Magnetic Field Distribution of a Novel Variable

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The novel variable inductor consist of a vacant winding and a toroidal core winding, the ... material, the B-H loops shows a “shearing” with increasing dc current.
PIERS Proceedings, Cambridge, USA, July 5–8, 2010

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Magnetic Field Distribution of a Novel Variable Inductor Based on Orthogonal Magnetization Zhengrong Jiang1 , Zhengxi Li1 , and Jianye Chen2 1

Department of Electrical & Mechanical Engineering, North China University of Technology Beijing 100144, China 2 Department of Electrical Engineering, Tsinghua University, Beijing 100084, China

Abstract— A computation method for the magnetic field distribution of a novel variable inductor based on orthogonal magnetization is presented. The inductor includes two windings, one is an ac winding for exciting ac field, another is a dc winding for creating dc bias field, the latter is perpendicular to the former. The vector combination results in a semi-rotating field in the core and make the hysteresis “shearing”. This feature makes the variable inductor safely and have linearly characteristic in case application on HVDC. The effect on material magnetic characteristic caused by orthogonal bias field is explained and the field distribution is computed, the calculated results are consistent with the experimental data well. 1. INTRODUCTION

With the development of HVDC transmission, a greater demand for high quality variable inductor is expected. The safety and linearity are essential to the application of voltage variation, VAR compensator, harmonic filtering and DC-AC converter. Several magnetic devices for variable inductor have been presented [1]. However, the harmonics of the output current can not be neglected. In this paper, we present an approach to control the permeability of an inductor core made of toroidal grain oriented Fe-Si laminations. This approach is based on the vectorial magnetization response of the core under two orthogonal field components. The vectorial sum results in a semirotating field in the inductor core. This method brings about many good virtues. Details of the inductor under consideration, its analytical aspects, numerical simulations and control characteristic are given in the following sections. 2. INDUCTOR STRUCTURE AND MAGNETIZATION MECHINISM

The novel variable inductor consist of a vacant winding and a toroidal core winding, the former is the main coil and connected with AC exciting current, the latter is placed in the former and connected with DC control current. Due to the two windings orthogonal orientation, there is no inductance voltage in the DC control winding, hence the DC control element is safe even if under a high voltage application. As for the oriented Fe-Si lamination core, it is subjected to two direction magnetic fields, one ~ is the shifting H(t) in the axis direction (often as easy axis of Fe-Si silicon sheet) creating by AC ~ current, another is circumaxile H⊥ which derives from DC current. It is perpendicular to the H(t), thus a semi-rotating field is created in the Fe-Si core. Conventionally the magnetic properties of material are analysed assuming that the directions of B and H are parallel. However, under the orthogonal fields the magnetic properties of the oriented lamination core are related by tensor permeability since B vector is not parallel to H vector in the core and permeability depend on magnetic flux density [2], the effective core permeability µ can be described phenomenally by a complex permeability µ = µ0 − jµ00 , the permeability tensor consists of an anisotropic matrix involving the permeabilities µx and µy and a rotating matrix, ~ which describes the perpendicular component H⊥ by shifting H(t) with an angle α in space. The relationship of B, H and permeability µ can be described as µ ¶ µ ¶ cos α sin α µ 0 x ~ = ~ =↔ ~ B · ·H µ·H (1) − sin α cos α 0 µy ~ − arc(B). ~ where, α is the loss angle and α = arc(H) As for the rotating matrix, the diagonal terms represent for alternating flux permeability tensors and the off-diagonal terms denotes the rotational ones [3]. When the phase difference between B

Progress In Electromagnetics Research Symposium Proceedings, Cambridge, USA, July 5–8, 2010

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and H caused by rotational hysteresis is considered the permeability tensor becomes the full tensor as follows: µ ¶ · ¸µ ¶ Bx µ µxy Hx = xx (2) By µyx µyy Hy The two-dimensional governing equation including two dimensional magnetic property is written as follow: µ ¶ µ ¶ µ ¶ µ ¶ ∂ ∂A ∂ ∂A ∂ ∂A ∂ ∂A vyy + vxx − vyx − vxy = −J0 − Jm (3) ∂x ∂x ∂y ∂y ∂x ∂y ∂y ∂x where, A is the magnetic vector potential, υ is the reluctivity tensor, J0 is the current density and Jm is the equivalent magnetizing current density. The non-linear Equation (3) is solved using the Newton-Raphson method and the field distribution of flux in the grain oriented lamination core can be calculated. 3. B-H HYSTERESIS AND FIELD DISTRIBUTION

Figure 2 shows the hysteresis loops of the grain-oriented lamination core under the various DC bias currents. The measurements are performed under dc and ac field simultaneously. It is clearly apparent that the orthogonal bias field (dc field) changed the hysteresis behavior of the magnetic material, the B-H loops shows a “shearing” with increasing dc current. The magnetization at maximum applied field, the remanence and the coercivity all decreased with increasing orthogonal bias field. Whence the orthogonal bias field alters the inductance of the device. Figure 3 shows the finite model of the grain oriented core. The circumcolumnar arrows denote the ac exciting current, the dc control current is divided into four sections toroidally. Figure 4 shows the flux distribution. According to Neel’s phase theory [4], the hysteretic magnetization curve is dependent on the direction of the applied field relative to the easy axis. Looking at above B-H measurement results, the B-H loop became less slope with increasing dc bias current. it is realized that the orthogonal dc bias field affects the magnetization process by enhancing the anisotropy of the grain oriented laminations and gives rise to a decrease in effective inductance of the device. The role of dc bias field is like a “magnetic valve” on the path to control the flux. It can be seen from Figure 4.

(a)

(c) Figure 1: Inductor based on orthogonal magnetization.

(b)

(d)

Figure 2: B-H loop with various dc bias current (a)0 A, (b) 1 A, (c) 2 A, (d) 3 A.

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PIERS Proceedings, Cambridge, USA, July 5–8, 2010

Figure 3: Loading current density in finite element model.

Figure 4: Flux distribution of grain-oriented core.

Figure 5: Control characteristic. 4. CONTROL CHARACTERISTIC

Under various main ac currents from 98.95 mA to 390.5 mA, the inductor is subject to series dc control currents from 0 A to 10 A respectively. Write down the voltages and currents of the inductor accordingly, then the efficient inductance can be given as: L=

U˙ (mH) 2πf · I˙

(4)

The following is the control characteristic curve. From the control characteristic, we found that the control ability of DC current to the main inductance decrease with the main current increasing, it is because that when the field caused by the main current is much larger than the dc bias MMF, the domain wall rotation is prevailing subject to ac exciting field and the dc bias field has no significant effect on the overall effective inductance any more. 5. CONCLUSION

The permeability of magnetic materials can be changed by applying a orthogonal dc magnetic field which is oriented perpendicular to the main flux direction, in this way the inductance of the main coil can be controlled. This method has the effect of lowering the permeability by adding anisotropic of the magnetic material without affecting the linearity of the magnetizing process [5]. Due to

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maintaining magnetization linearity no additional harmonics are produced on the application of HVDC. REFERENCES

1. Cho, G. C., G. H. Jung, N. S. Choi, and G. H. Cho, “Analysis and controller design of static var compensator using three-level GTOinverter,” IEEE Trans. Power Electron., Vol. 11, 57–65, 1996. 2. Enokizono, M., K. Yuki, and S. Kawano, “An improved magnetic field analysis in oriented steel sheet by finite element method considering tensor reluctivity,” IEEE Transactions on Magnetics, Vol. 31, No. 3, May 1995. 3. Enkinono, M. and K. Yuki, “An improved magnetic field analysis in oriented steel sheet by finite element method considering tensor reluctivity,” Proceedings ofthe 6th CEFC, P3C04, 1994. 4. Fiorillo, F. and L. R. Dupre, “Comprehensive model of magnetization curve, hysteresis loops, and losses in any direction in grain-oriented Fe-Si,” IEEE Transactions on Magnetics, Vol. 38, No. 3, May 2002. 5. Jiang, Z. R. and J. Y. Chen, “Semi-core variable inductor based on DC excitation field,” Automation of Electric Power Systems, Vol. 31, No. 5, Mar. 10, 2007.