Development of a Grey-box model for a Multi-Residential Passive Building incorporating Radiant Wall and Radiant Floor Heating Systems” Jordi Macia, International Energy Research Center

This article presents the development of a Grey-box type model, specifically an RC thermal-electrical circuit equivalent model, tailored for MPC to optimize energy operation of buildings. Efficient MPCs necessitate models with short computational time and low resource consumption for iterative short time-horizon simulations.

The model represents a residential 5-storey block containing 20 dwellings in Switzerland, with high thermal insulation, low air infiltration, and a glass winter garden in the south façade. Two HVAC variations are considered: one with radiant wall heating (RWH) installed in the external layer of the façade, and the other with a radiant floor heating (RFH) paired with individual air conditioning (AC) units in each zone. Given the centralized nature of both HVAC systems, the model considers the whole building as one single thermal zone.

Calibration data was generated using a TRNSYS model with a single thermal zone per dwelling. A Pseudo-random Binary Sequence (PRBS) is used to excite the heat dynamics at several ranges of frequencies in which the time constants of the building are expected to be, and it is not correlated to other inputs. Model parameters were identified employing the minimization function from the Scipy Python library to minimize the error between simulated and estimated data.

The proposed RC model for the radiant wall extends the conventional R2C2 model with indoor and mass temperature states, by introducing a third state for the heating loop connected to the mass, resulting in an R3C3 model. Validation against TRNSYS simulated data from the cold season achieved a 1.7% normalized root mean square error (NRMSE).

Similarly, the R3C3 model for radiant floor with AC extends the R2C2 by adding a third state for the heating loop connected to the indoor air. The AC is added as a heat gain in the indoor air temperature. Since this model aims to be used for both heating (RFH) and cooling (AC), it has to be adjusted to cold, shoulder, and warm seasons. Therefore, the model resulted in three sets of parameters for each of the seasons with NRMSE values of 1.19%, 1.26%, and 1.21%, respectively.

The results demonstrate an excellent alignment with the reference model, successfully accommodating both a radiant wall and three distinct seasonal adjustments. With minimal adjustment error and precise visual alignment of output profiles, the model effectively captures the building dynamics, particularly the behavior of the internal temperature—a critical control variable for MPCs.

Session Chair:

Jordi Macià Cid, IREC