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a generalized network flow model with application to power supply‐demand problems
Author(s) -
Liu ChenChing,
Wu Felix F.
Publication year - 1984
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230140110
Subject(s) - flow (mathematics) , flow network , constraint (computer aided design) , mathematical optimization , mathematics , power (physics) , set (abstract data type) , power flow , maximum flow problem , point (geometry) , topology (electrical circuits) , computer science , electric power system , combinatorics , geometry , physics , quantum mechanics , programming language
The conventional network flow model is generalized by replacing the capacity constraints on the flow of each arc by a constraint that the set of flows lies in a compact set; the resulting model is called the compact flow network model. A necessary condition for the maximal compact flow is presented. The max‐flow‐min‐cut theorem is generalized to compact flow networks. The condition that is required for the maximal flow to be equal to the minimal cut is examined. The max‐flow‐min‐cut theorem is used to derive a necessary and sufficient condition for feasibility of the multiterminal supply‐demand problem based on the compact flow model. As an application, the electric power supply‐demand problem is discussed from the compact flow point of view.