Practical static stability assessment for smart MicroGrids: a comparison between the MVEE and the Convex Hull

This paper provides a comparative analysis of two advanced methodologies for offline evaluation of feasible operating regions of MicroGrids (MGs): the Minimum Volume Enclosing Ellipsoid (MVEE) and the Convex Hull (CH). These methods construct analytical regions in a multidimensional space, representing only the operating points that ensure system stability. Stability is initially assessed through Load Flow (LF) analysis, and the results are validated against relay protection settings. The approaches classify operational conditions, derived from dispatching algorithms, as feasible or infeasible based on their geometric position in Euclidean hyperspace, defined by active and reactive power components. This study evaluates and compares both methodologies in terms of their accuracy and computational efficiency, offering insights into selecting the most suitable method for specific system requirements. The results provide valuable guidance for the application of stability assessment tools in the management of Smart MicroGrids.