MATEC Web of Conferences 22 , 020 0 9 (2015)
DOI: 10.1051/ m atec conf/ 201 5 2 2020 0 9
C Owned by the authors, published by EDP Sciences, 2015
Analysis of Magnetic Field Intensity and Induced Current under Live
Working Based on Charge Simulation Method
Yuanxiang Luo
School of Electrical Engineering, Northeast Dianli University, Jilin, Jilin, China
Ruiguo Chen
State Grid Liaoning Electric Power Supply Company, Shenyang, Liaoning, China
Yidong Zhu
State Grid Liaoning Academe of Electric Power Science, Shenyang, Liaoning, China
Jingui Cheng
Xi'an Qin Ping Power Technology Development Limited Company, Xi'an, Shanxi, China
Meixia Wei
Liaoning Annuoxin Power Technology Limited Company, Xi'an, Shanxi, China
ABSTRACT: To the problem that safety distance is insufficient for 500 kV substation live working, a magnetic
field analysis method for overhead line bus is given based on the charge simulation method. In the method,
charge is calculated firstly, and the space field intensity distribution calculation is completed by overlying charge.
The space field intensity distribution rule is carried out based on the appropriate analysis, and space field intensity distribution rule of substation is obtained. Then according to the calculation formula of inducing current, the
human body induction current under a substation busbar is simulated based on MATLAB. The simulation results
have a certain guidance function for actual live working.
Keywords:
live working; charge simulation method; field intensity distribution; induced current
1 INTRODUCTION
As an important skill of power transmission and
transformation industry, charge detection plays an
important role in improving power supply reliability
of power transmission, transformation system and
especially important substation [1]. But high density
and electromagnetic fields in charged body under live
working do harm to live working personnel physically
and psychologically. In the dense decorated substation,
in order to save investment and save floor space, it
may appear that the electromagnetic field density is
higher, and may bring greater harm. So before living
working, it is necessary checking on safety distance
and carrying out electromagnetic field analysis.
About substation and overhead line analysis, a lot of
experts and scholars have done detailed research on it.
And a series of research results can be obtained. In [2],
power frequency electromagnetic field
distribution of the certain northeast substation equipment is
measured through the measured method. In [3], the
electric field intensity of a single transmission line is
analyzed using charge simulation method. It is used
for the analysis of human body inducing current, and
good results have been achieved. In [4-5], the field
strength distribution of horizontal and vertical conductor is based on dipole field theory.
In this paper, the conclusion is different from
charge simulation method. It says that field size is
proportional to the current size, rather than voltage. It
provides a new perspective for the field intensity
analysis theory. In [6-7], the human body induction
current distribution under the overhead based on numerical analysis method makes a detailed discussion
on distribution rule of human body induction current.
In [8], the induced current of the body is calculated
using the simplified calculation formula proposed by
the international conference on power grid (CIGRE)
36.01 group.
In this paper, taking the measured parameters of a
500 kV substation as the prototype, on the basis of the
prototype, appropriate simplification is made. The
corresponding simplified harmonic analysis model can
be obtained.
The corresponding space field intensity distribution
can be obtained based on the simplified analysis model. Using the steps above to obtain field intensity and
human body induced current is calculated based on the
simplified induced current calculation formula. And
human body induced current affected by space position is analyzed.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152202009
MATEC Web of Conferences
Where, U [U 0]; τ' is the line charge density of
matching point;
2 ELECTRIC FIELD INTENSITY ANALYSIS
THEORY
2.1 Calculation principle of line charge
Usually the slender conductor is equivalent as the line
model. The voltage and current are generally known
as the quantity of wire conductors in engineering, but
analysis of electric field intensity needs charge density.
So we need to study the relationship between charge
density and voltage or current, which usually means
the relationship between voltage and line charge density as follows:
U =Pτ
(1)
Where, U is n 1 order voltage vector, P is
n n potential coefficient matrix, and it can be obtained based on the principle of the image. τ is
n 1 order line charge density vectors.
All that said, usually voltage vector is known, so
Equation (1) needs to be appropriately transformed to:
τ =HU
(2)
-1
Where, H=P .
