A General fractional-order heat transfer model for Photovoltaic/Thermal hybrid systems and its observer design

Abstract

This paper presents the results of heat transfer process modelling for Photovoltaic/Thermal PV/T hybrid system in state-space. The heat transfer process in solid materials can be described by an integer-order partial differential equation. However, in Photovoltaic (PV/T) hybrid systems, which is characterized by heterogeneous media due to the multilayers that make up the 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 (PV/T) 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 Linear Matrix Inequality (LMI) formulation.