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The mathematical model of a building as a single heat energy system by the decomposition method is represented by three interconnected mathematical models: the first is a mathematical model of the energy interaction of a building’s shell with an outdoor climate; the second is a mathematical model of energy flows through the shell of a building; the third is a mathematical model of optimal control of energy consumption to ensure the required microclimate. Optimization problems for three mathematical models with objective functions are formulated. Methods for solving these problems are determined on the basis of the calculus of variations and the Pontryagin maximum principle. A method for assessing the skill of an architect and engineer in the design of a building as a single heat energy system is proposed.

OPTIMIZATION PROBLEMS OF MATHEMATICAL MODELLING OF A BUILDING AS A UNIFIED HEAT AND POWER SYSTEM