Chapter 19
Study of the Transversality Conditions of the BCU Method
19.1 INTRODUCTION
The transversality condition plays a significant role in the development of the dynamical system theory. The condition is one of the three ingredients in the so-called Morse–Smale systems. The violation of the transversality condition often leads to a global bifurcation, making the task of verifying the transversality condition important. In the past, significant efforts have been directed to the development of tools for verifying the transversality condition. Despite these efforts, little progress has been made on this matter. It is now well recognized that the task of verifying the transversality condition is very challenging. There are no useful tools available for verifying the transversality condition except for computationally extensive numerical methods.
The one-parameter transversality conditions play an important role in the theoretical foundation of the conceptual BCU method. Violation of the one-parameter transversality conditions can cause a violation of dynamic property (D2) required in the BCU method; consequently, it may cause incorrectness in the BCU method when computing the controlling unstable equilibrium point (UEP). However, due to the complexity of practical power system models, the one-parameter transversality conditions may not be always satisfied. Several counterexamples showing that the BCU method may fail to give correct stability assessments, predicting stability ...
