Energy Harvesting from Ambient Vibrations

(1)

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Frédéric Giraud

To cite this version:

(2)

Introduction Modelling of a piezoelectric energy harvester An Example of inverter

Energy Harvesting from Ambient Vibrations

Fr´ed´eric Giraud

L2EP – University Lille1

November 27, 2012

(3)

1 Introduction

What is Energy Harvesting ?

Generator Technologies

Summary

2 Modelling of a piezoelectric energy harvester

Presentation of the system

EMR of the system

Power Extraction on a load resistor R

L

from harmonic oscillation

3 An Example of inverter

Introduction

SSHI: Synchronized Switch Harvesting on Inductor

(4)

Introduction

Modelling of a piezoelectric energy harvester An Example of inverter

What is Energy Harvesting ? Generator Technologies Summary

What is Energy Harvesting ?

We extract energy from an ambient and free source:

(5)

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

(6)

Introduction

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

z

}|

{

EnergyConversion

(7)

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

z

}|

{

EnergyConversion

LOAD

(8)

Introduction

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

z

}|

{

EnergyConversion

LOAD

P

1 P

2

(9)

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

z

}|

{

EnergyConversion

LOAD

P

1 P

2 We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than

1W .

(10)

Introduction

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

z

}|

{

EnergyConversion

LOAD

P

1 P

2 We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than

1W .

η =

P

2

P

1

= 1 −

P

1

−P

2

P

1

−→ Losses in the energy converter should be

as small as possible.

(11)

Objectives: Sensors Network

www.perpetuum.com

(12)

Introduction

Objectives: Sensors Network

www.perpetuum.com

Guti´erriez,A Heterogeneous Wireless Identification Network for the Localization of Animals Based on Stochastic Movements

(13)

Objectives: Sensors Network

www.perpetuum.com

Guti´erriez,A Heterogeneous Wireless Identification Network for the Localization of Animals Based on Stochastic Movements

http://www.rfwirelesssensors.com, 2012

Roundy et Al.:A study of low level vibrations as a power source for wireless sensor nodes.

(14)

Introduction

Objectives: Power, just where you need it

http://enocean.com Wireless Reduce Cost, and is reconfigurable Better Waste Cycle (Information from Enocean)

(15)

Objectives: Power, just where you need it

Innowattech’s systems produces power with vehicles

http://www.innowattech.com

(16)

Introduction

Objectives: Power, just where you need it

Innowattech’s systems produces power with vehicles

http://www.innowattech.com

The economist – April 28th 2007

(17)

Objectives: Marketing Purpose

Experience:

Same Remote

controller energized by human

power, but with different packaging.

”No need for Batteries”

”Green”

”Fun”

(18)

Introduction

Objectives: Marketing Purpose

Experience:

Same Remote

controller energized by human

power, but with different packaging.

”No need for Batteries”

”Green”

”Fun”

54% of people Will choose the first

one because it is eco-friendly.

(Jansen, Human power empirically explored)

(19)

Objectives: Marketing Purpose

Experience:

Same Remote

controller energized by human

power, but with different packaging.

”No need for Batteries”

”Green”

”Fun”

54% of people Will choose the first

one because it is eco-friendly.

(Jansen, Human power empirically explored)

Several projects are born from

this fact: Metis Produces energy

from dancers’ movements.

In Toulouse, the system VIHA

proposes Smart Tiles to energies

street lights.

(20)

Introduction

The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

LOAD

(21)

The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

LOAD

z

}|

{

EnergyConversion

Electricity

Elec.

(22)

Introduction

The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

LOAD

z

}|

{

EnergyConversion

Electricity

Elec.

Generator

(23)

The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...











SOURCE

LOAD

z

}|

{

EnergyConversion

Electricity

Elec.

Generator

Inverter

(24)

Introduction

Solar Harvesters:

(25)

Solar Harvesters:

This sensor measures IntraOccular Pres-sure http://cymbet.com

Handbag to recharge electronic devices http://www.neubers.de

(26)

Introduction

Solar Harvesters:

Solar Energy Harvester Evaluation Kit http://ti.com

Power and current as

a function of voltage:

I

,

P

V

(27)

Solar Harvesters:

Solar Energy Harvester Evaluation Kit http://ti.com

Power and current as

a function of voltage:

I

,

P

V

MPPT strategies,

require Energy

management of the

system

(28)

Introduction

Thermoelectric

A Peltier module from http://www.tellurex.com

V

DC

R

DC

_I

_DC

(29)

Thermoelectric

V

DC

R

DC

_I

_DC

I

DC

V

DC

I

DC

P

T

1

(30)

