The problem of frequency dependence in transmission line modelling

In this work, the accurate representation of transmission lines for the digital simulation of electromagnetic transients in power systems has been examined. A model has been developed that accounts for the frequency dependence and distributed nature of the line parameters over the entire frequency range. This model can easily be incorporated into a time-domain network solution of the complete power system. The model consists simply of a constant resistence in parallel with a current source evaluated at each time step of the solution. The equivalent resistance results from a finite-step-width discretization of the differential equations of a resistance-capacitance (R-C) network that simulates the line characteristic impedance. The equivalent current source accounts for the time delays and attenuations of the different frequency components of the travelling waves and for the discretization of the time-domain equations. Rational-function approximations are used to synthesize the R-C network and the line propagation ("weighting") function in the frequency domain. These rational approximations allow the corresponding time-domain functions to be obtained directly in a closed-form, thus circumventing the need for numerical inverse Fourier transformations. The numerical technique used to obtain the rational functions yields very accurate, high-order approximations. This technique is based on a direct, step-by-step allocation (and reallocation) of poles and zeros and avoids the instability problems which can be encountered with optimization techniques based on search methods. A series of analytical evaluations and simulation tests were performed in order to assess the validity of the model. The results of these tests show that the model is accurate, fast, and reliable. The model was incorporated into the code of the University of British Columbia's version of Dr. H.W. Dommel's Electromagnetic Transients Program (EMTP). iApplied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat