Matviienko O. Mathematical modeling and optimization of operating modes of water systems

Subject matters of the study are stochastic processes of the quasi-stationary modes of operation of the water supply systems. Research methods - the methods of mathematical modeling of nonlinear stochastic systems to develop a stochastic model of the quasi-stationary modes of operation of the water supply and distribution systems; methods of optimal stochastic control, theories of probability; mathematical statistics and random processes for solving the problems of optimization. Theoretical and practical results - a stochastic model of the quasi-stationary modes of operation of the water supply and distribution systems developed in the dissertation let take into account the stochastic nature of the object of control and environment, adequately describes the actual modes of operation of the water supply system at a given time interval and can be used as a base model for formulating and solving of the problems of optimal stochastic control of the development and operation of the water supply and distribution systems. Approximate methods of solving of these problems are developed in the present work. As the studies have shown as a result of zoning and using of adjustable pressure valves for a test example the sum of the squares of excess pressures in the nodes of the water supply system for the selected zone has decreased by 73%. As a result of solving of the problem of optimization of the modes of operation of the pumping station the energy consumption by this pumping station has reduced by 11%. Economic effect as a result of the transition from the current systems of control of the modes of operation in the water supply and distribution systems to the systems of optimal stochastic control with a three-band tariff for the electricity for one of the largest water mains in Ukraine came up to 6.5%. Scientific novelty of the obtained results is in the fact that a mathematical model of the quasi-stationary modes of operation of the water supply and distribution systems, taking into account the stochastic nature of the object of control and environment, and adequately describing the processes of transportation and distribution of water in the water supply system at a given time interval has been developed for the first time; a mathematical model of the problem of optimal stochastic control of the modes of operation of the water main with extreme and probabilistic constraints on the phase variables the solving of which let get minimal mathematical expectation of the cost of the electricity at a three-band tariff at the interval of control has been formulated for the first time; an approximate method of solving of the problem of optimal stochastic control of the modes of operation of the water main based on the formulation of its deterministic equivalent and use of the method of the branches and borders has been developed; a method of optimal stochastic control of the development of the water supply and distribution systems by zoning of the water distribution systems for the cities with complex terrain of the land and buildings of different high has got its further development; a mathematical model of the problem of optimization of the modes of operation of the pumping station at a given time interval the solving of which provides minimal mathematical expectation of the electricity cost and the stability of the solution to the predictable level of the stochastic disturbance. The dissertation work has been performed on the Chair of Applied Mathematics of Kharkiv National University of Radioelectronics of the Ministry of Education and Science of Ukraine in accordance with the plans of scientific research works of the state budget theme № 293 "Elaboration of the methodology and mathematical models of social and economic systems within the implementation of the concept of its stable development" (№ SR 0115U001522) , in the implementation of which the author was directly involved as a researcher. Moreover, the author was the executive in charge of the business agreement №16-3 "Estimation of the potential of the resource saving of the water mains of the complex of waterpreparation "Donets" a separate department of the communal enterprise "Kharkivvodokanal "(265/3-HP / 16 №0116 U007035).