Then we need to discuss clear expression given by
potential coefficient matrix. According to the principle
of mirror image, it is not difficult to obtain expression
of the main diagonal and other position in P :
2hi
ln R (i j )
i
p ij ln ri , j (i j )
ri , j
(3)
Where, hi is the height of the wire i to the ground,
and wire is a single phase conductor; Ri is the radius
of the wire i; When the wire is a split conductor, Ri is
the equivalent radius; ri,j is the distance between the
wire ith and wire jth; r’i,j is the distance that wire j is
from the wire i.
According to the Equation (2), the simulation of
electrical charge and numerical mirror charge can be
obtained.
Suppose there are n simulation charge, τ is n * 1
column, H is n * n phalanx, and U is n * 1 column. To
solve the analog electrical charge, the image electrical
charge can be converted into the problem n that linear
equations are to be solved.
But it still exists in a kind of constraint and special
field with known points (such as ground and ground
wire) which need to be added into Equation (1), and
they are called matching points. The augmented matrix added into the matching point is called (4) :
U=Pτ
P
P P21
P12 P22 ,
P12 is the line charge of simulation point and potential coefficient matrix of the matching point; P21
is line charge of matching point and potential coefficient matrix of simulation point; the line of the
matching point P22 is the line charge of matching point
and the potential coefficient matrix of matching point,
U [ τ τ']; , and τ' is the linear charge density of the
matching point.
From Equation (3) in inverse processing, the density of simulation charge and matching charge can be
obtained as follows:
τ = P U 1
(5)
2.2 The calculation of electrostatic field strength
under the action of line charge
According to the theory of electrostatic field, the expression of the relationship between electric field intensity and the line charge density of infinite long
conductor wire in the y axis parallel to the direction
can be shown in the following:
1
Ex 4
E 1
z 4
x xi xi x
)
R2
R2
i 1
n
zz zz
i ( 2 i 2 i )
R
R
i 1
n
(
i
(6)
Where, n is the number of phase of power transmission lines; xi and zi are the coordinates of the
equivalent electric charge respectively; x and z
are the coordinates of calculating point respectively; R’
is the distance between calculating point and image
electrical charge.
Combing with Equations (5) and (6), the expression
of electric field intensity about voltage can be concluded that:
1
Ex 4
E 1
z 4
x xi x xi m
) hl ul ]
R2
R2 l 1
i 1
n
z xi z xi m
[(
) hl ul ]
R2
R2 l 1
i 1
n
[(
(7)
Where, m is the dimension of H matrix. Ul is the
voltage vector elements.
(4)
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9
4.1
2.7
2.2
1. 7
3.2
2.7
5.5
4.6
3.6
h/m
5.1
3.2
2.2
2.7
4
1.7
3.6
Line height is 9m from the ground, and the distance of
different phase conductor is 4m. The bus voltage level
is 500 kV.
5
5.1.6
44.1
3.6
2
3.
2. 2
3. 6
4.1
6
4 EXAMPLE ANALYSIS
3.2
2.2 2.7
7
..283
08.9
.4
.9
.5
.061
1112116574573.4
.5
11422.....62772
111100 .83
199...38
88.4
.61
3.2 34.
4.6
6.0
46.5
7.7.0
34.6.1
2.2
3.2
6.56. 0 5.5
1.7
8
2.7
2. 2
Where, I is induced current, and the unit is μA; f
is frequency, and the unit is Hz; ω=2πf, which is angular frequency, and the unit is (rad/s); ε0 is the dielectric constant, and the value is 10-9/36/π; h1 is head
height, and h2 is trunk height.
7.
9
(8)
3.2
5.1
7.0
7.4
I t 0 E
˄2h12 h22 )
2.7
When people are in a 500 kV substation charge operation, a certain induction voltage is produced additionally. The induction loop is likely to be formed between the line and earth, and it forms a certain induced
current. It is more significant for current than the induced voltage to impact on the human body. Thus it is
necessary to make reasonable assessment on the induced current when live working, so as to ensure the
safety of live working personnel.
