Topology Optimization of Energy Harvesting Devices – The

D. Hoffmann / 28.05.10 / Slide 1www.hsg-imit.de

Topology Optimization of Energy Harvesting Devices –

The Quest for Maximum Power Output

Daniel HoffmannInstitut für Mikro- und Informationstechnik der Hahn-Schickard Gesellschaft e.V.

HSG-IMITWilhelm-Schickard-Str. 10, D-78052 Villingen-Schwenningen, Germany

phone: +49 7721 943-187 fax: +49 7721 943-210 email: [email protected]


Outline

Introduction to energy harvesting• Motivation• Examples of demonstrators• Energy harvesting from vibrations• Energy conversion principles• Workflow

Optimization of electrostatic energy harvesting devices• Active principle• Design constraints• Optimization using modeFRONTIER• Conclusions


Motivation

Industrial Environment

Object to be monitored

(Pump, Mould)

Sensor node• Intelligent• Wireless• Maintenance free• Unlimited lifetime• Robust & Reliable

• Highly cost-efficient condition-based maintenance of industrial devices (machines, pumps, plants, etc.)

• Condition monitoring:• Optimization of operation processes• Protection / Prevention• System state, Object position, etc.

Energy autonomous SystemEnergy harvesting technologies


Motivation

• Energy Harvesting Harvesting of electrical energy through conversion of ambient non-electrical energy

Radiation (light), thermal gradients, kinetic motions (vibrations)

• Research and Development at HSG-IMITDevelopment of application specific vibration generators

Continuous improvement of performance (effectiveness & efficiency)

Broadband systems, adaptive systems


Intelligent Fluid Quick Connector

Vibration transducer


Concrete Products Mould


Energy Harvesting in Railroad Applications


• Coupling of kinetic vibration energy• Mechanical to electrical energy conversion• High effectiveness of energy conversion• High efficiency of power management circuits• Minimum output ratings: voltage, current, power (given by application)• Size limited to available construction volume (given by application)• Adjustable to the specific conditions of the target environment• Self adaptation to changes in the vibration profile (frequency)• Dynamic long-term stability (reliability, durability)• No affection by environmental influences (temperature, materials,

moisture, )• …

General requirements

Energy Harvesting from Vibrations


Vibration Source

Vibration Generator Electronics Energy

Storage Consumer

Losses LossesLosses

Optimization Efficiency

Optimization Effectiviness

Energy Harvesting from Vibrations

m

me ccc +=k

)(tx

)(tz

)(ty

Generator components• Oscillating mass• Suspension springs• Transduction mechanism


Parameter Electromagnetic Piezoelectric Electrostatic

Voltage (AC Peak) 1 V … 10 V 5 V … 50 V 0.5 V … 5 V Current (AC Peak) 1 mA … 15 mA 10 µA … 200 µA 0.5 µA … 10 µA Power (AC Peak) 1 mW … 150 mW 50 µW … 10 mW 0.2 µW … 50 µW Operation frequency 30 Hz … 500 Hz 50 Hz … 500 Hz 1000 Hz … 5000 Hz Size 3 cm³ … 250 cm³ 5 cm³ … 50 cm³ 0.2 cm³ … 0.5 cm³ Mass of proof mass 10 g … 500 g 1 g … 10 g 500 µg … 1000 µg Displacement limit 0.5 mm … 3 mm 0.5 mm … 1 mm 10 µm … 40 µm

Energy Conversion Principles

+ + + + ++ + + + +

+ ++ +

--

--

--

--

--

--

--m

me ccc +=k

)(tx

)(tz

)(ty

Performance strongly dependent on excitation conditions!


0.2cm³, 1-10µW

200cm³, 100-800mWParameter Electromagnetic Piezoelectric Electrostatic

Excitation 39 m/s² 13 m/s² 59 m/s² Voltage (AC) 9 V 39 V 1.1 V Current (AC) 90 mA 385 µA 1.9 µA Power (AC) 800 mW 15 mW 2.2 µW Frequency 30 Hz 150 Hz 1220 Hz Size 190 cm³ 18 cm³ 0.2 cm³

Energy harvesting from vibrations

Device Range & Examples


Analysis of the target environment

Choice of a transduction mechanism

Modelling, Design and Optimization

Workflow

Manufacturing and Characterization

86 87 88 89 90 91 92 93 94

-200

0

200

Time (s)

acc

(m/s

²)

Acceleration Profile

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

Frequency (Hz)

PSD

(dB

/Hz)

