System approach to mathematical modeling of thermal processes in buildings - Куценко, Александр Сергеевич; Коваленко, Сергей Владимирович; Товажнянский, Владимир Игоревич (Eastern-European Journal of Enterprise Technologies, 2014)
An approach to constructing a mathematical model of the heat supply process of building, consisting of interconnected premises is proposed in the paper. The approach is based on replacing heat-conduction equations, describing heat transfer processes between the elements of buildings and the environment, by a finite-dimensional system of ordinary differential equations. Substantiation of the dimension of the approximating system, based on comparing the analytical solution of the heat-conduction equation and the results of the numerical integration of the approximate differential equation system is carried out. Numerical experiments have shown that for different values of the criteria with sufficient accuracy for practical purposes one can content himself with the system of the 2nd order. It is shown that the time constants of thermal processes of air of premises, partitions and filling of premises are by 2-3 orders lower than the time constants of the processes in the outer perimeter. This allows to replace the system of differential equations of heat balance for air, partitions and filling by static equations. The obtained structure of the mathematical model of the thermal process in a complex system is a linear model of controlled processes. This allows to effectively adapt all the basic methods of analysis and synthesis of automatic control systems to the problems of heat supply management.