Research Article: |
An Extensive Tensor Algebraic Model of Transformer |

Author: |
Asst. Prof. Dr. Rawid Banchuin |

Email: |
rawid.ban@siam.edu |

Department/Faculty |
Graduate School of IT, Siam University, Bangkok 10160 |

Published: |
ECTI Transactions on Computer and Information Technology (ECTI-CIT), 2020 (indexed by SCOPUS) |

### Citation

Banchuin, R., & Chaisrichaoren, R. (2020). An extensive tensor algebraic model of transformer. *ECTI Transactions on Computer and Information Technology (ECTI-CIT)*, *14*(1), 79-91. Retrieved from https://doi.org/10.37936/ecti-cit.2020141.153727

### ABSTRACT

An extensive s-domain multilinear algebraic model of the transformer has been proposed. This model is alternatively a tensor algebraic model because the multilinear algebra is alternatively the tensor algebra. Unlike the traditional matrix-vector approach, which relies on conventional linear algebra, this model, which in turn uses the multilinear algebra that is of higher dimension and is thus more generic, is applicable to those recently often cited transformers which often have unconventional characteristics such as frequency variant parameters, time variant parameters, and fractional impedance. Examples of such transformers are on-chip monolithic transformers, dynamic transformers, and transformers with fractional impedances. The imperfect coupling has been considered, and a multiple winding transformer has also been assumed. Applications of the proposed model to the chosen recent transformers with unconventional characteristics is presented. The effects of failure of Kron’s postulate on power invariant and validity of duality invariant, which pertain to the mentioned issues, are also discussed. The proposed extensive model is more inclusive and up to date than the matrix-vector based model and previous algebraic models. However, it is more complicated.

**Keywords: Dynamic Transformer, Fractional Mutual Inductance, Multilinear Algebra, On-chip Monolithic Transformer, Tensor Algebra**

## An Extensive Tensor Algebraic Model of Transformer

Graduate Schools, Siam University, Bangkok, Thailand

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