Métodos de función de energía aplicados al problema del margen de seguridad al colapso de tensión en redes de potencia

Abstract

In this work we analyze the application of energy function methods to the problem of defining security margins to voltage collapse in power systems. After reviewing the matematical theory of voltage collapse and the Liapunov' s theory of stability of dynamical systems, we describe how these theories may be applied to define a security margin to voltage collapse (the energy margin) in a power system model. We describe some basic properties of the energy margin, and its relationship with another security margin (the load margin) frequently used in power systems' planning and operation. Taking into account that the effective calculation of the energy margin requires the previous calculation of the unstable equilibria of the system's steady state equations (the so called load flow equations),we review its main calculation methods and,in particular,the theoretical foundations of the methods based on the rectangular formulation of the load flow equations. We present, finally, the main results of some test applications of the corresponding calculation software. We include in this work some specific original contributions to the theory and the calculation methods .In particular:we propose a modification to the basic theory of energy functions of power system's structure preserving model, we analyze the invariance properties of the energy margin in reference to the load dynamics, we describe how to incorporate some additional power devices to the general system's model,and we propose slight modifications to some of the classical calculation methods. Keywords : Voltage stability, Voltage collapse, Energy function