Energy Harvesting using Piezoelectric Generators. Dagur Gretarsson s021235

Transcription

1 Energy Harvesting using Piezoelectric Generators Dagur Gretarsson s February 7, 2007

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3 Preface This thesis was made in collaboration with Noliac A/S. Noliac specializes in designing, developing and manufacturing multilayer piezoelectric solutions. Noliac was founded in 1997, is located in Kvistgaard, Denmark, and has currently around 50 employees. The company has a high growth rate and is the world leading provider of piezo technology. The thesis was done after being in internship at Noliac. The internship had the focus of energy harvesting with piezoelectric generator which this thesis will continue. Dagur Gretarsson, s Copenhagen, 7. February 2007 Instructors: Michael A.E. Andersen, Ørsted DTU Flemming Jensen, Jean Nicolay Bruland and Bjørn Andersen, Noliac A/C i

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5 Contents 1 Introduction 1 2 Piezoelectric generators Introduction to piezoelectric generators Multilayer generators Harvesting calculations Piezoelectric components Piezoelectric model Electromechanical model design Impedance response Electromechanical components Simulation model Tests and measurements Measurements on S Measurement on S Measurement on H Energy level Energy demand Energy of piezoelectric generators Discussion 26 7 Conclusion 27 A Datasheets I A.1 PMEG6010AED Low V f Schottky barrier diode I A.2 MKT1813 Metallized Polyester Film Capacitor VIII A.3 BYV10-60 Small Signal Schottky Diode XIII ii

6 List of Figures 2.1 Polarization [4] Example of an energy harvester circuit Mechanical model to electromechanical model Electromechanical model for a piezoelectric generator Electric equivalent of a piezoelectric generator and resonance frequencies Impedance response for S1, S3 and H Simulation circuit in LTSpice Simulation graph in LTSpice Measurement setup Voltage and energy measurements for S Depolarisation of S Voltage and energy measurements for S Depolarisation of S Voltage and energy measurements for H Repeated measurement and voltage in relation with variable external capacitor Simulation diagram of regulator current and C ext Simulation of regulator current and C ext Voltage and energy changes due to capacitor ratio How changes in layer thickness affects voltage and energy How fewer layers affects voltage and energy iii

7 List of Tables 2.1 Data for piezoelectric components Material data [1] Relationship between units [2] Measured values and calculated equivalent components Voltage and energy difference between calculations and measurements Capacitance of S Voltage and energy difference between calculations and measurements Voltage and energy difference between calculations and measurements Capacitance of S Voltage and energy difference between calculations and measurements Voltage difference between calculations and measurements Capacitance of H Voltage and energy difference between calculations and measurements iv

8 List of symbols A m 2 Surface areal A A m 2 Actual areal C 0 F Internal capacitor C ext F External capacitor D 3 C/m 2 Dielectric charge displacement d 33 C/N Piezoelectric charge constant E 3 V/m Generated electrical field F N Force g 33 V m/n Piezoelectric voltage coefficient k 33 Coupling factor L m Length n Number of layers Q C Electrical charge Q ext C Charge of external capacitor Q 3 C Total generated charge (open circuit condition) S 3 Strain s 33d m 2 /N Elastic compliance T 3 N/m 2 Axial stress T h l m Thickness of one layer T h m Thickness U 3 V Generated voltage (open circuit condition) W m Width E el J Electrical energy (open circuit condition) E mec J Mechanical energy E ext J Electrical energy in external capacitor X 3 Pa Stress level / Actual stress T h m Change of thickness ɛ 0 F/m Permittivity of free space K Relative dielectric constant η % Efficiency v

9 Specification This project is a part of a project that Noliac A/C is working on. This project studies how energy can be harvested using a piezoelectric generator. The harvester is to be used in a projectile where the piezoelectric generator is compressed and the energy generated harvested. The objective of this project is to analyze the energy generation the piezoelectric generator produces under a compressive load. A calculation model and a simulation model of the piezoelectric generator will be examined and developed. vi

