Analysis of the effectiveness of flow distribution optimization methods in water supply systems with a large number of pumping stations

Abstract

Relevance. Currently, optimization methods for a small number of active sources working on the network have been studied. However, when developing operational control systems for water supply systems (WSS) of large cities, one has to deal with a large number of pumping stations (PS) simultaneously working to the network. The complexity of solving the problem of optimization of flow distribution in WSS increases with the increase in the number of active sources working together, which are variables of the optimization of the problem under consideration.

Goal. In the problem of operational control of the modes of operation of the WSS, the task of optimizing flow distribution in a large-scale water supply network occupies an important place. The purpose of the task is to distribute the load (expenditure) between the stations in such a way that, while ensuring the specified quality of water supply to all consumers, the minimum amount of energy consumption at the pumping stations is achieved. The formulation of the problem, the methods of its solution for the WSS of a large city, for which a large number of pumping stations work, are considered. It is necessary to conduct a comparative analysis of the effectiveness of the use of various optimization methods to solve the problem of optimal load distribution among a large number of pumping stations simultaneously working to the water supply system of the metropolis.

Research methods. This problem can be solved by methods of nonlinear mathematical programming or search optimization based on the hydraulic calculation of the water supply network. Its specific feature is the algorithmic task of the goal function. When working to a network of two active sources, this problem is reduced to a problem of one-dimensional search optimization. With a larger number of variables, it is necessary to use methods of multidimensional optimization. The most effective and common methods were used to study the effectiveness of solving the problem of flow distribution optimization in the WSS: coordinate descent; scanning with a variable step; deformed Nelder-Mead polyhedron; Hook and Jeeves direct search; Rosenbrock; Powell.

The results. The conducted research showed that the method of direct search of Hook and Jeeves was the most effective according to the criteria of the minimum expenditure of computer time and the amount of computer memory.

Conclusions. It is advisable to use the obtained results for the development and operation of systems for the operational management of the operation modes of the WSS of large cities, the control systems of dispatchers of water supply networks, CAD of water supply systems to determine the optimal modes of operation of the WSS.