Higher-Order Normal Form Analysis of Stressed Power Systems: A Fundamental Study

Abstract

A systematic procedure based on normal form theory is proposed to investigate nonlinear effects arising from the perturbation model of the power system dynamic representation. Using this method, a third-order model of the power system is proposed in which weak system nonlinearities are explicitly represented. Analytical expressions are then obtained that provide approximate solutions to system performance near a singularity, and techniques for interpreting these solutions in terms of modal functions are given. New insights into the nature of nonlinear oscillations are offered and criteria for characterizing nonlinear effects are discussed. Attention is also focused on assessing the effect of system stress on nonlinear dynamic performance. The application of these procedures is illustrated on a single-machine infinite-bus system using a classical model, but the results can be extended to accommodate more complex system representations. Numerical calculations are presented and discussed to check the accuracy of the method of analysis.

A Novel Method for Accelerating the Analysis of Nonlinear Behaviour of Power Grids using Normal Form Technique

“…By prescribing as above and solving for linear and nonlinear static solutions, P NL is obtained from (14). Then from (6) and (12) we can write set of linear equations as…”

A Comparative Analysis of Methodologies for the Representation of Nonlinear Oscillations in Dynamic Systems

“…This difference is due principally to the linear approximation; however, the degree of accuracy is a function of level stress and initial perturbation in the system [9]. The normal forms and modal series methods both are more specific for analyzing small perturbation and lower stress levels introduced to the power system.…”

A New Fast Track to Nonlinear Modal Analysis of Power System Using Normal Form

“…is the factorial of integer N . Furthermore, the number of coefficients C pqr and D pqrs in the modal model (7) that have to be computed using (8) is again N c . Equation (15) shows that the computational burden increases with the power of four of the number of degrees of freedom of the initial system.…”

“…As a result, most studies are based on inclusion of 2nd order terms with few works on inclusion of third order terms. Current researches emphasize the deficits of 2nd order NF in the light of nonlinearly growing power systems [5], [8], [18]. Moreover, 2nd order NF cannot be used for stability studies [6].…”