Rational Modeling of Multiport Systems via a Symmetry and Passivity Preserving Mode-Revealing Transformation

Modeling of frequency-dependent components and subnetworks is often based on a terminal description by an admittance matrix in the frequency domain. One challenge in the extraction of state-space models from such data is to prevent possible error magnification when the model is to be applied in time-domain simulations. The error magnification is a consequence of inaccurate representation of small eigenvalues of the admittance matrix. This paper resolves the problem by introducing a similarity transformation matrix which better reveals the eigenvalues of the admittance matrix. The chosen transformation preserves the passivity and symmetry of the original data, allowing the modeling to be performed by standard methods for model extraction and passivity enforcement. The approach is demonstrated for the wideband modeling of subnetworks and power transformers. The new technique is shown to accurately capture the large and small eigenvalues alike, thereby avoiding error magnifications in time-domain simulations.

[1]  T. Dhaene,et al.  Orthonormal Vector Fitting: A Robust Macromodeling Tool for Rational Approximation of Frequency Domain Responses , 2007, IEEE Transactions on Advanced Packaging.

[2]  A. M. Gole,et al.  Dynamic system equivalents: A survey of available techniques , 2009, 2009 IEEE Power & Energy Society General Meeting.

[3]  Giuseppe C. Calafiore,et al.  Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels , 2012, IEEE Transactions on Microwave Theory and Techniques.

[4]  R. Achar,et al.  Stability, Causality, and Passivity in Electrical Interconnect Models , 2007, IEEE Transactions on Advanced Packaging.

[5]  J. Martí,et al.  Accuarte Modelling of Frequency-Dependent Transmission Lines in Electromagnetic Transient Simulations , 1982, IEEE Transactions on Power Apparatus and Systems.

[6]  B. Gustavsen,et al.  Enforcing Passivity for Admittance Matrices Approximated by Rational Functions , 2001, IEEE Power Engineering Review.

[7]  Stefano Grivet-Talocia,et al.  Passivity enforcement via perturbation of Hamiltonian matrices , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Gene H. Golub,et al.  Matrix computations , 1983 .

[9]  L. Marti,et al.  Simulation of transients in underground cables with frequency-dependent modal transformation matrices , 1988 .

[10]  B. Gustavsen,et al.  Improving the pole relocating properties of vector fitting , 2006, 2006 IEEE Power Engineering Society General Meeting.

[11]  M. Paolone,et al.  Lightning-Induced Overvoltages Transferred Through Distribution Power Transformers , 2009, IEEE Transactions on Power Delivery.

[12]  B. Gustavsen.  Fast Passivity Enforcement for Pole-Residue Models by Perturbation of Residue Matrix Eigenvalues , 2008, IEEE Transactions on Power Delivery.

[13]  Athanasios C. Antoulas,et al.  A New Approach to Modeling Multiport Systems From Frequency-Domain Data , 2010, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[14]  A. Semlyen,et al.  Fast and accurate switching transient calculations on transmission lines with ground return using recursive convolutions , 1975, IEEE Transactions on Power Apparatus and Systems.

[15]  M. Nakhla,et al.  Enforcing passivity for rational function based macromodels of tabulated data , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[16]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[17]  T. Dhaene,et al.  Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method , 2008, IEEE Microwave and Wireless Components Letters.

[18]  A. S. Morched,et al.  A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables , 1999 .

[19]  A. S. Morched,et al.  Multi-port frequency dependent network equivalents for the EMTP , 1993 .

[20]  Taku Noda,et al.  Phase domain modeling of frequency-dependent transmission lines by means of an ARMA model , 1996 .

[21]  A. S. Morched,et al.  A high frequency transformer model for the EMTP , 1993 .

[22]  Christoph Heitz,et al.  Fast realization of the modal vector fitting method for rational modeling with accurate representation of small eigenvalues , 2009, 2009 IEEE Power & Energy Society General Meeting.

[23]  B. Gustavsen.  Passive macromodeling via mode-revealing transformation , 2012, 2012 IEEE 16th Workshop on Signal and Power Integrity (SPI).

[24]  Bjorn Gustavsen.  Frequency-dependent modeling of power transformers with ungrounded windings , 2004 .

[25]  S. Grivet-Talocia,et al.  Package macromodeling via time-domain vector fitting , 2003, IEEE Microwave and Wireless Components Letters.

[26]  Bjorn Gustavsen.  Wide band modeling of power transformers , 2004 .