10 Chapter 1 Introduction Piezoelectric energy harvesting is increasingly being used in portable devises and wireless sensors were power supplies are undesirable. Most of the applications use dynamic stress to generate energy while in this case there is use of static stress. Chapter 2 introduces the piezoelectric generator. It goes through the calculations behind a piezoelectric generator from studies made during the practical period. The studies are examined and several changes made. Different examples of piezoelectric generators are chosen to work with in calculations, simulations and measurements. Chapter 3 goes trough the principles of an electromechanical model and how it has been used to imitate the function of a piezoelectric generator. Results of measurements are compared with calculations and simulations in Chapter 4. The stage at which the harvesting circuit is coupled to an external circuit is presented in Chapter 5 Dimensions of piezoelectric generator are varied and voltage and energy changes are examined. Chapter 6 gives an idea for why the measurements, calculations and simulations are not identical. Chapter 7 summaries the results of the thesis with suggestions to improvements and future work. 1

11 Chapter 2 Piezoelectric generators In this chapter general theory behind the piezoelectric generator is presented. It is based on the Internship report made during internship period at Noliac A/S 2.1 Introduction to piezoelectric generators Piezoelectric generators convert mechanical energy into electrical energy. There are several factors that effect the energy conversion. The way a component is fitted directly affects the energy conversion. The more space the more conversion. Another factor is the impedance of the load. If the charge does not have the possibility to get away quickly, it tends to act against depolarisation because of the electrical field it generates. During depolarisation the component releases the maximum energy and afterwards it has to be polarized if it is to be used again. To depolarize a component, static or quasi static force is applied. Figure 2.1 shows how polarization occurs. Figure 2.1 a shows an unpolarized component, to polarize a component high voltage is applied, Figure 2.1 b, and Figure 2.1 c displays a polarized component. To depolarize the procedure is reverse. A polarized component is applied with enough force in a close circuit to allow the energy to be harvested. If a piezoelectric component is applied with compressive stress in an open circuit condition depolarization does not occur. The voltage generated when a piezoelectric generator is applied with a static force and no load, can be on the scale of kilo volts. Equation 2.1 shows the relationship between the open circuit voltage and the force that is applied to the component. U 3 = g 33 T h X 3 (2.1) 1

12 Figure 2.1: Polarization [4] Q 3 A = D 3 = d 33 T (2.2) A piezoelectric energy harvesting circuit could look like the circuit in Figure 2.2. Diode D 1 prevents the charge from flowing from C ext to the piezoelectric component during decompression and diode D 2 protects D 1 against reverse voltages. As mentioned above the voltage that a piezoelectric component D 1 C O PZT D 2 C ext Figure 2.2: Example of an energy harvester circuit generates under static force is very high. If this harvesting approach, seen in Figure 2.2, is to be used in low voltage application the parallel capacitor, C p, has to be much larger than the internal capacitor of the piezoelectric generator, C 0. The downside to this is that C p not only lowers the voltage level it also lowers the available energy. This is because of the relationship between the voltage, the total capacitance (Equation 2.3) and the energy (Equation 2.4). U = Q/C (2.3) W = 1 2 C U 2 = 1 Q 2 2 C (2.4) 2

13 2.2 Multilayer generators A multilayer piezoelectric generator has a lower output voltage than a single layer and a higher capacitance and therefore makes it more suitable for low voltage applications. Multilayer technology generates a higher charge than a single layer generator. The voltage generated is lower in multilayer technology because of bigger inner capacitance C 0. To get a desirable voltage to work with, the parallel capacitor C exp, see Figure 2.2, typically has to be much bigger than the inner capacitor C 0. The drawback is that the maximum energy harvest is when the capacitors are equal, and under those conditions it is possible to get 25% efficiency. 2.3 Harvesting calculations To find the output energy in the parallel capacitor C exp, the output energy for the piezoelectric generator is calculated [3]. The first step is calculating the stress level from the force applied divided by the areal of the generator: X 3 = F A (2.5) Thereby it is possible to calculate the electrical field from the piezoelectric voltage coefficient and the stress level: E 3 = g 33 X 3 (2.6) And the generated voltage is calculated from the thickness of one layer: U 3 = E 3 T h layer (2.7) The generator is without a load (open-circuit) and in that condition the strain is calculated from the elastic compliance: S 3 = s D 33 X 3 (2.8) After calculating the strain the thickness change is calculated: T h = n T h l S D 3 (2.9) With the known thickness change the mechanical energy can be calculated: E mec = 1 2 F T h = 1 F 2 T h l n 2 sd 33 A (2.10) 3