Power Spectral Density

86 87 88 89 90 91 92 93 94

-200

0

200

Time (s)

acc

(m/s

²)


0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

Frequency (Hz)

PSD

(dB

/Hz)


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

40 45 50 55 60 65

Frequency (Hz)

Pow

er (m

W)

Excitation: 2 m/s²

Excitation: 3 m/s²

Excitation: 4 m/s²

N

S I II III IV V VI VII VIII0

2

4

6

8

P opt (m

W)

0 20 40 60 80 100 120 140 160 180 200-60

-40

-20

0

20

40

60

Time (s)

acc

(m/s

²)


0 50 100 150 200 2500

10

20

30

Frequency (Hz)

PSD

(dB

/Hz)


0 20 40 60 80 100 120 140 160 180 200-60

-40

-20

0

20

40

60

Time (s)

acc

(m/s

²)


0 50 100 150 200 2500

10

20

30

Frequency (Hz)

PSD

(dB

/Hz)



• Size: 0.2 cm³• Voltage: (1 – 2) V• Power: (1 – 3) µW• Eigen frequency: 1460 Hz• Excitation: (40 – 125) m/s²

0

0,5

1

1,5

2

2,5

3

3,5

4

0 5 10 15 20 25Excitation (g)

R1 P

eak

Pow

er (µ

W)

50 V

40 V

30 V

20 V

10 V

Hoffmann et al., Fabrication, characterization and modelling of electrostatic micro-generators, J. Micromech. Microeng. 19 (2009)

Electrostatic Micro-GeneratorsMechanical Guidance

Interdigidated Comb Electrodes

Proof MassIsolation Trench

Metal tracks


Electrostatic Conversion Principle

0)(

21

1

111 =−

+++ B

BV

VC

qqxC

qdtdqR

0)(

21

2

222 =−

+++ B

BV

VC

qqxC

qdt

dqR

ymFFFkxxbxm esesS &&&&& −++−−−= 21

Kirchhoff’s second law:

Newton’s second law:

)sin(2 tYmy ωω=&&

i

R

RV

P i

2

=


x-x

C1(t)

R1 R2C

Calculation Capacitance

Values

C1(t)C2(t)x(t)

Calculation Electrostatic

Forces

Ci(x), Ci(t)

Fi(t)

dC1(x)/dx dC2(x)/dx

VC1(t)

VR(t)

C2(t)VC2(t)

VC1(t)VC2(t)

PR(t)

Feedback

Excitation

Electrical DomainTransducer DomainMechanical Domain

aC1(x) C2(x)

Model of Electrostatic Transducer

System model implemented in Matlab / Simulink

Prediction of the power outputDynamic system behavior


General Design Constraints

Transducer Design Area

WTDA = 3500

6000

Wiring & Waferbond Rim

• Limited spaceChip sizeDesign area

• Available energyExcitation accelerationFrequency

• Design objectiveMaximize power outputOptimization of design parameters

i

R

RV

P i

2

=


4500

d 1

WIE

WAWGA

WTS

LTS

WR

Design Parameters

dxxdCVF i

Ciesi)(

21 2 ⋅⋅=

( )LBFEEF RVHxNgfP ,,,,, max=

HF

gF

xmax

NEE


Parameter Symbol Constraints Reason

Gap between fingers gF Minimum value: 2.5 µm Technology

Number of electrode elements NEE Maximum value: 1968 Limited design area

Displacement limit xmax Maximum value: 50 µm Material stress

Height HF Maximum value: 50 µm Technology

Bias voltage VB Maximum value: 50 V Component ratings

Load resistor RL Maximum value: 1 MΩ Electronics

Parameter Constraints


Workflow in modeFRONTIER

=0

PRMS

EMG_EGV1_OptmF

NF BVLR

Vmax

Exit9

ZM

Scheduler:MOGA-II

Gap

DOE

HF

MaxPower

NEE xmax gF HF VB RL

DOE Scheduler Matlab Node Exit

PRMS VRMS

Design Objective: Maximize

Input Variables

Output Variables

• Single objective, multi-parameter optimization• DOE: quasi-random Sobol sequence, 15 designs• Scheduler: MOGA-II, 100 generations


