Power follows a quadratic relationship to input amplitude because P~V^2 minus some losses due to electronic components
Power follows a quadratic relationship to input amplitude because P~V^2 minus some losses due to electronic components
Vibration Energy Harvesting: Going Beyond Idealization
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Experimental analysis of a piezoelectricenergy harvesting system forharmonic, random, and sine on randomvibration JACKSON W. CRYNS B.S. Applied Mathematics, Engineering and Physics University of Wisconsin - MadisonResearch conducted under Brian K. Hatchell (PNNL) in fulfillment of DOE Office of Science, ScienceUndergraduate Laboratory Internship (SULI) and to support projects contracted by the U.S. ArmySigma Xi - Student Research Showcase 2013March, 2013 Sigma Xi - Student Resarch Showcase 1
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Abstract Advancements in low power electronics in the past decade allow systems to run off of progressively less energy and even eliminate the need for external power supplies completely. The key to self-sustaining electronics is the ability to harness energy from the surrounding environment and turn it into usable electrical energy, or Energy Harvesting. In many industrial applications, ambient energy is readily available in the form of mechanical vibrations. Piezoelectric ceramics provide a compact, energy dense means of transducing mechanical vibrations of the environment to electrical power. Harvesting power with a commercially available piezoelectric vibration powered generator using a full-wave rectifier conditioning circuit is experimentally compared for varying sinusoidal, random and sine on random (SOR) input vibration scenarios. Much of the available literature focuses on maximizing harvested power through theoretical predictions and power processing circuits that require accurate knowledge of generator internal electromechanical characteristics and idealization of input vibration, which cannot be assumed in general application. Characteristics of complex vibration sources significantly alter power generation and processing requirements, likely rendering idealized analysis inaccurate. Going beyond idealized steady state sinusoidal and simplified random vibration input, SOR testing allows for more accurate representation of real world ambient vibration and is an invaluable tool in harvester development.March, 2013 Sigma Xi - Student Resarch Showcase 2
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BackgroundWhat is Energy Harvesting?Application GoalsVibration Powered Generators (Transducers)Piezoelectric EffectPower ConditioningMarch, 2013 Sigma Xi - Student Resarch Showcase 3
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What is Energy Harvesting?• Every process dissipates waste energy to the surrounding environment• Ambient energy comes in many usable forms [5] Electromagnetic Radiation (1) Thermal Gradient (2) Potential Energy Forms (3) Vibration (Potential + Kinetic) (4)• Convert ambient energy to usable electrical energy – transducers • Small amounts of power – mW or µW (milli-Watts or micro-Watts) [3] (5) (6) (7) (8)• Not a new idea!March, 2013 Sigma Xi - Student Resarch Showcase 4
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Application Goals Supply power to off grid devices Remote equipment Monitors in hazardous environments (9) Wireless data logging and transmission Reduce maintenance requirements and costs Relieve dependence on primary batteries (10) Fits into national “green” initiativesMarch, 2013 Sigma Xi - Student Resarch Showcase 5
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Vibration Powered Generators (Transducers) Machines, moving parts and large power generators present significant vibration energy [2, 3, 8] Three transduction mechanisms [1, 8, 10]: Electrostatic – parallel plate capacitor Electromagnetic – magnetic induction Piezoelectric – piezoelectric effect Numerous studies have been conducted on power transduction [15,3,9] (11) (12) (13) Driving and Biking Walking Numerical and Theoretical Simulations Piezoelectric transducers are the most energy dense [8,12] March, 2013 Sigma Xi - Student Resarch Showcase 6
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Piezoelectric Effect Electric charge accumulates in certain materials in response to applied mechanical stress [11] (14) (15) This study analyzes a commercially available bimorph transducer Two piezoelectric layers Two electrical signals of opposite sinesMarch, 2013 Sigma Xi - Student Resarch Showcase 7
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Power Conditioning Conditioning circuitry – the components necessary to supply power from the transducer to the target electronics with specified current and voltage characteristics (16) Example conditioning circuit This study includes the target electronics in the conditioning circuitMarch, 2013 Sigma Xi - Student Resarch Showcase 8
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Research OverviewResearch Goals {10}Energy Harvesting Architecture {11 – 18 }Literature Review and Harvester Validation {19 – 36}Expanded Vibration Testing {37 – 46}Discussion and Design Implications {47 – 50}March, 2013 Sigma Xi - Student Resarch Showcase 9
