Energy and Power Engineering, 2013, 5, 20-23
doi:10.4236/epe.2013.53B005 Published Online May 2013 (http://www.scirp.org/journal/epe)
Energy Harvesting Based on Magnetic Dispersion for
Three-Phase Power System
Tarcisio Oliveira de Moraes Júnior, Yuri Percy Molina Rodriguez, Ewerton Cleudson de Sousa Melo,
Maraiza Prescila dos Santos, Cleonilson Protásio de Souza
Federal Institute of Paraíba - IFPB, Cajazeiras, Brazil
Department of Electrical Engineering, Federal University of Paraíba - UFPB, João Pessoa, Brazil
Received 2013
ABSTRACT
This paper presents a comparative study on Magnetic-Dispersion based Energy Harvesting Systems (MD-EHS) on
electrical conductors that supply power for a three-phase AC motor. It introduces two MD-EHS which are based on
magnetic cores of different material, named, nanocrystalline, ferrite and iron powder. The first one consists of harvest-
ing energy from magnetic flux through three symmetrical magnetic cores installed on each power conductors of a
three-phase AC motor. The second one consists of a single magnetic core for harvesting energy from magnetic flux of
only one of these conductors. Both ones have an AC/DC converter and a variable resistor based load. Experimental re-
sults have agreed with the theoretical analysis and show that the first proposed MD-EHS is capable of supplying 14
times more energy than the second MD-EHS, considering nanocrystalline cores and phase current of 3 A, and 7.5 times
more energy, considering ferrite cores and phase current of 9 A. Such energy can be applied to various low-power de-
vices, especially in wireless sensor network.
Keywords: Energy Harvesting; Magnetic Dispersion; Magnetic Cores
1. Introduction
Energy Harvesting is the process of capturing small
amounts of energy from energy sources available in en-
vironment, for instance: thermal, solar, mechanical,
magnetic induction, and others, and it is specially applied
in supplying energy to low-power devices particularly
those from wireless sensor networks. Energy harvesting
system based on magnetic induction is receiving consid-
erable attention since it is also applicable in measuring
variable in power lines.
An example of application of energy harvesting by
magnetic induction can be seen in [1] in which a system
composed basically of a magnetic flux device is capable
of transmitting to a base station the values of temperature
variations of the power line where itself is installed. In [2]
is proposed a system to harvest energy from electrostatic
field created between a power line and the ground. Ex-
perimental results have shown that the system can har-
vest 16 mW. In [3] was studied an energy harvester
based on magnetic induction on power line using a sim-
ple circuit model to validate the obtained theoretical re-
sults. As a result, 1mW of power was achieved consider-
ing air-core and 6.32 mW considering an iron core from
a magnetic field of 21.2 uT. Recently, in [4] it was stud-
ied a tube shaped energy harvester from power lines
where the power conditioning circuit is constraint for
constant voltage. As a result, the circuit efficiency does
influence the level of its output voltage. For constant
output power, the voltage level of the power conditioning
circuit decreases while the voltage of the transmission
line increases.
In this work, it is presented a comparative study on
Magnetic-Dispersion based Energy Harvesting Systems
(MD-EHS) on electrical conductors that supply power
for a three-phase AC motor. It was developed two MD-
EHS’s which are based on magnetic cores of different
material, named, nanocrystalline, ferrite and iron powder.
The first one, called 3F-MD-EHS, consists of harvesting
energy from magnetic flux through three symmetrical
magnetic cores installed on each power conductors of a
three-phase AC motor. The second one, called 1F-MD-
EHS, consists of a single magnetic core for harvesting
energy from magnetic flux of only one of these conduc-
tors.
This work is organized as follows: Section II describes
the essential theory of magnetic field regarding the cores
specifications, Section III shows the experimental analy-
sis, Section IV, the experimental results, and Section V,
the main conclusions.

