Inclusion of Higher Order Terms for Small-Signal (Modal) Analysis: Committee Report—Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis

Abstract

Abstract-This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.Index Terms-Method of normal forms, modal analysis, modal damping, modal frequency, nonlinear modal interaction.

Small-signal stability of wind power system with full-load converter interfaced wind turbines

“…Thus, the results from the modal analysis are only valid in proximity of the linearization point and should be perceived as a snapshot of the dynamic system behavior. The method of normal forms offer a framework for extending the modal analysis to include higher order terms and thereby capture dynamics not captured by a linear model [27], [28]. This method is especially important for stressed, highly nonlinear power systems which are not accurately described by the linear approximation in (1).…”

Research of the Mechanism of Low Frequency Oscillation Based on Dynamic Damping Effect

“…However, the bifurcation theory which is still at the exploratory stage cannot be applied to the large-scale system. Quadratic term is used to study the interactive effect between deferent modes based on the theory of normal forms method [15,16] and the modal series method [17,18]. However, these methods are complicated, and they can only reflect the nonlinear characteristics of equilibrium point and points nearby, but cannot count greater-range nonlinear factors in.…”

An Improved Poincaré-like Carleman Linearization Approach for Power System Nonlinear Analysis

“…It is shown that the eigenvalue space of Carleman linear model is formed by the eigenvalues from the linear space of the matrix 1 1 A , 2 1 A and the matrix 1 A N , which contain eigenvalues associated with the higher-order modal interaction.…”

“…Reconsider (8) and (12), it is found that the higher-order terms 1 A k have been replaced by 1 A k in the process of obtaining eigenvalues and solution. In other words, the 2 nd order combined eigenvalues belong to 2 1 A but do not belong to 1 2 A .…”

“…It is shown that the nonlinear effect should not be neglected, and quite a lot of researches are conducted to deal with this issue, e.g., normal form and modal series [1][2][3], or other nonlinear analysis methods are developed to perform higher order modal analysis of nonlinear power system model. However, these methods still deal with the state equations of original model, in which the complex nonlinear system theory has to be used.…”