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This paper describes the implementation of a full frequency-dependent model for transmission lines and cables in a state-space-based solver for electromagnetic transients. This implementation is for real-time simulation of power system switching transients. It is based on the wideband universal line model with modifications being incorporated to meet the computational speed requirements of real-time applications. The real-time performance of the implementation is demonstrated through application examples.

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This book provides a detailed description of some of the most widely used rational fitting techniques for approximation of frequency domain responses. The techniques are: Bode's asymptotic approximation, the Levy method, iteratively reweighted least squares, the Sanathanan-Koerner method, the Noda method, Vector Fitting, the Levenberg-Marquardt method, and the Damped Gauss-Newton method. A MATLAB routine for each technique is presented. These techniques are tested by approximating synthetic frequency domain responses. Then, they are applied to the rational approximation of the frequencydependent parameters corresponding to a single-phase transmission line. The effect of the rational function-based models is evaluated, considering transients in three cases: Open-ended, short-circuited, and perfectly matched lines. The error levels obtained in time domain simulations are consistent with the fitting deviations of the frequencydependent parameters. The book concludes by showing main advantages and disadvantages for each technique.