T. O. de M. JÚNIOR ET AL. 21
2. Magnetic Field Theory
According to Ampere's law, the magnetic flux density at
a given distance r from a infinitely long conductor car-
rying an alternating current with a peak amplitude I and
frequency ω is given by:
sin( )
2
m
I
t
Br



 (1)
where B is the magnetic flux density in a distance r of the
conductor and µm is the magnetic permeability of the
material between the conductor and the point r.
Figure 1 shows a laminated core on the power con-
ductor in a transversal way which the proposed MD-
EHS’s are based on. This core provides the magnetic
path for the magnetic flux and consists of about 50 thin
strips that are electrically separated by a thin layer of
insulating material. A coin, not shown in the figure, is on
the laminated core and is where the inducted voltage
takes place.
Based on Figure 1, the concatenated magnetic flux,
ϕ ,
across the laminated core, with sectional area A, is given
by:
BdA   (2)
where
dA wdr (3)
Substituting (1) and (3) in (2), it is obtained:
sin( )
2
f
L
r
m
Lr
It dr
wr

  (4)
which can be reduced as follows:
()ln
2
mL
L
L
Isent wrh
r







(5)
where
L

: magnetic flux of the magnetic L-th strip of
the core (where 0 < L < NL, NL = number of core strips)
P
rimary
conductor
Figure 1. Laminated cor e on a power conductor.
and
L
r is the radius of the L-th strip.
Concern the magnetic flux into the insulating material
between the laminated core strips, it is obtained from a
similar way and it is obtained:
0()ln
2
P
P
P
Isent wrS
r








(6)
where ϕ
P: magnetic flux of the magnetic P-th strip of the
core (where 0 < P < NL-1) and rP is the radius of the P-th
strip.
Considering now that is a coin wounds around the core
with N2 turns. In this way, the output voltage of coin ter-
minals, according to Faraday's Law, is expressed as:
2T S
d
VN
dt

 (7)
where T

is the total magnetic flux. T

can be ob-
tained by the summation of the magnetic flux through the
magnetic and insulating blades:
1
11
Ln Pn
TL
LP
dd d
dt dtdt
P







(8)
where:
cos() ln
2
m LL
L
Itw dr
dt r
  





h


(9)
0cos()ln
2
PP
P
Itw dr
dt r
  





S


(10)
To obtain theoretical results, it was considered as pa-
rameters the core dimensions: w, h, S, and r1 (internal
radius), as shown in Figure 1.
3. Experimental Study
In order to design the proposed MD-EHS, it was used
magnetic cores of three different materials: iron powder,
ferrite and nanocrystalline. The first proposed MD-EHS,
called 3F-MD-EHS, consists of harvesting energy from
magnetic flux through three symmetrical magnetic cores
installed on each power conductors of a direct start
three-phase AC motor, as can be seen in Figure 2.
In Figure 3, it is shown the power conditioning cir-
cuits (PCC) for the 3F-MD-EHS and in Figure 4 it is
shown for the 1F-MD-EHS.
The second proposed MD-EHS, called 1F-MD-EHS,
consists of a single magnetic core for harvesting energy
from magnetic flux of only one of these conductors.
It was carried out several experiments considering
cores of iron powder, ferrite and nanocrystalline and load
values, Rv, ranging from 10  up to 10 k. In all ex-
periments, the phase current of each conductor is 3 A for
the nanocrystalline cores, 9 A for ferrite and 12 A for
iron powder. The main parameters of the used cores are
described in Table 1.

