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In this paper is presented the physical model and mathematical approach which describe the equation system used in system calibration and design optimization. The system proposed for study is built from heat pump, for energy demand delivery, together with auxiliary heating source to face in all low temperature days, when heat pump work at maximum load but the required demand by the building is higher. The paper present few of the common used systems in market for which the mathematical equation system will be proposed to come in help designers for in simulation and cost optimization. Simulation of proposed design is realized and results are delivered. The system construction, is optimized by comparison study of design and simulation data for each system type proposed. The comparison study is used for cost estimation of system and energy balance.

Numerical approach regarding functional and design optimization for a residential building heating system composed by heat pump and auxiliary