Input Variables

Parameter Symbol Range Step

Gap between fingers gF 2.5 µm … 4.5 µm 0.5 µm

Number of electrode elements NEE 100 … 2000 5

Displacement limit xmax 10 µm … 50 µm 5 µm

Height HF 10 µm … 50 µm 5 µm

Bias voltage VB 10 V … 50 V 2 V

Load resistor RL 100 kΩ … 1 MΩ 5 kΩ


10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

100

147

195

242

289

337

384

432

479

526

574

621

668

716

763

811

858

905

953

10.0

12.1

14.2

16.3

18.4

20.5

22.6

24.7

26.8

28.9

31.1

33.2

35.3

37.4

39.5

41.6

43.7

45.8

47.9

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

0.0000

0.4842

0.9684

1.4526

1.9368

2.4211

2.9053

3.3895

3.8737

4.3579

4.8421

5.3263

5.8105

6.2947

6.7789

7.2632

7.7474

8.2316

8.7158

0.00

0.21

0.42

0.62

0.83

1.04

1.25

1.46

1.66

1.87

2.08

2.29

2.49

2.70

2.91

3.12

3.33

3.53

3.74

HF

50.00

10.00

NF

2000

100

RL

1000

100

VB

50.0

10.0

gF

4.5

2.5

xm

50.00

10.00

PRMS

9.2000

0.0000

Vmax

3.95

0.00

Parallel Coordinates: All Designs


Parallel Coordinates: Best Design

10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

100

147

195

242

289

337

384

432

479

526

574

621

668

716

763

811

858

905

953

10.0

12.1

14.2

16.3

18.4

20.5

22.6

24.7

26.8

28.9

31.1

33.2

35.3

37.4

39.5

41.6

43.7

45.8

47.9

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

1.2900

1.2902

1.2904

1.2906

1.2907

1.2909

1.2911

1.2913

1.2915

1.2917

1.2918

1.2920

1.2922

1.2924

1.2926

1.2928

1.2929

1.2931

1.2933

1.2935

0.00

0.09

0.17

0.25

0.33

0.41

0.50

0.58

0.66

0.74

0.83

0.91

0.99

1.07

1.16

1.24

1.32

1.40

1.49

HF

50.00

10.00

NF

2000

100

RL

1000

100

VB

50.0

10.0

gF

4.5

2.5

xm

50.00

10.00

PRMS

1.2935

1.2900

Vmax

1.57

0.00

Excitation amplitude: 2g


10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

100

147

195

242

289

337

384

432

479

526

574

621

668

716

763

811

858

905

953

10.0

12.1

14.2

16.3

18.4

20.5

22.6

24.7

26.8

28.9

31.1

33.2

35.3

37.4

39.5

41.6

43.7

45.8

47.9

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.8

3.9

4.0

4.1

4.2

4.3

4.4

10.00

12.11

14.21

16.32

18.42

20.53

22.63

24.74

26.84

28.95

31.05

33.16

35.26

37.37

39.47

41.58

43.68

45.79

47.89

9.1900

9.1905

9.1909

9.1914

9.1919

9.1923

9.1928

9.1932

9.1937

9.1942

9.1946

9.1951

9.1956

9.1960

9.1965

9.1969

9.1974

9.1979

9.1983

0.00

0.21

0.41

0.62

0.83

1.03

1.24

1.45

1.65

1.86

2.07

2.27

2.48

2.69

2.89

3.10

3.31

3.51

3.72

HF

50.00

10.00

NF

2000

100

RL

1000

100

VB

50.0

10.0

gF

4.5

2.5

xm

50.00

10.00

PRMS

9.1988

9.1900

Vmax

3.93

0.00

Parallel Coordinates: Best Design

Excitation amplitude: 6g


Parameter Symbol Design Rule

Gap between fingers gF Minimize

Number of electrode elements NEE Optimize

Displacement limit xmax Optimize

Height HF Maximize

Bias voltage VB Maximize

Load resistor RL Maximize (Optimize)

Conclusions on Design Parameters

Dimension of the parameter space can be reducedReduction of computation time for optimizationPerformance increase of 380% over not optimized design


D. HoffmannInstitut für Mikro- und Informationstechnik der Hahn-Schickard Gesellschaft e.V.

HSG-IMITWilhelm-Schickard-Str. 10, D-78052 Villingen-Schwenningen, Germany

phone: +49 7721 943-187 fax: +49 7721 943-210 email: [email protected]

Contact


Size of bubble is proportional to the excitation amplidtude(ielectromagnetic ipiezoelectric)

equals 40 m/s²

equals 1m/s²

0.00

0.01

0.10

1.00

10.00

0 25 50 75 100 125 150 175 200 225 250 275 300

frequency (Hz)

pow

er d

ensi

ty (m

W/c

m³)

Range of generators

Documents

Topology Optimization of Energy Harvesting Devices – The