Dynamic modeling of indoor air temperature based on power spectral density method

The control of indoor thermal conditions needs dynamic modeling of indoor air temperature in buildings. The indoor air temperature is influenced by four factors: outdoor weather conditions occupants; plug-in electric load used in air-conditioning zones; and cooling and heating energy consumed by air-conditioning system. Weather conditions, occupants and plug-in electric load are considered as random variables, while cooling and heating energy consumption are marked as deterministic variables. Step response method is a commonly method used for modeling. But step signals of random variables in real operation can hardly generated. This paper presents a power spectral density method for dynamically modeling of indoor air temperature response which contains a numerous of random variables. In order to simplify the analysis, this paper selects the ambient temperature and total solar radiation as the input variables and the indoor temperature as the output variable for analysis. Power spectral density and cross spectral density of different is calculated and transfer function is established. In the case of multiple input variables, the state space method is used to establish the transfer function. The proposed method was applied in a real room, and then model predictive control (MPC) strategy was applied based on this model. The result shows that the accuracy and the practicality of the model are all satisfactory.