A Time-Delayed Model and Estimation in Parabolic-Trough Solar Collectors

The dynamics of the parabolic-trough solar collectors are described by a differential equation model. Based on this model, different control strategies have been proposed to manage the heat production. However, the time delay between the solar irradiance (input) and the outlet temperature (output) has not yet been incorporated into the model. Considering this parameter will improve the model-based control techniques that strongly depend on the solar irradiance function. This paper develops a mathematical model for the parabolic-trough solar collectors in which the time delay is included. Since this parameter is unknown in practice, a method based on a cross-convolution approach is proposed to estimate it accurately. Moreover, the efficiency of the proposed method is improved by combining it with a filtering methodology. The proposed model's effectiveness and the estimation method's performance are demonstrated through numerical simulations.