电力系统自动化2026，Vol.50Issue(5)：110-124,15.DOI:10.7500/AEPS20240926001
Hilbert泛函视角下谐波线性化方法的特性分析
Characteristic Analysis of Harmonic Linearization Method from Perspective of Hilbert Functional
摘要
Abstract
The harmonic linearization method is an extensively utilized method in the field of broadband oscillation analysis of new power systems.However,the problem of unclear applicability arises in the application of this method.To this end,the harmonic linearization method is analyzed from the perspective of Hilbert functional.Firstly,the existing real physical systems can be abstracted as an idealized two-terminal algebraic-component system.Aiming at the orthogonality issues of multi-frequency inputs,combined with the Hilbert basis defined by the greatest common factor,the mathematical essence of harmonic linearization method is explained,which is the projection of high-dimensional function space to low-dimensional subspace.Secondly,the harmonic linearization method is explained to describe the approximate linear characteristics of the system in the desired base direction,which is different from the traditional linearization method.Thirdly,it is illustrated that the harmonic linearization method is only an approximate analysis method.The stability of the concerned components of the approximate system cannot guarantee the stability of the original high-dimensional system or the components that are not concerned.Meanwhile,the applicability of the method is analyzed in the bounded-input bounded-output(BIBO)system,the small gain stable system and the grid-connected converter system,Finally,a norm-based evaluation method is given for evaluating the approximation degree of harmonic linearization of polynomial systems.关键词
新型电力系统/宽频振荡/谐波线性化/Hilbert泛函/投影/近似分析方法/多项式系统Key words
new power system/broadband oscillation/harmonic linearization/Hilbert functional/projection/approximate analysis method/polynomial system引用本文复制引用
汪云涛,薛安成,张哲,冯宇辰..Hilbert泛函视角下谐波线性化方法的特性分析[J].电力系统自动化,2026,50(5):110-124,15.基金项目
智能电网国家科技重大专项(2030)资助项目(2024ZD0801100). This work is supported by Smart Grid-National Science and Technology Major Project(2030)of China(No.2024ZD0801100). （2030）
