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TIMESCALES IN INTERCONNECTED SYSTEMS
SINGULAR PERTURBATIONS AND TIMESCALES
MODELING OF TWOTIMESCALE SYSTEMS
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16 machine system 48 machine aggregable with respect aggregate model aggregate variables angles in area approximation A2 area partition Assumption asymptotic analysis asymptotically stable boundary layer capacitors Chapter coherent groups coherent with respect connection form conservation property coordinate vectors Corollary damping decoupled defined Difference variables dy/dt dynamic manifold eigenbasis matrix eigenspace eigenvalue approximation eigenvectors electromechanical model entries equation external connections fast dynamics fast modes fast subsystems fast time-scale fast variables Gaussian elimination grouping algorithm identity matrix illustrate Individual machine angles Lemma mass-spring system near-coherent nodes nonlinear dynamic networks nonsingular null space obtain order dynamic networks oscillatory partition matrix power systems quasi-steady RC-circuit example Riccati equation row spaces row vectors second order dynamic SECONDS Figure Section singular perturbation form slow and fast slow coherency slow modes slow subsystem slow time-scale slow variables storage elements system in Figure Theorem time-scale modeling methodology transformation two-time-scale system voltage weak connections weakly