A Crank–Nicolson Galerkin approach to the analysis of electromechanical oscillations in stressed power systems

The primary goal of this research is directed toward the study and characterization of nonlinear power system transient phenomena following large perturbations. A novel analytical framework based on a nonlinear Galerkin method and a finite difference scheme is introduced. The proposed method is designed primarily to capture strong nonlinear behavior and may be applied to model reduction, nonlinear characterization and control design.A nonlinear system model is first developed by Galerkin projections onto basis of eigenfunctions obtained from the proper orthogonal decomposition (POD) method that includes the representation of higher-order nonlinear effects. The scheme is coupled with a modified Crank–Nicolson finite difference method to characterize the nonlinear system dynamics following severe perturbations. Several extensions and generalizations of the method are suggested and tested and criteria are then developed for systematically analyzing complicated system oscillations.The theory is illustrated on two test power systems. Results obtained using the Galerkin procedures are compared with transient stability simulations. Factors that influence the quality of the nonlinear Galerkin approximations are discussed and issues concerning the implementation of the method and numerical calculations are also highlighted.

► A new semi-numerical technique for the analysis and characterization of electromechanical oscillations in power systems that combines the Crank–Nicolson Galerkin approach with proper orthogonal decomposition is proposed. ► The method can be used to analyze complicated phenomena and is shown to be robust over a range of operating conditions and is well suited for treating large amplitude motions. ► Preliminary results of this study are found to be in quantitative agreement with the exact system response even at conditions far from normal behavior. ► The proposed representation allows the error estimate to be minimized and yields a low-dimensional dynamical model with the smallest possible number of degrees of freedom.