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Research Goals Convince the reader that accurate experimental testing is an invaluable and essential tool in harvester development Determine implications of complex vibration characteristics on harvester performance Show that theoretical power harvesting predictions and numerical simulations require assumptions that cannot be made in general application: Oversimplifying assumptions of input vibration Exact knowledge of transducer internal electrical and mechanical characteristicsMarch, 2013 Sigma Xi - Student Resarch Showcase 10
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Energy HarvestingArchitectureMarch, 2013 Sigma Xi - Student Resarch Showcase 11
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Energy Harvesting Architecture Piezoelectric transducer V25w QuickPack® actuator produced by Midé [24,25] AC signal Proof mass (for frequency tuning) Rigid clamp (fixed-free cantilever beam) Vibration Source Exact transducer internal electrical and mechanical characteristics unknown LDS V721 – 1000 L shaker Closed loop vibration control [17] Power conditioning circuitry Standard circuitMarch, 2013 12
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Energy Harvesting Architecture Piezoelectric Transducer Set-Up Mount in cantilever configuration Input vibration at base Natural frequency [18] Tune with proof mass to match source vibration Modal analysis allows for accurate natural frequency determination Bare natural frequency of 124.5 HzMarch, 2013 Sigma Xi - Student Resarch Showcase 13
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Energy Harvesting Architecture Power Conditioning Duties AC-DC conversion [19] Transducer creates AC signal (oscillatory) Most microelectronics require DC Full-wave bridge rectifier Signal smoothing A time varying signal is damaging to DC electronics [20] Provide power to load Microelectronics Resistor Secondary (rechargeable) battery http://www.electronics-tutorials.ws/diode/diode_6.html http://www.eleinmec.com/article.asp?18March, 2013 Sigma Xi - Student Resarch Showcase 14
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Energy Harvesting Architecture Power Conditioning Circuitry [3,7,14-16,26] Standard (linear) Interface Target electronics (load) modeled represented by resistor Net transfer of energy through transient components is null, thus equivalent resistance is sufficient Capacitance is constant, locate optimal impedance by varying resistance CR = 600 µF, RL -> variable. Non-linear processing not considered in this study Designed for steady sinusoidal vibration only Dissipates extra power Application specific designs require additional voltage control Additional control circuitry always dissipates extra power Circuit used here finds the maximum available power for harvesting (except for loses in rectifier bridge and capacitor leakage)March, 2013 Sigma Xi - Student Resarch Showcase 15
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Energy Harvesting Architecture Test multiple scenarios Impedance head Harmonic, Random – simplified SOR – sine and random superposition for accurate testing Characterize and control the input vibration by acceleration Acceleration response is the most Shaker armature common form of vibration measurement and characterization Allows for subsequent validation in other experiments Method assumes harvester does not alter input dynamics (source is much larger than harvester) [31] Monitor force and acceleration with PCB impedance head 288D01March, 2013 Sigma Xi - Student Resarch Showcase 16
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Energy Harvesting ArchitectureMarch, 2013 Sigma Xi - Student Resarch Showcase 17
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Energy Harvesting ArchitectureFundamental Objective: How does power harvesting vary with input acceleration characteristics, transducer natural frequency, and load resistance? Measure voltage and current delivered to load to find harvested power Measure input acceleration and force to find input power, when neededMarch, 2013 Sigma Xi - Student Resarch Showcase 18
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Literature Review andHarvester ValidationGeneralSinusoidal input vibration*Flat random vibration**Analytical relations for purely sinusoidal and flat broadband vibration have been developed in otherworks for custom developed harvesters and simulations [6, 9 ,18-20]March, 2013 Sigma Xi - Student Resarch Showcase 19
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Literature Review and Harvester Validation Properly developed harvesters can harvest tens to hundreds of mW of power [1, 3, 6-9] Vibration Energy Harvesters (VEH) require careful development for effective power conversion Characterization of ambient source vibration Tuning of transducer to achieve resonance Determination of optimal impedance Harvesting electrical power induces mechanical damping and alters the transducer vibration dynamics, creating an electromechanical system [9]March, 2013 Sigma Xi - Student Resarch Showcase 20
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Literature Review and Harvester Validation Conditioning circuitry designs can range from a few analog components to complex architectures controlled by firmware [3,7,14- 16,26] Non-linear power processing has been shown to significantly increase harvested power over passive (standard) power processing Synchronized Charge Extraction (SEC) Synchronized Switch Harvesting with Inductor (SSHI) Additional control circuitry dissipates extra power, reducing efficiency [21]March, 2013 Sigma Xi - Student Resarch Showcase 21
