Complex Frequency Propagation along Transmission Lines

The paper proposes a Complex Frequency Continuum Model (CFCM) to represent the propagation of voltage dynamics along transmission lines. The proposed CFCM is based on the concept of Complex Frequency (CF), recently proposed by the second author. This model removes the assumption of small voltage magnitude an phase angles in the transmission system, which are the basis for a Linear Continuum Model (LCM) also recently proposed by the second author. The paper identifies two major differences between the CFCM and the LCM. On the one hand, the former captures the nonlinearity of the spatial rate of change of the CF. On the other hand, it recognizes the cross-dependence between the real and imaginary parts of the CF along a line. Time-domain simulations are carried out in a case study whose transmission system operates highly loaded, and the performance of the CFCM and the LCM are compared to a PLL-based estimation of the CF at different points of a line. Simulation results verify the accuracy of the proposed approach, and show the errors introduced by the LCM in estimating the CF at an intermediate point of a line.