A Tensor Algebraic Model of On-chip Monolithic Transformer

Banchuin, Rawid; Chaisricharoen, Roungsan

doi:10.1109/ecticon.2018.8620056

Cited by 2 publications

(14 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a result, I P ik , I Sik , V P ik and V Sjk are functions of complex frequency only, and the obtained current/voltage tensors are able to model the time dependencies of current/voltage functions caused by those of the circuit parameters despite the fact that these tensors are purely in the s-domain. This cannot be achieved if an order 1 tensor has been assumed similarly to [19], [20] and [24] because a tensor of order 1 is mathematically equivalent a vector. Before we proceed further, it should be mentioned here that the dimensions of I P ik and V P ik are N ×K, but those of I Sjk and V Sjk are M × K.…”

Section: The Proposed Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the last few decades, a very powerful mathematical tool entitled multilinear algebra, or tensor algebra, which is the generalization of the matrixvector algebra, has been applied to electrical engineering [18]- [24]. Tensor algebraic modelling attempts of the transformer have been proposed [19], [20], [24]. Unfortunately, the results of [19] and [20] are also inapplicable to recent transformers because these works used order 2 tensors as the impedance and current/voltage transformation arrays and used order 1 tensors for current/voltage arrays.…”

Section: Introductionmentioning

confidence: 99%

“…Despite the failures of [19] and [20], tensor algebra is still very promising due to its greater generality compared to matrix-vector algebra. Therefore we de-rived a tensor algebraic model of the on-chip monolithic transformer in [24] where the effects of imperfect coupling and frequency dependent circuit parameters, which are common to the on-chip transformer, have been taken into account. However, this previous work used order 2 tensors for the impedance and current/voltage transformation arrays and used order 1 tensors for current/voltage arrays similarly to [19] and [20].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the effects of failure of Kron's postulate on power invariant and validity of duality invariant [22] to the voltage-current relationships of the transformer, which merit concern for the mentioned issues, have also been discussed. The proposed extensive tensor algebraic model is more inclusive than its predecessor [24]. It is an efficient and up to date approach for modelling recent transformers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Extensive Tensor Algebraic Model of Transformer

Banchuin

Chaisrichaoren

2020

ECTI-CIT

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: The Proposed Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Extensive Tensor Algebraic Model of Transformer

Banchuin

Chaisrichaoren

2020

ECTI-CIT

Self Cite

View full text Add to dashboard Cite

show abstract

Vector SDE Based Stochastic Analysis of Transformer

Banchuin

Chaisricharoen

2021

ECTI-CIT

Self Cite

View full text Add to dashboard Cite

In this research, the stochastic behaviours oftransformer have been analysed by using the stochasticdifferential equation approach where both noise in thevoltage source applied to the transformer and the randomvariations in elements and parameters of transformers havebeen considered. The resulting vector stochasticdifferential equations of the transformer have been bothanalytically and numerically solved in the Ito sense wherethe Euler-Maruyama scheme has been adopted fordetermining the numerical solutions which have been theirsample means have been used for verification. With theobtained analytical and numerical solutions, the stochasticproperties of the transformer’s electrical quantities havebeen studied and the influences of noise in the voltagesource and random variations in elements and parametersof transformers to those electrical quantities have beenanalysed. The causes of high and low frequency stochasticvariations of such electrical quantities in both transient andsteady state have been pointed out. Moreover, furtherextension of our stochastic differential equations and therelated mathematical formulations has also been given.

show abstract

A Tensor Algebraic Model of On-chip Monolithic Transformer

Cited by 2 publications

References 21 publications

An Extensive Tensor Algebraic Model of Transformer

An Extensive Tensor Algebraic Model of Transformer

Vector SDE Based Stochastic Analysis of Transformer

Contact Info

Product

Resources

About