Open Access

ARTICLE

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

Loc Vu-Quoc^1,*, Yuhu Zhai² and Khai D. T. Ngo³

1 Aerospace Engineering, University of Illinois at Urbana-Champaign, Illinois, 61801, USA
2 Princeton Plasma Physics Laboratory, Princeton, New Jersey, 08542-0451, USA • yzhai@pppl.gov
3 Electrical and Computer Engineering, Virginia Tech, Virginia, 24061, USA • ktn@vt.edu

* Corresponding Author:Loc Vu-Quoc. Email:

(This article belongs to the Special Issue: Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister)

Computer Modeling in Engineering & Sciences 2021, 129(3), 1441-1486. https://doi.org/10.32604/cmes.2021.016784

Received 26 March 2021; Accepted 14 July 2021; Issue published 25 November 2021

Abstract

The Generalized Falk Method (GFM) for coordinate transformation, together with two model-reduction strategies based on this method, are presented for efficient coupled field-circuit simulations. Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors, called trial vectors, to construct a vector basis for coordinate transformation. The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems. We also show that, unlike the Pad´e-via-Lanczos (PVL) method, the GFM does not generate unstable positive poles while reducing the order of circuit problems. Further, the proposed GFM is also faster when compared to methods of the type Lanczos (or Krylov) that are already widely used in circuit simulations for electrothermal and electromagnetic problems. The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods. Further, we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system. The implementation of these equivalent circuit networks in circuit simulators is discussed. With the proposed model-reduction strategies, significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

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