14 The electrical energy for a open circuit condition is: E el = 1 2 k2 33s D F 2 T h l n 33 A = k 2 33E mec (2.11) During closed circuit condition a further compression of the ceramic is at same force. This additional strain results in the electrical energy: Thereby the total energy is: E ex = 1 2 k4 33s E F 2 T h l n 33 A (2.12) E t = 1 2 k2 33(k 2 33s E 33 + s D 33) F 2 T h l n A (2.13) With a harvesting circuit coupled to the piezoelectric generator the factor for elastic compliance in short circuit condition, s E 33, will be somewhat lower because of the load of the harvesting circuit. The charge generated is: Q 3 = 2 E t C 0 (2.14) The voltage over C ext can then be calculated with voltage drop over diode D 1 if the harvesting circuit has a half wave rectifier as in Figure 2.2. U ext = Q 3 C 0 + C ext U D1 (2.15) After calculating the voltage, the energy stored in the external capacitor is calculated. E ext = 1 2 C extu 2 ext (2.16) When the piezoelectric component is applied with a compressive load its thickness changes. Those changes in thickness have direct influence on its capacitance. The calculations behind the capacitor changes start with the change in thickness: t = Stroke free F block F n (2.17) The free stroke is the displacement reached by an actuator without any load, at a given voltage level. While the blocking force is the force needed to push an actuator to its original state. 4

15 The capacitance is dependent on the number of layers, n, the active areal of the component, A k A, and the changes in thickness, t. The capacitance can be calculated by using this formula: c 0 = n K ε 0A k A T h l t (2.18) 2.4 Piezoelectric components The multilayer piezoelectric generators that will be used in the calculations, simulations and measurements are shown in Table 2.1. They were chosen with similar dimensions and constructions but of different material, which should show the variation between the materials. Batch ML ML A ML-03-33(8)-A Material H1 S1 S3 Dimensions L W T h [mm] Number of layers n Thickness of layer T h l [µm] Capacitance C 0 [nf] Stroke [µm] Blocking Force [N] Table 2.1: Data for piezoelectric components The different materials are suitable for different applications. Hard materials as the H1 are for high power applications. Whereas soft materials, as the S1 and S3, have high sensitivity and are therefore good for sensing applications. The material data is shown in Table 2.2 Symbol Unit H1 S1 S3 Relative dielectric constant K33(ε t r ) Coupling factor k Piezoelectric charge coefficient d 33 [10 12 m 2 /N] Piezoelectric voltage coefficient g 33 [10 3 V m/n] Elastic compliance (short circuit) s E 33 [10 12 m 2 /N] Elastic compliance (open circuit) s D 33 [10 12 m 2 /N] Mechanical Quality factor Q > Table 2.2: Material data [1] 5

16 Chapter 3 Piezoelectric model A basic electromechanical model of a piezoelectric generator was developed and used for simulations. 3.1 Electromechanical model design A mechanical system can be described with an equivalent diagram with electrical components. In this application s context the piezoelectric generator can be described with Figure 3.1. Were the mechanical system is described with an equation: dv F = m m dt + r mv + 1 t vdt (3.1) c m 0 And the equivalent electrical system can be described by this equation: F = L di dt + RI + 1 Idt (3.2) C 0 From these equations the relationship between a mechanical system units and an electronic system units. The units are shown in Table 3.1 Mechanical system Electronic system Force F [N] Voltage U [V] Velocity v [m/s] Current I [A] Mechanical mass m m [kg] Inductance L [H] Mechanical resistance r m [Ns/m] Resistance R [Ω] Mechanical compliance c m [m/n] Capacitance C [F] t Table 3.1: Relationship between units [2] Because a piezoelectric generator converts mechanical energy to electrical energy an ideal transformer is implemented. One the secondary side of the 6

