Download Optimum Design of Magnetic Inductive Energy Harvester and its AC-DC Converter

Optimum Design of Magnetic Inductive Energy
Harvester and its AC-DC Converter
Qian Sun, Sumeet Patil, Stephen Stoute, Nian-Xiang Sun, Brad Lehman
Department of Electrical and Computer Engineering
Northeastern University
Boston, MA, 02115, USA
Abstract—The design of a new-type of inductive magnetic
energy harvesting system with high permeability magnetic
material combined with a dual polarity boost converter is
presented. By using the strong magnetostatic interaction
between the coils and permanent magnets, the output power
and power density of the energy harvester is enhanced
compared to conventional air cored inductive harvesters. In
the proposed dual polarity boost converter, the coil leakage
inductor of the harvester is utilized to form the input inductor
of the boost converter to minimize the converter size.
Therefore, the magnetic energy harvester and the power
converter share the same magnetic core. Optimum system
design becomes a balance of core size, required leakage
inductance and required magnetizing inductance in order to
extract maximum energy.
I.
induced voltage. Using strong magnetostatic interaction
between magnets and coils with high permeability magnetic
material cores, the output power can be enhanced
significantly. Our proposed vibration and rotation energy
harvesters show enhanced output power and power density
compared to piezoelectrics, as well as widen working
bandwidth [6].
A difficulty with extracting energy in the majority of
inductive magnetic energy harvesters is that they produce
low AC voltage at low frequency (typically around 100Hz),
where step-up transformers cannot be used directly because
of their large size. At the same time, the voltage requirement
for low voltage, low power, electronic devices is typically
1.8~3.3VDC. Thus, rectification losses cannot be avoided in
power processing circuit of magnetic harvester. Recently, a
number of high step up converters topologies have been
presented, especially for piezoelectics applications [3]-[4],
[7]-[17]. Conventional approaches to rectify the AC
harvester voltage is to feed it to a diode bridge rectifier at the
first stage and then to a dc-dc converter in the second stage
[3]-[4]. However, this is inefficient due to the power losses
in the first stages to overcome the diode bridge voltage drops
[16]. This has led to the beginning of research to design
bridgeless power electronic and other circuits for air cored
inductive energy harvesters to avoid some of the losses [4],
[15]-[17]. As the first work on inductive magnetic energy
harvesting system, a direct AC/DC boost converter is
designed utilizing the harvester coil leakage inductance.
Since the detailed analysis on the equivalent model of
inductive magnetic harvester has not been presented, there is
insufficient research on how the harvester and converter
design influences each other. Furthermore, these types of
converters require bidirectional switches and additional
external magnetic cores for boost inductors.
INTRODUCTION
Vibration and rotation energy harvesting technologies
have been developing rapidly, and have shown great
potential in many different applications. However, these
applications are often limited by the amount of energy that
can be harvested. Generally, piezoelectric energy harvesting
technologies are considered the most commercially mature
[1]-[3]. Alternatively, inductive magnetic energy harvesters
with air cored coils are also available [4], but they have
much lower power density than their piezoelectric based
counterparts. However, there is an emerging classification of
inductive energy harvesters that propose to replace the air
cored coils with high permeability magnetic materials [5][6]. Theoretically this leads to energy density 105-106 times
that in piezoelectrics. The full potential of high permeability
inductive magnetic energy harvester has not yet been
realized.
The main challenge to design inductive magnetic energy
harvester is how to increase its output power and power
density to higher level. Although the output voltage and
power can be increased by making a large size harvester with
thousands of turns, it will eventually lead to low efficiency
and low power density caused by high energy loss on
increasing coil resistance. The high permeable cores
dramatically increase the magnitude of magnetic flux
through the coils. Thus, a larger flux change is expected to
be generated through each core, which results in larger
978-1-4673-0803-8/12/$31.00 ©2012 IEEE
In this paper, a new dual polarity boost converter with
magnetic fully integrated into the harvester is proposed. By
utilizing the leakage inductance of the proposed high
permeability magnetic harvester, no external inductor cores
need to be added as the boost inductor of the AC/DC
converter cascaded after the harvester. Further, by adding a
diode in series with each center tapped coil, rectification can
be achieved with low power loss. The fact that internal
394
vs
Fig. 2 Inductive magnetic energy harvesters in equilibrium
(a)
(b)
Fig. 1 Inductive magnetic energy harvesters. (a) Vibration harvester. (b)
Rotation harvester
leakage inductance is utilized to form input inductance of
boost converter, dramatically reduces converter size. Further,
no bi-directional switch is needed in the converter, which
leads to smaller power loss on control and drive circuits and
simpler control scheme. In Section II, the design and
modeling of the inductive magnetic energy harvester and its
AC-DC converter is presented. By analyzing an equivalent
model of harvester, it is shown how the dual polarity boost
converter can utilize the leakage inductance of the harvester
to achieve the maximum extracted energy of the whole
harvesting system. The experiment results are presented in
Section III. The efficiency and power loss of each switching
device are calculated in this section.
