AI 中文总结
针对基于换流器的电力系统的谐波稳定性，提出结合BIBO与内部稳定性的控制理论定义，证明非线性系统局部谐波稳定性由其LTP近似的稳定性蕴含，开发HSS框架与LMI条件并在网侧换流器系统验证其有效性。
AI 中文摘要
谐波相互作用已成为基于换流器的电力系统（CBPS）中一种具有决定性意义的动态稳定性现象，但迄今为止，尚未有针对非线性动力系统语境下谐波稳定性概念的形式化定义。本文提出一种谐波稳定性的定义，该定义结合了两种标准稳定性概念，即针对任意标称周期轨迹的有界输入有界输出（BIBO）稳定性与内部稳定性特性。此外，本文严格证明，非线性CBPS的任意标称周期轨迹的局部谐波稳定性，由其线性时周期（LTP）近似的稳定性特性所蕴含。为实现可计算的稳定性评估，本文开发了一种基于LTP模型的谐波状态空间（HSS）表示的框架，具体而言，提供了用于验证谐波稳定性的时不变线性矩阵不等式（LMI）条件。所提方法在一个网侧换流器系统上得到验证，基于HSS的分析数值证实了该系统在周期运行轨迹附近的谐波稳定性。
英文摘要
Harmonic interactions have become a defining dynamic stability phenomenon in converter-based power systems (CBPSs). However, a formalization of the notion of harmonic stability in the context of nonlinear dynamical systems is not available thus far. In this paper, we propose a definition of harmonic stability formulated as a combination of two standard stability notions, namely, bounded-input bounded-output (BIBO) and internal stability properties with respect to any nominal periodic trajectory. Moreover, we rigorously show that the local harmonic stability of any nominal periodic trajectory of nonlinear CBPSs is implied by the stability properties of its linear time-periodic (LTP) approximation. In addition, to enable computationally tractable stability assessment, we develop a framework based on harmonic state-space (HSS) representations of LTP models. In particular, we provide time-invariant linear matrix inequality (LMI) conditions to certify harmonic stability. The proposed methodology is illustrated on a grid-following converter system, where the HSS-based analysis numerically confirms harmonic stability around the periodic operating trajectory.
