Low-order gray-box modeling of heating buildings and the progressive dimension reduction identification of uncertain model parameters

Heating buildings have a huge heat capacity and have abilities to accept fluctuating heat supply from renewables. Creating a low-order scalable model that describes the thermal dynamics of coupled heat transfer, charge, and discharge processes among heating buildings is essential to unlocking the thermal storage potential of building mass and achieving space heating decarbonization. White-box models tend to be too complex and black-box models lack scalability. Thus, a low-order gray-box model with uncertain lumped parameters is proposed based on comprehensive heat transfer analyses and necessary assumptions. Thermal mass in heating buildings is divided into four independent heat storage units. The building envelope that can be heated directly or not is regarded as a different heat storage unit. To reduce the search space dimension of model identification, the decision variables are downsized to essential model parameters based on the sensitivity analysis. Moreover, a progressive dimension reduction method is introduced to further improve the probability that the optimization algorithm converges to a global minimum. Case studies show that the calibrated model with global optimal solutions of uncertain model parameters has a good performance on the prediction of the average temperature of indoor air, the average absolute error is only 0.1 °C.