II.
Lk
is
vs
Lw
Rc
Lm
im
Rw
ii
Lk
is
vi
vs
Rw
Lm
im
ii
vi
(a)
(b)
Fig. 3 Equivalent model of inductive magnetic energy harvester
transformers, hard drives and magnetic resonance imaging
equipment to prevent magnetic fields from affecting nearby
electronic equipment. However, these high permeability
materials have the potential, as shown in this paper, to
provide significantly enhanced inductance performance with
high inductance, low volume, high quality factor, etc. When
introduced in inductive energy harvesters, this leads to
significantly enhanced power/energy density compared to
air core coil based energy harvesters [5]-[6].
DESIGN OF ENERGY HARVESTING SYSTEM
In this section, the design and modeling of the inductive
magnetic energy harvester and its dual polarity boost
converter is presented. The converter is designed to utilize
the internal leakage inductance of the magnetic energy
harvester in order to reduce the size of harvesting system.
A. Inductive Magnetic Harvester Design and Modeling
Two inductive magnetic harvesters are shown in Fig. 1
(vibration harvester in Fig. 1(a) and rotation harvester in Fig.
1(b)). The inductive magnetic harvesters typically consist by
magnets, coils, and rotation or vibration mechanical
structure. Despite different motion types, the mechanical
energy changes to electrical energy by the changing flux
through magnetic core by vibrating or rotating. Thus, they
can be modeled by the same equivalent model with different
parameters.
Fig. 2 shows the inductive magnetic energy harvester in
equilibrium. The magnetic cored coil is expected to generate
a much larger flux change than air cored coil (typically
designed as in [1]) by providing a high permeability path for
the flux.
According to Faraday’s law, the electromotive force
(EMF) is induced by the flux change through the coil
winding, which is represented by in the equivalent model.
And is the voltage measured across coil windings of the
harvester.
Since the permeability of the core material is finite, the
magnetic reluctance is non-zero. According to Ampere’s
Law:
is =
Hl ΦRm
=
+ ii = im + ii
n
n
(1)
is source current of equivalent model and is excitation
current (Fig. 3). This current can be modeled as magnetizing
inductance in parallel.
Due to finite permeability, a small amount of flux does
not go through magnetic core, which is called leakage flux
(Fig.2). The leakage flux is from two parts. One part from
permanent magnets can be modeled as series leakage
inductor . is mainly related to the permeability of the
magnetic core material, and the gap between magnets and
coils. The leakage flux generated by coil windings can be
modeled as a series inductor , which generally is
negligible compared to . Once the core material has been
decided, leakage inductance and magnetizing inductance
are mainly decided by the gap between permanent
magnets and coils (Fig. 2). When the gap increases, The key component of the harvester is the high
permeability (high- µ ) core inside the coil. This high
permeability magnetic material is normally composed of
nickel-iron alloy (~77%), iron (16%), copper (5%) and other
materials (2%) and has relative permeability close to 106.
Traditionally, the material has been used to form thin sheets
of magnetic shields for shells/protection of electric power
395
is = 0
Lk
Rw ii = 0
vi = vs
vs
(a)
Lk
is
Rw
vs
(b)
Fig.4 Open and short circuit of harvester
5
x 10
-3
iin
Lk
ii
Lk
Leakage Inductance
4.5
iin
Leakage Inductance Lk (H)
4
3.5
3
2.5
2
θc
2π
1.5
t
D f Ts
1
DTs
0.5
0
90
Ti
95
100
105
Frequency (Hz)
110
115
Fig. 5 Leakage inductance increases and decreases. By choosing a gap small
enough, can be made to become a large quantity and can
be neglected. The following section of converter design will
be under this limited gap range.