Introduction

Thermoelectric

V

DC

R

DC

_I

_DC

I

DC

V

DC

I

DC

P

T

1

T

2

(31)

Thermoelectric

V

DC

R

DC

_I

_DC

I

DC

V

DC

I

DC

P

T

1

T

2

(32)

Introduction

Thermoelectric

V

DC

R

DC

_I

_DC

I

DC

V

DC

I

DC

P

T

1

T

2

=

(33)

Thermoelectric

V

DC

R

DC

_I

_DC

I

DC

V

DC

I

DC

P

T

1

T

2

=

Temperature Gradient (residential). Lindsay Miller, http://uc-ciee.org

plumbing application from http://www.nextreme.com

(34)

Introduction

Magnetic

stopper

coil

stopper

φ

x

(35)

Magnetic

stopper

coil

stopper

φ

x

(36)

Introduction

Magnetic

stopper

coil

stopper

φ

x

(37)

Magnetic

stopper

coil

stopper

φ

x

(38)

Introduction

Magnetic

stopper

coil

stopper

φ

x

(39)

Magnetic

stopper

coil

stopper

φ

x

(40)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

_dt

(41)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

(42)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

(43)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

(44)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

=

∼

(45)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

(46)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

(47)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1

1) Diode turns ON

(48)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

(49)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2 3

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

(50)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2 3

hii

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

(51)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2 3

hii

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

v

B

hii,

P

(52)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2 3

hii

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

v

B

hii,

P

_{= hv}

B

i

i = v

B

hii

Fr´ed´eric Giraud Master E2D2 November 27, 2012 10 / 40

(53)

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

t

e

,

v

B

,

i

1 2 3

hii

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

v

B

hii,

P

_{= hv}

B

i

i = v

B

hii

(54)

Introduction

Magnetic

stopper

coil

stopper

φ

x

e

_{= −N}

dφ

_dt

= N

dφ

_dx

dx

dt

v

e(t)

L

i

v

B

=

∼

e

_t

,

v

B

,

i

1 2 3

hii

1) Diode turns ON

2)

_dt

di

_{= 0 because e − v}

B

= 0

3) i = 0, diode turns OFF

v

B

hii,

P

_{= hv}

B

i

i = v

B

hii

(55)

Piezoelectric

An electronic lighter, http://freepatentsonline.com

Piezoelectric crystals

(56)

Introduction

Piezoelectric

An electronic lighter, http://freepatentsonline.com Piezoelectric crystals

Cantilever beam

w(t) = Wsin(ωt)

(57)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

(58)

Introduction

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v im

i

m

is a current proportional

to the deformation speed

(59)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v im

i

m

is a current proportional

to the deformation speed

(60)

Introduction

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v im

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

(61)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v im

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

Roundy, A piezoelectric vibration based generator for wireless

electronics (2004)

(62)

Introduction

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v

im RL

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

electronics (2004)

(63)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v

im RL

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

electronics (2004)

ω

P

ω0

(64)

Introduction

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

v

im RL

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

electronics (2004)

ω

P

ω0

R

Lopt

PMax

R

L

P

(65)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Energy Management

Equivalent electrical circuit

v

im RL

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

electronics (2004)

ω

P

ω0

R

Lopt

PMax

R

L

P

(66)

Introduction

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Energy Management

Equivalent electrical circuit

v

im RL

=

∼

i

m

is a current proportional

to the deformation speed

Comparison Magn. Piezo

Magnetic

Piezo.

Voltage source

Current

source

Inductive

capacitive

Large Stroke

Small

Stroke

Remote action

electronics (2004)

ω

P

ω0

R

Lopt

PMax

R

L

P

(67)

There is no ”one fit all” solution

Each solution may be efficient in a certain range of Power.

Meanwhile, shrinking Chips consumption come at a time when energy harvesting becomes efficient and practical (source: IDtechex.com)

(68)

Introduction

1 Introduction

What is Energy Harvesting ?

