Transmission line model with frequency dependency and propagation effects: A model order reduction and state-space approach

A new and comprehensive transmission line model for the study of power systems electro-magnetic transients based on a highly effective model order reduction, is presented in this paper. The model takes the form of a state-space representation and differs fundamentally from the well-known family of transmission line model based on the wave-travelling concept. The core principles of the model order reduction procedure are the application of singular approximations, balancing-free square-roots and the computation of projection matrices. Grammian factors in combination with a Cholesky factorization are applied to the solution of the Lyapunov equations and, hence, to the calculation of the projection matrices. Commensurate with state-of-the-art transmission line models for the study of electromagnetic transients, the new model includes full frequency dependency, propagation effects and geometric imbalances.While its frequency dependency characteristic is modelled using a set of parallel RL branches, the long-line effects are incorporated by discretizing its distributed parameters with respect to the line distance. Newtonpsilas method is used to fit the set of parallel RL branches and Singular Value Decomposition is employed to solve cases where the Jacobian becomes ill-conditioned. The effectiveness of the proposed transmission line model is demonstrated using a non-transposed version of the Jaguara-Taquaril three-phase transmission line system.