Fig. 6 Proposed circuit and input current
Open and short circuit test can be done with the
harvester under certain frequency. Open circuit voltage and
short circuit current can be measured with the setup shown
in Fig. 4. Since there is no current going through the
harvester in open circuit condition, we can get:
As shown in Fig. 3(a), in series with represents
winding resistance. In order to increase the output voltage of
the harvester, the harvester winding usually is made up of
large number of turns. Thus, generally, the winding
resistance cannot be ignored and it is key factor that affects
the efficiency of the harvesting system. The winding
resistance should be as small as possible to achieve less
power loss.
vi = vs
(2)
In short circuit condition, the winding resistance and
the leakage inductance can be seen as the load of the
harvester. For a general load composed of RL elements
under sinusoidal-steady-state excitation follows the
following equation:
Since the magnetic core is highly permeable, there exists
core loss. A resistor in parallel with represents eddy
current loss and hysteresis loss. Compared to and , the
effect of core loss is negligible. Thus, is large enough to
be neglected in following analysis.
is ( SC ) =
It can be seen from Fig. 3 that the leakage inductance is
one of the key parameter affecting output power of harvester.
At the same time, the leakage inductance is used as the
input inductance of dual polarity boost converter in the
converter design. The value of also influences the
converter power loss. In order to gain maximum energy out
from the energy harvesting system, needs to be
controlled to an optimum value.
Theoretically, the leakage inductance can be only
calculated by finite element analysis. However, it can be
roughly estimated with the simplified equivalent model.
396
vs ( OS )
jω Lk + Rw
(3)
Thus, the leakage inductance can be estimated under
each fixed frequency with known winding resistance. It can
be seen in Fig. 5 that the leakage inductance of proposed
inductive magnetic harvester is around 2mH.
B. Dual Polarity Boost Converter
We propose to center tap the harvester coil in Fig. 1.
Then according to the harvester equivalent model, we
introduce a new type of converter, in Fig. 6, that is a dual
polarity boost converter that utilizes the leakage inductance
of the center tapped coils as the two boost inductors. Since
Lk 1
D1
Lk 2
D2
dramatically reduce the converter size since no external
inductor is needed. Further, with a center tapped coil,
rectification is achieved by adding the two diodes in Fig. 6,
instead of a diode bridge rectifier. Therefore, rectification
voltage drop will lower by 50%, and further, there is no bidirectional switch needed (simplifying and improving the
efficiency of the control and drive).
D3
vs1
vs 2
Lk1
D1
The main losses in the circuit are due to the winding
resistance of coil, ON-state resistance of the MOSFETs, and
the input and output diodes:
D3
vs1
2
(4)
Ploss = I s2( rms ) ⋅ Rw + 2 ⋅ V f ⋅ I din ( avg ) + V f ⋅ I dout ( avg ) + I SW
( rms ) ⋅ Rds
where , , , and are input current, input diode
current ( and ), output diode current ( ) and
MOSFET current, respectively. Consider the kth switching
cycle for the converter, the input voltage can be seen as
constant, since vibration period .
vs 2
Lk 2
D2
Lk 1
D1
(a)
D3
vs1
vsk = Vp ⋅ sin(2π k ⋅
∆isk =
vs 2
Lk 2
Lk 1
D2
D1
Ts
)
Ti
vsk DTs
Lk
where is the peak voltage of harvester. The RMS value of
the source current over a switch cycle can be derived as:
D3
vs1
 2 1 2
1 vsk2 D 3Ts2
1
 I sk = isk ( D + D f ) =
3
3 L2k 1 − vsk / Vo


v 2 D 2T 2

I sk2 = I sk2 ( avg ) + sk 2 s

12 Lk
vs 2
Lk 2
(5)
D2
(6)
( DCM )
(CCM )
Suppose the converter works in CCM during . The
RMS value of input current can be calculated by taking
average of half cycle integration:
(b)
Fig. 7 Principle of Operation. (a) Positive half cycle of AC voltage.
(b) Negative half cycle of AC voltage
I s2( rms ) =
the diodes are located after the leakage inductance, their
voltage drop will not have dominant power loss, and hence
this topology is suitable for ultra-low voltage, low power
application. Since the output voltage of the harvester is
similar to a sine waveform, the EMF will be considered as
sinusoid in the analysis to simplify the process.