Based on Equation [4], simplify the induced current
calculation method when upright body in power frequency electromagnetic field can be obtained as follows:
in Y direction attenuates, that is, field strength in the
range of live working does not obviously attenuate. In
China, occupational exposure of the electric field intensity that is limited by the power frequency electromagnetic field exposure rule is 6 kv/m. Obviously, under the
condition of each phase, the electric field intensity does
not exceed this limit. The field intensity change trend is
shown in Figures 1-4, and the field strength that is
placed in area from 4m to 5.7m shown in Figure 1 and
Figure 3 is weak. The dense regions of field lines are
mainly concentrated in the area of more than 6m, and a
phase is equal to 0 °. The maximum electric field intensity density area lies in between a and b phase, and a
phase is equal to 180 °. The maximum electric field
intensity density area is between b and c phase. When a
phase is equal to 90 ° and 270 °, regional field strength
in 4m and 5.7m is stronger. But the electric field line is
relatively sparse. Figure 2 and Figure 4 similarly lie in
the center of the field which is located in the b phase.
4. 6
3 CALCULATION OF INDUCED CURRENT
3
4.1 Analysis of field intensity distribution of line
1.01. 1
11
.2.3
0.8 0.9
7.
22.9
2
.2.1
.1.22.8
.35.26.7
0
6
12.6
111
.7
.4
1.
1.23
1.1
0.7
0.2
0.2
0.
1
0.1
0.7
0.6 4
0.
0.2
1
0
-10
0.1
-8
-6
-4
-2
0
2
4
6
-6
-4
0
2
4
6
1.7
2.2
3. 2
-2
8
10
Figure 2. The a phase distribution of field intensity when the
phase is 90 °
0.
3
0.80.9
0.3
0.010.7. 0
30..6
0.7 1.0
2
0.4
1.1
1.2
1.3
0.2 0.1
0.3
0.
2
0.1
11.3
.2
1.1.0
1
-8
x/m
0.1
h/m
0
-10
3. 2
2
0. .4
0
.30.6
00.7
3
0.
0.1
2
0.2
3
1
0.1
0.4
0.6
4
0.09.8
0.4
5
2..76
2.35
22..1.2
2
2.0 8
12.191.7.
1.6
1.4
0.3 0
0..7
6
0.
4
0.6
0.4
.1
7. 10
.0
.7
.6
.4
90.9
12567430.4
.1
.2
4.9
775.4 19
8
37890.9
3..5
.90.123567
8
..4.8
78.2.8
...4.
..1
76.7
295
.0
6.
6.8
6908 98132567
6.
.4
6655.2
.1
723
.
.
6
5
.
55.
8 00..89
33..0 1.0
6
98
1.0698753..23.13.03.93.83.73.6.35.33.212.20..
544..4.7
44533210.9 11.1
8.17.6
.4
.6
2.2. 1
2.
2.
0.822.
0.
8
1.2
6
0.
7
0.9
0.7
8
33.
3..3
.8
.2
510.9 7.6
3.0
2.8
2.9
2.7
2.6
2.5
2.3
2.2
2.1
2.0
1.1.9
1.
1.8171.6.4
1
1.0
2.7
9
2.7
2
8
10
x/m
Figure 1. The a phase distribution of field intensity when the
phase is 0 °
It can be shown in Figures 1-4, the space field intensity constantly attenuates, with three buses as the core.
The field intensity from 2m height to ground is vertical
distribution. And it is evident distortion of field strength
around 2m radius of conductor. The 4m to 5.7m height
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55..56
0.80.9
2
2.0
2
.35
.1
..2
.26.7 2
1.4
1.6
11
12.9
2
.8
.7
1.2
1.3
1.
0
0.7
The field/kV/m
0.
2
0.
3
0.9
0.8
0.
1
0.3
0.2
0.1
0.20.1
0. 3
0. 100.70
.03..6
0.7
20.8
1.1
1.2
1.3
0.1
0.1
h/m
2
0.
3
0.
0. 1
2
1
4
0.7
0.6
0.4
The field when h=4m
The field when h=5.7m
1.2
0.3
0.
7
0.
2
3
1..2
1 0
1.1
1.
3
0.1
.
0.60
4
1.1.
416.7
0.4
0.6
2
0.
0. 90. 8
0.4
5
1.4
2..67
2.35
2220...12
2
.
2.98
11.
0.4
. 30.6
0
0.7
5 00..89
3232...21908 1.1
33.
33.3.2
22.10.9
.8
0.6
0.4
5.
1
9.8.76.5
.40..987.654.33.2.13.033. 3
0.6
0.8
6
8.8
79
.9.6
.5
.4
.1
.0
64778.031254.1
77..4
119899800.3
4.56.79012356.0
...9
7.2
7.1
38
7656.0
967878 ..4.7
665.65.8.5..2490718
465321
44.7
4.2.
