Open AccessStability Analysis by means of Discrete Abstraction. Application to Voltage Stability of Distributed Generators**This study has been carried out in the RISEGrid Institute (www.supelec.fr/342 p 38091/risegrid-en.html), joint scienti_c program between CentraleSupelec and EDF (‘Electricit_e de France’) on smarter electric grids.
Author(s) -
Marjorie Cosson,
Hervé Guéguen,
Didier Dumur,
Cristina Stoica,
Vincent Gabrion,
Gilles Malarange
Publication year - 2015
Publication title -
ifac-papersonline
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 72
eISSN - 2405-8971
pISSN - 2405-8963
DOI - 10.1016/j.ifacol.2015.11.201
Subject(s) - reachability , abstraction , undecidable problem , bisimulation , stability (learning theory) , piecewise , computer science , decidability , control theory (sociology) , mathematics , affine transformation , theoretical computer science , pure mathematics , control (management) , mathematical analysis , artificial intelligence , philosophy , epistemology , machine learning
International audienceThis 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
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