Bifurcation analysis of power system load characteristics with continuation methods

Power systems are capable of exhibiting complex dynamics. Sometimes critical ones are, e.g. nonlinear incidents like collapse and swing phenomena. Many efforts are made by researchers and operators in order to prevent and dominate these undesirable effects. It is well known that parameter variations have influences on the system behavior and its stability. Sometimes they can cause incidents like the ones mentioned above. Because of former studies (e.g. in the field of catastrophe theory) it is also known that very often only a few parameters dominate the system behavior. An identification of these main parameters is desirable in order to get more information about the underlying mechanisms. On this basis an improvement or developement of adequate strategies in order to prevent critical system states is possible. Limit induced problems due to parameter variations as well as effects of generator controls on the system have been investigated in several papers. This paper neglects the limit induced problems and considers influences of different load characteristics on the system behavior. Therefore, an appropriate load model is needed. It is desirable that the chosen model represents the physical behavior as well as influences of individual parameter. The presented analysis uses continuation methods and the concepts of bifurcation theory. Therewith an investigation due to parameter of interest is possible and furthermore properties of the solution points can be investigated and classified, too. Moreover, appropriate network models are needed. An often-used, three-node power system model is chosen here. It represents the main system behavior and the physical dependencies in principle. Additionally it is clearly arranged and easy to handle. This paper presents two major results. At first bifurcation-studies are made. These studies regard especially load parameter variations. In contrast to other solutions these results are transformed into so-called power diagrams. It is possible to use this well known representation to derive or adapt control schemes. Secondly, the usage of flexible AC transmission devices (FACTS) is analyzed in order to avoid critical bifurcations. Although this was studied in several papers before, this work analyzes again the influences of different load characteristics. As a result, one gets information about possible limits. In special cases gain—intervals of the used FACTS—device can be determined within the system is independent of load parameter variation.