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Frequency-Dependent Equivalent Based on Idempotent Decomposition and Grouping

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Accurate representation of Frequency Dependent Equivalent (FDE) has received a great deal of intense research in the time-domain transient analysis. Nowadays, a multi-input multi-output pole residue model is applied for the frequency domain realization. One common challenge to this approach is the accurate representation of small eigenvalues which tend to be poorly fitted. In some cases, a given FDE may presents a large ratio between eigenvalues at the lower frequency range, thus being characterized as a stiff system.

In this work, we propose an alternative approach to improve the observability of these small eigenvalues. First, we use the idempotent decomposition of an FDE which is then grouped accordingly the behavior of the associated eigenvalues at the lower frequency range. These grouped idempotent are then fitted independently. A discussion of possible passivity enforcement in the rational approximation is also presented. A nonuniform line associated with a wide river crossing is used to illustrate the application. This configuration was chosen due the large ratio between eigenvalues at the lower frequency range.

Author(s):

Antonio Lima    
Universidade Federal do Rio de Janeiro
Brazil

Felipe Camara    
Furnas
Brazil

Joao P.L. Salvador    
Federal Center of Technological Education "Celso Suckow da Fonseca", CEFET/RJ
Brazil

Teresa Correia de Barros    
IST ULisboa
Portugal

 

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