Frequency-dependent modeling of transmission lines using bergeron cells

This paper proposes using Bergeron's equivalent circuit with traveling time equal to the simulation time step as an element for frequency-dependent modeling of transmission lines for electromagnetic transient (EMT) simulations of power systems. According to the simulation time step used, a transmission line is divided into aforementioned Bergeron's equivalents, each of which is called a ‘Bergeron cell’ in this paper. In this way, the traveling-wave nature of a line is represented by the cascaded Bergeron cells. Then, the frequency-dependent loss nature of the line is represented by a matrix partial fraction expansion, and this is inserted at each connection point of the Bergeron cells in the form of a multiphase Norton equivalent. Since the frequency-dependent loss is modeled in the dimension of impedance, the change of the line length is easily taken into account by a simple multiplication. This methodology thus allows variable-length modeling and completely avoids modal decomposition in both model identification and EMT simulation stages. The proposed methodology is applied to the frequency-dependent modeling of overhead and submarine-cable transmission lines, and its accuracy is assessed.