• Stochastic model
• Model-based analysis
• Smart Grids
• Power Flow Equations
• Optimization
• Stochastic Activity Networks
• Stochastic Petri Nets

The electrical infrastructure can be considered nowadays as a meta-critical infrastructure: in fact it is the basis for almost all the critical infrastructures a modern nation can have, such as water, oil, gas and transportation.
To allow pervasive control and monitoring towards resilience and performance enhancements, the Smart Grid is emerging as a convergence of information and communication technology with power system engineering. In particular, the ever increasing level of distributed energy resources penetration calls for more and more sophisticated monitoring and control facilities.
So, studying the influence of distributed energy resources, of new control policies and ICT on the dependability of distribution grids can offer valuable insights on how to improve the design of Smart Grids.
In addition to standard dependability measures such as reliability and availability, among greatly relevant measures specifically defined for electrical distribution systems there are the voltage quality and the energy required, but not supplied, by the distribution system.
A popular approach to assess electrical distribution specific measures, in presence of failures or attacks to the ICT system and/or to the electric infrastructure, is the stochastic model-based analysis. Although several studies have been already proposed, the research in this context still faces a number of challenges, mainly due to the need: i) to consider both the ICT subsystem and the controlled electrical infrastructure, to properly account for (inter)dependencies through which operations (and failures/attacks) propagate; ii) to model and analyze the SG components at a sufficiently detailed level of abstraction, targeting realistic representation of their structure and behaviour in view of promoting accuracy of the assessment itself. Both nominal and a variety of faulty behaviours are to be investigated, since the interest is on assessing resilience and quality related attributes; iii) to tackle realistic segments of SG in terms of topology size, to make the evaluation study of real interest to stakeholders involved in the field.
Copying with all these needs results in huge and complex models, to be typically defined in a modular fashion and requiring sophisticated compositional operators. Moreover, model solution through simulation-based evaluation becomes unavoidable in presence of non-Markovian behaviour of the involved components, thus preventing the use of analytical approaches.
Given the above premises, the stochastic model-based analysis of realistic SG topologies is a research area where further investigations and enhancements are highly desirable. In this context, this thesis offers contributions in the direction of promoting efficient evaluation of SG in realistic scenarios from a resilience perspective.
Specifically, starting from a preliminary development of a model-based framework for SG evaluation already available at the ISTI SEDC Lab in Pisa, the work progressed in three major directions:
- finalization of a basic SG evaluation framework, carried on taking into account the challenges described above, especially in terms of detailed representation of structure and behaviour of electric components and how they are impacted by the behaviour of cyber components, as well as (inter)dependencies and failure phenomena. This was a valuable effort to start exercising the framework on a variety of grid topologies and failure scenarios, which helped greatly to understand strengths but also limitations of the current solution and pointing out directions for refinement steps. In particular, efficiency was identified as the major obstacle to deal with grid topologies representative of realistic regional segments, so further advancements concentrated on this aspect;
- compositional operators adopted in the modular development of models were identified as a major weakness from efficiency viewpoint, and therefore as a research area where available solutions need improvements. In particular, new non-anonymous replication techniques for constructing the system model starting from template models of its components have been formalized, implemented and tested within the Mobius modeling framework.
Among the available possibilities, the best from the point of view of performance has been selected to replace the one adopted in the basic model.
- state estimation computations were also identified as highly executed operations and so another promising aspect for performance improvement. Several methods, all based on the Newton-Raphson method, to estimate the state of the electrical infrastructure have been investigated and among those the best approach has been selected.
- control logic, implemented as the solution of an optimization problem, requires several calls to the electrical state estimation process and then a fine tuning, aimed at minimizing the computational cost, has been carried out. The benefits in efficiency brought by the newly developed solutions have been quantified through a comparison study between the basic evaluation framework and the enhanced one equipped with such solutions.