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Stable compact modeling of piezoelectric energy harvester devices

Chengdong Yuan (Department of Engineering, Jade University of Applied Sciences, Wilhelmshaven, Germany and Institute for Electronic Appliances and Circuits, University of Rostock, Rostock, Germany)
Siyang Hu (Department of Engineering, Jade University of Applied Sciences, Wilhelmshaven, Germany and Institute for Electronic Appliances and Circuits, University of Rostock, Rostock, Germany)
Tamara Bechtold (Department of Engineering, Jade University of Applied Sciences, Wilhelmshaven, Germany and Institute for Electronic Appliances and Circuits, University of Rostock, Rostock, Germany)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 27 April 2020

Issue publication date: 20 May 2020

83

Abstract

Purpose

Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”

Design/methodology/approach

Piezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. 

Findings

This contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.

Originality/value

The stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.

Keywords

Acknowledgements

This paper forms part of a special section “12th International Conference on Scientific Computing in Electrical Engineering (SCEE 2018)”, guest edited by Vittorio Romano.

Citation

Yuan, C., Hu, S. and Bechtold, T. (2020), "Stable compact modeling of piezoelectric energy harvester devices", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 2, pp. 467-480. https://doi.org/10.1108/COMPEL-07-2019-0305

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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