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Literature Review and Harvester Validation Previous research heavily focused on two idealized vibration cases: steady state sinusoidal vibration sources and flat, broadband random profiles [1, 6, 7, 9, 12, 13, 16, 17] Analysis and modeling are simplified in these cases Non-linear SSHI requires steady state sinusoidal Non-linear SEC performance drops in non-sinusoidal vibration environments Many studies omit inclusion of the significant power loss from additional control circuitry that can be on the order of hundred of μW [] No studies addressed voltage fluctuations induced by random vibration [22] [23]March, 2013 Sigma Xi - Student Resarch Showcase 22
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Literature Review and Harvester Validation Few studies incorporated more complex vibrational sources [2,18] Sinusoidal and flat random vibration inputs are scarce in application Real ambient conditions can be accurately modeled by incorporating both random and sinusoidal content Acceleration Spectral Density of a typical Apache Helicopter flight is significantly more complex than sinusoidal or flat random vibration • Peaks are accounted for by sinusoidal components superposed on top of a random profileMarch, 2013 Sigma Xi - Student Resarch Showcase 23
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Literature Review and Harvester ValidationExperimental Sinusoidal Input Validation Unless otherwise stated, harvester is driven at the transducer natural frequency Sinusoidal vibrations are characterized by driving frequency and amplitude “Amplitude” refers to acceleration amplitude, zero to peakMarch, 2013 Sigma Xi - Student Resarch Showcase 24
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Literature Review and Harvester Validation Sinusoidal – Amplitude variation Theoretical Expectations: Displacement and voltage scale linearly with input amplitude Power scales quadratically with voltage and thus amplitudeQuadratic trend is clearly exhibitedat two natural frequencies. March, 2013 Sigma Xi - Student Resarch Showcase 25
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Literature Review and Harvester ValidationFor identical input amplitudes:lower natural frequencies harvestmore power. ** Consequence of input power variations March, 2013 Sigma Xi - Student Resarch Showcase 26
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Literature Review and Harvester Validation Sinusoidal – Impedance Variation Theoretical Expectations: Resistance (impedance) effects harvested power Optimal resistance varies with natural frequency Optimal resistance is around 40 kΩ and 15 kΩ for 58.3Hz and 124.5 Hz respectivelyMarch, 2013 Sigma Xi - Student Resarch Showcase 27
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Literature Review and Harvester Validation Sinusoidal – Impedance Variation (cont’d)As natural frequencyincreases, optimal impedancedecreases and peak narrows March, 2013 Sigma Xi - Student Resarch Showcase 28
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Literature Review and Harvester Validation Sinusoidal –Frequency Response Function (FRF) for power Theoretical expectations: All mechanical vibratory systems have a frequency dependent transfer function Deviating from natural frequency lowers the resulting transducer dynamic amplitudes and thus harvested powerHarvested power drops byapproximately 50% within 1 Hz deviationfrom natural frequency, reinforcing theimportance of accurate tuning oftransducerImplies that there is an approximatenon-negligible transducer bandwidth of+/- 3 Hz in which power is generated March, 2013 Sigma Xi - Student Resarch Showcase 29
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Literature Review and Harvester ValidationExperimental Random Input Validation The terms broadband and random vibration are often used interchangeably, but random vibrations need not be broad in general Power is averaged of 100s samples to increase repeatability Random vibrations vary statistically in time [18] Random vibrations are characterized by Power Spectral Density (PSD), or acceleration spectral density, profile in units of [g2/Hz] Integrating the PSD over a frequency range and taking the square root results in the Root Mean Square (RMS) level of vibration in g’s for that filtered frequency range “Amplitude” refers to spectral density near the transducer natural frequency It is shown later that spectral densities far from the resonant frequency negligibly influence the harvesterMarch, 2013 Sigma Xi - Student Resarch Showcase 30
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Literature Review and Harvester Validation Random – Amplitude Variation Theoretical Expectations: Power scales linearly with spectral density Power scales inversely with natural frequency, as with sinusoidalAs derived in [18], harvested powervaries linearly with spectral density March, 2013 Sigma Xi - Student Resarch Showcase 31
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Literature Review and Harvester Validation Random – Impedance Variation Theoretical Expectations: Random vibration has higher optimal resistance than sinusoidal vibration Optimal impedance scales inversely with natural frequencyOptimal resistance is higher forrandom vibration thansinusoidal vibration for bothfrequencies, and decreaseswith natural frequency foreach vibration type March, 2013 Sigma Xi - Student Resarch Showcase 32
