Chapter 12

Controlling UEP Method: Computations

12.1 INTRODUCTION

It is now well recognized that the controlling unstable equilibrium point (controlling UEP) method is the most viable method for direct stability analysis of practical power systems. The success of applying the controlling UEP method hinges upon the ability to find the correct controlling UEP. However, the task of finding the controlling UEP of a given fault for general power system transient stability models is very challenging.

From a theoretical viewpoint, the existence and uniqueness of the controlling UEP with respect to a fault-on trajectory are assured. From a computational viewpoint, computing the controlling UEP is very challenging as summarized into seven challenges in the following section. These computational challenges should be taken into account during the development of numerical methods for computing the controlling UEP. These challenges collectively serve to explain why previous methods proposed in the literature fail to compute the controlling UEP. We note that since the controlling UEP is independent of the energy function used in the direct stability assessment, the tasks of constructing an energy function and of computing the controlling UEP are not interrelational.

In this chapter, we focus on the computational aspects of the controlling UEP method. Specifically, the following will be described:

  • The computational challenges in computing the controlling UEP are described. A total of seven challenges ...

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