Assessing placement of controllers and nonlinear behavior using normal form analysis

Normal form (NF) theory is used to characterize and quantify nonlinear modal interaction near critical equilibria. This study focuses on the analysis of second-order modal interaction and the study of nonlinear aspects of system behavior which are of interest to the design and location of system controllers. A systematic approach to deriving second-order NF representations in the neighborhood of equilibrium points is presented. On the basis of this model, nonlinear interaction measures are then obtained to assess the extent and distribution of nonlinearity in the system. Analytical criteria are developed to predict the existence of nonlinear modal interactions that significantly affect system dynamic performance. To demonstrate the effect of nonlinear interaction, a case study of locating controllers to damp electromechanical oscillations is developed. Examples of application of the developed approaches on a two-area four-machine test system are presented to determine the strength of nonlinear interactions in the system response, and estimating its effects on system dynamic performance and control design.