1
Increasing Inductor Power Density Using
Controllable Electropermanent Magnets
M. E. Lawniczak, Student Member, IEEE
Abstract-- Inductive components are used widely in the power
grid for the purpose of controlling power flow, regulating fault
current, and providing compensation. Magnetics are also a
principal component of power electronics circuits. In both cases,
inductor design focuses on achieving a desired impedance while
maintaining the component within its saturation limits. Recent
research has shown that permanent magnets or electromagnets
can be used to counteract internal flux, thus altering the saturation
characteristics of the inductor.
Permanent magnets exhibit a fixed magnetic field, and
therefore are not controllable. Electromagnets require current to
maintain the field, and therefore generate significant steady-state
power loss.
Electropermanent
magnets
differ from
electromagnets in that they have zero steady-state power losses
and heating issues, while maintaining the ability to electronically
control the magnetic field.
An electropermanent magnet consists of a permanent magnet
and an electromagnet. The winding current of an
electropermanent magnet can be programmatically controlled to
create a magnetic field that is either on or off. Once the
electropermanent magnet is switched on there is zero power being
consumed while it is energized. Furthermore, there is no heat
generated during the on state of the electropermanent magnet
allowing the device to be low maintenance. Currently,
electropermanent magnets are being used on a large scale to lift
heavy objects with no chance in dropping the load in the event of
a power failure. On a small scale, electropermanent magnets are
being used in modular devices. Companies such as Google are
working on modular cell phones where components can be added
and interchanged using electropermanent magnets. Through
research and analysis of permanent magnetic materials and their
operational characteristics, this project will examine the use of
electropermanent magnets in power electronics and power
systems applications as a more power efficient means of
implementing devices currently being used in motors, switched
mode power supplies, and the power grid.
that explain how the flux flows through a given inductor.
Sections are also devoted to the experimental set up and results
of measuring the saturation current of an inductor when an EPM
is applied and not applied.
II. DECREASING INDUCTOR SIZE
When designing an inductor the size of the inductor is
an unfortunate tradeoff that must be made in order to have a
large inductance. Methods such as the Kg method can be used
to determine the minimum core size to withstand a given
maximum current, inductance and maximum flux density. An
example of large inductor size is pictured below in Figure 1.
Almost half of the area in the inverter is made up of inductors.
Using an electropermanent magnet to cancel internal flux
within the core of an inductor would enable a decrease in
inductor size, decrease costs as well as decrease size of power
electronics such as this inverter.
Fig. 1. Approximately half of the surface area of this inverter circuit consist of
inductors.
III. MAGNETIC PROPERTIES OF MATERIALS
Index
Terms—electropermanent
magnet,
coercivity,
remanence, inductor, saturation current, magnetic field strength,
flux density.
I. INTRODUCTION
T
HIS document explores the construction and application of
electropermanent magnets for the purpose of decreasing
inductor size while increasing the saturation current level of the
core. It contains information regarding the characteristics of
magnetic materials used to construct an electropermanent
magnet, how to construct the electropermanent magnet, testing
the effectiveness and application of the electropermanent
magnet to an inductor. Magnetic circuit models are provided
An entire branch of physics is dedicated to the study
of the effects produced when a magnetic field is applied to a
material. Some of the characteristics that classify these effects
are permeability, remanence, intrinsic coercivity and saturation
[1]. All of these characteristics are relevant in the construction
and functionality of an electropermanent magnet and are
described in greater detail in the paragraphs below.
An electropermanent magnet is made of two magnets.
The Neodymium Iron Boron magnet is a permanent magnet
classified as a “hard” magnetic material. A hard magnetic
material is a material that has a high coercivity. The coercivity
of a magnet determines the ease with which a magnetic field
can be reversed. The units for coercivity are amps per meter.
The second magnet within the electropermanent magnet is the
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Alnico 5 magnet. The Alnico 5 magnet is classified as a “soft”
magnetic material, meaning it has a low coercivity. The low
coercivity characteristic means that it takes a lower magnetic
field strength to flip the magnetic field in the opposite direction.
The low coercivity of the Alnico 5 is what allows the
electropermanent magnet to switch on and off with a current
pulse. The remanence characteristic classifies the
magnetization left behind in a magnetic material when an
external magnetic field is removed. Figure 2 compares the
coercivity and remanence values of each of the magnets.
remanence values add and the magnetization is permanent.
When a negative current pulse is applied the magnetic field of
the Alnico 5 magnet is flippd and is opposite to the magnetic
field of the Neodymium Iron Boron magnet, turnng the EPM
off. Figure 6 includes the magnetic circuit models for the
electropermanent magnet in the on and off state.
Fig. 2. Comparison of magnetic characteristic between NIB and Alnico 5.
