Current distribution reconstruction in switching arcs by means of regularization based on GSVD

Abstract

The knowledge of the variation of arc current is helpful in improving the breaking performance of a vacuum circuit breaker. As a novel non-intrusive method, arc magnetic performance testing technology has attracted attention. In view of the widely used regularization method of the standard form in arc current reconstructions cannot fully overcome the ill-posed nature of the Biot-Savart equation, the regularization approach based on generalized singular value decomposition (GSVD) is proposed to improve the situation. Moreover, a discrete 3-D arc model with the help of the finite element technique incorporating the current divergence-free and boundary conditions is introduced to improve the authenticity of the model. The performance of the truncated generalized singular value decomposition (TGSVD) and general-form Tikhonov regularization with derivative operators L₁ and L₂ are studied in numerical tests. In addition, the effectiveness of generalized cross validation criterion, quasi optimality criterion and normalized cumulative periodic graph method in selecting regularization parameters are compared. The methodology can help improve arc control and guide the design of vacuum circuit breakers with improved performance parameters.

KEYWORDS:

• Electromagnetic inverse problems
• arc inversion
• finite element technique
• GSVD
• regularization parameter selection

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65J22
• 65F22
• 65M60
• 35Q61

Acknowledgements

We thank the reviewers and editors for their warm work in the paper revision process. Meanwhile we thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51777136].