Power System Nonlinear Modal Analysis Using Computationally Reduced Normal Form Method

Abstract

Increasing nonlinearity in today’s grid challenges the conventional small-signal (modal) analysis (SSA) tools. For instance, the interactions among modes, which are not captured by SSA, may play significant roles in a stressed power system. Consequently, alternative nonlinear modal analysis tools, notably Normal Form (NF) and Modal Series (MS) methods are being explored. However, they are computation-intensive due to numerous polynomial coefficients required. This paper proposes a fast NF technique for power system modal interaction investigation, which uses characteristics of system modes to carefully select relevant terms to be considered in the analysis. The Coefficients related to these terms are selectively computed and the resulting approximate model is computationally reduced compared to the one in which all the coefficients are computed. This leads to a very rapid nonlinear modal analysis of the power systems. The reduced model is used to study interactions of modes in a two-area power system where the tested scenarios give same results as the full model, with about 70% reduction in computation time.

Nonlinear Technologies in Advanced Power Systems: Analysis and Control

“…The contribution of Ugwuanyi and others is reported in [6], where a very interesting approach in the modal analysis of large-scale power systems is presented. Modal analysis has been a widely discussed theme in the study of the dynamical behavior of the power plant.…”

Fundamental study of oscillations in the Nigerian power system

“…Where 𝑢 𝑖𝑗 is the element in the ith row and jth column of the right eigenvector U. If higher-order terms are considered in the linearisation, say order 2, a specific transformation [17,18,19] is applied, in addition to the linear transformation, and the solution is obtained in another new coordinate. At last, the solution will be of the form:…”

“…The details of the transformation leading to (8) overshoot the mark of the present work. Interested readers can please refer to [17,18,19]. However, important developments from (8) used in this work are presented.…”

“…The detailed techniques for confirming modal interaction in an interconnected system have been documented in [17,18,19]. Those techniques cannot be treated rigorously within the framework of the present paper.…”

Fundamental Study of Oscillations in the Nigerian Power System

“…The details of the transformation leading to (8) overshoot the mark of the present work. Interested readers can please refer to [17], [18]. However, important developments from (8) used in this work are presented.…”