17 a) mm F b) U + - I L R C c) v cm mm cm rm rm v F + - Figure 3.1: Mechanical model to electromechanical model F + v mm rm cm 1:N R0 C0' - Figure 3.2: Electromechanical model for a piezoelectric generator transformer a parallel resistance and a capacitor are implemented, Figure 3.2. To find the values for these electromechanical equivalent components the electrical equivalent is calculated using the impedance response of the piezoelectric generator Impedance response The first step in finding the electromechanical components, shown in Figure 3.1, is to measure the impedance characteristic for the piezoelectric generator. A gain-phase analyser is used for the measurements. The measuring probe is placed on the external electrodes of the piezoelectric generator and impedance response is measured. Figure 3.1.1(a) shows the electric equivalent of the measured components, where the transformer is short circuited. At low frequencies the capacitance of the generator is dominant. By finding 7

18 log Z Ls Rs Cs fp fs Cp (a) (b) f Figure 3.3: Electric equivalent of a piezoelectric generator and resonance frequencies the impedance, z t, at a chosen low frequency, f t, it is possible to calculate that capacitance with Equation 3.3 or using a function on the gain phase analyser. C t = C s + C p = 1 (3.3) 2πf t z t The series resonance frequency, f s Figure 3.1.1(b), is the measurement which is related to the length/width dimensions of the piezoelectric generator. The parallel resonance frequency is also measured. The formulas for these frequencies are: 1 f s = 2π (3.4) L s C s f p = 1 (3.5) 2π C p L s C s C p +C s After measuring z t, f s and f p the formulas 3.3, 3.4 and 3.5 can be used to find the equivalent components C s, C s and C p. C s = C t (1 f s 2 ) (3.6) fp 2 1 L s = (3.7) 4πC s fs 2 C p = C t C s (3.8) The result for the chosen piezoelectric generators are shown in Table 3.2. The resistance, R s, is adjusted to match the measured impedance response. In Figure 3.4 the impedance response for each piezoelectric generator is shown. 8

19 Measurements ML ML A ML-03-33(8)-A z t [Ω] f t [khz] f s [khz] f p [khz] Calculations C t [nf] C s [nf] L s [µh] C p [nf] Table 3.2: Measured values and calculated equivalent components 1000,00 100,00 100,00 10,00 10,00 Z [ohm] 1,00 Z [ohm] 1,00 0,10 0,01 Simulation - 5x5x2.3 H1 Measurment - 5x5x2.3 H1 0,10 Simulation - 5x5x2.1 S1 Measurement - 5x5x2.1 S1 0,00 0, f [khz] f [khz] (a) (b) Z [ohm] 1 0,1 Simulation - 5x5x2.0 S3 Measurment - 5x5x2.0 S3 0, f [khz] (c) Figure 3.4: Impedance response for S1, S3 and H1 9

20 3.1.2 Electromechanical components The electromechanical components are calculated using the coupling factor, k 33. The turn ratio of the transformer equals 1/k 2 33 and thereby capacitor, C m, equals C s multiplied by (k 2 33) 2 [2]. The equations for the electromechanical components are: 3.2 Simulation model C m = C t k33(1 4 f s 2 ) = C fp 2 s k33 4 (3.9) M m = 1 = L s 4πC m fs 2 k33 4 (3.10) C 0 = C t C m (3.11) R m = 1 Mm Q C m (3.12) The model of the piezoelectric generator, seen in Figure 3.2, is simulated in LTSpice. Figure 3.5 portrays a screenshot of the model setup in LTSpice. On the left side under the headline Parameters, measured values in Section and material constants from Section 2.4 are keyed in. Equations from Section Figure 3.5: Simulation circuit in LTSpice are under the headline Calculations of parameters, where the values of 10

21 the equivalent components are calculated. In the upper left corner calculations for the force are made from pressure applied, X, on the piezoelectric generator and its areal, A. The time constant, t, determines the duration of the impact curve, V(force) on Figure 3.6. On Figure 3.6 the output of the model, V(u0), is displayed. This simulation is of S3(ML A), Figure 3.6: Simulation graph in LTSpice compressed with 1500N which result in 46.8V. In Chapter 4 The accuracy of the of the model will be verified. 11

