Modelling indoor air carbon dioxide concentration using grey-box models

Predictive control is the strategy that has the greatest reported benefits when it is implemented in a building energy management system. Predictive control requires low-order models to assess different scenarios and determine which strategy should be implemented to achieve a good compromise between comfort, energy consumption and energy cost. Usually, a deterministic approach is used to create low-order models to estimate the indoor CO2 concentration using the differential equation of the tracer-gas mass balance. However, the use of stochastic differential equations based on the tracer-gas mass balance is not common. The objective of this paper is to assess the potential of creating predictive models for a specific room using for the first time a stochastic grey-box modelling approach to estimate future CO2 concentrations. First of all, a set of stochastic differential equations are defined. Then, the model parameters are estimated using a maximum likelihood method. Different models are defined, and tested using a set of statistical methods. The approach used combines physical knowledge and information embedded in the monitored data to identify a suitable parametrization for a simple model that is more accurate than commonly used deterministic approaches. As a consequence, predictive control can be easily implemented in energy management systems.