542
.7
111.8
.4
1.9
1.6
2.2. .01.0
.92.
42.
00.
1.1
1.2
0.9
7
0. 7
8
33.9
.5
..1
32
.0
.8
223.5
.7
.6
2.2.2..0.3
111.
89712
1.6
1.4
1.0
11.11 1
. 0 . 2. 3
9
0.8
0.6
0.4
0.
2
0.2
1
0.1
0
-10
-8
-6
-4
-2
0
2
4
6
8
0
-10
10
x/m
1.7
2.7
2. 2
2
2. 7 . 2
1.7
2. 2
2.7
4. 1
3.2
-6
-4
-2
0
2
4
6
1.7
2.7
3. 2
2.2
-8
2.7
1
3.2
2
2.2
3.6
h/m
3.6
3
0
-10
3.2
1
4.
4
5.1
4.6
3.6
3.2
2.2
1.7
2.7
5
5. 56. 0 6. 56.9
6
6
6.0
3.2 4455.5
..1
3..16
6
4.6
3.2
.6
43.1
4.6
5.5
5. 1
6.
0
6.
594
6.
7.
.1
5
7. 4
2.7
7
3.2
.8
26278960.8
.2
118
19.2
.8
111121.6
.3.7
3354...6.05.49.93
1
.17..73
1.0.9
1
.8
1112121
0.92
.384
8.8
7.. 9
2.7
2.2
1.7
2
3.
2.2
9
4.6.1
4.6
3
-6
-4
-2
0
2
4
6
8
10
x/m
Figure 3. The a phase distribution of field intensity when the
phase is 180 °
8
-8
8
Figure 5. A field intensity distribution of different heights
when the a phase is 0 °
And obvious field intensity changes exist in relatively sparse segmented regions among the three
phases. As shown in field intensity change trending
from Figures 1-4, maximum density area of the electric field changes with phase. It proves that the field
intensity produced by the alternating current (ac) is
time-varying.
When live working, workers need to stand on the
4m high insulation. As the average height of the human body is 1.7m, it is estimated that person’s head is
about 5.7m height to the ground. So in this article, two
representative heights that are 4m and 5.7m are taken
to estimate the space field intensity.
Because the field strength is continuous, so according to the field intensity of the head and foot height,
whether the field strength of the head and foot in the
middle area is overweight can be estimated.
10
x/m
Figure 4. The a phase distribution of field intensity when the
phase is 270 °
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sistent more than 90 ° + k*180.
5
5
4.5
4.5
4
The field/kV/m
The field/kV/m
4
3.5
3
3
2.5
2.5
The field when h=4m
The field when h=5.7m
2
1.5
-10
3.5
-8
-6
-4
-2
0
2
The field when h=4m
The field when h=5.7m
2
4
6
8
1.5
-10
10
-8
-6
-4
-2
0
x/m
Figure 6. A field intensity distribution of different heights
when the a phase is 90 °
2
4
6
8
10
x/m
Figure 8. A field intensity distribution of 4m and 5.7m height
when a phase is 270 °
4.2 Analysis of induced current of human body
Taking 1.5m as human body height, and the head
height is 0.2m. The electrical field strength changes
with the position.
9
00
0
2.
.0.
4.5.4
50.6
0
.3
0. 3 0
0.2
0.0
0.1
0.20.3
0.1
0.1
0.1
0.0
0.
0
h/m
The field/kV/m
.0
5
0.3
0.2
0.
1
0.0
0.2
0.1
0.4
0.1
0.6
0.1
0 .1
0. 1 0
0.2
6
0.6
0..55
0
0.04.4
0.3
6
0.
0.
2
7
0.8
.5
.4
.3
1
1.6 2112212..2
0..0.7199080188..89900
11..5
64 1 .1.7.1.1
1.5
1.
3
111..4
3
2
.
1.0 2.0
7
00.
.770.2 1..7
0.6
0.6
0.5
0.5
00.4
.40.3
87.7.6
.000.09.9.080. .0 0 .4.3
.21.6
1.0.
54 00
50.
11.10
0.
0.2
8
0.1
1
0.
1
0.0
1.2
0.2 0.
3
0.2
The field when h=4m
The field when h=5.7m
0.2
1.4
4
0
-10
0.1
2
-8
-6
-4
-2
0
2
4
6
8
0.0
0.1
3
0.2
0.
