Leakage Inductances of Transformers at Arbitrarily Located Windings

Jaraczewski, Marcin; Sobczyk, Tadeusz

doi:10.3390/en13236464

Cited by 8 publications

(12 citation statements)

References 14 publications

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“…The second problem leads to the Neumann boundary conditions on the blue boundaries in Figure 1, but some modification of the ampere-turns function is required, which was proved in Jaraczewski and Sobczyk (2020). The Neumann zero conditions can be stated at the blue boundaries only for balanced ampere-turns of the HV and LV windings; otherwise, some modification of the ampere-turn function would be needed to achieve the balanced ampere-turns.…”

Section: Solving Boundary Conditions Formentioning

confidence: 99%

“…For starters, DPDO, developed in Sobczyk (2019) and Jaraczewski and Sobczyk (2020), was briefly characterised. They relate the values of the functions z ( x , y ) of two periodic variables to the values of its partial derivatives in points regularly located on the rectangular area in which the function is defined.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Discrete partial differential operators (DPDOs) for 2D problems were proposed by Sobczyk (2019). They have been successfully tested by Jaraczewski and Sobczyk (2020-E) to calculate the leakage inductances of power transformers. Those DPDOs are based on the general assumption that the solution in its original area repeats in each direction outside of it and is determined by two-variable functions, periodic with respect to each of them.…”

Section: Introductionmentioning

confidence: 99%

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Solving 2D boundary-value problems using discrete partial differential operators

Jaraczewski

Sobczyk

2021

COMPEL

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Purpose Discrete differential operators of periodic base functions have been examined to solve boundary-value problems. This paper aims to identify the difficulties of using those operators to solve ordinary linear and nonlinear differential equations with Dirichlet and Neumann boundary conditions. Design/methodology/approach This paper presents a promising approach for solving two-dimensional (2D) boundary problems of elliptic differential equations. To create finite differential equations, specially developed discrete partial differential operators are used to replace the partial derivatives in the differential equations. These operators relate the value of the partial derivatives at each point to the value of the function at all points evenly distributed over the area where the solution is being sought. Exemplary 2D elliptic equations are solved for two types of boundary conditions: the Dirichlet and the Neumann. Findings An alternative method has been proposed to create finite-difference equations and an effective method to determine the leakage flux in the transformer window. Research limitations/implications The proposed approach can be classified as an extension of the finite-difference method based on the new formulas approximating the derivatives. This method can be extended to the 3D or time-periodic 2D cases. Practical implications This paper presents a methodology for calculations of the self- and mutual-leakage inductances for windings arbitrarily located in the transformer window, which is needed for special transformers or in any case of the internal asymmetry of windings. Originality/value The presented methodology allows us to obtain the magnetic vector potential distribution in the transformer window only, for example, to omit the magnetic core of the transformer from calculations.

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Section: Solving Boundary Conditions Formentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving 2D boundary-value problems using discrete partial differential operators

Jaraczewski

Sobczyk

2021

COMPEL

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“…The leakage reactance between the pair of low voltage and zig winding can be calculated by using (7) o…”

Section: Reactance In Zigzag Transformersmentioning

confidence: 99%

“…Reluctance network modeling is faster but less accurate as compared to the numerical method. Due to the higher accuracy, compared to the other analytical method, the Rogowski method is one of the efficient analytical techniques that can be used effectively to evaluate leakage reactance [7].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Analytical Method and Different Finite Element Models for the Calculation of Leakage Inductance in Zigzag Transformers

Dawood

Isik²,

Kömürgöz

2022

ELEKTRON ELEKTROTECH

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A zigzag transformer is a key segment of the electric power system. The optimal design of the zigzag transformer is important for transformer designers to provide a required return path for earth faults and to ensure proper operation of a power system. The two most important parameters of the zigzag transformers are no-load losses and leakage impedance. The accurate calculation of both factors helps to minimize the overall cost of the transformer. Therefore, the prediction of leakage reactance in the zigzag transformer using analytical or numerical methods is an essential part of the early designing stages of the transformer. This paper provides several two- and three-dimensional finite element models. The main purpose of these models is to evaluate the accuracy of the different models for the calculation of the leakage reactance. An analytical formula and a complete procedure for the calculation of the leakage reactance in the zigzag transformer are also provided, which will help the researchers and transformer designer to optimize this type of transformer. The prototype is also manufactured and tested to verify the accuracy of the analytical method and finite element models for the calculation of the leakage reactance. The simulation and experimental results show that the finite element calculation cannot only obtain accurate leakage reactance values (magnetostatic analysis), but also provides better accuracy in the no-load losses (transient analysis).

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Calculation of the losses in the shunt reactor at nominal and rated power with experimental verification

Dawood

Kömürgöz

Isik³

2022

2022 5th International Conference on Power Electronics and Their Applications (ICPEA)

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Leakage Inductances of Transformers at Arbitrarily Located Windings

Cited by 8 publications

References 14 publications

Solving 2D boundary-value problems using discrete partial differential operators

Solving 2D boundary-value problems using discrete partial differential operators

Comparison of Analytical Method and Different Finite Element Models for the Calculation of Leakage Inductance in Zigzag Transformers

Calculation of the losses in the shunt reactor at nominal and rated power with experimental verification

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