| Summary: | <p>The ever-growing presence of renewable energy sources has started a radical transformation of power grids worldwide.
Their dynamical characteristics, the connections via power electronics, and their geographically distributed locations render their connection to the power grid substantially different from the traditional synchronous machines.
Household solar panels are a striking example of this transition:
their distribution is extremely sparse, and individual devices have a negligible contribution to the global electricity network; however, the presence of a large population of such devices influences the power grid in ways yet to be fully understood.</p>
<p>In the first part of this thesis we test the behaviour of a variety of solar devices, in order to develop models representing the aggregated, heterogeneous population that is connected to the power network.
We then present a model of the power grid whose parameters depend on the amount of solar devices connected to the grid.
In particular we focus on the network frequency, and we study how features of the PV population affect the overall frequency signal. </p>
<p>We investigate the frequency response after a generation loss contingency at varying levels of renewable penetration. We aim at identifying scenarios that lead to significant frequency deviations which activate a load shedding procedure.
Simulations of critical circumstances are useful to highlight potential issues, yet are often not sufficient to guarantee the reliability of a complex, stochastic system as the power grid.
In the second part of this dissertation we introduce formal methods, a suite of techniques to model complex systems as mathematical entities and to outline tight requirements about such systems. In particular we rely on the formal abstraction technique, which translates a stochastic system into a Markov model.
By means of model checking, we assess the satisfaction of given requirements and we provide a formal guarantee of correctness. </p>
<p>Our formal tests must specify a significant number of parameters as we consider various populations of solar devices.
The perfect tuning of such parameters is a cumbersome, handmade responsibility.
Finally, we automate this task proposing a parameter synthesis framework which automatically returns the values of parameters that satisfy the predefined requirements.</p>
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