scholarly journals How scaling of the disturbance set affects robust positively invariant sets for linear systems

2017 ◽  
Vol 27 (16) ◽  
pp. 3236-3258 ◽  
Author(s):  
Moritz Schulze Darup ◽  
Rainer Schaich ◽  
Mark Cannon
Keyword(s):  
Linear Systems ◽  
Invariant Sets ◽  
Positively Invariant Sets

scholarly journals Transient stability analysis of power grids with admissible and maximal robust positively invariant sets

2020 ◽  
Vol 68 (12) ◽  
pp. 1011-1021
Author(s):  
Tim Aschenbruck ◽  
Willem Esterhuizen ◽  
Stefan Streif
Keyword(s):  
Power Systems ◽  
Transient Stability ◽  
Energy Transition ◽  
Power Grids ◽  
Invariant Sets ◽  
Admissible Sets ◽  
Major Fault ◽  
Bounded Disturbances ◽  
One Machine ◽  
Positively Invariant Sets

AbstractThe energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid’s bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.

On the algebraic characterization of invariant sets of switched linear systems

Automatica ◽  
2010 ◽  
Vol 46 (6) ◽  
pp. 1047-1052 ◽  
Author(s):  
P. Riedinger ◽  
M. Sigalotti ◽  
J. Daafouz
Keyword(s):  
Linear Systems ◽  
Invariant Sets ◽  
Algebraic Characterization ◽  
Switched Linear Systems
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