The remanence values are utilized in the off and on
stage of the electropermanent magnet. When the
electropermanent magnet is in the off stage the remanence
values of the two magnets cancel and the net magnetization is
zero. When the electropermanent magnet is on the remanence
values are added together created a strong magnetization.
The permeability of a material describes the ability of
flux to flow through a material. The permeability of the
Neodymium and Alnico 5 magnet is 2.1 and 1.05, respectively.
The permeability will be brought up again later in this paper
when the reluctance is calculated. The linearity and nonlinearity
of the permeability is characterized in the hysteresis loop. The
magnetic characteristics of a material are evident in the shape
of the hysteresis loop. Figure 3 illustrates the hysteresis loop
for a soft and hard magnetic material. The hysteresis loops for
Alnico 5 and Neodymium would look similar to the hysteresis
loops below, however the height y-intercept of the loops would
be at the same, 1.2 [T].
Fig.5. The different phases of the electropermanent magnet. The polarity of the
current pulse applied to the coil is related to the location of the flux density at
that moment [6].
Fig.6. The magnetic circuit on the left represents the electropermanent magnet
in the ON state. The magnetic circuit on the right represents the
electropermanent magnet in the OFF state.
IV. CONSTRUCTING THE ELECTROPERMANENT MAGNET
Fig. 3. Hysteresis Loop for a soft and hard magnetic material.
The phases of the electropermanent magnet are illustrated in
Figure 4. In the first phase when zero current is applied to the
coil the remanence values cancel and the magnet is off. When a
positive current pulse if provided the direction of the current
flow determines the direction that the magnetic field strengths
will point. When the current is removed from the coil the
When constructing an electropermanent magnet the
magnetic characteristics described above are critical to the
EPM’s ability to switch on and off using a minimum amount of
current. If the coercivity of the magnetic material is too large
than the initial current pulse may exceed the overall power
consumption of simply using an eletromagnet. Great care
should be taken when selecting the materials to be used. The
magnets used need to be the same length and not necessarily the
same width. This is due to the inverse relationship between the
area of the magnet and the reluctance. This is explained in more
detail in the calculations section. In this project, two
electropermanent magnets were constructed using 10mm and
6.35mm length magnets. Figure 7 is a photo of each othe EPMs.
The 10mm is on the right and the 6.35mm model on the left.
Throughout the paper the EPMs will be referred to as EPM A
and EPM B. EPM B was not used because it was later
discovered that an Alnico 8 magnet had been epoxied to the
component instead of Alnico 5 . The coercivity of the Alnico 8
magnet is approximately 1000 kA/m and required a large
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current pulse to flip the magnetic field strength. The small
length of the magnets left a small window area and an adequate
amount of turns could not be wrapped around in order to obtain
a reasonable current. Attempts were made to build other EPMs
however the ferrite was very brittle and shattered when cutting/
sanding. The Alnico 5 material was also very difficult to cut
through. Since long rods of the material were ordered small
nicks were placed where the magnet was intended to be
shortened and then using leverage and a chisel the magnet was
snapped. The ferrite pieces on either side of the magnet were
constructed from ETD cores and have a width of 12.7 mm and
thickness of 5.08 mm. The length of the ferrite pieces for the
6.35 mm length magnet should have been extended to create a
larger window area for wrapping the copper wire.
determined by the intrinsic coercivity, H [kA/m] and the length
of the magnet, 𝑙 [m] .
𝑚𝑚𝑓 = 𝐻𝑙
The reluctance of the material is determined by Equation (4)
ℛ=
𝑙𝑚
𝜇0 𝜇𝑟𝐴𝑐
(4)
Where 𝑙 m [m], is the mean length of the material, 𝜇0 is the
permeability of free space[𝐻 ∙ 𝑚−1 ], 𝜇𝑟 is the relative
permeability of the material and the cross-sectional area, 𝐴𝑐
[m2]. Combining Hopkinson’s Law with equation (5), the flux
can be controlled by the area of the magnetic material.
𝑚𝑚𝑓 = Фℛ
Fig. 7. The model on the left consists of 2 10mm length magnets (EPM A). The
model on the right consists of 2 6.35 mm length magnets (EPM B).
(3)
(5)
Increasing the length of the magnet has no effect on the flux
generated by the EPM. Notice the mmf and reluctance both have
a linear relationship to the length of the magnet. The increase in
both mmf and reluctance has no effect on the flux. Increasing
the area of the magnet however does have an inverse
relationship with Reluctance. Therefore increasing the cross
section area of the material decreases the reluctance and
increases the flux.
A. Calculating the current required to switch the EPM
V. USING FEMM TO SIMULATE FLUX DENSITY
The flux density, B [T] is related to the magnetic field, H
[A/m] using equation 3.