22 Chapter 4 Tests and measurements This chapter contains results of compressive load measurements of the three piezoelectric generators chosen, H1, S1 and S3. The setup for the measurements are shown in Figure 4. The piezoelectric generator is placed in a stiffness tester. The stiffness tester has an piezoelectric stack built inside. A power supply provides voltages for the stack and thereby a compressive load to the piezoelectric generator. A force transducer measures the force applied. The force transducer output is measured with a data collection card PCI900. The piezoelectric generator is connected to a half wave rectifier with a capacitor on the output. The output voltage was measured with the data collection card PCI900 and oscilloscope HM507. The highest possible force reached with the equipments is around 3750N or 140MPa for the chosen generators of 25mm 2, Equation 2.5. All the measure- Figure 4.1: Measurement setup 12

23 ments are made with a half wave rectifier, Figure 2.2, of small signal Schottky diodes BYV10-60(D 1,D 2 ) and an external polyester capacitor (MKT 1813), C ext. Simulations have diodes of type PMEG60-10AED because it was already available in LTSpice and has similar characteristics as the BYV Measurements on S1 The measurements of piezoelectric generator S1 were done with an external capacitor, C ext, of 713nF. Figure 4.2 shows the result of Measurement 1. For pressure up to MPa, the curves for calculation and measurements are linear and reach a voltage difference of 2.47V and 0.08mJ, Table 4.1. At a pressure higher than MPa the piezoelectric generator reaches depolarisation but the calculations do not take the depolarisation effect into the equation and continue to clime linearly Calc. - C0=881nF Cext=713nF - S1 Meas. - C0=881nF Cext=713nF - S1 1,8 1,6 Calc. - C0=881nF Cext=713nF - S1 Meas. - C0=881nF Cext=713nF - S1 60 1,4 U [V] ,82; 48,87 107,82; 46,4 E [mj] 1,2 1 0,8 0,6 107,82; 0,85 107,82; 0, ,4 10 0, Compressive load [MPa] (a) Compressive load [MPa] (b) Figure 4.2: Voltage and energy measurements for S1 S1 U E Measured Voltage 46.40V 0.77mJ Calculated Voltage 48.87V 0.85mJ Difference 2.47V 0.08mJ Table 4.1: Voltage and energy difference between calculations and measurements The internal capacitor, C 0, changes are drastic between measurements. Tabel 4.2 shows how the capacitor changes between Measurement 1 and Measurement 2. As this component has been used for several measurements 13

24 the capacitance has increased from 768nF to 915nF. This means that the compressive load has a permanent effect on the piezoelectric generator. The relationship between changes in thickness and capacitance can been seen in Equation 2.18, the more thickness change the higher capacitance. After S1 Measurement 1 Measurement 2 Before 881nF 898nF After 915nF 915nF Table 4.2: Capacitance of S1 depolarisation was reached the measurement was repeated and as seen in Figure 4.3 it is clear that the generator has changed. Less voltage is generated but the voltage increases linearly and generates almost the same voltage level as at the last measurement were polarisation occurred Meas. - C0=881nF Cext=713nF - S1 Meas. - C0=898nF Cext=713nF - S U [V] Compressive load [MPa] Figure 4.3: Depolarisation of S1 14

25 Figure 4.4: Measurements versus simulations In Figure 4.4 simulations are compared to two measuring points, at 52.53MPa and at MPa. The difference is 0.53V and 4.32V, Table 4.3. S1 U E Measured Voltage 21.1V 46.40V Simulated Voltage 20.57V 42.08V Difference 0.53V 4.32V Table 4.3: Voltage and energy difference between calculations and measurements 4.2 Measurement on S3 The external capacitor used in measurements of piezoelectric generator S3 was 987nF. Figure 4.5 shows the results of Measurement 1. The difference between measured and calculated voltage is 1.9V at 66.57MPa and 0.05mJ. At 140MPa the depolarisation of S3 starts which results in high voltage difference between measurement and calculation. S3 U ext 66.57@MPa E ext 66.57@MPa Measured Voltage 26.2V 0.34mJ Calculated Voltage 24.3V 0.29mJ Difference 1.9V 0.05mJ Table 4.4: Voltage and energy difference between calculations and measurements As for piezoelectric component S1 the capacitance changes are quite high 15

26 60 50 Calc. - C0=1072nF Cext=987nF - S3 Meas. - C0=1072nF Cext=987nF - S3 1,6 1,4 Calc. - C0=1072nF Cext=987nF - S3 Meas. - C0=1072nF Cext=987nF - S3 1, U [V] 30 66,57; 26,2 E [mj] 0, ,57; 24,30 0,6 66,57; 0,34 0,4 10 0,2 66,57; 0, Compressive load [MPa] (a) Compressive load [MPa] (b) Figure 4.5: Voltage and energy measurements for S3 between measurements. Table 4.4 shows the difference between capacitor values before and after measurement. S1 Measurement 1 Measurement 2 Before 1072nF 1189nF After 1209nF 1196nF Table 4.5: Capacitance of S1 The measurement was repeated after depolarisation was reached. Figure 4.6 shows that the generator has clearly changed. The same occurs for S3 as for S1, the second measurement goes towards the final measuring point of Measurement 1. Measurements versus simulations The difference between measurements and simulation is greater than for S1. In Figure 4.7 two measuring points, at 32.30MPa and 66.57MPa, are shown and the results of the simulation at same compressive load. The difference is 3.28V and 6.41V, where simulations are about 25% higher. S3 U E Measured Voltage 12.5V 26.2V Simulated Voltage 15.78V 32.61V Difference 3.28V 6.41V Table 4.6: Voltage and energy difference between calculations and measurements 16

27 Meas. - C0=1072nF Cext=987nF - S3 Meas. - C0=1189nF Cext=987nF - S U [V] Compressive load [MPa] Figure 4.6: Depolarisation of S3 Figure 4.7: 17

28 4.3 Measurement on H1 In Figure 4.8 a measurement and calculation of material H1 is shown. A capacitor, C ext of 614nF was used to harvest the energy from the piezoelectric generator Calc. - C0=653nF Cext=614nF - H1 Meas. - C0=653nF Cext=614nF - H1 140,41; 67,2 1,6 1,4 Calc. - C0=653nF Cp=614nF - H1 Meas. - C0=653nF Cp=614nF - H1 140,41; 1, , ,41; 62, ,41; 1,21 U [V] 40 E [mj] 0,8 30 0,6 20 0,4 10 0, Compressive load [MPa] Compressive load [MPa] (a) (b) Figure 4.8: Voltage and energy measurements for H1 In Table 4.7 the highest measuring point is compared with the calculation in voltage and energy. That point is chosen because it is the point where the difference between calculation and measurement is the highest (both in voltage and percentage). U E Measured 67.2V 1.39mJ Calculated 62.86V 1.21mJ Difference 4.34V 0.18mJ Table 4.7: Voltage difference between calculations and measurements At MPa the calculated voltage is 4.34V lower than the measured voltage and the energy 0.18mJ. H1 Measurement 1 Measurement 2 Before 650nF 684nF After 702nF 702nF Table 4.8: Capacitance of H1 The capacitance of the piezoelectric generator is measured before and after the measurements, and as with the other generators the capacitance 18

29 is higher after the measurement. Capacitance changes for H1 are shown in Table 4.8. Figure 4.9 (a), compares Measurement 1 and Measurement 2. Though the inner capacitance is slightly bigger it has little effect on the performance. Figure 4.9 (b) shows how the eternal capacitor, C ext, effects the voltage. The smaller the capacitor is the higher voltage is generated Meas. - C0=650nF Cext=614nF - H1 Meas. - C0=684nF Cext=614nF - H Meas. - C0=702nF Cext=614nF - H1 Meas. - C0=702nF Cext=325n - H1 Meas. - C0=702nF Cext=1312nF - H1 U [V] 40 U [V] Compressive load [MPa] Compressive load [MPa] (a) (b) Figure 4.9: Repeated measurement and voltage in relation with variable external capacitor Measurements versus simulations The simulations for H1 are quite different from the measurements as can been seen in Figure 4.10 and in Table 4.9. The reason could be that the material of the piezoelectric generator is harder than in the other two and might therefore give this difference. Figure 4.10: 19

