Stability Analysis by means of Discrete Abstraction. Application to Voltage Stability of Distributed Generators

Marjorie Cosson (1, 2) , Hervé Guéguen (3) , Didier Dumur (1) , Cristina Stoica Maniu , Vincent Gabrion (2) , Gilles Malarange (2)

1 L2S - Laboratoire des signaux et systèmes
2 EDF R&D - EDF R&D
3 IETR - Institut d'Électronique et des Technologies du numéRique

This paper proposes a stability analysis method for discrete-time piecewise affine systems based on the reachability study of the equivalent discrete abstraction. The finite discrete abstraction eases reachability analysis but does not allow to conclude on system instability. To be able to conclude, this abstraction is refined by bisimulation calculation until the system is found to be unstable or the discrete abstraction is found to be equivalent to the system. This method allows to conclude both on the stability and the instability of the system, avoiding the undecidable situations. This approach is illustrated on voltage stability of a distribution feeder hosting distributed generators equipped with piecewise affine control laws.

Keywords: Hybrid systems; Transition systems; Nonlinear systems; Piecewise linear analysis; Electric power systems; Reactive power; Voltage stability

Domains: Engineering Sciences [physics]; Engineering Sciences [physics]; Automatic

Marjorie Cosson, Hervé Guéguen, Didier Dumur, Cristina Stoica Maniu, Vincent Gabrion, et al.. Stability Analysis by means of Discrete Abstraction. Application to Voltage Stability of Distributed Generators. 5th IFAC Conference on Analysis and Designe of Hybrid Systems (ADHS), Oct 2015, ATLANTA, United States. pp.364-370, ⟨10.1016/j.ifacol.2015.11.201⟩. ⟨hal-01259498⟩