Optimization of electricity costs in residential heat supply systems

Currently, there is a large number of objects related to recirculation of material flows, mixing of reagents of liquid and gaseous media, etc. Among them are residential heating systems. Their dynamics are described by differential equations with a deviating argument. The main task of energy-saving management of heat supply systems of residential buildings is to increase energy efficiency with the help of the optimal mode of their operation. In the case of heat supply systems for residential buildings, the optimality criterion must take into account the need to maintain the required temperature regimes when the ambient temperature varies. Optimizing the operation of such objects using known methods is quite difficult. In this work, a dummy variable method is proposed to reduce the original system of differential equations with a deviating argument to a system of ordinary differential equations and transfer equations, for which known optimization methods can be applied. The method is generalized to systems with a non-stationary deviating argument and to systems with several processes having an aftereffect. The practical use of the dummy variable method is shown on the example of solving the problem of optimal control of the heat exchange process in a private residential building. Ref. 21, pic. 3