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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 aggregability condition aggregable with respect aggregate model aggregate variables approximation A2 area partition Assumption asymptotic analysis boundary layer capacitors Chapter coherent groups coherent with respect connection form conservation property coordinate vectors Corollary damping decoupled defined denote difference variables dy/dt dynamic manifold eigenbasis matrix eigenspace eigenvalue approximation eigenvectors electromechanical model entries external connections fast dynamics fast modes fast subsystems fast time-scale fast variables Gaussian elimination grouping algorithm identity matrix illustrate Lemma mass-spring system near-coherent nodes nonlinear dynamic networks nonlinear systems nonsingular null space obtain order dynamic networks oscillatory parameter partition matrix power systems quasi-steady RC-circuit example Riccati equation row spaces row vectors satisfies second order dynamic 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 ys(t