Generator Technologies

Summary

2 Modelling of a piezoelectric energy harvester

Presentation of the system

EMR of the system

Power Extraction on a load resistor R

L

from harmonic oscillation

3 An Example of inverter

Introduction

SSHI: Synchronized Switch Harvesting on Inductor

(69)

Coordinates and assumptions

moving Case

Bender

(70)

Introduction

Modelling of a piezoelectric energy harvester

An Example of inverter

Presentation of the system EMR of the system

Power Extraction on a load resistor RLfrom harmonic oscillation

Coordinates and assumptions

moving Case

Bender

The bender is attached to a vibrating and rigid case,

(71)

Coordinates and assumptions

moving Case

Bender

M

A mass M is attached to increase power harvesting,

(72)

Introduction

Coordinates and assumptions

moving Case

Bender

M

_w

_(t)

w(t) is the deflection of the beam,

(73)

Coordinates and assumptions

moving Case

Bender

M

_w

_(t)

ℜ

w(t) is the deflection of the beam, We define ℜ a fixed reference frame,

(74)

Introduction

Coordinates and assumptions

moving Case

Bender

M

_w

_(t)

ℜ

′

w(t) is the deflection of the beam, We define ℜ a fixed reference frame, And ℜ′

a reference frame affixed to the vibrating case.

(75)

Coordinates and assumptions

moving Case

Bender

−

→

_F

p→M

M

w

(t)

ℜ

′

− →

Fp→mis the force of the Bender onto the mass M.

(76)

Introduction

Coordinates and assumptions

moving Case

Bender

−

→

_F

p→M

M

w

(t)

ℜ

′

− →

The case is supposed to be controlled in position, and we have yc= Asin(ωt) the amplitude of the case’s vibration.

(77)

Coordinates and assumptions

moving Case

Bender

−

→

_F

p→M

M

w

(t)

ℜ

′

− →

The case is supposed to be controlled in position, and we have yc= Asin(ωt) the amplitude of the case’s vibration. Gravity is neglected, as well as Inertia momentum of the bender,

(78)

Introduction

Coordinates and assumptions

moving Case

Bender

−

→

_F

p→M

M

w

(t)

ℜ

′

v im i

− →

The case is supposed to be controlled in position, and we have yc= Asin(ωt) the amplitude of the case’s vibration. Gravity is neglected, as well as Inertia momentum of the bender, Actuator electrical convention.

(79)

Equations

Dynamic of the mass M:

Glossary

Mthe mass f, the force onto M A, vibration’s amplitude ω, vibration’s pulsation faccis the inertial force icurrent of the device (actuator convention) immotional current fpinside piezo force NPiezoelectric force factor (depends on geometry) fpPiezo internal force fsMaterial internal elastic force

Ksequivalent stiffness (depends on geometry) DsViscous coefficient

(80)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

Glossary

(81)

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Glossary

(82)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

Glossary

(83)

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Glossary

(84)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

Glossary

(85)

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

Glossary

(86)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

while v produces an internal force

f

p

= Nv

Glossary

(87)

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

while v produces an internal force

f

p

= Nv

Material’s behaviour

Glossary

(88)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

while v produces an internal force

f

p

= Nv

Material’s behaviour

The material is elastic: fs

= Ks

R

w dt

˙

Glossary

(89)

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

while v produces an internal force

f

p

= Nv

Material’s behaviour

The material is elastic: fs

= Ks

R

w dt

˙

With some friction inside:

f

s

= Ks

R

˙

w dt

+ Ds

w

˙

Glossary

(90)

Introduction

Equations

Dynamic of the mass M:

M

_dt

d

22

(w (t) + Asin(ωt)) = Fp→M

= f

M

w

¨

(t) = f + MAω

2 sin

(ωt) = f + facc

Electrical Behaviour:

Capacitive

v

=

_Cb

1 R

(i − im)dt

Piezoelectric effect

i

m

derives from deflection: im

= N ˙

w

while v produces an internal force

f

p

= Nv

Material’s behaviour

The material is elastic: fs

= Ks

R

w dt

˙

With some friction inside:

f

s

= Ks

R

˙

w dt

+ Ds

w

˙

These actions are opposite to the PE

effect: f = fp

− fs

Glossary

(91)

EMR of the system

v= 1 C_b Z (i − im)dt | {z }

(92)

Introduction

EMR of the system

v= 1 C_b Z (i − im)dt | {z } i v

SE

(93)

EMR of the system

v= 1 C_b Z (i − im)dt | {z } i v im v

SE

z }| { fp= Nv, im= N ˙w

(94)

Introduction

EMR of the system

SE

z }| { fp= Nv, im= N ˙w ˙ w fp ˙ w f ˙ w= 1 M Z (f − facc)dt | {z }

(95)

EMR of the system

SE

z }| { fp= Nv, im= N ˙w ˙ w fp ˙ w f ˙ w= 1 M Z (f − facc)dt | {z } z }| { f= fp− fs z }| { fs= Ks Z ˙ w dt+ Dsw˙ ˙ w fs

(96)

