How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computatio...How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computational burden of probabilistic security assessment is even more unimaginable.In order to solve such problems,a security region(SR)methodology is proposed,which is a brand-new methodology developed on the basis of the classical point-wise method.Tianjin University has been studying the SR methodology since the 1980s,and has achieved a series of original breakthroughs that are described in this paper.The integrated SR introduced in this paper is mainly defined in the power injection space,and includes SRs to ensure steady-state security,transient stability,static voltage stability,and smalldisturbance stability.These SRs are uniquely determined for a given network topology(as well as location and clearing process for transient faults)and given system component parameters,and are irrelevant to operation states.This paper presents 11 facts and related remarks to introduce the basic concepts,composition,dynamics nature,and topological and geometric characteristics of SRs.It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way.Thus,this article provides support for the systematic understanding,future research,and applications of SRs.The most critical finding on the topological and geometric characteristics of SRs is that,within the scope of engineering concern,the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes.Based on this finding,the calculation time for power system probabilistic security assessment(i.e.,risk analysis)and power system optimization with security constraints can be decreased by orders of magnitude.展开更多
This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hype...This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.展开更多
In an integrated electricity-gas system(IEGS),load fluctuations affect not only the voltage in the power system but also the gas pressure in the natural gas system.The static voltage stability region(SVSR)method is a ...In an integrated electricity-gas system(IEGS),load fluctuations affect not only the voltage in the power system but also the gas pressure in the natural gas system.The static voltage stability region(SVSR)method is a tool for analyzing the overall static voltage stability in a power system.However,in an IEGS,the SVSR boundary may be overly optimistic because the gas pressure may collapse before the voltage collapses.Thus,the SVSR method cannot be directly applied to an IEGS.In this paper,the concept of the SVSR is extended to the IEGS-static stability region(SSR)while considering voltage and gas pressure.First,criteria for static gas pressure stability in a natural gas system are proposed,based on the static voltage stability criteria in a power system.Then,the IEGS-SSR is defined as a set of active power injections that satisfies multi-energy flow(MEF)equations and static voltage and gas pressure stability constraints in the active power injection space of natural gas-fired generator units(NGUs).To determine the IEGSSSR,a continuation MEF(CMEF)method is employed to trace the boundary point in one specific NGU scheduling direction.A multidimensional hyperplane sampling method is also proposed to sample the NGU scheduling directions evenly.The obtained boundary points are further used to form the IEGSSSR in three-dimensional(3D)space via a Delaunay triangulation hypersurface fitting method.Finally,the numerical results of typical case studies are presented to demonstrate that the proposed method can effectively form the IEGS-SSR,providing a tool for IEGS online monitoring and dispatching.展开更多
Background External knowledge representations play an essential role in knowledge-based visual question and answering to better understand complex scenarios in the open world.Recent entity-relationship embedding appro...Background External knowledge representations play an essential role in knowledge-based visual question and answering to better understand complex scenarios in the open world.Recent entity-relationship embedding approaches are deficient in representing some complex relations,resulting in a lack of topic-related knowledge and redundancy in topic-irrelevant information.Methods To this end,we propose MKEAH:Multimodal Knowledge Extraction and Accumulation on Hyperplanes.To ensure that the lengths of the feature vectors projected onto the hyperplane compare equally and to filter out sufficient topic-irrelevant information,two losses are proposed to learn the triplet representations from the complementary views:range loss and orthogonal loss.To interpret the capability of extracting topic-related knowledge,we present the Topic Similarity(TS)between topic and entity-relations.Results Experimental results demonstrate the effectiveness of hyperplane embedding for knowledge representation in knowledge-based visual question answering.Our model outperformed state-of-the-art methods by 2.12%and 3.24%on two challenging knowledge-request datasets:OK-VQA and KRVQA,respectively.Conclusions The obvious advantages of our model in TS show that using hyperplane embedding to represent multimodal knowledge can improve its ability to extract topic-related knowledge.展开更多
Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible c...Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.展开更多
针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityreg...针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityregion,SVSR)临界点,然后基于该临界点处空间切向量的空间角与最大空间角阈值的关系,对SVSRB进行初始分段近似,以SVSR临界点到初始近似边界的距离与最大距离误差阈值的关系为依据,对初始近似边界进行二次近似,计及SVSRB曲率的变化,得到更为精确的SVSR分段超平面近似边界,实现SVSRB近似解析表达式的构建,该方法可有效提高SVSRB近似精度,增强电力系统电压稳定的态势感知能力。最后,将所提方法应用于WECC3机9节点测试系统和欧洲电网13659节点测试系统,结果表明,所提方法可有效实现SVSRB精确近似解析表达和准确构建。展开更多
文摘How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computational burden of probabilistic security assessment is even more unimaginable.In order to solve such problems,a security region(SR)methodology is proposed,which is a brand-new methodology developed on the basis of the classical point-wise method.Tianjin University has been studying the SR methodology since the 1980s,and has achieved a series of original breakthroughs that are described in this paper.The integrated SR introduced in this paper is mainly defined in the power injection space,and includes SRs to ensure steady-state security,transient stability,static voltage stability,and smalldisturbance stability.These SRs are uniquely determined for a given network topology(as well as location and clearing process for transient faults)and given system component parameters,and are irrelevant to operation states.This paper presents 11 facts and related remarks to introduce the basic concepts,composition,dynamics nature,and topological and geometric characteristics of SRs.It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way.Thus,this article provides support for the systematic understanding,future research,and applications of SRs.The most critical finding on the topological and geometric characteristics of SRs is that,within the scope of engineering concern,the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes.Based on this finding,the calculation time for power system probabilistic security assessment(i.e.,risk analysis)and power system optimization with security constraints can be decreased by orders of magnitude.
