Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output....Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.展开更多
Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvex...Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.展开更多
The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as si...The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as single point failure and slow response speed,have led to utilization of measures such as distributed OPF methods.The OPF problem is non-convex,which makes it difficult to obtain an optimal solution.The second-order cone programming(SOCP)relaxation method is widely utilized to make the OPF problem convex.It is difficult to guarantee its exactness,especially when line constraints are considered.This paper proposes a penalty based ADMM approach using difference-of-convex programming(DCP)to solve the non-convex OPF problem in a distributed manner.The algorithm is composed of distributed x iteration,z iteration and A,/i iteration.Specifically,in the distributed z iteration,the active power flow injection equation of each line is formulated as a difference of two convex functions,and then the SOCP relaxation is given in a different form.If the SOCP relaxation is inexact,a penalty item is added to drive the solution to be feasible.Then,an optimal solution can be obtained using a local nonlinear programming method.Finally,simulations on a 14-bus system and the IEEE 123-bus system validate the effectiveness of the proposed approach.展开更多
最小二乘支持向量机(LS-SVM)是一种基于超平面的分类器,由于LS-SVM缺乏特征选择能力,因此在高维小样本数据集上的泛化表现不佳,所以有必要提高LS-SVM的特征选择能力。在LS-SVM的目标函数中引入?_(0 )-范数正则项,提升模型的特征选择能...最小二乘支持向量机(LS-SVM)是一种基于超平面的分类器,由于LS-SVM缺乏特征选择能力,因此在高维小样本数据集上的泛化表现不佳,所以有必要提高LS-SVM的特征选择能力。在LS-SVM的目标函数中引入?_(0 )-范数正则项,提升模型的特征选择能力。然而由于?_(0)-范数的引入,导致新的模型不仅是非凸非光滑的,而且是NP-难问题。为了克服这些困难,首先用一个非凸非光滑连续函数近似?_(0)-范数,再对该近似函数进行DC(difference of convex functions)分解,将问题转化为DC规划问题,从而利用DCA(difference of convex functions algorithm)求解该问题。该新方法的主要优点在于DCA的子问题具有解析解,从而使得训练速度得到很大地提升。数值实验表明,本文所提出的新方法不仅具有较好的泛化性能和特征选择能力,而且计算速度快。展开更多
针对DC(difference of convex)规划,结合最优化理论和算法的相关知识,用不同的方法对DC规划中已有的一些定理和结论进行了证明。在此基础上,对其中一些结论进行了推广,并且阐述了一类DC规划和其对应的反凸规划的最优解之间的联系。最后...针对DC(difference of convex)规划,结合最优化理论和算法的相关知识,用不同的方法对DC规划中已有的一些定理和结论进行了证明。在此基础上,对其中一些结论进行了推广,并且阐述了一类DC规划和其对应的反凸规划的最优解之间的联系。最后利用L-次微分等相关知识,提出并讨论了一类特殊DC规划和其相关的一类凸规划的最优解之间的联系与区别。展开更多
Non-convex optimization can be found in several smart manufacturing systems. This paper presents a short review on global optimization(GO) methods. We examine decomposition techniques and classify GO problems on the b...Non-convex optimization can be found in several smart manufacturing systems. This paper presents a short review on global optimization(GO) methods. We examine decomposition techniques and classify GO problems on the basis of objective function representation and decomposition techniques. We then explain Kolmogorov's superposition and its application in GO. Finally,we conclude the paper by exploring the importance of objective function representation in integrated artificial intelligence, optimization, and decision support systems in smart manufacturing and Industry 4.0.展开更多
基金supported by NSFC(No.11301570)Basic and Advanced Research Project of CQ CSTC(No.cstc2013jcyjA00003)+1 种基金China Postdoctoral Science Foundation Funded Project(No.2013M540697)Research Fund of Chongqing Technology and Business University(No.2013-56-03)
基金supported by the National Natural Science Foundation of China(Grant No.51977080)the Natural Science Foundation of Guangdong Province(Grant No.2022A1515010332)supported by the U.S.National Science Foundation(Grant#2124849).
文摘Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.
基金supported by the National Natural Science Foundation of China under Grant 52177086the Fundamental Research Funds for the Central Universities under Grant 2023ZYGXZR063the Science and Technology Program of Guizhou Power Grid Coorperation under Grant GZKJXM20222386.
文摘Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.
基金supported in part by the National Natural Science Foundation of China(51477070)National Key Research and Development Program of China(2018YFB0905000)Jiangsu Electric Power Company(J2019087).
文摘The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as single point failure and slow response speed,have led to utilization of measures such as distributed OPF methods.The OPF problem is non-convex,which makes it difficult to obtain an optimal solution.The second-order cone programming(SOCP)relaxation method is widely utilized to make the OPF problem convex.It is difficult to guarantee its exactness,especially when line constraints are considered.This paper proposes a penalty based ADMM approach using difference-of-convex programming(DCP)to solve the non-convex OPF problem in a distributed manner.The algorithm is composed of distributed x iteration,z iteration and A,/i iteration.Specifically,in the distributed z iteration,the active power flow injection equation of each line is formulated as a difference of two convex functions,and then the SOCP relaxation is given in a different form.If the SOCP relaxation is inexact,a penalty item is added to drive the solution to be feasible.Then,an optimal solution can be obtained using a local nonlinear programming method.Finally,simulations on a 14-bus system and the IEEE 123-bus system validate the effectiveness of the proposed approach.
文摘最小二乘支持向量机(LS-SVM)是一种基于超平面的分类器,由于LS-SVM缺乏特征选择能力,因此在高维小样本数据集上的泛化表现不佳,所以有必要提高LS-SVM的特征选择能力。在LS-SVM的目标函数中引入?_(0 )-范数正则项,提升模型的特征选择能力。然而由于?_(0)-范数的引入,导致新的模型不仅是非凸非光滑的,而且是NP-难问题。为了克服这些困难,首先用一个非凸非光滑连续函数近似?_(0)-范数,再对该近似函数进行DC(difference of convex functions)分解,将问题转化为DC规划问题,从而利用DCA(difference of convex functions algorithm)求解该问题。该新方法的主要优点在于DCA的子问题具有解析解,从而使得训练速度得到很大地提升。数值实验表明,本文所提出的新方法不仅具有较好的泛化性能和特征选择能力,而且计算速度快。
文摘针对DC(difference of convex)规划,结合最优化理论和算法的相关知识,用不同的方法对DC规划中已有的一些定理和结论进行了证明。在此基础上,对其中一些结论进行了推广,并且阐述了一类DC规划和其对应的反凸规划的最优解之间的联系。最后利用L-次微分等相关知识,提出并讨论了一类特殊DC规划和其相关的一类凸规划的最优解之间的联系与区别。
文摘Non-convex optimization can be found in several smart manufacturing systems. This paper presents a short review on global optimization(GO) methods. We examine decomposition techniques and classify GO problems on the basis of objective function representation and decomposition techniques. We then explain Kolmogorov's superposition and its application in GO. Finally,we conclude the paper by exploring the importance of objective function representation in integrated artificial intelligence, optimization, and decision support systems in smart manufacturing and Industry 4.0.