V p2 D 3Ts2
3L2k
(
2
∫
π − θc
π −θ c
sin 2 θ
2
0
1 − V p sin
θ
 (1 − D )4 V p2 D 2Ts2 
sin θ c
+
dθ ) + 
)
 (1 +
θc
12 L2k 
 RL
(7)
Vo
 (1 − D ) 4 V p2 V p2 D 2Ts2 
sin θ c
sin θ c
(1 −
)+
)
=
+
 (1 +
2
π − θ c  2 RL2
θc
6 Lk
24 L2k 
14442444
3 14444442444444
3
V p2 D 3Ts2
DCM
CCM
Similarly, the MOSFET current, input diode current (
and ) and output diode current ( ) can be calculated:
The principle of operation is shown in Fig. 7. Each
winding operates during a half cycle of the input AC
voltage, with the control scheme each half cycle similar to a
fixed duty ratio boost converter. The converter can work in
both continuous (CCM) and discontinuous (DCM) current
mode. As shown in Fig. 6, when the input voltage is low,
the converter works in DCM and when the input voltage
builds up, the converter transfers to CCM.
2
2
I SW
( rms ) = DI s ( rms ) =
Vp2 D4Ts2
2
k
6L
DVp  (1 − D)4 D2Ts2 
sin θc
sin θc
)+
+
)

 (1 +
π − θc
2  RL2
12L2k 
θc
2
(1 −
θ
I din ( avg ) =
DI s ( avg )
2
=
I dout ( avg )
The proposed converter is designed to be integrated to
the inductive magnetic energy harvester by using leakage
inductance as the input inductance of boost converter. The
leakage inductance can be designed so that it is large
enough to be used for the input inductance, which can
θ
c
c
V p D 3Ts 1 − sin( 2 ) V p D sin( 2 )
(
)+
2 Lk
π − θc
RL (1 − D ) 2 θ c
θ
(8)
(9)
θ
c
c
V 2 D 2Ts 1 − sin( 2 ) 2V p sin( 2 )
= p
(
)+
Lk (1 − D) π − θ c
RL (1 − D )θ c
(10)
It can be seen from (7), (8), (9) and (10), the power loss
on the MOSFET switches, winding resistance and diodes
decreases when the leakage inductance increases. And if
the harvester enters CCM, the power loss reduces. However,
397
120
TABLE I.
Harvester Output Power
Converter Output Power
System Output Power
100
PARAMETER OF MAGNETIC HARVESTER
Parameters
Induced voltage (RMS)
Output Power (W)
80
Gap
Magnet diameter
Coil numbers
Coil inductance
Coil resistance
60
40
20
0
0
5
10
Leakage Inductance (H)
15
1V
2mm
8mm
4
1mH
4.5 Ω
C. Optimum Leakage inductance
Traditionally, magnetic harvester design and converter
design are separated. However, the maximum output cannot
be achieved for both harvester and converter at the same .
20
Fig. 8 Variation of harvester and converter output power with
Value
!
MATLAB/Simulink models are built according to Fig.
3(b) and Fig. 6 in order to observe how the harvester and
converter output power change with leakage inductance .
The harvester output power is measured under optimal
resistance in order to gain maximum power transfer. Fig. 8
shows the simulation result. The output energy of magnetic
energy harvester drops with the increase of . The output
power of the converter rises with the increase of due to
lower power loss, which verifies (7)-(10). The energy
harvesting system net energy output is shown in the red
curve. When the leakage inductance is small, the system
output power is limited by high power loss of converter.
And when the is large, the output power output power
with is limited by the harvester output capacity. The
maximum system net energy occurs when two curves cross
each other.
Fig. 9 Experimental setup
Frequency (Hz)
0.14
0.13
0.12
Output Power (W)
0.11
Generally, magnetic energy harvesters are designed to
be operated close to the vertical axis ( as small as
possible) to gain higher voltage and power output. However,
this is no longer desirable if no external inductor added.
There is no need to maintain the minimum gap, which often
leads to a high requirement on the mechanical design of
magnetic energy harvester [1],[7]-[8]. Near the maximum
point of system output power in Fig. 7, system output power
drops slowly with increasing . Thus, there is a tolerance
on for magnetic harvester design. Therefore, the gap can
be maintained in a small range, and needs not be a precise
value, adding more convenience on harvester mechanical
design. In the proposed harvesting system, the coils are
mounted on the holder of inductive magnetic energy
harvester with superglue (Fig. 1 (b)). Since the gap can
hardly be adjusted by changing the position of coils once
they are fixed to the harvester, several sets of harvester were
built with different mechanical and electrical parameters.
