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Analysis and simulations of the model show that it is a realistic abstraction, and quantitatively indicate that heterogeneity is necessary to enable the overall network to function in safe conditions and to avoid load shedding.

This project will provide extensions of this recent research. Prerequisites: Computer-Aided Formal Verification, Probabilistic Model Checking Stochastic Hybrid Systems (SHS) are dynamical models that are employed to characterize the probabilistic evolution of systems with interleaved and interacting continuous and discrete components.

This work investigates the behaviour of a large, heterogeneous population of photovoltaic panels connected to the grid.

We employ Markov models to represent the aggregated behaviour of the population, while the rest of the network (and its associated consumption) is modelled as a single equivalent generator, accounting for both inertia and frequency regulation.

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Courses: Computer-Aided Formal Verification, Numerical Solution of Differential Equations Prerequisites: Some familiarity with dynamical systems, working knowledge of MATLAB and C Sensorisation and actuation in smart buildings and the development of smart HVAC (heat, ventilation and air-conditioning) control strategies for energy management allow for optimised energy usage, leading to the reduction in power consumption or to optimised demand/response strategies that are key in a rather volatile market.

Abstractions come in the form of lumped, aggregated models, which are beneficial in being easier to simulate or to analyse.

Key to the novelty of this work, the proposed abstractions are quantitative in that precise error bounds with the original model can be established.

Formal analysis, verification, and optimal control of SHS models represent relevant goals because of their theoretical generality and for their applicability to a wealth of studies in the Sciences and in Engineering.

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In a number of practical instances the presence of a discrete number of continuously operating modes (e.g., in fault-tolerant industrial systems), the effect of uncertainty (e.g., in safety-critical air-traffic systems), or both occurrences (e.g., in models of biological entities) advocate the use of a mathematical framework, such as that of SHS, which is structurally predisposed to model such heterogeneous systems.MPL models are specified in MATLAB, and abstracted to Labeled Transition Systems (LTS).

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