Solving optimization problems when designing power supply circuits

Abstract

One of the quickly developing trends in the optimization of electric power grids is system development of operation and optimization of branch circuits which are based on linear programming problems. One of its categories is traffic problem. The paper discusses the formulation of various types of transport optimization problems used in the design of the most efficient power supply systems in the real sector of economy. The construction of arithmetic models of problems is carried out. Their optimality criterion is cost minimization for the design of electrical network diagrams consisting of power lines connecting sources and consumers. Examples of designing optimization power layout in mathematical problems considering the transmission capacity of power lines is given. The paper also touches upon a mathematical problem considering possible transit of capacities. The task is to build a mathematical model and solve problems that ensure minimization of process losses and losses of power when designing electrical networks. The results of solving problems are presented in the form of power supply circuits corresponding to the most optimal linking of source and consumer nodes. The work is of a scientific and practical significance as it considers the problem of optimizing economic costs when designing electric power network schemes. Moreover it is based on a qualitatively different level of use of the traffic problem algorithm. The algorithm for solving the minimization problem obtained in this paper allows developing the necessary computing operations as well as quickly obtaining the results of solving the cost optimization problem in the designed electric power network. P GWh. It is also known that the costs of transmitting power over power transmission lines between stations and settlements are ij z c.u./GW·h ( 600 11 = z , 700 12 = z , 400 13 = z , 320 21 = z , 300 22 = z , 350 23 = z , 500 31 = z , 480 32 = z , 450 3 = z ). At certain times of the year, the need for electricity in each of these three settlements increases by 20%. In this case, it is assumed that the lack of electricity can be replenished from another power supply network at a higher cost (1000 c.u./GW·h). However, the third settlement cannot join another power grid. Power plants are planning to design a more cost-effective program that provides electrical balance between consumers. It is necessary to plan the lowest-cost electrical network (it is possible to lay air lines only from the source to the loads) and determine the cost of additional electricity for each of these settlements at a certain time of the year.