文摘This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.
基金funded by the National Natural Science Foundation of China(52222704 and 52177107).
文摘In an integrated electricity-gas system(IEGS),load fluctuations affect not only the voltage in the power system but also the gas pressure in the natural gas system.The static voltage stability region(SVSR)method is a tool for analyzing the overall static voltage stability in a power system.However,in an IEGS,the SVSR boundary may be overly optimistic because the gas pressure may collapse before the voltage collapses.Thus,the SVSR method cannot be directly applied to an IEGS.In this paper,the concept of the SVSR is extended to the IEGS-static stability region(SSR)while considering voltage and gas pressure.First,criteria for static gas pressure stability in a natural gas system are proposed,based on the static voltage stability criteria in a power system.Then,the IEGS-SSR is defined as a set of active power injections that satisfies multi-energy flow(MEF)equations and static voltage and gas pressure stability constraints in the active power injection space of natural gas-fired generator units(NGUs).To determine the IEGSSSR,a continuation MEF(CMEF)method is employed to trace the boundary point in one specific NGU scheduling direction.A multidimensional hyperplane sampling method is also proposed to sample the NGU scheduling directions evenly.The obtained boundary points are further used to form the IEGSSSR in three-dimensional(3D)space via a Delaunay triangulation hypersurface fitting method.Finally,the numerical results of typical case studies are presented to demonstrate that the proposed method can effectively form the IEGS-SSR,providing a tool for IEGS online monitoring and dispatching.
基金Supported by National Nature Science Foudation of China(61976160,61906137,61976158,62076184,62076182)Shanghai Science and Technology Plan Project(21DZ1204800)。
文摘Background External knowledge representations play an essential role in knowledge-based visual question and answering to better understand complex scenarios in the open world.Recent entity-relationship embedding approaches are deficient in representing some complex relations,resulting in a lack of topic-related knowledge and redundancy in topic-irrelevant information.Methods To this end,we propose MKEAH:Multimodal Knowledge Extraction and Accumulation on Hyperplanes.To ensure that the lengths of the feature vectors projected onto the hyperplane compare equally and to filter out sufficient topic-irrelevant information,two losses are proposed to learn the triplet representations from the complementary views:range loss and orthogonal loss.To interpret the capability of extracting topic-related knowledge,we present the Topic Similarity(TS)between topic and entity-relations.Results Experimental results demonstrate the effectiveness of hyperplane embedding for knowledge representation in knowledge-based visual question answering.Our model outperformed state-of-the-art methods by 2.12%and 3.24%on two challenging knowledge-request datasets:OK-VQA and KRVQA,respectively.Conclusions The obvious advantages of our model in TS show that using hyperplane embedding to represent multimodal knowledge can improve its ability to extract topic-related knowledge.
基金the National Natural Science Foundation of China (Grant No. 10671009)
文摘Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.
文摘针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityregion,SVSR)临界点,然后基于该临界点处空间切向量的空间角与最大空间角阈值的关系,对SVSRB进行初始分段近似,以SVSR临界点到初始近似边界的距离与最大距离误差阈值的关系为依据,对初始近似边界进行二次近似,计及SVSRB曲率的变化,得到更为精确的SVSR分段超平面近似边界,实现SVSRB近似解析表达式的构建,该方法可有效提高SVSRB近似精度,增强电力系统电压稳定的态势感知能力。最后,将所提方法应用于WECC3机9节点测试系统和欧洲电网13659节点测试系统,结果表明,所提方法可有效实现SVSRB精确近似解析表达和准确构建。
