Bilinear reduced order approximate model of parabolic distributed solar collectors. (June 2016)

• Record Type: Journal Article
• Authors: Elmetennani, S.; Laleg-Kirati, T.M.
• Is Part Of: Solar energy. Volume 131(2016)
• Page Start: 71
• Page End: 80
• Publication Date: 2016-06
• Subjects: Solar collector -- Solar energy -- Model reduction -- Bilinear model -- Hyperbolic partial differential equation; Solar energy -- Periodicals; Solar engines -- Periodicals; 621.47
• DOI: 10.1016/j.solener.2016.02.021
• Languages: English
• ISSNs: 0038-092X

Abstract

Highlights: We propose a new approximate reduced model of the parabolic distributed collector. The approximate model is obtained by a dynamical Gaussian interpolation. We validated the proposed approximation numerically. We analyzed model accuracy with respect to different factors. We obtained satisfactory results are with reduced computational complexity. Abstract: This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, based on a modified Gaussian interpolation along the spatial domain. The proposed reduced model, written in a form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the Gaussian interpolation has been studied.