ENERGY HARVESTING TRANSDUCERS - ELECTROSTATIC · •Electrostatic energy harvesters based on an air...
Transcript of ENERGY HARVESTING TRANSDUCERS - ELECTROSTATIC · •Electrostatic energy harvesters based on an air...
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ENERGY HARVESTING TRANSDUCERS - ELECTROSTATIC
(ICT-ENERGY SUMMER SCHOOL 2016)
Shad Roundy, PhD
Department of Mechanical Engineering
University of Utah
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Three Types of Electromechanical Lossless Transduction
1. Electrodynamic (also called electromagnetic or inductive): motor/generator action is produced by the current in, or the motion of an electric conductor located in a fixed transverse magnetic field (e.g. voice coil speaker)
2. Piezoeletric: motor/generator action is produced by the direct and converse piezoelectric effect – dielectric polarization gives rise to elastic strain and vice versa (e.g. tweeter speaker)
3. Electrostatic: motor/generator action is produced by variations of the mechanical stress by maintaining a potential difference between two or more electrodes, one of which moves (e.g. condenser microphone)
Credit: This classification and much of the flow from Electromagnetic section is based on the 2013 PowerMEMS presentation by Prof. David Arnold at the University of Florida
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Outline for Short Course
• Introduction and Linear Energy Harvesting
• Energy Harvesting Transducers
– Electromagnetic
– Piezoelectric
– Electrostatic
• Wideband and Nonlinear Energy Harvesting
• Applications
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FUNDAMENTALS OF ELECTROSTATICTRANSDUCTION
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Basic Capacitor Relationship
For a parallel plate capacitor
𝐶 =𝜖𝐴
𝑑
𝑈 =1
2𝐶𝑉2 =
𝑄2
2𝐶
where 𝜖 is the permittivity between the plates (usually air 𝜖0 = 8.85𝑥10−12), 𝑉 is the voltage across the plates, and 𝑄 is the charge stored on the plates (𝑄 = 𝐶𝑉).
If capacitance changes due to external excitation, the energy stored in the capacitor will change, and this energy can be harvested.
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Three Types of Electrostatic Harvestersoscillation
+ + + + + + + + + +
- - - - - - - - - -
Vdc
current
oscillation
+ + + + + + + + + +
- - - - - - - - - -
Vdc
current
oscillation
+ + + + + + + + + +
- - - - - - - - - -
Vdc
current
Out of plane
Overlapping area change
Permittivity change
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Energy Conversion CyclesVoltage Constrained
Cmax
Cmin
Vmax
(2)
(1)
(3)
Q
V𝐸1231 =
1
2𝐶𝑚𝑎𝑥 − 𝐶𝑚𝑖𝑛 𝑉𝑚𝑎𝑥
2
(1) – (2) Capacitor charged at Cmax to Vmax.
(2) – (3) Voltage held at Vmax while capacitance reduces to Cmin. Charge is either returned to voltage source or to an external circuit.
(3) – (1) Remaining charge recovered at capacitance of Cmin.
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Energy Conversion CyclesCharge Constrained
Cmax
Cmin
Vmax
(2’)
(1)
(3)
Q
V
𝐸12′31 =1
2𝐶𝑚𝑎𝑥 − 𝐶𝑚𝑖𝑛 𝑉𝑚𝑎𝑥𝑉𝑖𝑛
𝐸1231 =1
2
1
𝐶𝑚𝑖𝑛−
1
𝐶𝑚𝑎𝑥𝑄02
(1) – (2’) Capacitor charged at Cmax to Vin.
(2’) – (3) Capacitor is open circuit (constant charge) while capacitance reduces to Cmin. In order for charge to remain the same, voltage on capacitor increases to Vmax.
(3) – (1) Charge is recovered at much higher voltage (Vmax) and therefore higher energy than it was injected.
