ieee electrical power and energy conference · 2018. 12. 11. · sneha lele, robert sobot,...

Numerical Modelling of Piezoelectric Transformers for LowFrequency Measurement and Disturbance Monitoring

Sneha Lele, Robert Sobot, Tarlochan Sidhu

IEEE Electrical Power and Energy Conference(EPEC 2012)

October 12, 2012

implantable systemsl a b o r a t o r y

Table of Contents

1 Introduction

2 Mathematical understanding of piezoelectric transformer(PT) model

3 PT – Experimental results

4 Modelling set–up and simulation results

5 Conclusions

6 References

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Numerical Modelling of Piezoelectric Transformers for Low Frequency Measurement and Disturbance Monitoring


Table of Contents

1 Introduction




5 Conclusions

6 References

3 / 25


Background

Two main types of inputs to the power relay hardware are ACvoltage and AC current inputs.

Auxiliary electromagnetic transformers transform 50/240Vdown to a workable voltage of 5/10V to be fed to processor.

Piezoelectric transformer is explored in place of conventionalelectromagnetic transformer.

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Piezoelectric transformer (PT)

PT operation is based on the principle of electromechanicalconversion of energy.

PolarizationVoutLoad

Vin

t

w

side plated

end plated2l

Physical diagram of a piezoelectric transformer

Advantages : low cost, high efficiency, no electromagneticinterference, good input–output isolation [Chi97].

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Finite element modelling (FEM) of PT

A novel application of PT in a low frequency region forvoltage transformation and line monitoring [LSS12].

FEM analysis is an useful method for behavioural modelling inorder to encompass a large sample set of PTs.

Important characteristics of PT even for low frequencies like50Hz can be studied using the FEM analysis.

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Finite element modelling (FEM) of PT

[Ler90] discussed one of the first methods for static,eigenfrequency, harmonic and transient analysis of 2D and 3Dpiezoelectric elements.

Rosen–modal, unipoled–disk and ring type PTs were discussedin later years [Ho07], [YCCL08] with effects of externalloading [TKea01].

The main objective of this work is to develop and verify a 3Dnumerical model for PT and compare the results with theexperimental findings.

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Table of Contents

1 Introduction




5 Conclusions

6 References

8 / 25


Mathematical understanding of PT model

The relationship of strain (S) depending on the stress (T )with an electric field (E ) applied across its electrodes is givenby [Sye01],

Sj =∑

sEjkTk +∑

dijEi (1)

Where i=1,2,3 and j=k=1,2,...,6

Electric displacement (D) is expressed as a function of E andT .

Dj =∑

dEij Tj +

∑εTil El (2)

Where i=l=1,2,3 and j=1,2,...,6

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Table of Contents

1 Introduction




5 Conclusions

6 References

10 / 25


PT – Experimental results

‘Rosen piezoelectric transformer’, a passive electricalenergy–transfer device was first introduced in [RFR58].

We experimented with PT from ‘Fuji Ceramics’ made of leadzirconate titanate material with dimensions in the range of16mm x 4mm x 1mm.

Step–up transformation at resonance but step–down behaviourin the 10Hz to 250Hz range with a linearity of ±1%.

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PT – Experimental results

0.2

0.6

1.0

50 150 250

[V]

Frequency, [Hz]

Vin=10VVin=75V

Vin=150V

0.1

0.5

3.0

12.0

10k 100k 200k

Ou

tpu

t vo

lta

ge

, [V

]

Vin=1V

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Table of Contents

1 Introduction




5 Conclusions

6 References

13 / 25


Modelling set–up

A 3D model with tetrahedral meshing depicting the input andoutput sections of PT.

Dimensions equal to the actual dimensions of PT used in theexperiment.

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Simulation results

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Simulation results

0.000

0.002

0.004

10 500 1000

[mS

]

Frequency, [Hz]

0.0

10.0

20.0

160k 190k 220k

Su

sce

pta

nce

, [m

S]

Susceptance plots near resonance (top) and in low frequency region(bottom)

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Simulation results

50.485

50.488

50.491

10 500 1000

[V]

Frequency, [Hz]

0.0

4000

8000

160k 190k 220k

Ele

ctr

ica

l p

ote

ntia

l, [

V]

Electrical potential plots near resonance (top) and in low frequencyregion (bottom)

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Simulation results

The velocity of propagation v through a piezo is proportional tothe propagation length l and the resonant frequency fr , fr = v

2·l[Sye01].

Effect of length of PT (l) on resonant frequency (fr )

l (mm) fr COMSOL (kHz) Actual fr (kHz)

10.07 315.54 325.516.07 209.04 201.420.06 161.63 161.037.19 73.32 88.450.07 62.271 66.46

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Table of Contents

1 Introduction




5 Conclusions

6 References

19 / 25


Conclusions

The 3D finite element modelling was employed forcharacterizing the Rosen–type rectangular PT.

The susceptance and output potential at resonance and inpower–line frequency range were demonstrated.

PT at low frequency can be considered for purposes of linemonitoring and accurate frequency measurement.

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Conclusions

A more practical design incorporating loss factors, optimumdamping constants and loading is the next step in our project.

The model will also be tested for transient effects to refine itssensitivity to unwanted high frequencies.

Time–domain and frequency spectrum analysis will be donewith real–time signals to characterize the model.

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Table of Contents

1 Introduction




5 Conclusions

6 References

22 / 25


References I

L. Chihyi.Design and Analysis of Piezoelectric Transformer Converters.PhD thesis, Virginia Polytechnic Institute and State University, July1997.

GE-Multilin.Reference guide - Protection, Control, Metering, Communications,Instrument Transformers.GE Multilin, 2008.

GE-Multilin.350C Feeder Protection System.GE Multilin, 2009.

S. Ho.Modeling and analysis on ring–type piezoelectric transformers.IEEE transactions on ultrasonics, ferroelectrics, and frequencycontrol, 54(11):2376–2384, November 2007.

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References II

R. Lerch.Simulation of piezoelectric devices by two– and three–dimensionalfinite elements.IEEE transactions on ultrasonics, ferroelectrics, and frequencycontrol, 37(3):233–247, May 1990.

S. Lele, R. Sobot, and T. Sidhu.Frequency measurement and disturbance monitoring usingpiezoelectric transformers.IEEE Power and Energy Conference at Illinois, 2012 (PECI 2012),2012.

C. A. Rosen, K. A. Fish, and H. C. Rothenberg.Electromechanical transformer, 1958.

E. M. Syed.Analysis and modeling of piezoelectric transformers.Master’s thesis, University of Toronto, 2001.

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References III

T. Tsuchiya, Y. Kagawa, and et al.Finite element simulation of piezoelectric transformers.IEEE transactions on ultrasonics, ferroelectrics, and frequencycontrol, 48(4):873–878, July 2001.

Y. Yang, C. Chen, Y. Chen, and C. Lee.Modeling of piezoelectric transformers using finite–elementtechnique.Journal of the Chinese Institute of Engineers, 31(6):925–932, 2008.

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ieee electrical power and energy conference · 2018. 12. 11. · sneha lele, robert sobot,...

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