1
2D and 3D magnetic shielding simulation
methods and practical solutions
Oriano Bottauscio
Istituto Elettrotecnico Nazionale Galileo Ferraris Torino, Italy
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Summary
Part I – General principles of magnetic field mitigation
Part II - Mathematical models for shielding problems
Part III – Magnetic material properties and influence of geometrical parameters
Part IV – Examples of applications
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Part I: General principles of magnetic field
mitigation
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Concept of passive shielding
One strategy for reducing magnetic fields in a specific region is to make use of material properties for altering the spatial distribution of the magnetic field from a given source. A quantitative measure of the effectiveness of a passive shield in reducing the magnetic field magnitude is the shielding factor, s , defined as:
shield field Magnetic
shield field Magnetics
with
ofabsence in
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Two basic physical mechanismsTwo separate physical mechanisms can contribute to materials-based magnetic shielding.
1) Magnetostatic shielding, obtained by shunting the magnetic flux and diverting it away from a shielded region.
2) Eddy current shielding, obtained in presence of time-varying magnetic fields by inducing currents to flow whose effect is to "buck out" the main fields.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Magnetostatic shielding
It is realized by the introduction of ferromagnetic materials having high magnetic permeability, which create a preferential path for the magnetic field lines
A considerable reduction of the magnetic field is generally reached in the region beyond the shield
This is the only passive shield solution in presence of d.c. magnetic fields
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Magnetostatic shielding
Without shield
Shield
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ideal cases: infinite cylinder and spherical shieldsFor cylindrical and spherical shields with relative permeability µr inner radius a and thickness the shielding factor in presence of a uniform magnetic field is:
r
2
2r2
r
4144
11
rrs
ar
2
Cylinder
Sphere
r
23
2r
rr
916128
12122
rrrs
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ideal case: infinite cylinder and spherical shields
Large relative permeability and large ratio of thickness to diameter produce good shielding.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Eddy current shieldingTime varying magnetic fields induce electromotive forces and, consequently, eddy currents are forced to circulate in the conductive material.
Induced currents constitute an additional field source, which is superimposed to the main magnetic field.
The global effect is a compression of the flux lines on the source hand and a reduction of the magnetic flux density beyond the shields.
Obviously, this kind of shield is not effective for d.c. fields and its efficiency increases with the supply frequency.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Eddy current shielding
Without shield
Shield
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ideal case: infinite cylinder shield
For a long cylindrical shield with permeability μo, conductivity , inner radius a, and thickness ∆ in a sinusoidally varying field at angular frequency , the shielding factor is given by:
21 o
a
is
At the increasing of conductivity, radius, and thickness the shielding efficiency increases.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
From ideal to actual shields
The analysis of ideal shields having cylindrical or spherical shapes is useful as a first approach to understand the factors affecting the shielding mechanism.
Anyway, in most cases actual shielding configurations are far from these idealized geometries.
In order to reproduce actual conditions, more sophisticated models have to be implemented.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Part II: Mathematical models for shielding
problems
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Peculiarities of shielding problems
Main peculiarities of the problem:o the shields usually have small
thickness with respect to other dimensions scale problem
o The field is usually not limited in a defined volume open boundary problems
o Presence of significant electromagnetic effects
o Possible complex geometrical situations Analytical formula are not always available
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Possible approaches to simulation
o The solution of Maxwell equations is needed.