Introduction

EMR of the system

SE

z }| { fp= Nv, im= N ˙w ˙ w fp ˙ w f ˙ w= 1 M Z (f − facc)dt | {z } facc ˙ w z }| { f= fp− fs z }| { fs= Ks Z ˙ w dt+ Dsw˙ ˙ w fs

SM

(97)

EMR of the system

SE

SM

pe

= v .i

is the output power,

(98)

Introduction

EMR of the system

SE

SM

pe

= v .i

is the output power,

p

m

= f

acc

w

˙

is the mechanical input power

and both should be < 0

(99)

EMR of the system

SE

SM

pe

= v .i

is the output power,

p

m

= f

acc

w

˙

is the mechanical input power

and both should be < 0

v i e i

SE

Ω T Tr Ω

SM

Comparison with a DC motor

Things are not so differerent.

(100)

Introduction

EMR of the system

SE

SM

pe

= v .i

is the output power,

p

m

= f

acc

w

˙

is the mechanical input power

and both should be < 0

v i e i

SE

Ω T Tr Ω

SM

Comparison with a DC motor

Things are not so differerent.

(101)

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

(102)

Introduction

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

(103)

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

(104)

Introduction

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

(105)

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

(106)

Introduction

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

for example, f

_acc

= MAω

2 _e

j ωt

_{and |f}

acc

| = MAω

2 .

(107)

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

for example, f

_acc

= MAω

2 _e

j ωt

_{and |f}

acc

| = MAω

2 .

v

_{= −R}

L

i

(108)

Introduction

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

for example, f

_acc

= MAω

2 _e

j ωt

_{and |f}

acc

| = MAω

2 .

v

_{= −R}

L

i

(109)

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

for example, f

_acc

= MAω

2 _e

j ωt

_{and |f}

acc

| = MAω

2 .

v

_{= −R}

L

i

v RL im

i

(110)

Introduction

Asumption

f

acc

= MAω

2 sin

(ωt) for harmonic oscillations

complex notation: x is the complex phasor of x(t), means

x

_{(t) = ℑ(x)}

since oscillations are harmonic, we will write:x = X e

j ωt

for steady state operation, X is constant, leading to

dx

dt

= jωX e

j ωt

|x| = |X | = X

for example, f

_acc

= MAω

2 _e

j ωt

_{and |f}

acc

| = MAω

2 .

v

_{= −R}

L

i

v RL im i

And R

L

≪

_C

1

_b

_ω

, yields

v

_{≃ −R}

L

i

m

(111)

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

(112)

Introduction

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

f

= Nv − Ks

w

(113)

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

f

= Nv − Ks

w

v

_{= −RL}

i

_m

_{= −RL}

N

w

˙

(114)

Introduction

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

f

= Nv − Ks

w

v

_{= −RL}

i

_m

_{= −RL}

N

w

˙

M

w

¨

+ N

2 _R

L

w

˙

+ Ks

w

= f

acc

(115)

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

f

= Nv − Ks

w

v

_{= −RL}

i

_m

_{= −RL}

N

w

˙

M

w

¨

+ N

2 _R

L

w

˙

+ Ks

w

= f

acc

−→ RL

acts as a damping

P

2 = −

1 ₂

R

L|im|

2

(116)

Introduction

For an ideal generator (D

s

= 0)

M

w

¨

= f + f

_acc

f

= Nv − Ks

w

v

_{= −RL}

i

_m

_{= −RL}

N

w

˙

M

w

¨

+ N

2 _R

L

w

˙

+ Ks

w

= f

acc

−→ RL

acts as a damping

P

2 = −

1 ₂

R

L|im|

2 |im| = N| ˙w| =

ω.

N .|facc|

√

(Ks−Mω

2

₎

2

_+(N

2

_RL

ω

)

2

Energy Harvesting from Ambient Vibrations

HAL Id: hal-02495300

https://cel.archives-ouvertes.fr/hal-02495300

Submitted on 1 Mar 2020

HAL is a multi-disciplinary open access

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abroad, or from public or private research centers.

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scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Frédéric Giraud

To cite this version:

Energy Harvesting from Ambient Vibrations

Fr´ed´eric Giraud

L2EP – University Lille1

November 27, 2012

Table of contents

1

Introduction

What is Energy Harvesting ?

Generator Technologies

Summary

2

Modelling of a piezoelectric energy harvester

Presentation of the system

EMR of the system

Power Extraction on a load resistor R

L

from harmonic oscillation

3

An Example of inverter

Introduction

SSHI: Synchronized Switch Harvesting on Inductor

What is Energy Harvesting ?

We extract energy from an ambient and free source:

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...























SOURCE

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...























SOURCE

z