T. O. de M. JÚNIOR ET AL.
22
Motor
S
y
mmetrical Cores
PCC
Figure 2. 3F-MD-EHS.
Motor
M
Source
380 V 60 Hz
3PH
T1
T2
T3
680uF
Rv
XSC1
AB
Ext Trig
+
+
_
_+_
Figure 3. Power conditioning circuit of the 3F-MD-EHS.
Motor
M
Source
380 V 60 Hz
3PH
T1
680uF
Rv
XSC1
AB
Ext Trig
+
+
_
_+_
Figure 4. Power conditioning circuit of the 1F-MD-EHS.
4. Experimental Results
After performing experiments considering the different
cores and the set of values of Rv, it was possible to obtain
the maximum obtained power and the voltages values.
The best results are described in Tables 2 and 3 and the
results considering the variations of Rv can be seen in
Figure 5 for the 3F-MD-EHS and Figure 6 for the 1F-
MD-EHS showing the power obtained for each value of
the load, Rv.
Table 1. Parameters of the used cores.
Core’s Parameters
Material w
[mm]
h
[mm]
r
[mm] S r

Ferrite 8 4.2 6.85 0.00062300
Nanocrystalline10.35 4.4 22.5 0.00061000000
Iron Powder 18 11.3 12.05 0.000675
Table 2. Experimental results from 3F-MD-EHS.
3F-MD-EHS
Material V
[mV]
I
[mA]
P
[mW]
Rv
[]
Ip
[Arms]
Ferrite 560 11.3 6.3 50 3.0
Nanocrystalline 374 37.4 14 10 9.0
Iron Powder 5.7 0.57 0.0032 10 12.0
Table 3. Experimental results from 1F-MD-EHS.
1F-MD-EHS
Material V
[mV]
I
[mA]
P
[mW]
Rv
[]
Ip
[Arms]
Ferrite 310 4.6 1.5 70 3.0
Nanocrystalline 602 1.5 0.9 400 9.0
Iron Powder 18.5 1.85 0.034 10 12.0
50100 150 200 250 300
0
2
4
6
8x 10
-3
Load (Ohms)
P ower (W )
Ferrite
50100 150 200 250 300
0
0.005
0.01
0.015
0.02
Load (Ohms)
P ower (W)
Results first system
Nanocrystalline
50100 150 200 250 300
0
1
2
3
4x 10
-6
Load (Ohms)
P ower (W)
Iron Powder
Figure 5. Power levels – first system.

T. O. de M. JÚNIOR ET AL.
23
50 100150 200 250300 350 400
0
1
2x 10
-3
Load (Ohm s)
Power (W)
Ferrite
100 200 300400 500 600 700 800 9001000
0
0. 5
1x 10
-3
Load (Ohm s)
Power (W)
Res ul t s second system
Nanocrystalline
20 406080100120140
0
2
4x 10
-5
Load (Ohm s)
Pow er (W)
Iron P owder
Figure 6. Power levels – second system.
5. Conclusions
In this work, it was presented two proposed Magnetic-
Dispersion based Energy Harvesting Systems, called
3F-MD-EHS and 1F-MD-EHS, where the former works
on three phase conductors and the latter on one phase
conductor. Both are based on magnetic cores of different
material, named, nanocrystalline, ferrite and iron powder.
The obtained experimental results have shown that, con-
sidering the 3F-MD-EHS, it was capable of harvesting up
to 14 mW at a load of 10  for a nanocrystalline core
with 3 A RMS current on the power line; up to 6.3 mW
at a load of 50  for a ferrite cores with 9 A RMS current
on the power line; and up to 3.2 W at a load of 10 for
a core of iron powder with 12 A RMS current. Consider-
ing the 1F-MD-EHS, it was capable of harvesting up to
0.9 mW at a load of 400  for the nanocrystalline core
with 3 A RMS current on the power line; up to 1.5 mW
at a load of 70  for ferrite cores with 9 A RMS current
on the power line, and up to 34 W for a load of 10  for
an iron powder core with 12 A current on the power line.
In this way, it can be observed that the power harvested
from the nanocrystalline core 3F-MD-EHS is 14 times
higher than the nanocrystalline core 1F-MD-EHS and 7.5
times higher considering ferrite core. However, consid-
ering iron powder cores, the obtained power of the
3F-MD- EHS was 10 times less than in the 1F-MD-EHS.
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