This paper presents the application of bifurcation method on the steady state three-phase load-flow Jacobian method to study the voltage stability of unbalanced distribution systems. The eigenvalue analysis is used to...This paper presents the application of bifurcation method on the steady state three-phase load-flow Jacobian method to study the voltage stability of unbalanced distribution systems. The eigenvalue analysis is used to study distribution system behavior under different operating conditions. Two-bus connected by asymmetrical line is used as the study system. The effects of both unbalance and extreme loading conditions are investigated. Also, the impact of distributed energy resources is studied. Different case studies and loading scenarios are presented to trace the eigenvalues of the Jacobian matrix. The results exhibit the existence of a new bifurcation point which may not be related to the voltage stability.展开更多
We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and...We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr（. ） is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang （2013）, which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field （SCF） iteration to be presented and analyzed in detail in Part II of this paper.展开更多
文摘This paper presents the application of bifurcation method on the steady state three-phase load-flow Jacobian method to study the voltage stability of unbalanced distribution systems. The eigenvalue analysis is used to study distribution system behavior under different operating conditions. Two-bus connected by asymmetrical line is used as the study system. The effects of both unbalance and extreme loading conditions are investigated. Also, the impact of distributed energy resources is studied. Different case studies and loading scenarios are presented to trace the eigenvalues of the Jacobian matrix. The results exhibit the existence of a new bifurcation point which may not be related to the voltage stability.
基金supported by National Natural Science Foundation of China(Grant Nos.11101257 and 11371102)the Basic Academic Discipline Program+3 种基金the 11th Five Year Plan of 211 Project for Shanghai University of Finance and Economicsa visiting scholar at the Department of Mathematics,University of Texas at Arlington from February 2013 toJanuary 2014supported by National Science Foundation of USA(Grant Nos.1115834and 1317330)a Research Gift Grant from Intel Corporation
文摘We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr（. ） is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang （2013）, which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field （SCF） iteration to be presented and analyzed in detail in Part II of this paper.
