The holomorphic embedding method(HEM)stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables.The key idea behind the HEM is to ...The holomorphic embedding method(HEM)stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables.The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion involving one or multiple embedded complex variables.This transformation empowers the utilization of complex analysis tools to tackle the original problem effectively.Since the 2010s,the HEM has been applied to steady-state and dynamic problems in power systems and has shown superior convergence and robustness compared to traditional numerical methods.This paper provides a comprehensive review on the diverse applications of the HEM and its variants reported by the literature in the past decade.The paper discusses both the strengths and limitations of these HEMs and provides guidelines for practical applications.It also outlines the challenges and potential directions for future research in this field.展开更多
What is known as StahPs Theorem in power engineering circles is used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to powerflow(PF)problem.In this two-part paper,we examine i...What is known as StahPs Theorem in power engineering circles is used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to powerflow(PF)problem.In this two-part paper,we examine in more detail the implications of Stahl's theorems to both theoretical and numerical convergence for a wider range of problems to which these theorems are now being applied.We show that the difference between StahPs extremal domain and the function's domain is responsible for theoretical nonconvergence and that the fundamental cause of numerical nonconvergence is the magnitude of logarithmic capacity of the branch cut,a concept central to understanding nonconvergence.We introduce theorems using the necessary mathematical parlance and then translate the language to show its implications to convergence of nonlinear problems in general and specifically to the PF problem.We show that,among other possibilities,the existence of Chebotarev points,which are embedding specific,are a possible theoretical impediment to convergence・The theoretical foundation of Part I is necessary for understanding the numerical behavior of HEM discussed in Part II.展开更多
What has become known as Stahl's Theorem in power-engineering circles has been used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to the power-flow problem.In this,the se...What has become known as Stahl's Theorem in power-engineering circles has been used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to the power-flow problem.In this,the second part of a two-part paper,we examine implications to numerical convergence of the HEM and the numerical properties of a Pade approximant algorithm.We show that even if the point of interest is within the convergence domain,numerical convergence of the sequence of Pade approximants computed with finite precision is not guaranteed.We propose a convergence factor equation that can be used to both estimate the convergence rate and the capacity of the branch cut.We also show that the study of convergence properties of the Pade approximant is the study of the location of the branch-points of the function,which in turn dictate branch-cut topology and capacity and,therefore,convergence rate.展开更多
The power flow(PF)calculation for AC/DC hybrid systems based on voltage source converter(VSC)plays a crucial role in the operational analysis of the new energy system.The fast and flexible holomorphic embedding(FFHE)P...The power flow(PF)calculation for AC/DC hybrid systems based on voltage source converter(VSC)plays a crucial role in the operational analysis of the new energy system.The fast and flexible holomorphic embedding(FFHE)PF method,with its non-iterative format founded on complex analysis theory,exhibits superior numerical performance compared with traditional iterative methods.This paper aims to extend the FFHE method to the PF problem in the VSC-based AC/DC hybrid system.To form the AC/DC FFHE PF method,an AC/DC FFHE model with its solution scheme and a sequential AC/DC PF calculation framework are proposed.The AC/DC FFHE model is established with a more flexible form to incorporate multiple control strategies of VSC while preserving the constructive and deterministic properties of original FFHE to reliably obtain operable AC/DC solutions from various initializations.A solution scheme for the proposed model is provided with specific recursive solution processes and accelerated Padéapproximant.To achieve the overall convergence of AC/DC PF,the AC/DC FFHE model is integrated into the sequential calculation framework with well-designed data exchange and control mode switching mechanisms.The proposed method demonstrates significant efficiency improvements,especially in handling scenarios involving control mode switching and multiple recalculations.In numerical tests,the superiority of the proposed method is confirmed through comparisons of accuracy and efficiency with existing methods,as well as the impact analyses of different initializations.展开更多
We propose an approach to learning sample embedding for analyzing multi-dimensional datasets.The basic idea is to extract rules from the given dataset and learn the embedding for each sample based on the rules it sati...We propose an approach to learning sample embedding for analyzing multi-dimensional datasets.The basic idea is to extract rules from the given dataset and learn the embedding for each sample based on the rules it satisfies.The approach can filter out pattern-irrelevant attributes,leading to significant visual structures of samples satisfying the same rules in the projection.In addition,analysts can understand a visual structure based on the rules that the involved samples satisfy,which improves the projection’s pattern interpretability.Our research involves two methods for achieving and applying the approach.First,we give a method to learn rule-based embedding for each sample.Second,we integrate the method into a system to achieve an analytical workflow.Cases on real-world dataset and quantitative experiment results show the usability and effectiveness of our approach.展开更多
K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度...K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度量的二维单项式多面体与具有平坦度量的复欧氏空间不存在公共的K hler子流形,即二维单项式多面体与复欧氏空间是不相关的。展开更多
随着分布式新能源大量接入配电网,主网潮流变轻,静态电压偏高且难以控制,而现有的集中式光伏电站静止无功发生器(static var generator,SVG)设备的无功补偿能力却未充分利用。针对以上问题,提出一种基于改进全纯嵌入法的含光伏电站主动...随着分布式新能源大量接入配电网,主网潮流变轻,静态电压偏高且难以控制,而现有的集中式光伏电站静止无功发生器(static var generator,SVG)设备的无功补偿能力却未充分利用。针对以上问题,提出一种基于改进全纯嵌入法的含光伏电站主动调节的无功补偿策略,对传统全纯嵌入潮流法进行改进,构建改进全纯嵌入潮流模型,充分利用集中式光伏电站的无功补偿能力,并进行额外无功补偿设备的选址定容,提高电力系统电压稳定性,降低无功补偿设备的投资成本。以改进后的IEEE 39节点系统为算例,仿真结果表明,电力系统电压稳定性得到有效提高,同时无功补偿装置配置总容量减少了约20%。展开更多
文摘The holomorphic embedding method(HEM)stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables.The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion involving one or multiple embedded complex variables.This transformation empowers the utilization of complex analysis tools to tackle the original problem effectively.Since the 2010s,the HEM has been applied to steady-state and dynamic problems in power systems and has shown superior convergence and robustness compared to traditional numerical methods.This paper provides a comprehensive review on the diverse applications of the HEM and its variants reported by the literature in the past decade.The paper discusses both the strengths and limitations of these HEMs and provides guidelines for practical applications.It also outlines the challenges and potential directions for future research in this field.
