Some modeling problems for four-phase power transmission systems

In the last years, a great effort has been paid in the exploitation of renewable energy resources, an attractive solution for satisfying the growing energy demand. This is considered one of the most interesting challenges in the future for guaranteeing the sustainability and for dramatically reducing the environmental impact. In this context, one of the most crucial aspects to take into account, for effectively allowing the competitiveness of renewable resources with respect to the conventional ones, is the improvement of the capability of the existing transmission systems. In fact, as a consequence of the renewable resource massive employment, transmission congestions could arise, compromising the reliability of the overall power system. At this aim, multiphase power transmission is a natural candidate to increase the capability of the existing corridors, avoiding in this way the search for land availabilities for new overhead transmission lines. A viable alternative solution to traditional three-phase transmission lines is provided by four-phase transmission lines. In recent papers some advantages with respect to the traditional systems have been discussed. However, some modeling problems have to be deeply investigated for demonstrating the worth of employing the four-phase transmission system. More specifically, the problem of the interface between the three-phase section and the four-phase one is very complex, since it involves a proper description of the special transformers required. A detailed mathematical model of the special transformers and their connections is needed for understanding the relationship between the symmetrical components of the two different systems. This is also indispensable for properly describing the transient stability margins against large disturbances as short circuits. In the paper, starting from the equivalent mathematical representation of the special transformers in terms of nodal admittance matrix, the authors derive some fundamental results which could be very useful for extending some standard methodologies and for properly evaluating the robustness characteristics of this new kind of transmission system. More specifically, the proposed methodology allows to outline the sensitivity of the system to some transformer parameters and to perform robust transient stability analysis in spite of semizero and zero sequence transformer parameters uncertainty.