AI 中文总结
研究电网稳定性与对称性关系，创新运用群论，发现电网对称性含网络和组件对称性两方面，得出不同类型电网稳定性排序及组件对称性对稳定性的影响，对含分布式资源和可控发电机的现代电网控制有重要意义。
AI 中文摘要
电网稳定性主要取决于多个发电机组的同步。目前，电网稳定性与对称性之间的关系尚不明晰。本文创新性地运用群论这一数学工具填补了研究空白。发现电网对称性涉及网络和组件对称性两方面，分别反映网络结构和发电机组的同质性。电网稳定性与网络和组件对称性密切相关，相应自同构群和对称子群阶数分别反映其对称程度。从网络对称性看，四发电机电网稳定性排序为K4 > C4 > K13 > R4 > P4 > X4 ，与网络对称性排序一致。从组件对称性看，电网稳定性大多受益于组件对称性提升，但R4 是例外，建议避免单个发电机的集中作用。这些结论对含分布式资源和可控发电机的现代电网控制有重要意义。
英文摘要
The stability of power grids principally depends on the synchronization of multiple generating units. So far, the relationship between grid stability and symmetries remains unclear. This article fills in the research gap by innovatively using the mathematical tool of group theory. We find that grid symmetries involve two aspects-network and component symmetries, which reflect the homogeneities of network structures and generating units, respectively. As disclosed, the stability of power grids has a tight bearing on network and component symmetries, where corresponding automorphism group and symmetric subgroup orders reflect their levels of symmetries, respectively. In the perspective of network symmetries, where grid stability and synchronization speed are dictated by the algebraic connectivity, the stability ranking list of grids with four generators is K4 > C4 > K13 > R4 > P4 > X4, which fully agrees with that of network symmetries. In terms of component symmetries, the stability of power grids largely benefits from improved component symmetries yet with R4 as an exceptional case, where it is recommended to avoid the centralized effort of a single generator. These conclusions have significant implications for the control of modern power grids with distributed resources and controllable generators, including energy storage and renewable power generators interfaced by grid-following/-forming converters.
Comments22 pages, 13 figures