o Standard Finite Element codes are usually not adequate for two main reasons:
o Open boundary domainso Scale problem introduced by thin shields
o Possible alternative approaches:o Analytical methods (only for simple
geometries)o Hybrid Finite Element – Boundary Element
formulations (mainly for 2D open boundary nonlinear problems)
o Thin shield formulation (2D-3D open boundary linear problems)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Analytical methodsTwo possible alternative analytical
approaches:Separation of variables• Simple geometrical configurations:
• Closed cylindrical or spherical shields• Infinite planar shield
• More complex material properties (linear behaviour)
Conformal mapping • More complex geometrical configurations• Idealized material properties:
• Ideal pure conductive (PES)• Ideal pure ferromagnetic (PMS)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Separation of variables: Planar one-layer shield
0 1
)(02 )(cos2
4 M
mm
ytykmx dkxxke
IWB m
0 1
)(02 )(sin2
4 M
mm
ytykmy dkxxke
IWB m
k 20 21
21 jpk
2
11
1
WkW
r
12
kW r
tt eWeW 11 22
22 )1()1(
Imx
y r , , t
L
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Limit of the assumption of infinite shield
Infinite shield (analytical)
Actual solution
No shield
h x
y
+I-IL
12
h
L
62
h
L
Infinite shield (analytical)
Actual solution
No shield
Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Transformal mapping: planar shield
PMS (perfect magnetic shield) 0, r + ))(log())(log(
2*
00 jtjtttttI
w
dz
dwH x Im
dz
dwH y Re
PES (perfect electric shield) +, r = 1
jt
jt
tt
ttIw loglog
2 *0
0
2
2
1
1
t
tlz
x
jy plane z
- l +l
+I
x0
jy0
Negligible tickness
= 0 = 2
jv plane t
-z = -l
z=+l
z = -l
+u0
jv0+I
- I (0,j)
w = complex magnetic
potential
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Limit of the assumption of PMS
h = 0.6 m
h x
y
+I-IL
PMS
Actual solution No shield
PMS
Actual solution No shield
h = 0.15 m
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
2D Hybrid FEM-BEM formulationTo handle open-boundary fields, the domain is
fictitiously subdivided into:o An “internal” limited region i (including the
shields)o An “external” unlimited region e (including
field sources)
i e
ni
ne
J0
Magnetic field h is expressed as the sum of two terms:
mhhh 0
Field of the sources Shield effects
c
dvgrad00 jh
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Internal” region
Linearization of B-H curve by Fixed Point technique
dsS
aa 1M
Introduction of magneticvector potential a
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“External” region
Green formulation applied to am:
abh curl00 0aaa m
c
dvja 000
0
ee
dsn
aadsn
aaa
eo
e
mo
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Complete set of equations
By introducing continuity conditions at FEM-BEM boundaries we obtain:
02
1
i e
oi ie
mo
i,ei,e
dsn
aadsn
aaa
niti
tene p
p+1
FEM
BEM
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Effect of magnetic material nonlinearity
Two busbars leading high current are shielded by a cylindrical Fe-Ni alloy
Shield
Busbars
Measurement point
The material of the shield is modeled assuming:
- linear behaviour (μr = 300000)- First magnetisation B-H curve
0.1 1 10 100 10000.0
0.2
0.4
0.6
0.8
B (
T)
H (A/m)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Effect of magnetic material nonlinearity
No shield L NL No shield L NL0.1
1
10
100
1000
Current = 100 kA
B (T
)
Current = 10 kA
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:basic principle
The goal of this approch is to remove the shield thickness, by substituting the 3D shield with an equivalent 2D structure
This results is obtained by acting on two geometrical scales: a “microscopic” scale on the shield thickness and a “macroscopic” scale on the shield surface
Working on the “microscopic” scale the shield thichness is substituted by suitable interface conditions
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation: assumptions
The two sides of the shield are indicated with (a) and (b), assuming n oriented from (a) to (b)
v
w
ud
t1
t2
n
(a)
(b)
Shield:Magnetic permeability Electrical conductivity
Working at the “microscopic” scale, the field behaviour inside the shield is assumed to depend only on the w coordinate
