Multi-Scale and Frequency-Dependent Modeling of Electric Power Transmission Lines

A frequency-dependent transmission line model for multi-scale simulation of diverse transients over a wide range of frequencies is developed, implemented, and validated. Itmakes use of the concept of frequency-adaptive simulation of transients in which the Fourier spectra are adaptively shifted in the frequency domain to reduce the discretization time-steps in the time domain. The transients are modeled through dynamic phasors comprising the real and imaginary parts of analytic signals to facilitate the frequency shifting. In the proposed line model, all mathematical operations such as numerical recursive convolutions are, therefore, expressed in terms of analytic signals. A modal decomposition is performed to attain decoupled modes for the multi-phase case. The transition from the representation of electromagnetic traveling waves with time-steps below the wave propagation time to the tracking of slower electromechanical transients at time-steps above the wave propagation time is achieved by the automatic insertion of a p-segment to represent the galvanic coupling within one time-step. Accurate and efficient simulation of both electromagnetic and electromechanical transients within a simulation run is so supported. The validation is verified through comparison with a staged field test covering the diverse transients of line energization, transient recovery voltage, and steady state.