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Assessment of dynamic stability of large‐scale power system by Rayleigh's quotient
Author(s) -
Kakimoto Naoto,
Sugano Keiji
Publication year - 1996
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.4391160207
Subject(s) - rayleigh quotient , eigenvalues and eigenvectors , control theory (sociology) , electric power system , quotient , stability (learning theory) , oscillation (cell signaling) , expression (computer science) , diagonal , mathematics , torque , rayleigh scattering , rayleigh quotient iteration , diagonal matrix , power (physics) , representation (politics) , mathematical analysis , computer science , physics , inverse iteration , geometry , pure mathematics , artificial intelligence , optics , biology , genetics , control (management) , quantum mechanics , machine learning , thermodynamics , programming language , law , political science , politics
A method of assessing dynamic stability of large‐scale power system by Rayleigh's quotient is proposed. One‐machine infinite‐bus systems show damping torque characteristics similar to diagonal components of operational transfer matrices for original multimachine systems, which means that design of PSS with one‐machine systems controls those components. An expression for damping constants of oscillation modes is derived based on an energy function and its time derivative for a simplified system representation. This expression demonstrates that oscillations do not necessarily become unstable even if there are some generators with negative damping; and the effect of damping torque is determined by eigenvectors. The expression is generalized with Rayleigh's quotient, and a method of estimating eigenvalues of large‐scale power systems is proposed. With this method, approximate eigenvalues are refined to accurate eigenvalues. Only a specified number of eigenvalue analyses are required irrespective of the number of generators, hence much calculation is saved. Finally, this method is applied to a 107‐machine system to verify its effectiveness.