f
1 penetration depth
H C C 1 2exp exp w w
C1, C2 = integration constants
1 j 1j
An expression of H inside the shield is found:
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:I interface equation
Starting from the Maxwell equation:
the I interface condition is obtained:
)()()()( at
btS
o
an
bn div
jHH HH
dd
dwjdw00
nBnE
)()(1 at
btSdiv HH
)()( b
na
no HH
j
2dtgh
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:II interface equationConsidering an infinitesimal cylinder of volume V:
V
(b)
(a)
n
t
0)()()(
)()()()( latba
dSdSdSdV bbaa
V
tBnBnBB
V
tdVdSlat
BtB)(
)(bnB)(a
nB
the II interface condition is obtained:
)()()()( bt
atS
o
an
bn div
jHH HH
2dtghj
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Resulting interface conditionsThe resulting interface conditions:
link the normal and tangential components of the magnetic field the two sides of the shield
)()()()( bt
atS
o
an
bn div
jHH HH
)()()()( at
btS
o
an
bn div
jHH HH
v
w
ud
t1
t2
n
(a)
(b)
(I)
(II)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Field equations on the shield surfaceIn the two homogeneous external regions (a) and (b), where field source are present, the magnetic field H can be written as:
)()( ssm grad HHHH
Curl-freereduced field Source field
Reduced scalar potential
baSS
o
sn
anm
bnm graddiv
jHHH
2)(,,
baS
sS
o
anm
bnm graddiv
jHH
H2,,
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Multilayered screensIn presence of multilayered screens, the field equations obtained by the interface conditions can be generalized.For the generic i-th layer, the following interface conditions are deduced:
)a(
i,tS
)a(i,n
i,i,
i,i,)b(
i,tS
)b(i,n
div
B
TT
TT
div
B
HH 2221
1211
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Multilayered screens
The layers are connected in cascade, by multiplying the matrices of each single layer:
)(1,
)(1,
1,221,21
1,121,11
,22,21
,12,11
,22,21
,12,11)(
,
)(,
....
..........
atS
an
ii
ii
NN
NNbNtS
bNn
div
B
TT
TT
TT
TT
TT
TT
div
B
H
H
)a(
tS
)a(n
)b(tS
)b(n
div
BTT
TT
div
B
HH 2221
1211
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Resulting FEM equationsThe field equations on the shield surfaces are solved by FEM, discretizing the screens into 2D elements (for 3D problems) or 1D elements (for 2D problems).The weak formulation (w=test function) leads to:
SS
S
wdsHjwdsHHj
dswgradgrad
sn
bnm
anm
Sba
S
2o,,
o
wdsgradwdsHHj
wdsgradgrad
SS
S
Ss
ta
nmb
nm
Sab
S
H2,,o
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Thin-shield” formulation:Integral equationsIn the two external regions, integral equations can be written, applying the Green theorem:
dsdsP aaa nn )()()(
dsdsP bbb nn )()()(
Side (a)
Side (b)nFEM equations on shield surface
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Codes available at IEN
2D Code PowerField(2D thin-shield formulation)
Sally2D Code(Hybrid nonlinear FEM-BEM formulation)
Sally3D Code(3D thin-shield formulation)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Part III: Magnetic material properties and influence of geometrical
parameters
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ferromagnetic shieldsInfluence of material properties
The behaviour of ferromagnetic materials is defined by the first magnetisation curve
In principle, all ferromagnetic materials can be in principle used for passive shielding
In many applications (e.g. open shields) shielding devices are characterized by giving rise to low magnetic flux density values inside the materials
The shielding efficiency strongly depends on the value of the initial permeability (Rayleigh region)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Nickel-Iron alloys
Nickel-Iron alloys (mumetal, permalloy) exhibits very high permeability (r~105).They are available as bulk or thin (up to 10 m) laminations.Their use is justified in the shielding of limited regions and when a high shielding efficiency is needed.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Low cost” magnetic materials“Electrical steels”: iron, low carbon steel alloys, silicon-iron alloys (oriented and non oriented) with a thickness of some hundreds of micrometers.
