STATE-SPACE TRANSMISSION LINE MODEL WITH FREQUENCY-DEPENDENCY AND LONG-LINE EFFECTS BASED ON A SINGULAR APPROXIMATION AND BALANCING-FREE SQUARE-ROOT APPROACH

摘要

This paper presents a new and comprehensive transmission line model, in state-space form, suitable for power systems electromagnetic transients, employing a highly effective model order reduction approach. The backbone of the model order reduction procedure relies on the computation of projection matrices, which enables a very considerable reduction in the dimensions of the original model. The determination of the projection matrices is based on the solution of the Lyapunov equations using the Gramian factors and a Cholesky factorization. The transmission line model incorporates full frequency dependency, long-line effects and geometric imbalances and it is quite different from the highly-developed family of transmission line models based on the travelling wave concept The frequency dependency of the transmission line is modelled using a set of parallel RL branches, whilst the long-line effects are modelled by discretizing its distributed parameters with respect to the line distance. A Newton-Raphson method is used to fit the parallel RL branches and Singular Value Decomposition is applied to solve cases where the Jacobian becomes ill-conditioned. Validation of the results obtained with this transmission line model is presented for the Jaguara-Taquaril three-phase transmission line system, considering both ideally transposed and non-transposed conditions.