𝐵 = 𝑢𝐻
(1)
The magnetic field strength for EPM A was designed to have
twice the magnetic field strength of the coercivity to ensure the
magnet would be completely demagnetized or magnetized. If
too low of a magnetic field strength is applied the EPM will not
retain its intended state. Using H=100 [kA/m] and 𝑙=10 [mm]
and n= 62, which was determined simply be wrapping as many
turns as possible around the magnet. Using the following
equation
𝐻𝑙 = 𝑛𝑖
The femm software was used to provide a visual of how
the flux generated by the electropermanent magnet would
distribute through the core of the inductor. The flux in the
femm simulations were consistent with the flux calculated in
LT spice and hand calculations and were therefore reliable. The
magnetic circuit model for the electropermanent magnet
attached to an inductor is pictured in the figure below.
(2)
the current needed to switch the Alnico 5 magnet in EPM A was
calulated to be 16[A]. When applying current to flip the magnet,
at 8[A] the magnet exhibited some magnetization or
demagnetization (depending on the polarity of the current
pulse). However, when the current was removed from the EPM
the magnetization disappeared. The current level had to reach
16[A] in order to be permanently magnetized or demagnetized.
B. Calculating the Flux Generated by the Electropermanent
Magnet
The magnetic materials each have an internal magneto
motive force, 𝑚𝑚𝑓 [A] and reluctance, ℛ [H-1]. The mmf is
Fig. 8. The magnetic circuit model for the EPM attached to an inductor.
Figure 9 shows the femm simulation for the magnetic circuit
model pictured above. The EPM is placed across an air gap. The
high reluctance of the air gap encourages the flux generated
from the EPM to flow in the opposite direction. The
configuration is effective and flux is passed through each leg of
the inductor. The model could be further improved by
distributing more of the flux in the empty spaces around the
electropermanent magnet. This could be achieved by
decreasing the length of the magnet. The area of the magnet
could then be increased ensuring that the flux generated from
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the electropermanent magnet remains the same. Figures 10 and
11 are other examples of femm simulations.
Ultimately, the flux from the EPM will need to be distributed
such that the maximum flux is subtracted from the internal flux
of the inductor. If flux from the EPM is in the same direction as
the internal flux that portion of the core is in danger of
saturating, having an effect on the performance of the inductor.
The flux from the EPM has a canceling effect with the flux
generated by the inductor coil in the middle and right leg of the
inductor (enclosed in purple), the flux flowing to the left leg
however has a summing effect (enclosed in red).
Fig. 9. An effective geometry for applying the EPM to the inductor such that
the flux is distributed through each leg of the core.
Fig. 12. The areas where the flux generated by the EPM is canceling internal
flux of the inductor is enclosed in purple. The red enclosure indicates where
flux from the EPM is adding to the internal flux, which could saturate that leg
of the core.
VI. MEASURING THE INDUCTANCE EXPERIMENTALLY
Fig. 10. This simulation was modeled experimentally and had the greatest effect
on the inductance than any other configuration. This configuration is not as
practical however because so much excess flux is surrounding the inductor.
This flux may interfere with other components in the circuit.
Fig. 11. This simulation has large air gaps near the base of the inductor. The
flux looks for the path of least reluctance and therefore flows through only a
short segment below where the EPM is placed.
An RLC machine was used to measure the inductance of
different sized cores, with and without EPMs attached. The
simulation in Figure 9 was tested experimentally. The inductor
used an ETD29 core with .0075 mill air gaps. The inductance
measured was 1.3 mH. When EPM A was attached to the side
of the core the inductance fell to 940 𝜇𝐻. This was less of a
change than was expected. This may be due to the mismatched
widths of the EPM and the inductor and poor contact being
made. This low drop in inductance compared to the next setup
described is still being investigated. Another configuration
measured experimentally is shown in Figure 12. The inductor
has no air gaps and an inductance of 1 mH. When EPM A was
applied on the top of the inductor the inductance fell to 330 𝜇𝐻.
This suggests that the flux generated by EPM A is saturating
the core causing over a 50% decrease in inductance.
Fig. 13. EPM A causes the 1 mH inductor to drop to 330 𝜇𝐻. Confirming the
influence an EPM can have on internal flux of an inductor.
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This shows that the EPM is in fact strong enough to have a great
effect on the internal flux of the inductor. The next step will
involve using pieces of ferrite material constructed around the
inductor in such a way that the EPM’s flux is always canceling
the internal flux of the inductor.
flux within the inductor’s core.
VII. MEASURING THE SATURATION CURRENT
Using the ETD 29 core with an inductance of 1.3 mH the
saturation current was measured with the inductor alone and
with EPM A attached to the side. The hypothesis was that when
the core saturated at a calculated current, a drop in inductance
would occur. After applying the EPM, the flux from the EPM
would cancel some of the internal flux of the inductor allowing
a greater current to be applied to the inductor before saturating.
