Analyzing dynamic performance of power systems over parameter space using normal forms of vector fields. Part I: Identification of vulnerable regions

This is the first part of a two-part paper discussing the dynamic performance of power systems over parameter space using the method of normal forms. A new normal form transformation is derived under the second order resonance condition. By using the resonance condition as a guide to indicate detrimental system dynamic performance, the authors propose a computationally efficient method to study the system under varying parameters. An approach to determine the resonance and near-resonance region in the parameter space is developed. For the resonance case, conclusions are drawn by simply examining the analytic solutions. For the near-resonance case, the machine states showing poor performance can be found by tracing the dominant nonlinear modal interaction and mode-machine interaction. The method is tested on the IEEE 50-generator system. The results reveal many interesting characteristics of the system related to resonance and near-resonance, which validates the effectiveness of the method as a useful analytical tool for system operation and design. Further work on quantifying the effect of the modal interactions on the machine states is presented in Part II.