DEVELOPMENT OF MODEL OF OPTIMAL CONTROL OF WATER SUPPLY SYSTEM

Abstracts: This paper considers the problem of optimal control of branched water supply systems. To control the system, the problem of optimal distribution of products is developed whereas non-linear programming problems are applied. We consider a system for providing products, consisting of magistral and distribution pipelines, taking products from the magistral pipeline. Each distribution line has many warehouses. Products are taken into the system using the main intake facility and transferred between the warehouses using intermediate distribution facilities. To eliminate the deficiencies in management, tasks are set to determine the necessary intensities of product supply in the facilities, allowing timely provision of consumers with the necessary volume of products, to minimize losses, product discharges of facilities in the system during a certain control period.


Introduction
The introduction of modern management systems in the water management provides enterprises with an unprecedented opportunity to control and manage all aspects of water intake, transportation, and distribution from a centralized management system. A new method for optimizing this system in real time is proposed, formulated as an integer quadratic programming problem. The proposed method for solving this problem is very successful in achieving an almost optimal solution. Modern water management enterprises should be a single system, operating with information-computing system [1]. Benefits resulting from these actions can include improving the quality of water supply by reducing water loss, minimizing energy costs, and increasing system performance without compromising operational reliability. The real-time demand management strategy is applied to water supply enterprises to reduce the target cost function as low as possible [2].

Characteristics of the object
In this work, we consider a product supply system, which consists of a madistral line (ML) and K the number of distribution lines (DL) taking products from the ML. In each DL there are J k number of warehouses (QW). Products are taken into the system with the help of the main fence (С-00) and transferred between the warehouses with the help of intermediate distribution structures (С-kj, Excessive pro ducts can be removed from the system using emergency facilities (C-kJk) at the end of each line. On each j-t section of the q line there are İ kj the number of consumers (T). To control such systems, the necessary intensities of product supply at each structure are calculated, which are supported by an automated control system [3]. But the incorrect calculation of these intensities causes large losses, product discharges, excessive switching of equipment and untimely provision of consumers. As a result of this, the system management efficiency is reduced.

Statement of the problem
To eliminate the above disadvantages, the following statement of the problem of determining the necessary intensities is given: It is required to find such intensities of supply of products in structures that can provide consumers with the necessary volume of products in a certain manner, minimize losses, product discharges and the number of changes in the operating modes of structures in the system during the control period (t 0 , T] [4].
We divide the period (t 0 , T] into Z the number of intervals (t z-1 , t z ], on each of which the intensi- As the objective function, the sum of the costs associated with the discharge of products from the automation system Denote 00 00 , ' 2 , , Then, the objective function is transformed to the form: The following restrictions apply: The relationship between the change in stock of products and the balance of consumption in the sections of lines: Here K j is the set of DL numbers taking products from ML.

∑∑ ∑
Given the notation (7), the total number of control parameters and restrictions will be as follows:  (6) to support systems, the number of control parameters and restrictions is obtained too much. With this in mind, it is necessary to choose or develop as simple and effective a solution to the problem as possible [6].
The solution of the problem Problem (1) - (6) has been solved for a system consisting of ML and two DL powered by ML. Each line consists of two sections, one consumer in each (Fig. 1).
The control period is divided into three consecutive intervals and the mathematical formulation of the problem is obtained in the following form: