OPTIMIZATION OF ENERGY FIELD PARAMETERS

Abstract

Resolving energy saving tasks is an urgent problem of our time. Geometric modelling of energy processes makes it possible for the designer or architect to solve such problems and to consider the energy costs of a project in advance. It is important for practice to solve a number of optimization tasks, in which it is possible to choose the best solution from a set of criteria. The way of solving one of such tasks is proposed in this study. In a mathematical model of an energy field, which is represented in the form of an equation, some of the specified parameters can be set, and the rest are free. If the number of free parameters exceeds the number of given parameters by one, the mathematical model of the energy field will be underdetermined, and it will be possible to find its optimal solution from the one-parameter set of possible parameters. A mathematical model can be represented by a single equation, if the parameters of energy sources are given. If the parameters of the energy field points are set, but the parameters of the energy sources are unknown, the mathematical model of the field is represented by a system of equations. If the unknowns are the coordinates of the given points of the field, the specified system of equations is non-linear. Most of practical tasks of energy field optimization are connected with energy saving. Optimization criterion in this case is minimization of power of energy sources under fulfillment of given task conditions. Dependence between parameters of a target function is described by a single equation or a system of such equations. The optimization problem in this case becomes single-criteria. Variable parameters of an equation or system of such equations are optimization parameters. In this publication one of several problems of energy field parameters optimization connected with practice of architectural design of interiors and exteriors is solved - minimization of energy source powers to provide given potentials in given points of field or minimization of power of given number of identical energy sources as for artificial illumination of rooms.