Temperature evolution in heated premises and external boundary wall with dynamic control of heating systems

The study presents a mathematical model for building heating control. The buildings are connected to district heating or to central heating. The task of the heating control is to maintain a preset constant indoor air temperature. Control disturbance is caused by external meteorological conditions, firstly by outdoor air temperature. The control action can be the change in heat transfer capacity of the radiators, whereby the indoor air temperature can be commanded back to the present value to offset the effect of the disturbance. Just the control can be a follower or of predictive type. The expected indoor air temperature can be calculated from the energy balances. These are composed of differential equations, describing dynamic equilibrium of heat transfer through the external walls, as well as heat storage in the walls and indoor air. Type of differential equations is linear, inhomogeneous, of first or second order. Solution of the differential equation results in describing the change in indoor air temperature in time as a function of outdoor air temperature. Further on, the equation determines the function of the necessary heating capacity to keep the indoor air temperature constant. By the model several heating programs can be evaluated. The physical model is shown in Fig. 1. Intermediate variable is the average temperature of the external walls. Heat conduction and convection through the walls is calculated by the difference of the indoor air temperature and of the average wall temperature by using relevant R 1 and R 2 heat resistance factors. The model is adequate when the heat transport within the building sections is neglectable, and the thermodynamic and heat transfer characteristics of the walls are identical. Thereby the model describes the heat balance of representative premises, but the results can be transferred to similar other premises, too.