Modeling of a Large-Scale Water Distribution System

by Nien-Sheng Hsu, Natl Taiwan Univ, Taipei, Taiwan,
Peter W. F. Louie, Natl Taiwan Univ, Taipei, Taiwan,
William W-G. Yeh, Natl Taiwan Univ, Taipei, Taiwan,

Abstract: Metropolitan Water District of Southern California (MWD) imports water from the California State Water Project and the Colorado River, providing for supplemental water demands for six counties in Southern California. The total area served is about 5,100 square miles, with a population of approximately 15 million people. To assist in the planning and management of the water distribution system, a computer model is developed to simulate the flow of water in the system. An optimization model is then developed to optimize the planned operations of the system. A linear programming (LP) algorithm is used to solve for a 12-monthly-period problem. When more time periods are involved, e.g., weekly time periods, dimensionality prohibits a direct LP solution. A Dantzig- Wolfe decomposition scheme is formulated to handle the large-scale problem. It takes advantage of the special structure of the problem. The constraint set is divided into a time-dependent part and a time-independent part. The time-independent constraints have the same block structure and content. The variables in the time-independent constraint set are linked by time-dependent constraints. A master problem is formed which only considers the linking constraints. The master is linked to the subproblems that have the same block structure. A column-generation technique is developed for solving the master and subproblems. A subsystem of the MWD's water distribution system is first tested by the decomposition scheme. The results obtained show that a considerable savings in computer storage is achieved by the scheme.

Subject Headings: Water supply systems | Water storage | Hydrologic models | Water conservation | Hydraulic models | Computer models | Optimization models | Flow simulation | Computer programming | North America | California | United States | Colorado River

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