0
10
1
x/m
Figure 7. A field intensity distribution of 4m and 5.7m height
when a phase is 180 °
As we can conclude from Figures 5-8, the field
strength on the other side circuit below line also
changes with the phase angle. The maximum field
strength occurs near phase angles of 90° and 270°.
But field intensity distribution of 90°+k*180 and
0°+k*180 is slightly different. The field intensity distribution on the level surface of 90 ° + k * 180 is a
single peak. The field intensity distribution of 0 ° + k
* 180 is different. On the other hand, in addition to the
peak of the center, there are two small peaks on both
sides. The energy distribution of 0 ° + k * 180 is con-
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
x/m
Figure 9. The body induction current distribution (mA) of
500kV bus when the a phase is 0 °
As we can see from Figures 9-12, inducted current
law is similar to the field strength rule, and the human
body current is mA level. According to guide rules
that limit AC power field, magnetic field and electromagnetic field are published by the international
commission on non-ionizing radiation protection. And
the fundamental limit value of the current density of
professional personnel is 10mA/ m . Human skin area
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MATEC Web of Conferences
2
is about 3 m . So according to the data shown in Figure 3, the induced current of human body in the
working environment is safe.
9
0. 4
0
2
4
1.2
6
8
0. 6
0. 4
0.6
0.8
-6
-4
-2
0
2
4
6
8
10
x/m
0.4
0.6
-2
0.6
0.8
-4
1. 4
0. 8
1.0
1.2
1.1.
46
0.6
0.4
0.6
h/m
1.2
1.6
0.6
1. 0
0. 8
0.4
-6
-8
0.4
0.6
-8
0.8
0.6
1
0
-10
1
0.6
1.0
2
0.8
3
1.0
0.6
h/m
1. 6
4
11.2
.0
0.
8
0.8
0.6
0.6
1.0
4
0
-10
5
3
5
2
4.9
.3
334.1
4
23....13.759
9
2.08
.64
2.2
2
.
2. 1
0.8
1
0.4
6
0. 6
1.0
0.8
1.2
7
1.0
0.8
6
.9
3333..7
.531
232....964
22.20
2..8
1.0
1.4
1.4
0.6
0.8
0.4
7
9
8
0.6
8
10
Figure 12. The body induction current distribution (mA) of
500kv bus when the a phase is 270 °
x/m
Figure 10. The body induction current distribution (mA) of
500kV bus when the a phase is 90 °
9
0.2 0
.3
1
0. 5
. 50.6 .2
0.300.4
0.3
0.3
0.1
0. 0
0.2
0.1
0.2
0.0
0.0
h/m
0.3
0.2
0.
1
0.
0
0.1
0.1
0. 2
0
0.
5
0.0
0.1
0.1
0.1
0.1
0. 1
0.2
0.
07.
0.7
6
0.6
0..55
04
0.4
.
0
0.3
.2
6
00..7 0.20
8
211009.09.08.
7
6
.3
.2.7018984.
222.2
0
...0
11..6.65423111...00111.1
1111... .78899
1
11..7
..00.
111.1.0
.4.3
55
0.4 00
0..6
0.
21
0.0.
0.2
0.2
0. 1
8
0.6
..77
000..6
00.04..455
0.3
4
0.0
0.1
3
0.1
0.
0
2
1
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
5 CONCLUSIONS
In this paper, the field and induced current analysis of
problems are carried out based on charge simulation
method. This method has the advantage that the field
strength analysis and induction current laws can be
seen intuitively. And on the condition of computation
it can be accepted that high accuracy can be obtained.
The problems which need to be further discussed are:
(1) As to local eddy current problems of the human
body, more sophisticated numerical simulation method is needed to be verified. Especially, as to local
induced current intensive area, it should be more focused on. In addition, the various parts of the body to
stand the strength of the induced current are also different. So each part of the induction current needs to
differentiate with consideration and analysis.
(2) Although two-dimensional spatial distribution is
studied, the need to study the
distribution of the
three-dimensional space, further expansion of the field
intensity distribution and the change of the induced
current is urgent. Especially, the location of the lowest
body endurance value [9] and induced current peak of
the third dimension are focused on.
x/m
Figure 11. The body induction current distribution (mA) of
500kV bus when the a phase is 180 °
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