Model

The building behavior is modeled according to the commonly used RC-equivalent network technique, in this case, the 3R2C model variant is used as illustrated below.

The idea is to provide a rough approximation of the load profile using a minimum number of model parameters. The air capacitance (C_air) is calculated using the internal zone volume, the specific heat, and a default correction factor that takes into account convective airflow movement.

The equivalent thermal resistor (R_total) is calculated using the design load (P) from the prior building study, and the internal and external full load design temperatures (see formula below). 

The concentrated building structure capacitance (C_building) is approximated and related to the full load power by default values (heavy, medium, or light structure). Depending on the location of the insulation, the capacitance can be positioned using a θ factor which defines the location where the equivalent resistor is split to attach the capacitance. Both the auxiliary heat from the heating system, the solar gains, and the internal occupancy gains are directly connected to the internal air node. The solar gains depend on the orientation and the window area. The external temperature Te and the solar irradiation are retrieved from a weather data file. 

Despite the relative accuracy of this RC equivalent model, it is a quite satisfying approach when studying the controllability of the hydronic heating system. Particularly, the air capacitance is important in the small time scale plant dynamics and can be easily determined. The much slower and less accurate interaction with the building structure is less important when studying hydronic controllability aspects. Also for comparing the partial load energy efficiencies of alternative hydronic designs, the real load model accuracy is often of minor importance as long as the load is representative. 

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