The idea behind the first proposal of the fuzzy power flow (FPF) was to analyze the impact of the uncertainties in load and generation at the power flow level, when no statistical information is available. Further development of the field addressed the optimal power flow problem and the use of fuzzy methodologies to help planners of the composite generation-transmission system. In a market environment, transmission system adequacy may be defined as the ability of the system to meet reasonable demands for the transmission of electricity. The starting point of this paper is that FPF can be used as a tool to quantify this adequacy, without the need of making too many assumptions about load and generation uncertainties. However, some changes in the basic concept of the FPF are needed in order to accomplish this task - part of this paper is devoted to the description of the adequate formulation. We will also show that this formulation can be used both in the normal operation situation and in the reliability evaluation of the transmission system. An illustrative example completes this paper.

In this paper a tool for the evaluation of transmission system adequacy is presented. Although similar in the basic assumptions to the classic versions of the Fuzzy Power Flow (FPF), the approach has significant differences in the formulation. First, it is symmetrical (no influence of the slack bus in the results), so all the fuzzy power injections are in the same situation. Second, by including line constraints, only feasible deterministic power flows are accepted in the fuzzy variables calculations, leading to a more correct representation of the possible impact of uncertainty. Third, recalculation of the estimated node fuzzy injections leads to a clear picture of the repressed power flows and thus of the adequacy of the grid. On the other hand, the Constrained Fuzzy Power Flow (CFPF) separates completely the analysis of the network from the generation influence and costs, which is indispensable in a unbundled organization of the power system.

This paper aims to provide small- and medium-sized enterprises (SMEs) owned by families with a simple, achievable technical methodology for the assessment of sustainable mobility alternatives, in particular, the purchase of electric vehicles (EVs) and photovoltaic (PV) systems. By adopting a comprehensive comparative analysis approach, this research aims to empower SMEs to make highly informed decisions concerning the choice of vehicles and energy systems that provide strategic and sustainable value. Based on a quantitative analysis linked to the total costs over ten years, and considering the different types of vehicles (electric, hybrid, and combustion) and the integration of PV systems, practical formulas are used to calculate the total cost of ownership (TCO), energy consumption, and CO₂ emissions. The results show that adopting electric vehicles, especially those complemented by photovoltaic systems with storage for night-time charging, can significantly reduce operating costs and carbon emissions, generating economic and environmental value. This study provides an accessible and applicable approach to the context of family SMEs, facilitating the analysis and choice of mobility options based on simple and commercially available data. By focusing on value creation through informed and strategic decisions, this work offers a relevant contribution to the competitiveness and sustainability of SMEs, promoting the adoption of sustainable mobility technologies in an integrated and effective manner.