Vin
Q0
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Some Variable Capacitance Structures
Motion
Interdigitated Comb FingersGap Closing
Interdigitated Comb FingersChanging Overlap
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Some Variable Capacitance Structures
In plane, overlapping area harvester with patterned electrodes
Patterned electrodes
motion
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Some Intermediate Comments
• Natural for implementation in silicon MEMS where variable capacitance structures are common
– But, proof mass is extremely low, so power is usually very low
• Energy densities are usually low due to the low permittivity of air unless the voltages are very high
• Needs some sort of rechargeable battery to prime the capacitor, or quite complicated control circuitry
• So, recently, electret based harvesters have become much more common
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Electrets
• “Electret is a dielectric material that has a quasi-permanent electric charge or dipole polarisation. An electret generates internal and external electric fields, and is the electrostatic equivalent of a permanent magnet.” - Wikipedia
• Electrets are characterized by their surface charge density and stability over time
• SiO2 forms an electret with very high surface charge density, but its stability over time is a concern
• Perfluorinated polymers provide better stability
• CYTOP (Asahi Glass Co.) has become a highly used electret material for this application
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Electrets
S. Boisseau, G. Despesse and B. Ahmed Seddik, Electrostatic Conversion for Vibration Energy Harvesting, Small-Scale Energy Harvesting, Intech, 2012
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Example Electret Properties
Adapted from S. Boisseau, G. Despesse and B. Ahmed Seddik, Electrostatic Conversion for Vibration Energy Harvesting, Small-Scale Energy Harvesting, Intech, 2012
ElectretMax thickness
(mm)
Relative
permittivity
Charge density
[mC/m2]
Surface
voltage @ max
thick
Teflon 100 2.1 0.1 – 0.25 ~ 600
Si02 3 4 5 – 10 ~ 500
Parylene 10 3 0.5 - 1 ~ 200
CYTOP 20 2 1 - 2 ~ 1000
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Electret Harvester – Operating Principles
S. Boisseau, et. al. Small-Scale Energy Harvesting, Intech, 2012
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Electret Equivalent Circuit
S. Boisseau, et. al. Small-Scale Energy Harvesting, Intech, 2012
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Electret Harvester Theory
The governing equation for this circuit is:
𝑑𝑄2𝑑𝑡
=1
1 +𝐶𝑝𝐶 𝑡
𝑉𝑠𝑅− 𝑄2
1
𝑅𝐶 𝑡−
𝐶𝑝𝐶 𝑡 2
𝑑𝐶 𝑡
𝑑𝑡
where 𝐶𝑝 = 𝐶𝑝𝑎𝑟 is the parasitic capacitance
This can be re-written in terms of load voltage, 𝑉. (Note, this written as 𝑈 in the figure, which is confusing so I use 𝑉.)
𝑑𝑉
𝑑𝑡= −
1
𝐶𝑝 + 𝐶 𝑡𝑉
1
𝑅+𝑑𝐶 𝑡
𝑑𝑡−𝑑𝐶 𝑡
𝑑𝑡𝑉𝑠
The power is then just:
𝑃𝑟𝑚𝑠 =1
2
𝑉 2
𝑅
Note: electrets are sometimes characterized by surface voltage (𝑉𝑠) as in the equations above, and sometimes by charge density, 𝜎, where
𝑉𝑠 =𝜎𝑑
𝜖𝜖0.
where 𝑑 is the thickness of the electret, and 𝜖 is the relative permittivity of the electret material.
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Electret Harvester Mechanics
Electrostatic force will act to minimize energy in the system, or maximize capacitance.
𝐹𝑒 = −𝑑
𝑑𝑧𝑊𝑒𝑙𝑒𝑐 = −
𝑑
𝑑𝑧
1
2𝐶 𝑧 𝑉 𝑧 − 𝑉𝑠
2
where 𝑊𝑒𝑙𝑒𝑐 = electrostatic force, 𝑉(𝑧) = load voltage as a function of position
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Electret Harvester MechanicsRemember from Linear VEH theory
𝑚 ሷ𝑧 + 𝑏𝑚 + 𝑏𝑒 ሶ𝑧 + 𝑘𝑧 = −𝑚 ሷ𝑦
where 𝑏𝑒 ሶ𝑧 is the electrically induced force. Substituting:
𝑚 ሷ𝑧 + 𝑏𝑚 ሶ𝑧 + 𝐹𝑒 + 𝑘𝑧 = −𝑚 ሷ𝑦
And the governing equations for the system are:
𝑚 ሷ𝑧 + 𝑏𝑚 ሶ𝑧 −𝑑
𝑑𝑧
1
2𝐶 𝑉 − 𝑉𝑠
2 + 𝑘𝑧 = −𝑚 ሷ𝑦
ሶ𝑉 = −1
𝐶𝑝 + 𝐶𝑉
1
𝑅+𝑑𝐶
𝑑𝑡−𝑑𝐶
𝑑𝑡𝑉𝑠
This must be solved numerically as a simple expression for 𝐶 𝑧 is often not available.
