P2P market and the Distribution System Operator is required. This paper presents and compares three mutual-benefit coordination methods. The first method entails applying product differentiation on an iterative basis to avoid exceeding the lines thermal limits, which is performed through penalties on P2P exchanges that may be overloading the network. The second method uses the P2P market with an AC-OPF, ensuring network operation through a flexibility market via upward and downward flexibility. The last one proposes an integrated operation of the P2P market with AC-OPF. All methods are assessed in a typical distribution network with high prosumers integration. The results show that the second method is the one that, fulfilling the network constraints, presents greater social welfare.& COPY; 2023 Elsevier Ltd. All rights reserved.

Abstract