Phase-shifting transformers in a structure-preserving energy function

Abstract

With some exceptions, direct methods have so far not been properly able to assess the transient stability of general power systems with phase-shifting transformers (PSTs) because there were no energy functions that would include their action in a post-fault situation. In this paper, we propose two additional potential-energy function parts for the two most common PSTs that can be added to any existing structure-preserving energy functions (SPEF). In this way, modularity is achieved and other FACTS devices can easily be taken into consideration. Using the proposed energy functions, it is possible to apply direct methods to any system that consists of an arbitrary number of phase-angle regulators (PAR) and quadrature-boosting transformers (QBT). These new energy functions assume a constant controllable parameter; however, we extended the use of the presented energy functions by a simple procedure that makes the direct method able to consider any parameter change in a post-fault system. The proposed energy-function extensions were tested in a longitudinal system, because only in such a system will direct methods and a simulation give the same results. Another demonstration was made with an IEEE nine-bus test system using a potential-energy boundary-surface (PEBS) direct method.