This would be seen as a shift right of the original NO EPM
curve. The hypothesized graph is displayed in Figure 14. The
test set up is pictured in the schematic in Figure 15. An RLC
machine was used to measure the inductance. An ideal current
was emulated using a DC voltage source with an internal
resistance. A 1 mH inductor was placed in series with the DC
source to decrease any fluctuations in the signal. A large
capacitor was used in series with the RLC machine to ensure
that the small sinusoidal current produced by the RLC machine
to measure the inductance did not go back towards the DC
voltage source. The DC source was incremented by .1 [A] until
the core saturated. The DC source however interfered with the
readings of the RLC machine and the data was not reliable. The
data collected is pictured in Figure 16. Notice the inductor
immediately saturates whether the EPM is applied or not. The
shoulder drop off that was expected in the hypothesized graph
was not seen in the collected data. It is possible that if the
current values between 0 and .1 amps were zoomed in on the
expected shoulder drop off of the inductance could be seen.
However .1 amps is the smallest amount the DC source can be
incremented by and greater accuracy is not possible with this
particular set up. It should also be noted that using equation (6)
the saturation current for the inductor was hand calculated and
was expected to saturate around 2.3 [A].
𝐼𝑠𝑎𝑡 =
𝐵𝑠𝑎𝑡 𝐴𝐶
𝑛
(𝑅𝑐 +𝑅𝑔 )
(6)
Fig. 15. The experimental set up for testing the saturation current of the
inductor.
Fig. 16. The experimental results show an immediate saturation in the core
when the EPM is and is not applied. It is believed the DC source has distorted
the readings of the RLC meter.
The next experimental set up to measure the saturation
current of an inductor will apply transformer theory. The circuit
schematic is depicted in Figure 17. A second winding will be
put around the coil of the ETD29 and the dc voltage source and
series impedance will be reflected to the left and the saturation
current measured. The DC voltage source will need to begin at
5[A] and the impedance will be seen as 5X larger, which may
help alleviate the problem of the DC source interfering with the
RLC measurements. This experimental setup should provide
more reliable measurements.
Fig. 14. The hypothesized shoulder drop off of an inductor with and without
an EPM applied. The shift right of the curve suggest an internal cancelation of
Fig. 17. The next experimental set up to measure the saturation current of an
inductor will use transformer concepts to reflect a greater impedance of the DC
source to the left side.
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VIII. CONCLUSION
This research has shown that the electropermanent
magnet can generate enough flux to saturate a core. If this flux
can be routed in such a way that all of the flux generated by the
EPM cancels the internal flux of the core, then decreasing
inductor size while maintaining a higher saturation current will
be achievable. Future work on this project include obtaining
custom fabricated magnets with different magnetic field
directions so that innovative geometries can be created between
the inductor and the EPM. Furthermore, new EPMs that require
less power for the switching of the magnet will be configured.
This will include magnets with greater area and greater window
area (for more turns). Other experimental set ups will be
hypothesized and tested for greater accuracy. Also, inductors
with other geometries such as the toroid will be tested for
efficient flux distribution. During this phase of the research the
flux created from the current pulse was not considered, however
this will also be further investigated.
IX. REFERENCES
[1]
R. Clarke (2008, Aug.) "Magnetic Properties of Materials" [Online].
Available: http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/
[2]
R. Erickson, Fundamentals of Power Electronics Palo Alto, Calif., 1961,
p. 497-850.
J. T. Ludwig, (1960, July). Inductors Biased with Permanent Magnets,
p. 273-278.
G. M Shane, S. D. Sudhoff, “Design Paradigm for Permanent-MagnetInductor – Based Power Converters,” IEEE Transactions on Energy
Conversion, Vol. 28, No. 4 December 2013.
Z Dang, J. Qahouq, "Evaluation of High Current Toroid Power Inductor
with NdFeB Magnet for DC-DC Power Converters," Alabama, 2015.
A. N Knaian, "Design of Programmable Matter," Ph.D. dissertation, Dept.
of Electrical Engineering and Computer Science, Masachusetts Institute
of Tehcnology, Cambridge, MA, College Park, 2000.
[3]
[4]
[5]
[6]
X. BIOGRAPHIES
Maeve Lawniczak is a senior in Electrical
Engineering at the University of Tennessee. She is interested in
wearable technology and wearable devices. She has worked
with the Center for Biotechnology at the University of
Tennessee converting signals from detected bioluminescence
cells to a digital output. She is currently working with Dr.
Costinett researching applications of electropermanent magnets
into the power grid. Maeve is on the board of Systers, which
aims to recruit, mentor and retain women in EECS and is a
student ambassador of CURENT.