Methodology for Obtaining Linear State Space Building Energy Simulation Models

Abstract Optimal climate control for building systems is facilitated by linear, low-order models of the building structure and of its Heating, Ventilation and Air Conditioning (HVAC) systems. However, obtaining these models in a practical form is often difficult, which greatly hampers the commercial implementation of model predictive controllers. This work describes a methodology for obtaining a linear State Space Model (SSM) of Building Energy Simulation (BES) models, consisting of walls, windows, floors and the zone air. The methodology uses the Modelica library IDEAS to develop a BES model, including its non-linearities, and automates its linearisation. The Dymola function linearize2 is used to generate the state space formulation, facilitating further mathematical manipulations, or simulation in different environments. Optionally this model can then be reduced for control purposes using model order reduction (MOR) techniques. The methodology is illustrated for the zone air temperature in an office building. For this case, the absolute error between the non-linear BES and its SSM remains under 1 K and its yearly average is 0.21 K. The original 50 states SSM could furthermore be reduced to 16 states without significant loss of accuracy