Identification and tracing of oscillatory stability margin boundaries

The aim of the paper is to present a framework that can quickly identify and estimate the oscillatory stability margin under various system operating conditions. First we present a brief review of various existing methods that are available for oscillatory stability assessment. The methods are basically divided into direct and indirect methods. In direct method, the oscillatory instability point is directly estimated from a given base case operating point. Whereas in indirect method the instability point is estimated in sequence of steps for any given scenario. The indirect methods can be further divided into eigenvalue based and manifold based. The manifold approach not only identifies but also can trace the margin boundary. The manifold based methodologies presented in this paper facilitate the analysis contributing to fast oscillatory stability margin monitoring and control. Only with solving tangent vector of a test matrix: a linear transformation of system total Jacobian matrix, the Hopf bifurcation is easily detected by observing the sign change of scalar index in the tangent vector. Once the instability point is detected, how this point changes with respect to various control configurations is further analyzed. Actually the instability point can be traced for various control configurations and scenarios. To achieve this objective, a unified formulation for oscillatory stability margin boundary tracing in multiparameter space is proposed. The bifurcation related margin boundary could be traced along any control scenario in multicontrol parameter space combined with any given loading scenario. The manifold method based identification and tracing is further improved by combining this approach with a new dominant eigenvalue tracing method. This approach is further extended to trace damping margin boundaries. The techniques presented in this papers can lead to on line monitoring of these boundaries.