-GO Si-Fe alloys: 104
-Iron low carbon steel alloys, NO Si-Fe alloys: 102103
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
“Low cost” magnetic materials
Rapidly solidified alloys: amorphous materials, nanocristalline materials, produced as ribbons with a thickness of some tens of micrometers. The initial relative permeability is:- about 105 for Co-based alloys (comparable to Ni-Fe alloys)- about 104 for Fe-based alloys
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ferromagnetic shieldsInfluence of material properties
The choice of the material is connected with the specific application:
For small volumes screening (e.g. shielding of electronic devices for compatibility reasons) high quality and high cost materials can be employed (e.g. Ni-Fe alloys)
For large scale screening other materials are more useful both for economical and technical reasons (e.g. Low carbon steel, Fe-Si alloys)
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ferromagnetic shields:Effect of field nonunformity
1
10
100
1000
/(2a)=0.1
r=10000
/(2a)=0.01
r=10000
s Case1 Case2 Case3
/(2a)=0.01
r=1000
Case1
Case3
Case2
=thickness, 2a=diameter
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Closed/U-Shaped shield
1
10
100
1000
/L=0.1
r=10000
/L=0.01
r=10000
s Case1 Case2
/L=0.01
r=1000
Case1
Case2
=thickness, L=side
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Plane shield
0 2 4 6 8 101.00
1.25
1.50
1.75
2.00
2.25
2.50
s
L/d
/L=10-3, r=1000
/L=10-2, r=1000
/L=10-2, r=10000
d
source
shield Measurement point
=thickness, L=side
0 2 4 6 8 10
2
4
6
8
10
s
L/d
/L=10-3, r=1000
/L=10-2, r=1000
/L=10-2, r=10000
d
source
shield Measurement point
Distance of the measurement point = 0.1 L
Distance of the measurement point = 0.5 L
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Shielding factor: so BBk
Plane ferromagnetic shields:Influence of material properties
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Plane ferromagnetic shields:border effects
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.30
2
4
6S
hiel
ding
fact
or -
k
X Coordinate (m)
s = 1 mm s = 5 mm s = 10 mm
Plane shield (d = 5 cm)
x
y
d
source
shield
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
U-shaped shield
0 2 4 6 8 10
2
4
6
8
10
12
14
16
s
L/d
/L=10-3, r=1000
/L=10-2, r=1000
/L=10-2, r=10000
d
source
shield
Measurement point
0 2 4 6 8 10
10
20
30
40
50
60
70
80
s
L/d
/L=10-3, r=1000
/L=10-2, r=1000
/L=10-2, r=10000
Distance of the measurement point = 0.1 L
Distance of the measurement point = 0.5 L
d
source
shield
Measurement point
=thickness, L=side
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
U-Shaped ferromagnetic shields:Influence of material properties
Shielding factor: so BBk
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
U-shaped/Closed ferromagnetic shields:Influence of air-gaps
When the shielding configurations make an angle (U-shaped, closed), the assumption of a perfect material continuity is a condition unattainable in practice.
The angle, realized by approaching two different laminations, introduces unavoidable airgaps in the path of the magnetic flux flowing in the shield.
The lack of continuity gives rise to a significant reduction of the shielding efficiency, which mainly affects the high permeability materials.
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ferromagnetic shieldsInfluence of air-gaps
Shielding factor: so BBk
54
Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Ferromagnetic shields:“Source-side” shielding
x
y
d
source
shield
The influence of thickness and permeability is evident for “source” side shielding
“source” side
x
y
d
source
shield
-0.4 -0.2 0.0 0.2 0.41
2
4
6
810
20
Plane shield
s
x (m)
L = 0.6 m d = 0.1 m = 10 mm,
r=1000
= 1 mm, r=1000
= 10 mm, r=100
= 1 mm, r=100
Closed shield
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Part IV: Examples of applications
56
Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Design of the shielding for a MV/LV substation
A 3D computer model is implemented in order to identify the most important field sources
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
LV board30T
[T/A]
125T
57.6T15T
[T/A]
MV board
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
On the floor over the substation
8.4T
6.7 T
5 T
5.5 T
[T/A]
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
LV board shielding
After shielding
Before shielding
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
MV board shielding
After shieldingBefore shielding
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Double trefoil HV underground power line
1200
750
100
1500
3x1600 mmq cables
Dig boundary
Ground level
Junction area
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Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Possible shielding configurations in proximity of the junction area
2 mm Al shields
63
Outline
Part I: General principles of magnetic field mitigation
Part II: Mathematical models for shielding problems
Part III: Magnetic material properties and influence of geometrical parameters
Part IV: Examples of applications
Three dimensional plot around the junction area for shield configuration c)