Modal Series Method Research Articles

Analysis of Nonlinear Torsional Dynamics Using Second-Order Solutions

Based on the modal series method, this paper derives the second- and first-order solutions of torques for investigating nonlinear torsional dynamics. The derivatives of the two types of solutions are compared to explain the advantage of the second-order solutions. The index is given for evaluating the feasibility of solutions. Subsequently, several nonlinearity indices are defined to quantify the effects of nonlinear modal interactions on torsional dynamics, and the suitable indices are determined for analyzing nonlinear torsional dynamics. The systematic method is developed for the analysis of nonlinear torsional dynamics. Furthermore, the concept of nonlinear modal interactions is extended to deal with both the fundamental and the combination modes; the nonlinearity contribution factors are emphasized. The study is implemented on two modified cases from the IEEE first benchmark model, which validates the presented method for investigating torsional dynamics in the stressed case and gives new engineering insights into nonlinear torsional dynamics.

Extending the perturbation technique to the modal representation of nonlinear systems

After a brief review of perturbation technique, using this method an approach is developed to represent and study the behavior of nonlinear dynamic power systems. For the first time in this field, perturbation technique is applied to obtain an approximate closed form expression for the zero input response of stressed power systems. In order to show the superiority of the proposed method, it has been applied to a typical nonlinear system which is a single machine infinite bus (SMIB) power system with unified power flow controller (UPFC). The accuracy and competency of this method in comparison with Modal Series method will also be validated.

Analyzing dynamic performance of stressed power systems in vicinity of instability by modal series method

AbstractHighly stressed power systems exhibit complex dynamic behaviors such as inter‐area oscillations when subjected to large disturbances. In such conditions, nonlinear effects have dominant role in determining dynamic response of the systems. In this paper by using modal series method, dynamic behaviors of the stressed power systems in severe conditions and near instability have been studied. Also two measures, mode dominance measure (MDM) and most perturbed machine factor (MPF) have been introduced. They determine the most dominant modes and identify the most perturbed generators when the system is subjected to a given fault. Contribution factors have been used to show the links between identified modes and machines from the analysis. Time domain simulation has been helped for validation of the results. By using similarity transformation, state variables have been represented in modal space and utilized to check the results. The studies are carried out on the IEEE 50‐generator test system which demonstrates a wide range of dynamic characteristics at different loading levels and fault scenarios. Copyright © 2008 John Wiley & Sons, Ltd.

Validation of power system non-linear modal analysis methods

The validity of two power system non-linear modal analysis methods, i.e. normal form method and modal series method, are investigated in this work. The second-order participation factors are derived for modal series method and qualitatively compared with that of normal form method. To evaluate the validity of analysis methods, a valid region that satisfies certain error index is defined. The test results of a two-area four-generator power system show that the valid regions of both modal series method and linear modal method are not affected by second-order resonance condition, while that of normal form method is affected significantly. It is found that as the system stress increases, the error index and its growing speed of modal series method are the smallest, and that of normal form method take second place. A non-linearity index for normal form method is defined based on the original index and its validity is verified by the case studies using the same test system.