MIT Department of Electrical Engineering & Computer Science

EECS Fall 1995 Catalog Supplement

6.972 Nonlinear Dynamics in Power Systems (H)

MW 2:30-4, 34-301
3-0-9
Prof. Bernard Lesieutre, 10-039, x3934

Even in their simplest form, power systems models are large and nonlinear. These properties present many theoretical and practical challenges. In this course we will examine current research in the modeling and analysis of power systems. Nonlinear techniques will be emphasized. A background in dynamic systems is required (6.241 or equivalent). The specific topics to be covered and their applications in power systems are listed below.

1. Linear Systems: eigenvalues, eigenvectors, participation factors, invariant subspaces.
   --Computational issues involving small-signal stability studies and the determination of critical eigenvalues and eignevectors
   --Reduced-order modeling of large linear systems
   
   
2. Manifolds: unstable, stable, and center manifolds. Time-scale separation and slow and fast manifolds.
   --Power system models and reduced-order modeling using integral manifolds
   
   
3. Lyapunov Stability: Lyapunov functions/energy functions, region of attraction.
   --Critical fault-clearing time, transient stability, transient energy functions, PEBS method
   
   
4. Structural Stability: bifucation theory, continuation methods, limit cycles, chaos.
   --Load flow, voltage collapse, power system oscillations
   
   
5. Differential/Algebraic Equations: system index, solution properties
   --Bifurcations of the constrained manifold, impasse points
   
   
6. Projects