{"title":"Securing voltage stability in power grids via holomorphic dynamics","authors":"Bai Cui , Xu Andy Sun","doi":"10.1016/j.automatica.2025.112158","DOIUrl":null,"url":null,"abstract":"<div><div>Voltage instability is a complex dynamic phenomenon in today’s electric power systems. The onset of voltage instability is usually related to the loss of proper solutions to the nonlinear power flow equations, which express the fundamental law governing electric power and voltages in a power grid. Thus, studying the solvability of the power flow equations is at the heart of the voltage stability problem. In this paper, we transform the solvability problem of the power flow equations to a stability problem of a discrete dynamical system defined by a holomorphic mapping in several complex variables. Then, we show a general result on the fixed points of holomorphic functions invariant in a polydisc. Using these analytical tools, we obtain a strong explicit condition that certifies the existence and uniqueness of a proper solution to the nonlinear power flow equations. The new condition reveals in a precise way the interplay between voltage instability, the electrical and topological structures of the power grid, and the electric load characteristics. The new condition is proven to be stronger than existing ones. Extensive computational experiments further demonstrate the strength of the proposed condition for securing real-time voltage stability of large-scale high-voltage electric transmission systems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112158"},"PeriodicalIF":4.8000,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109825000494","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Voltage instability is a complex dynamic phenomenon in today’s electric power systems. The onset of voltage instability is usually related to the loss of proper solutions to the nonlinear power flow equations, which express the fundamental law governing electric power and voltages in a power grid. Thus, studying the solvability of the power flow equations is at the heart of the voltage stability problem. In this paper, we transform the solvability problem of the power flow equations to a stability problem of a discrete dynamical system defined by a holomorphic mapping in several complex variables. Then, we show a general result on the fixed points of holomorphic functions invariant in a polydisc. Using these analytical tools, we obtain a strong explicit condition that certifies the existence and uniqueness of a proper solution to the nonlinear power flow equations. The new condition reveals in a precise way the interplay between voltage instability, the electrical and topological structures of the power grid, and the electric load characteristics. The new condition is proven to be stronger than existing ones. Extensive computational experiments further demonstrate the strength of the proposed condition for securing real-time voltage stability of large-scale high-voltage electric transmission systems.
期刊介绍：
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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