A general fractional-order heat transfer model for photovoltaic/thermal (PVT) hybrid systems and its observer design
Résumé
This paper presents the results of modelling the heat transfer process for the new system called Photovoltaic/Thermal (PVT) hybrid systems in state-space. The heat transfer process in a solid material can be described by an integer-order partial differential equation. However, in the Photovoltaic/Thermal (PVT) hybrid systems, which is characterized by heterogeneous behaviour due to the materials that make up the layers of system, it can be described by a fractional-order partial differential equation. The major objectives of this study were to establish a new mathematical model of the Photovoltaic/Thermal (PVT) hybrid systems and their fractional-order observers in time domain. This model has been constructed in the context of a new consideration of heat conduction with a time fractional-order derivative. On the other hand, after obtained the general model of the system in state-space, the existence conditions of the fractional-order observer of such systems are given. Then, a necessary and sufficient condition for the asymptotic stability of the estimation error is given in a LMI formulation.