Decentralized thermal modeling of multi-zone buildings for control applications and investigation of submodeling error propagation

Abstract

Centralized model predictive control is a popular and optimal approach for thermal control of multi-zone buildings. In centralized control of large-scale, multi-zone buildings, decentralized thermal modeling (including identification) may be useful since it may hard and computationally demanding to obtain a single model for the overall system. Success of a centralized predictive controller depends highly on the prediction accuracy of the used control model during control design phase.In decentralized modeling, control-oriented thermal models of individual zones are obtained by taking the thermal interactions with adjacent zones as extra input signals. These submodels can be very accurate when validated at the zone level. However, when all submodels developed in a decentralized approach are combined to construct a model of the overall building system, modeling errors in submodels may be amplified through thermal interactions and the resulting multi-zone model may not have enough prediction accuracy to be used in a centralized model predictive control algorithm. The opposite is also possible: submodel errors may cancel out, to some degree, each other and hence the multi-zone model may have a better prediction accuracy than submodels.In this paper, first a set of state-of-the-art decentralized control-oriented thermal modeling/identification approaches (composable zones approach, graph theory-based decentralized identification approach, and determination of weakly-interacting zones approach) for multi-zone buildings is presented. Second, multi-zone building thermal models based on the composable zones approach and multi-input single output (MISO) ARMAX (AutoRegressive Moving Average with eXogenous input) model structure for submodels are obtained, and then the problem of submodeling error propagation is investigated through a set of case studies. The case studies are arranged with an increasing number of thermal interactions. For the considered case studies, it was found that the combination of composable zones approach with MISO ARMAX model structure for submodels was an appropriate way to obtain accurate control-oriented prediction models for multi-zone buildings. Moreover, it was observed that the error propagation sometimes can be significant when a multi-zone model was composed from submodels, and that there was no correlation between the number of thermal interactions and the level of submodeling error propagation.