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Moment-SOS hierarchy for large scale set approximation. Application to power systems transient stability analysis

Matteo Tacchi 1 
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This thesis deals with approximating sets using Lasserre’s moment-SOS hierarchy. The motivation is the increasing need for efficient methods to approximate sets of secure operation conditions for electrical power grids. Indeed, recent and ongoing changes in the European power network, such as the increase in renewable energy sources interfaced by power electronic devices, are bringing up new challenges in terms of power grid security assessment. The aim of the present thesis is to investig- ate the suitability of them moment-SOS hierarchy as a tool for large scale stability assessment.In this regard, the very scheme of moment-SOS hierarchies is analysed in-depth, and general results regarding the convergence and accuracy of the framework are stated, along with specific computational methods inspired from differential geo- metry and partial differential equations theory, in order to improve the convergence of the numerical scheme.From the computational viewpoint, the core of this thesis is the exploitation of problem structure to alleviate the computational burden of high dimensional, large scale industrial problems. The network structure of power grids leads us to consider general sparsity patterns and design methods which distribute our computations accordingly, drastically reducing computational costs in implementation.In addition to stability analysis, a special interest is put on the theoretical prob- lem of volume computation, whose applications rather concern the field of integral calculus and probability evaluation, as understanding this problem turns out to be a prerequisite for approximating stability regions of differential systems, such as regions of attraction or positively invariant sets, with the moment-SOS hierarchy. Indeed, the moment-SOS approach to volume computation is the core of moment- SOS stability analysis.
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Matteo Tacchi. Moment-SOS hierarchy for large scale set approximation. Application to power systems transient stability analysis. Automatic. INSA de Toulouse, 2021. English. ⟨NNT : 2021ISAT0028⟩. ⟨tel-03296221v2⟩

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