Maximal Positively 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; transient stability; invariant sets; occupation measures; Lasserre's relaxation; moment-sum-of-squares hierarchy

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

Antoine Oustry, Carmen Cardozo, Patrick Panciatici, Didier Henrion. Maximal Positively Invariant Set Determination for Transient Stability Assessment in Power Systems. IEEE 58th Conference on Decision and Control (CDC), Dec 2019, Nice, France. ⟨10.1109/CDC40024.2019.9029422⟩. ⟨hal-01923135v2⟩