The experiment results are based on one set of harvester
which has better performance.
0.1
0.09
0.08
0.07
0.06
0.05
0.04
80
85
90
95
Frequency (Hz)
100
105
110
Fig. 10 Harvester output power versus frequency
as mentioned previously, high output power of harvester
requires low . A tradeoff must be made on designing of a
value of value to obtain maximum system energy
extraction. As mentioned before, leakage inductance is
significantly affected by gap between coil and magnets.
That means, there is a tradeoff between power loss in the
switches and magnetic core energy harvester output.
398
TABLE II.
CIRCUIT PARAMETERS AND LOSS OF THE CONVERTER
Value
Parameters
(a)
Leakage Inductance
Winding Resistance
MOSFET
Output Capacitor
Input Diodes
Output Diode
(b)
Output Voltage
Lk1, Lk2
2mH
Rw
Rds_on
C
Vf
4.7Ω
0.22Ω
100µF
0.23V
Vo
Estimated Loss
0.113mW
0.0045mW
25.3mW
4.5mW
3.3V
machine. The output power of the harvester is calculated
from the voltage across the load resistance. The maximum
power is 130mW at 110Hz.
B. Energy Harvesting System
In this section, the experiment results of energy
harvesting system are presented. The design parameters of
the converter are shown in TABLE II. A MOSFET with low
gate drive voltage (FDV305N from Fairchild) is selected as
the main switching device. Schottky diode (NSR0320 from
ONsemiconductors) with low forward voltage drop is
chosen to be input and output diode. The typical forward
voltage drop is 0.23V.
Fig. 11 (a) Output voltage (2V/div). (b) Input current (200mA/div)
(a)
The converter is operated in open loop with fixed duty
ratio =0.85 at the switching frequency 25kHz. A nominal
load of " = 200 Ω is connected to the converter. The
magnitude of the output voltage is around 3.3V, which
means the output power around 54mW. The input current of
positive side is shown in Fig. 11. It can be seen that the
input current is blocked by the input diode during negative
half cycle. Due to the large value of input inductance
(around 2mH), there is small current ripple. The gate signal
is shown in Fig. 12.
(b)
Fig. 12 (a) Gate Signal (2V/div). (b) Output voltage (2V/div).
III.
Since the input voltage cannot be measured directly, the
input power and converter efficiency can hardly be found
from the input voltage and current. As shown in TABLE II,
the power loss is estimated according to (7)-(10). The
converter is considered to work under continuous current
mode and the effect of input diodes voltage drop is also
included. It can be seen that the most significant power loss
is from input and output diodes. The converter efficiency is
estimated to be around 64.4%.
EXPERIMENT RESULT
The inductive magnetic energy harvester (Fig. 1 (b)) and
dual polarity boost converter is designed according to above
analysis. The block diagram of experiment setup is shown in
Fig. 9. A milling machine is used to produce rotation for the
harvester. The harvester is fixed to the base of the milling
machine with the rotation wheel close to spindle, so that the
wheel can rotate with the spindle. The rotation speed of the
harvester is controlled by the milling machine. The
experiment result is presented under both conditions when
the harvester is connected with and without converter.
However, the harvester has maximum output power
130mW at 110Hz under optimal resistance 4.9Ω. There is
no impedance matching in the converter design. If the
harvester maximum output power is considered as input
power, the efficiency of the harvesting system is 41.5%.
A. Inductive Magnetic Energy harvester
The harvester design parameters are shown in TABLE I.
The frequency of harvester output voltage can be changed
from 0 to 120Hz with the milling machine.
IV.
CONCLUSION
In this work, the proposed energy harvesting system is
for extracting more energy from inductive magnetic energy
harvester. The presented inductive magnetic energy
harvester use high permeability material cores to achieve
The harvester output power is tested under the optimal
resistance 4.9Ω. The curve of harvester output energy
variation with frequency is shown in Fig. 10. The curve is
obtained by changing the rotation speed of the milling
399
[8]
more flux change through the coils, which leads to higher
output voltage. The proposed dual polarity boost converter
combined with the harvester can dramatically reduce the
rectification voltage drop compared to conventional diodebridge rectifier. The leakage inductance of coils is utilized
to form the input inductance of the boost converter to reduce
the converter size. Since high permeability cores are
employed, the leakage inductance is high enough and can be
adjusted to achieve higher efficiency of the harvesting
system.
[9]
[10]
[11]
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