Over the last few decades, we have witnessed an ever-increasing integration of renewable energy sources into the electrical system and a simultaneous reduction in the production of synchronous generators. This poses serious risks to the proper functioning of the grid and, in particular, to its stability, understood as the ability of the system to return to acceptable operating conditions after a disturbance. TThe problem of analyzing the stability of the electrical grid is today more relevant than ever in order to guarantee a reliable and safe operation of the grid. In particular, the availability of efficient techniques for evaluating the behavior of the network following a contingency is fundamental not only for the analysis, but also for the synthesis, i.e. the design of the parameters and control laws.

The report is structured as follows: first, an introduction is given to the different nuances that the concept of electrical system stability can encompass. Then, a distinction is made between the two main macro categories of stability analysis: small disturbance analysis and large disturbance analysis. Then, the most commonly used models in the literature for stability analysis in general are presented.

This year, the problem of small-signal variation analysis was addressed for an electrical grid characterized by the co-presence of synchronous and static generation and described by algebraic differential models. By extending some work in the literature, it is shown how, for this type of grid, stability (non asymptotic) is essentially always guaranteed, provided that the control parameters of the static converters satisfy certain requirements. The study does not exhaust the topic of small signal stability analysis: the models discussed are indeed simplified and require further extensions. However, it provides a basis on which future studies may be based.

The work described here is part of a broader three-year program whose objectives are to arrive at a large disturbance analysis of electrical systems characterized by a high penetration of static generation, with the aim of providing guidelines for the synthesis of the controls of the components present in them.