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A new formulation and solution method for the maximum loading point in electrical power systems
Author(s) -
Yorino Naoto,
Harada Shigemi
Publication year - 1997
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/(sici)1520-6416(199710)121:1<17::aid-eej3>3.0.co;2-2
Subject(s) - jacobian matrix and determinant , singularity , electric power system , mathematics , point (geometry) , saddle point , reduction (mathematics) , diagonal , newton's method , flow (mathematics) , operating point , control theory (sociology) , mathematical analysis , dimension (graph theory) , power (physics) , computer science , geometry , engineering , physics , nonlinear system , electronic engineering , control (management) , quantum mechanics , artificial intelligence , pure mathematics
This paper proposes a new efficient formulation and solution method for a maximum loading point or saddle node bifurcation point in electrical power systems. This point, corresponding to a tip of the P(Q)‐V curve, is characterized by singularity of the load flow Jacobian. The proposed formulation is of dimension n + 1, instead of 2 n + 1 in the standard formulation, for n ‐dimensional load flow equations. The proposed method uses a 1‐dimensional singularity condition, obtained from a reduction of the standard n + 1‐dimensional singularity conditions. For this reduction, one of the diagonal elements of the load flow Jacobian is selected. We also propose an index for this selection to make the proposed method reliable. The solution for the proposed formulation can effectively be obtained based on the Newton‐Raphson method with sparse matrix techniques. The computational performance of the proposed method is demonstrated on 6, 14, and 118 bus test systems. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 121(1): 17–25, 1997