Distributed Magnetic Flux Density on the Cross-Section of a Transformer Core

Lingzhi Li,Jing Zheng,Hai Huang,David Matthews,Adrian Keating,Xuhao Du,Jie Pan

doi:10.3390/electronics8030297

Abstract

In this paper, the magnetic flux density distribution on the cross-sections of a transformer core is studied. The core for this study consists of two identical U-shaped cores joint at their open surfaces with known air gaps. The magnetic flux density at one of their joint boundary surfaces was measured for different air gaps. A finite element model (FEM) was built to simulate the magnetic flux density and compared with experiment data. Using the validated FEM, the distributed magnetic flux density on the cross-section of the core structure can be obtained when the air gap approaches zero. An engineering model of the density based on the Ampere’s circuit law was also developed and used to explain the relationship between air gap and mean magnetic flux density on the cross-section. The magnetic flux density on the cross-section was found to have a convex-shaped distribution and could be described by an empirical formula. Using this approach, the magnetic flux density distribution in cores with different interlayer insulation was obtained and discussed. This method could also examine the leakage of magnetic flux density in the air gap region when the distance is non-zero, and the relationship between the leakage field and the field in the core structure. The proposed method and model can provide a more detailed understanding for the magnetic field of transformer cores and potential application in designing quiet transformers and condition monitoring.

Highlights

An understanding of the magnetic flux density distribution in a transformer core is important for transformer vibration analysis, noise prediction, core loss control, inductor design and manufacturing [1
Experimental results of U-shaped cores for 64 subsections under all investigated air gap distances were compared with the finite element model (FEM) results
Of each investigated location’s relative error is expressed as Equation (6), where LG is the set of investigated air gap distances with cardinality | LG |

Summary

Introduction

An understanding of the magnetic flux density distribution in a transformer core is important for transformer vibration analysis, noise prediction, core loss control, inductor design and manufacturing [1–3]. An understanding of the magnetic flux density distribution in a transformer core is important for transformer vibration analysis, noise prediction, core loss control, inductor design and manufacturing [1–. Measurements of flux density for individual core’s packages, using wires wound in each package of the limbs and yokes, have indicated that the centre package of the core had the minimum magnetic flux density [4]. Experiments based on wound-wires restricts the measurement to only the core’s local magnetic flux. The magnetic field inside the core can be measured by using a search coil placed inside holes drilled into the core [7]. Shilyashki measured the magnetic flux density inside the core by inserting a pin sensor with pickup coil to the measurement channels [1,8]. The large discontinuity in the magnetic flux within the holes may introduce unpredictable perturbations in the magnetic field, requiring detailed correction of the data

Objectives

Results

Conclusion