An Optimization Algorithm for Looped Water Networks

This paper contains the results, and represents the culmination of a six month study of the procedures and techniques for the optimization of operation of the City of Albuquerque Water System.

1.1 Primary Purpose of the Optimization Subsystem

The optimization subsystem for the AUTO 8 system has as its objective to deliver water to the Water System customers at the lowest possible cost to the city while maintaining reliability-of its components and certain safety standards. These safety standards include minimum levels in each of the reservoirs which must be maintained to insure adequate water for fighting fires.

1.2 Inherent Problems

With a network as complicated as a city water distribution system must necessarily be, there are many difficulties with designing a straightforward optimal solution to a pzoblem such as getting water from the ground to the ultimate users. A problem that any mathematical method for optimization will encounter with a system such as a municipal water system is the heavy degree of looping of the network. This redundancy of paths is necessary to ensure adequate channels for water to any portion of the system for safety and reliability reasons. The result is a problem that is very non-linear. In the design of a procedure for optimal control, this non linearity must be taken into consideration. The Albuquerque water network is made up of trunks which extend from the lower elevations in the Rio Grande Valley up toward the higher elevations o f the Sandia Mountains on the East side and toward the upper valley on the West. The trunks are connected by large intertrunk transfer lines which are connected to the distribution networks within the system. The network is divided into zones of elevation with each zone representing approximately 115 feet of elevation. The system is gravity fed from reservoirs in each zone. The Albuquerque system has many sources of water at least in the lower zones. Water may be pumped directly from wells which are local to the reservoirs in the lowest four zones, or boosted from the zone below, or in any combination. Each of the well fields and booster stations contains multiple pumps. Each of the pumps within the system has a different pumping rate and cost of pumping water. Therefore the well pumps located at one reservoir represent a source of water for that reservoir, and, through the boosters located at the site, can be considered a source for the reservoir on the same trunk in the zone above. In addition, because of the intertrunk transfer lines, sources for one reservoir may serve to some degree as sources for other reservoirs within the same zone on parallel trunks. The City currently has a contract with the power company which charges for electricity on a peak / off peak basis. The optimization algorithm must not only take this cost structure into consideration, but must also provide the flexibility for adaptation to future rate contracts.

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