Scientific Computing Seminar

Date:
Friday, June 17, 2005
Time:
1:00pm-2:00pm
Location:
50A-5132
Seminar Speaker:
Nelson Martins
CEPEL, Brazil
nelson (AT) cepel (DOT) br
http://www.nelsonmartins.com
Title:
Eigenvalue Applications/Computations in Electrical Power System Studies
Abstract:
Eigenvalue applications in electrical power system studies started in the sixties with matrix problems of dimension around 10, which has since then risen to more than 10,000. The following is a non exhaustive list of applications: 1) damping assessment and control of electromechanical oscillations, including poorly-damped, low-frequency inter-area oscillations that permeate across an entire interconnection (picking up one evidence, out of a myriad of others, on the engineering effort involved in monitoring, modeling and damping these oscillations: in the early nineties there existed the 0.7 Hertz Oscillation Ad Hoc Work Group, which reported to the WSCC Technical Studies Subcommittee and produced valuable reports); 2) subsynchronous resonance problems in series-compensated transmission networks, which in the early seventies damaged twice the rotor shaft of a large turbine-generator of the Mojave power plant, in Nevada; and 3) harmonic voltage distortion analysis, caused by multiple harmonic current loads that excite series and parallel resonances in the R, L,C transmission/distribution networks and degrade power supply quality.

Over the last 25 years, sparse eigensolution methods have been applied to large power systems nonsymmetric matrix problems. The methods in current use range from basic Inverse Iteration and Rayleigh Quotient Iteration to advanced subspace iteration and Krylov subspace methods. Methods developed at CEPEL in the last decade are also gaining acceptance, in particular the Refactored Bi-Iteration (RBI) and the Dominant Pole Spectrum Eigensolvers for both scalar and multivariable transfer functions. These methods have been used in several applications, including model order reduction that is needed in the design of large scale multivariable control systems.

Linear system models, whose matrix elements are non-linear functions of the Laplace variable s, have been proposed in the literature to adequately represent pure time delays, distributed and frequency dependent parameters. Electromagnetic transients induced by the energization of long transmission lines, which have frequency-dependent and distributed parameters (infinite systems), require such sophisticated modeling. Newton eigensolution algorithms have been recently developed at CEPEL to solve for the dominant pole spectrum (and associated residues) of these infinite systems. Reduced order models for these infinite systems are then realized in state space, to become External Equivalents that are connected to the Study Area, in order to speed-up simulations in computational intensive electromagnetic transients studies.

Sponsor of Seminar:
Osni Marques
Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov