Abstract: A method and device characterize linear properties of an electrical component having n>1 ports. The linear properties of the component are described in a matrix relating a voltage applied to the ports to a current through the ports. A frequency dependence of the matrix is approximated to preserve eigenvalues of the matrix by a pole-residual model. The method includes: (a) obtaining a set of values of the matrix at discrete frequencies, and obtaining eigenvalues and eigenvectors for each value; (b) fitting a set of vector equations to the eigenvalues and eigenvectors with a first set of pole frequencies; and (c) calculating a second set of pole frequencies by a vector fitting process for all modes of an element of the matrix. Steps (b) and (c) are repeated using the second set of pole frequencies in step (c) in a subsequent step (b) until a stop condition is met.

Abstract: Residue perturbation is used for enforcing passivity of a linear response model of an electrical component having n>1 ports. According to an exemplary embodiment, a modal perturbation approach can be used, which allows weighted perturbation of the individual modes by the inverse of the corresponding eigenvalues. This provides superior results if the admittance or impedance matrix of the device has a large eigenvalue spread.

Abstract: Residue perturbation is used for enforcing passivity of a linear response model of an electrical component having n>1 ports. According to an exemplary embodiment, a modal perturbation approach can be used, which allows weighted perturbation of the individual modes by the inverse of the corresponding eigenvalues. This provides superior results if the admittance or impedance matrix of the device has a large eigenvalue spread.

Abstract: Rational macromodeling of multiport devices is disclosed that can ensure high accuracy with arbitrary terminal conditions. This can be achieved by reformulating a vector fitting technique to fit eigenpairs rather than matrix elements, and weighting can be chosen equal to an inverse of an eigenvalue magnitude in order to achieve a relative accuracy criterion for the eigenvalue fit. The procedure can improve accuracy for cases with a large eigenvalue spread. Impedance characteristics of an adjacent network can be used to lessen the complexity of the fitting and to improve accuracy.

Abstract: To characterize an electrical component, namely a medium or high voltage transformer, electrical motor or generator, a two-step procedure is carried out. In a first step, a set of terminal configurations are applied to the terminals (p1, . . . , pn) of the component in order to obtain data describing the linear electrical response of the component to any pattern of voltages uk or currents ik applied to the terminals (p1, . . . , pn). Typically, such data is e.g. expressed in terms of an admittance matrix Y or impedance matrix Z or, by the set of current and voltage vectors (ik, uk). Using this data, the linear electrical response of the component 1 under a test terminal configuration can now be calculated in a second step. This procedure allows to determine the response under any desired test terminal configuration without the need to carry out the measurement under the test terminal configuration.