30 H1 U E ext @MPa Measured Voltage 33.6V 67.2V Simulated Voltage 20.03V 37.68V Difference 13.57V 29.52V Table 4.9: Voltage and energy difference between calculations and measurements 20

31 Chapter 5 Energy level In this chapter the energy demand for a projectile is investigated and energy level of piezoelectric generators are examined. 5.1 Energy demand A piezoelectric harvesting circuit placed in a projectile often has the requirement of delivering a couple of millijoules. An example could be a power stage driving a circuit that uses 30mJ at 3.3V. Where 15mJ are used the first period of 100msec and in the next period 15mJ are used in 2sec. A linear regulator is used to regulate the voltage from the harvesting circuit with a loss of 0.2V with a maximum input voltage of 30V. The current can then be calculated for the first period: I 1 = 15mJ 3.3V 100ms Current for the second period is then calculated: I 2 = 15mJ 3.3V 2s = 45.46mA/s (5.1) = 2.27mA/s (5.2) From Equation 5.4 it is possible to make the calculations for the value of the external capacitor, C ext. The maximum input voltage for the regulator is 30V and since the energy over the two periods is equally divided in two, the voltage for the calculations of the capacitor is also divided into two for each period. This means that the voltage used for calculation is the input voltage subtracted by the output voltage and the loss in the regulator: U Ccalc = 30V 3.3V 0.2V 2 21 = 13.25V (5.3)

32 Then the value of the external capacitor is calculated using Equation 5.4. C ext1 = I 1 dt 1 du ccalc = i c (t) = C du c dt 45.46mA/s 100ms 13.25V The capacitance is also calculated from current I 2 : (5.4) = 343µF (5.5) C ext2 = I 2 dt 2 du ccalc = 2.27mA/s 4s 13.25V = 343µF (5.6) Now that the capacitance is calculated from the two currents the value is set to 343µF. Energy level at 30V is then calculated with equation: E c (t) = 1 2 Cu2 c(t) = µF (30V )2 = 154.4mJ (5.7) The voltage curve from V1, 5.1, has a duration of 8msec peaking at 4msec. The curve imitates the output of a piezoelectric generator. Figure 5.2 shows the result of the simulation. This shows that a large capacitor is needed to supply an energy of this level. Figure 5.1: Simulation diagram of regulator current and C ext 22

33 Figure 5.2: Simulation of regulator current and C ext 23

34 5.2 Energy of piezoelectric generators Now that the piezoelectric generator has been studied by making a calculation model and simulation model, the nest step is to see how the energy level of a piezoelectric generator can be changed by adjusting some parameters. All calculations were made with 400MPa compressive load. In Figure 5.3 the , , Uext - S1 5x5mm Eext - S1 5x5mm 9,00 8, Uext - S1 10x10mm Eext - S1 10x10mm 9,00 8,00 U [V] ,00 6,00 5,00 4,00 3,00 E [J] U [V] ,00 6,00 5,00 4,00 3,00 E [J] 50 2,00 1, ,00 1,00 0 0,05 0,06 0,08 0,13 0, ,00 0 0,05 0,06 0,08 0,13 0, ,00 Cext/C0 Cext/C0 (a) (b) Figure 5.3: Voltage and energy changes due to capacitor ratio energy and voltage in external capacitor C ext is effected by the ratio between internal capacitance and external capacitance where there are 76 layers with layer thickness of 23µm. Figure 5.3 (a) shows the piezoelectric generator, S1-5x5, used in measurements in Chapter 4. Figure 5.3 (b) shows the same generator except it is 4 times bigger in areal, S1-10x10. By making the areal larger it results in the same energy level but half voltage level. This is because the capacitance becomes four times higher. Equation 5.8 and Equation 5.9 show the relationship between the capacitance, voltage and energy. C 0 = n K ε 0A k A T h l (5.8) E ext = 1 2 C extu 2 ext (5.9) In Figure 5.4 the layer thickness of S1-5x5 has changed. Figure 5.4 (a) has a thickness of 10µm and Figure 5.4 (b) has a thickness of 46µm and both have the same numbers of layers. This means that the thicker the layer is the more energy and voltage is generated. Figure 5.5 shows how the voltage increases with fewer layers and stays 23µm in thickness per layer. The energy stays the same as in Figure 5.3 (a) because of the relationship between the voltage and the capacitance. 24

