Maximal Positive Invariant Set Determination for Transient Stability Assessment in Power Systems

Antoine Oustry (1) , Carmen Cardozo (2) , Patrick Panciatici (2) , Didier Henrion (3, 4)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 RTE - Réseau de Transport d'Electricité [Paris]
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
4 FEL CTU - Faculty of Electrical Engineering [Prague]

This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is formulated as a semi-definitive program based on occupation measures and Lasserre's relaxation. An extension of the proposed method into a robust formulation allows us to handle Taylor approximation errors for non-polynomial systems. Results show the potential of this approach to limit the use of extensive time domain simulations provided that scalability issues are addressed.

Mots clés: power systems; convex optimization

Domaines: Optimisation et contrôle [math.OC]; Energie électrique; Automatique / Robotique

Antoine Oustry, Carmen Cardozo, Patrick Panciatici, Didier Henrion. Maximal Positive Invariant Set Determination for Transient Stability Assessment in Power Systems. 2018. ⟨hal-01923135v1⟩