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Capacitance Expressions
Example 1, gap closing oscillator:
𝐶(𝑧) =𝜖0𝐴
𝑧 + 𝑔 +𝑑𝜖
where 𝐴 is the total maximum electrode overlap area, 𝑔 is the thickness of the air gap, and 𝑑 is the thickness of the electret, 𝑧 is the displacement of counter electrode.
𝑑𝐶 𝑧
𝑑𝑧=
−𝜖0𝐴
𝑧 + 𝑔 +𝑑𝜖
2
𝐹𝑒 =1
2
𝜖0𝐴
𝑧 + 𝑔 +𝑑𝜖
2 𝑉 − 𝑉𝑠2
S. Boisseau, et. al. Small-Scale Energy Harvesting, Intech, 2012
𝑔
𝑧
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Capacitance Expressions
Example 2, overlapping area patterned electrodes:
The maximum capacitance is:
𝐶𝑚𝑎𝑥 =𝜖0𝐴
𝑔 +𝑑𝜖
where 𝐴 is the total maximum electrode overlap area, 𝑔 is the thickness of the air gap, and 𝑑 is the thickness of the electret.
See Boisseau et. al. 2012 for a discussion of minimum capacitance for the common overlapping area with patterned electrode architecture.
𝐶 𝑧 =𝐶𝑚𝑎𝑥 + 𝐶𝑚𝑖𝑛
2+𝐶𝑚𝑎𝑥 − 𝐶𝑚𝑖𝑛
2cos
𝜋
𝑤𝑧
where 𝑤 is the pitch width
motion
𝑤
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Capacitance Expressions
Example 2, overlapping area patterned electrodes:
𝑑𝐶 𝑧
𝑑𝑧= −
𝜋
2𝑤𝐶𝑚𝑎𝑥 − 𝐶𝑚𝑖𝑛 sin
𝜋
𝑤𝑧
And:
𝐹𝑒 = −𝜋
4𝑤𝐶𝑚𝑎𝑥 − 𝐶𝑚𝑖𝑛 sin
𝜋𝑥
𝑤𝑉 − 𝑉𝑠
2
motion
𝑤
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ELECTROSTATIC HARVESTER DEVICES
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Rotational Harvester - Boland - 2005
Boland J., Micro electret power generators. PhD thesis. California Institute of Technology. 2005
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Another Rotational Harvester – Nakano and Suzuki - 2015
Nakano, Komori, Hattori, Suzuki, PowerMEMS 2015
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Vibration Harvester- Y. Suzuki
Suzuki et. al. JM&M, 2010
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OMRON
http://techon.nikkeibp.co.jp/english/NEWS_EN/20081117/161303/
OMROM device has among the highest reported effectiveness (𝐸𝐻 =𝑃
𝑃𝑉𝐷𝑅𝐺), of around
30-40%.
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Vibration Harvester - Boisseau
S. Boisseau, et. al. Small-Scale Energy Harvesting, Intech, 2012
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Ferrofluidic Electrostatic – Galchev
Galchev, Raz, and Paul, PowerMEMS 2012
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Ferrofluidic Electrostatic – Kruupenkin
Krupenkin and Taylor, Nature Communications, 2012
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Summary
• Electrostatic energy harvesters based on an air gap, with no electret have low energy density
• Electret based harvesters have energy densities on par with electromagnetic and piezoelectric
• Well suited to MEMS implementation
• Voltages high enough to be easily conditioned
• Fabrication and balancing of electrostatic forces can be a challenge