35 80 1, , Uext - S1 5x5mm Eext - S1 5x5mm 1,60 1, Uext - S1 5x5mm Eext - S1 5x5mm 35,00 30,00 U [V] ,20 1,00 0,80 0,60 E [J] U [V] ,00 20,00 15,00 E [J] 20 0, , , ,00 0 0,05 0,06 0,08 0,13 0, ,00 0 0,05 0,06 0,08 0,13 0, ,00 Cext/C0 Cext/C0 (a) (b) Figure 5.4: How changes in layer thickness affects voltage and energy U [V] Uext - S1 5x5mm Eext - S1 5x5mm 10,00 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 E [J] 0 0,05 0,06 0,08 0,13 0, Cext/C0 0,00 Figure 5.5: How fewer layers affects voltage and energy 25

36 Chapter 6 Discussion This project started out with developing the calculation and simulation models. Measurements were made to verify the models. The difference between measurements and calculations is mainly because of the depolarisation. Both piezoelectric generators S1 and S3 get depolarised around 120MPa while the calculation continues to increase linearly. Between measurements and simulations there is more difference than between measurements and calculations. The simulations for S1 gives results closest to measurements while simulations for S3 and H1 are more apart. Material in S3 is closer to S1 since both are made from soft material while H1 is made of hard material. The models do have limitations due to material differences of piezoelectric generators and can only be useful when using material such as in S1. 26

37 Chapter 7 Conclusion The purpose of this project was to analyse the energy generation of a piezoelectric generator and develop calculation and simulation models of generating and harvesting that energy. To verify the models three different samples of piezoelectric generators were compared, S1, S3 and H1. The difference between the components is the material the components are made of. A linear calculation model was developed for piezoelectric generators. When comparing the three samples to the measurements the difference was within 12% in the linear area of measurements. A linear simulation model was studied and developed. The results were that S1 was the component closest to the measurements or within 10% in the linear area of measurements. This indicates that the model is suitable for predicting the behavior of S1. The same cannot be concluded for the other two components which deviate more than 20% from the measurements. For making the energy level suitable for driving low voltage circuits the dimensions and material of piezoelectric generators are crucial. The dimensions of the areal determines the voltage level, the more areal the lower the voltage while contributing the same energy. The thickness of each layer within the component affects both voltage and energy. The thicker the layers the higher the energy and voltage. Further work This projects provides good grounds for further research into the subject. Especially with regards to material choices of the piezoelectric generators. The hard material component H1 deviated the most from the measurements which indicates that other modeling methods could be developed which would be more specific for hard materials or strive for building a model which could be suitable for all material types. When looking into the material differences the point of depolarisation must be studied since that determines the energy harvesting level. 27

38 Bibliography [1] Ferroperm. Piezoceramics, July [2] K.Rasmussen. Analogier mellem Mekaniske, Akustiske og Elektriske Systemer. Polyteknisk Forlag, 4 edition, [3] A.J. Moulson and J.M. Herbert. Electroceramics. Chapman and Hall, [4] J.W. Waanders. Piezoelectric Ceramics - Properties and applications. Philips Components,

39 Appendix A Datasheets A.1 PMEG6010AED Low V f Schottky barrier diode I

40 II

41 III

42 IV

43 V

44 VI

45 VII

46 A.2 MKT1813 Metallized Polyester Film Capacitor VIII

47 IX

48 X

49 XI

50 XII

51 A.3 BYV10-60 Small Signal Schottky Diode XIII

52 XIV

53 XV

54 XVI

55 XVII