Optical Design of OCT with Gapped Magnetic Ring

doi:10.4236/epe.2013.53B003

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Energy and Power Engineering, 2013, 5, 11-14

doi:10.4236/epe.2013.53B003 Published Online May 2013 (http://www.scirp.org/journal/epe)

Optical Design of OCT with Gapp ed Magnetic Ring*

Xiaoyi Su, Qifeng Xu

College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China

Email: [email protected]

Received 2013

ABSTRACT

The mathematics and physics model of OCT (Optical Current Transformer) with a gapped magnetic ring is briefly dis-

cussed in the paper. And some proposals of how to select the magnetic materials and crystals and reduce the stress bire-

fringence of the crystal are also put forward in the paper. Based on the above, an OCT with 1000 A rated current is de-

signed by using the ANSOFT Maxwell tools.

Keywords: Ferromagnetic Collector Type; Optics Current Transformer; Magnetic Properties; Linear Birefringence

1. Introduction

Faraday magneto-optical effect is applied in optical cur-

rent transformer (OCT). Based on its sensing methodol-

ogy it can be divided into four types: fiber one, bulk

glass one, solenoid one, as well as gapped magnetic ring

one [1]. The one with a gapped magnetic ring utilizes a

small piece of magneto-optic crystal and other optical

elements to be placed in the gap of the magnetic ring

wounding around a current carrying conductor to form an

optical circuit. The gap magnetically induced by the cur-

rent flowing in the conductor and the crystal are the

“heart” of an optical current transformer head. Taken

together, the magnetic properties and the optical proper-

ties should be taken into consideration in the design. This

paper discusses the characteristics of the OCT with

gapped magnetic ring. Additionally, reasons and proce-

dures to select magnetic materials and crystals and miti-

gate stress birefringence are also represented specifically

in the paper. Depending on the analysis above and the

ANSOFT Maxwell tools, the optimized structure of an

OCT with 1000A has been achieved.

2. The Characteristics of OCT with Gapped

Magnetic Ring

When a linearly polarized light passes through a mag-

netic field paralleling to its propagation direction, a opti-

cal phase shift of the light called Faraday rotation angle

will created due to the Faraday effect

VHdl



 (1)

where V is the Verdet constant. Once deemed if a gap of

magnetic ring is small enough, the gap magnetic can be

regarded as same as the ring inherent magnetic induced

by the current flowing in the conductor. Additionally,

based on the Ampere circuital theorem the gap magnetic

strength is given by ()

ggaa

Il ulu



 (2)

where l is the polarized light effective optical passing

path in the gap, I is the primary current, lg is the air-gap

length, ug is the air permeability, ua is the gapped mag-

netic ring permeability, la is the gapped magnetic ring

average loop length. As ug is far less than ua, Equation (1)

is simplified as

Il (3)

Combined Equation (1) with Equatio n (3), the Faraday

deflection angle θ and the primary current I are given by

VHdluVIl l





 (4)



luVl



 (5)

in which lc is the crystal length. Set Pi to be the polarizer

output light intensity and P0 to be the analyzer output

light intensity. According to the Malus law, the relation-

ship between Pi and P0 is expressed as

0cos ()

PaP







 (6)

where α is the optical attenuation coefficient intensity; φ

is the difference optical phase shift between the two out-

put light waves.

Desiring to obtain the maximum outpu t power, φ is set

to 45°. If θ is small enough, sin2θ will approximately

equal to 2θ. Equation (6) transforms into

(1 )

uVIl

PP PP

 

CAC

(7)

*Project supported by the National Natural Science Foundation of China

(51177016).

X. Y. SU, Q. F. XU

where PAC, the alternate current signal, is expressed as

PAC = (aPiugVIlc)/lg, while PDC, the direct current signal,

is expressed as PDC = (aPi)/lg. Eliminating the fluctua-

tions of optical power by introducing the operation

U=PAC/PDC. The relationship between U and I is given

UIuVIll (8)

3. The Optimal Design of OCT

3.1. The Selection of Magnetic Material

The cold-rolled silicon steel, the permalloy alloy and the

amorphous alloy are commonly made on gapped mag-

netic rings. Their characteristics differences are reflected

in the magnetic permeability, the remanence density, the

saturation magnetization, the coercive force, the iron loss,

the Curie temperature, as well as the magnetostriction

coefficient. Considering that the OCT actual operation

environment temperature is less than the Curie tempera-

ture of magnetic materials, the iron loss and the magne-

tostriction coefficient are negligible under the 1000A

power frequency system, so these three factors, the iron

loss, the Curie temperature and the magnetostriction co-

efficient can be ignored. Table 1 shows the remainder

typical parameters.

Table 1. The comparison of typical parameters of the three

materials.

Typical Parameters

Materials Saturation

Mag-

netiz-ation

(T)

Magnetic

permeability

(*104)

Remanence

density

（T）

Co-

erci-ve

force

(A/m)

amorphous

alloy 1.5 0.25 1 2.0

permalloy

alloy 0.6 5.8 0.4 4.3

cold-rolled

silicon

steel 1.7 0.12 1.56 7

Permalloy alloy has the highest initial permeability,

the amorphous alloy has a lower one and the cold-rolled

silicon steel has a lowest one. Additionally, for closed

cores, a higher initial permeability is good for measure-

ment sensitivity. But the gapped magnetic rings are dif-

ferent. As the gap magnetic induction Bg is

()

aag g

Blu lu

 (9)

Once the air permeability is 104 to 105 times bigger

than magnetic rings’. Then la is 102 times larger than lg,

so la/ua is far less than lg/ug. Equation (9) is simplified as

BuIl (10)

In this case, the magnetic indu

ction Bg depends on the

imary current I, the gap length lg and the air permeabil-

ity ug . That is to say, the permeability ua is an unimpor-

tant factor to the magnetic properties of gapped magnetic

rings.

Static field simulations on three magnetic materials

shown in Table 1 are done respectively by using the

ANSOFT Maxwell tool. The simulation gapped magnetic

ring parameters as follow: the inner radius is 30 mm, the

outer radius is 70 mm, the height is 40 mm and, the gap

length is 20 mm. Their basic magnetization curve are

illustrated in Figure 1. When the primary current is less

than 4 KA, these three curves are overlapped and the

cold-rolled silicon steel one has the lo ngest current linear

region. Since normal load current flowing on the con-

ductor is usually under 1 kA level, associating with the

linear region length shown in Figure 1, cold-rolled sili-

con steel and amorphous alloy have better magnetic per-

formance compared to permalloy alloy.

The remanence of magnetic concentrator ring is given

by[2]:

()( 0)

ul ul

BfH fH

   (11)

where f(B) is a closed core magnetization curve function.

to select a suitable magnetic

The remanence in the Gapped magnetic ring are de-

pended on the average magnetic path length and the air

gap length. These dependencies make the necessity to

design a r ight ring overall size. A smaller remanence has

certain distinct advantages to maintain the response

characteristics of magnetization, decrease coercive force

and reduce hysteresis loss.

Taken together, the norm

material is the one having a small remanence, a small

coercive force and a large saturation magnetic flux den-

sity. Thereby, amorphous alloy is the most suitable mate-

rial.

Figure 1. The basic magnetization curve of the three gap

magnetic rin gs.

X. Y. SU, Q. F. XU 13

3.2. The Selection of Magneto-Optical Crystal

Since the Verdet constant varies with the dynamic tem-

perature, the temperature coefficient should be consid-

ered during the selection of magneto-optical crystal.

When the te mperatu re change s from -2 5℃ to +80℃, the

Verdet constant of FR-5, a paramagnetic material, is re-

duced by 30% throughout the mutative temperature and

YIG that is a ferromagnetic material has 25% irregular

variation, while ZF-7 that is an anti-magnetic material

only changes 0.79% [3]. Similarly, an anti-magnetic ma-

terial called MR1 almost has no effect on the Verdet

constant in the temperature ranging from -55 to +135℃.

Additionally, its Verdet constant is as high as 0.065 -

0.092 min/Oe.cm (@ 632.8 nm) which is helpful to

shorten the crystal length and reduce the line birefrin-

gence. Therefore, the MR1 is employed in this design.

As the OCT using light to measure the magnetic field

surrounding a current carrying conductor has a transfer

function with a sine wave characteristics which made the

OCT polarization interference be a non-linear portion.

An approximate linear relationship between sin2θ and 2θ

introduced in the section 2 can fix th is problem when θ is

small enough. Ultimately, the OCT accuracy level will

determine the maximum Faraday deflection angle and the

crystal length. Set X is the difference between lg and lc ,

Equations (5) could be transformed as







(12)

Assuming the OCT accuracy

Reduce Stress Birefringence

tion

ilar expansion coefficient with

mization Structure of Gapped

Magnetic Rings

eter-

mineurrent carrying conductor which

ner and outer radius N, the more uniform gap

is a 0.2 class and the

imary current is 1000 A, its measurement error is less

than 0.2%. Then the maximum Faraday deflection angle

θmax is 0.877°. Set the maximum X is 20 mm, (As the

prism and polarizer product class size are 7 mm and 2

mm respectively. The other 2mm space is reserved for

installation). Putting these data into Equation (12), l is

calculated to 16.72 mm. Therefore, the crystal maximum

length is 16 mm.

3.3. Methods to

During the process of magneto-optic crystal produc

and processing or the in teract ion between the sensor head

and the adjacent structure, residual stress will occur and

stress birefringence will created simultaneously.

Since expansion coefficient has a function with the

temperature when the temperature ch anges the di fferenc e

on the materials expansion coefficient will cause tem-

perature gradients owing to the uneven temperature dis-

tribution of the sens ing head. Then thermal stress is gen-

erated within the sensing head and a linear birefringence

appears. Line birefringence aliasing on the Faraday po-

larization angle can undermine the reliability and stabil-

ity of the OCT [4]. For example, an OCT sensing head

has a structure of 70 mm outer diameter, 30 mm inner

diameter, 40 mm height and 30 mm air gap length and

ZF-7 as the sensing element which is 10 mm long, con-

ducted by a 1000 A primary current, its Faraday rotation

angle is 4.81° and its line birefringence angle is about

0.560 and it introduces 11.64% measurement error. The

method to reduce the linear birefring ence is to reduce the

magneto-optical material length. For example, using a

200 um thick magneto-optical film that dopes with Ce3+

by using the technology of liquid phase epitaxial (LPE)

as the sensing element instead of ZF-7 [5], then the

Faraday deflection angle is turned to 28.60 and its line

birefringence angle is 0.0112° only and the corre-

sponding error drops to 0.039%. It turns that the influ-

ence of linear birefringence on Faraday deflection angle

is effectively weakened.

Further, filling asbestos in sensor head or utilizing

materials having the sim

e magneto-optical material can also free from the tem-

perature variation gradient and weaken the thermal stress

birefringence.

3.4. The Opti

Since the gapped magnetic ring’s inner radius r is d

d by the size of a c

is determined by the primary current. Depending on the

analysis, the rated current of an OCT designed in this

paper is 1000 A, so conductive rod radius is set to 18 mm.

Additionally, leaving a 10mm margin sp ace to fill asbes-

tos, the gapped magnetic ring inner radius r is 28 mm.

Assuming N is the difference between th e inne r and ou ter

radius of the gapped magnetic ring. So the outer radius R

can be expressed as the sum of r and N. Combing Equa-

tion (3) with Equation (11), the gap length not only de-

termines the gap induction, but also affects the remanent

density. when the magnetic material is certain, the

smaller the gap length, the greater the gap induction and

remanence. Since the crystal length is described in selec-

tion 3.2, the air gap has a length ranging from 20 mm to

36 mm. Depending on the ANSOFT Maxwell tool, mak-

ing simulations on three gapped magnetic rings with 25

mm, 30 mm and 35 mm penning gap length under the

1000 A system respectively. The result are illustrated in

Figure 2 and Figure 3 which show the effect of the dif-

ference between a gapped magnetic ring inner and outer

radius on the gap induction Bg , as well as on the rema-

nent Br.

The larger the difference between a gapped magnetic

ring’s in

agnetic field distribution and the smaller the magnetic

flux leakage [6]. When N exceeds the length 30 mm, the

gap magnetic distribution is completely uniform. Con-

sidering to decrease the volume of material and achieve

X. Y. SU, Q. F. XU

4. Conclusions

This paper discusses the characteristics of OCT with

gapped magnetic ring, and some considerations to select

the magnetic material and the magneto-optical crystal,

and reduce the stress birefringence. Depending on the

analysis in the paper, the optimized design of an OCT

with 1000 A rated primary current is designed by using

the ANSOFT Maxwell tools. This optimized sensing

head has a structure as follows: 28 mm inner radius, 58

mm outer radius, 15 mm height and 25 mm length gap.

Additionally, the magneto-optical crystal choose MR1

with the length of 5 mm. In a temperature range from -40

℃ to +80℃, the OCT designed can be employed suc-

cessfully.

Figure 2. The effect of the difference between a gapped mag-

netic ring’s inner and outer radius on th e gap induction.

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Figure 3. The effect of the difference between a gapped mag-

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0 mm

ereby, the gapped magnetic ring outer radius R is 58

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doi：10.1109/61.156982