Development and validation of a gray box model to predict thermal behavior of occupied office buildings

Due to the development of energy performance contracting and the needs for peak electric demand reduction, the interest for building energy demand prediction is renewed. Gray-box models are a solution for energy demand prediction. However, it is still difficult to find the best level of model complexity and the good practices for the training phase. Since models’ order and parameter identification method have a strong impact on the forecasting precision and are not intuitive, a comparative design approach is used to find the best model architecture and an adequate methodology for improving the training phase. The gray box models are compared on their ability to forecast heating and cooling demands and indoor air temperature. An objective function is proposed aiming to minimize both power and indoor temperature prediction errors. Moreover, for each model, several training period durations are tested. First, this study shows that a R6C2 (second order model) model is adapted to predict the building thermal behavior. Furthermore, the best fits are obtained with two weeks of data for the identification process. Second, a sensitivity analysis using total Sobol index calculation leads to validate the objective function and identify the most important parameters for prediction.

[1]  Henrik Madsen,et al.  Identifying suitable models for the heat dynamics of buildings , 2011 .

[2]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[3]  Lino Guzzella,et al.  EKF based self-adaptive thermal model for a passive house , 2014 .

[4]  Gilles Lefebvre,et al.  Using model size reduction techniques for thermal control applications in buildings , 2000 .

[5]  Jorge Nocedal,et al.  An interior algorithm for nonlinear optimization that combines line search and trust region steps , 2006, Math. Program..

[6]  Stéphane Bertagnolio.  Evidence-Based Model Calibration for Efficient Building Energy Services , 2012 .

[7]  Gerhard Czeplak,et al.  Solar and terrestrial radiation dependent on the amount and type of cloud , 1980 .

[8]  Nadia Ghrab-Morcos,et al.  Energy performance assessment of occupied buildings using model identification techniques , 2011 .

[9]  Ari Rabl,et al.  Parameter estimation in buildings: Methods for dynamic analysis of measured energy use , 1988 .

[10]  Henrik Madsen,et al.  Estimation of continuous-time models for the heat dynamics of a building , 1995 .

[11]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[12]  M. Jansen.  Analysis of variance designs for model output , 1999 .

[13]  Henrik Madsen,et al.  Identification of the main thermal characteristics of building components using MATLAB , 2008 .

[14]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[15]  Gilles Fraisse,et al.  Development of a simplified and accurate building model based on electrical analogy , 2002 .

[16]  James E. Braun,et al.  An Inverse Gray-Box Model for Transient Building Load Prediction , 2002 .

[17]  David Coley,et al.  Second order system identification in the thermal response of real buildings. Paper II: Recursive formulation for on-line building energy management and control , 1992 .

[18]  Mohcine Zouak,et al.  A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building , 2004, Neural Computing & Applications.

[19]  Stéphane Roger Roujol.  Méthodes de calcul prévisionnel des consommations d'énergie des bâtiments climatisés : incertitude et validation , 2003 .

[20]  Christian Ghiaus,et al.  Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part I – Building modeling , 2012 .