Open AccessEfficient method to compute all the type‐1 low‐voltage power flow solutions in distribution systems
Author(s) -
Zhang Gengwu,
Wang Chengmin,
Xie Ning
Publication year - 2019
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2018.6290
Subject(s) - jacobian matrix and determinant , flow (mathematics) , eigenvalues and eigenvectors , node (physics) , electric power system , voltage , type (biology) , power (physics) , mathematics , computer science , topology (electrical circuits) , mathematical optimization , control theory (sociology) , physics , engineering , electrical engineering , geometry , control (management) , artificial intelligence , ecology , quantum mechanics , combinatorics , biology
The power flow equations usually have multiple solutions including a high‐voltage solution and many low‐voltage solutions, among which only the type‐1 solutions (where the power flow Jacobian matrix has only one positive real‐part eigenvalue) are closely related to the voltage instability phenomenon. This study proposes an efficient method to compute all the type‐1 low‐voltage power flow solutions in distribution systems. First, the geometric properties of the power flow solution space of distribution systems have been studied. Second, the propositions which can guarantee to locate all the type‐1 power flow solutions have been suggested and proved. Finally, the conventional implicit Z‐bus method is modified to compute all the type‐1 germ solutions, based on the suggested propositions; and then the Newton–Raphson method is utilised to trace all the type‐1 low‐voltage power flow solution branches which originate from the known type‐1 germ solutions. The 7‐node, 33‐node, and 69‐node systems are used to validate and demonstrate the proposed method.