基金supported by the Science and Technology Project of SGCC(No.5455HJ160007).
文摘What is known as StahPs Theorem in power engineering circles is used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to powerflow(PF)problem.In this two-part paper,we examine in more detail the implications of Stahl's theorems to both theoretical and numerical convergence for a wider range of problems to which these theorems are now being applied.We show that the difference between StahPs extremal domain and the function's domain is responsible for theoretical nonconvergence and that the fundamental cause of numerical nonconvergence is the magnitude of logarithmic capacity of the branch cut,a concept central to understanding nonconvergence.We introduce theorems using the necessary mathematical parlance and then translate the language to show its implications to convergence of nonlinear problems in general and specifically to the PF problem.We show that,among other possibilities,the existence of Chebotarev points,which are embedding specific,are a possible theoretical impediment to convergence・The theoretical foundation of Part I is necessary for understanding the numerical behavior of HEM discussed in Part II.
基金supported by the Science and Technology Project of SGCC(No.5455HJ160007).
文摘What has become known as Stahl's Theorem in power-engineering circles has been used to justify a convergence guarantee of the Holomorphic Embedding Method(HEM)as it applies to the power-flow problem.In this,the second part of a two-part paper,we examine implications to numerical convergence of the HEM and the numerical properties of a Pade approximant algorithm.We show that even if the point of interest is within the convergence domain,numerical convergence of the sequence of Pade approximants computed with finite precision is not guaranteed.We propose a convergence factor equation that can be used to both estimate the convergence rate and the capacity of the branch cut.We also show that the study of convergence properties of the Pade approximant is the study of the location of the branch-points of the function,which in turn dictate branch-cut topology and capacity and,therefore,convergence rate.
文摘The power flow(PF)calculation for AC/DC hybrid systems based on voltage source converter(VSC)plays a crucial role in the operational analysis of the new energy system.The fast and flexible holomorphic embedding(FFHE)PF method,with its non-iterative format founded on complex analysis theory,exhibits superior numerical performance compared with traditional iterative methods.This paper aims to extend the FFHE method to the PF problem in the VSC-based AC/DC hybrid system.To form the AC/DC FFHE PF method,an AC/DC FFHE model with its solution scheme and a sequential AC/DC PF calculation framework are proposed.The AC/DC FFHE model is established with a more flexible form to incorporate multiple control strategies of VSC while preserving the constructive and deterministic properties of original FFHE to reliably obtain operable AC/DC solutions from various initializations.A solution scheme for the proposed model is provided with specific recursive solution processes and accelerated Padéapproximant.To achieve the overall convergence of AC/DC PF,the AC/DC FFHE model is integrated into the sequential calculation framework with well-designed data exchange and control mode switching mechanisms.The proposed method demonstrates significant efficiency improvements,especially in handling scenarios involving control mode switching and multiple recalculations.In numerical tests,the superiority of the proposed method is confirmed through comparisons of accuracy and efficiency with existing methods,as well as the impact analyses of different initializations.
文摘We propose an approach to learning sample embedding for analyzing multi-dimensional datasets.The basic idea is to extract rules from the given dataset and learn the embedding for each sample based on the rules it satisfies.The approach can filter out pattern-irrelevant attributes,leading to significant visual structures of samples satisfying the same rules in the projection.In addition,analysts can understand a visual structure based on the rules that the involved samples satisfy,which improves the projection’s pattern interpretability.Our research involves two methods for achieving and applying the approach.First,we give a method to learn rule-based embedding for each sample.Second,we integrate the method into a system to achieve an analytical workflow.Cases on real-world dataset and quantitative experiment results show the usability and effectiveness of our approach.
文摘随着分布式新能源大量接入配电网,主网潮流变轻,静态电压偏高且难以控制,而现有的集中式光伏电站静止无功发生器(static var generator,SVG)设备的无功补偿能力却未充分利用。针对以上问题,提出一种基于改进全纯嵌入法的含光伏电站主动调节的无功补偿策略,对传统全纯嵌入潮流法进行改进,构建改进全纯嵌入潮流模型,充分利用集中式光伏电站的无功补偿能力,并进行额外无功补偿设备的选址定容,提高电力系统电压稳定性,降低无功补偿设备的投资成本。以改进后的IEEE 39节点系统为算例,仿真结果表明,电力系统电压稳定性得到有效提高,同时无功补偿装置配置总容量减少了约20%。
