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

Abstract

-In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincaré transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.

Real Power Modulation Strategies for Transient Stability Control

“…Although the following methods are not discussed at length here, they have also attracted research interest. In [185], Wang et al study stability analysis techniques based on Carleman linearization. In [186], Loparo and Blankenship approximate the system dynamics using a Volterra series.…”

Transient Stability Analysis for a Multi-VSC Parallel System Based on the CFND Method

“…[11] proposed a normal form method that extends to the cubic term and is applied to transient stability analysis of a 2-zone 4-machine system. The Kalman linear method involves embedding a nonlinear system into an infinite dimensional linear model and analyzing it using linear theory to obtain information such as higher-order modes and nonlinear participation factors [12]. However, most of the current high-order modal analysis methods are limited to converting high-order nonlinear systems into the superposition of linear modes, and then using mature linear methods for analysis, making it difficult to provide specific ROA and effective transient stability judgment conclusions.…”