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Literature Review and Harvester ValidationRandom – Bandwidth Variation Theoretical Expectations: Power is independent of input bandwidth when significantly longer than that of transducer Unspecified results for short bandwidths or varying spectral density profile shapesExcept for random statisticaldeviations from one point thenext, average harvested poweris constant over all bandwidthsMarch, 2013 Sigma Xi - Student Resarch Showcase 33
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Literature Review and Harvester ValidationRandom – Frequency Variation Theoretical Expectations: Harvested power is inversely proportional to transducer natural frequency For identical input amplitudes and bandwidths, higher natural frequencies produced less powerMarch, 2013 Sigma Xi - Student Resarch Showcase 34
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Literature Review and Harvester Validation Harvester met and agreed with theoretical predictions for special cases Steady state sinusoidal vibration Flat broadband vibration Limitations of idealized studies Real sources commonly consist of numerous sinusoidal peaks, complex random profiles, nonlinear and transient interactions No found studies incorporated non-flat random profiles No found studies incorporated multiple sinusoidal components No found studies incorporated interactions of both sinusoidal and random content No found studies addressed time variations in random vibrationsMarch, 2013 Sigma Xi - Student Resarch Showcase 35
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Expanded Vibration TestingShort bandwidth and non-flat random profilesSinusoidal and random component interactionMultiple sinusoidal component interactionMarch, 2013 Sigma Xi - Student Resarch Showcase 36
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Expanded Vibration TestingRandom – Short Bandwidth Variation Test varying bandwidths with identical gRMS values Each random profile in the left plot has a 0.1414 gRMS acceleration level (note that 50 Hz and 500 Hz expand beyond plot window) Each scenario was supplied to the bare transducer to produce right plotThe harvester gets progressively worse at harvesting power as bandwidth increases, foridentical input power and gRMS levels.
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Expanded Vibration Testing Random – Non-Flat profile Test impact of spectral density profile variations Varying shape outside the transducer natural frequency Identical in the bandwidth of the transducer (124.5 Hz 3 Hz)Three profiles produced nearly identicaloutput powers of 0.65, 0.67, and 0.71μW respectively.Implies harvested power depends onlyon the spectral density near the naturalfrequency, other densities do not affectharvested power. March, 2013 Sigma Xi - Student Resarch Showcase 38
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Expanded Vibration Testing SOR – Constant Sinusoid, Variable Spectral Density Test the effects of noise when harvesting from sinusoidal peak 0.3 g sinusoidal peak and increasing spectral density, PSDs plotted on left Linear superposition suggests that power should increase, above the sinusoidal power, as seen in random vibrationHarvested power increases with spectral density, however differently from the randomcase due to time domain variations and imperfect super position in control software March, 2013 39
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Expanded Vibration Testing SOR – Optimal Resistance Determine the optimal resistance when both sinusoidal and random content is present Sinusoidal and random cases had significantly different optimal resistances Does SOR bridge this gap?Optimal resistance increases from~15kΩ for sinusoidal to ~45kΩ forrandom as spectral densityincreases.In other words, as vibrationdominance shifts from sinusoidal torandom, so does the optimalresistance March, 2013 Sigma Xi - Student Resarch Showcase 40
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Expanded Vibration Testing SOR – Multiple Sinusoidal Components Test interactions of two dominant sinusoidal components Two tones seen within 3 Hz of each other in Apache helicopter vibration More components increase input power in the transducer bandwidth FRF shows that harvested power value depends of frequency separation Test two tones of 0.3 g amplitude at 58.3 Hz natural frequencyAs frequency separationincreases, harvested power approachesthat of a single sinusoid at the naturalfrequency.At 0.25 Hz separation, average harvestedpower is 28% higherMore than 1 Hz separation, harvestedpower is only a few % higher March, 2013 41
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Expanded Vibration TestingSOR – Multiple Sinusoidal Components (cont’d) Multiple sine components induce significant amplitude beating in source vibration and output voltage With negligible random vibration levels, input vibration reaches zero (left) Filter capacitor prevents load voltage from dropping to zero and alters the input voltage from the transducer (right)March, 2013 Sigma Xi - Student Resarch Showcase 42
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Expanded Vibration Testing SOR – Multiple Sinusoidal Components (cont’d) Amplitude beating is dependent on frequency separation FRF suggests beating should decrease with separationAs frequency separationincreases, beat amplitude approacheszeroFor two sinusoidal components 0.25 Hzapart, load voltage beats at nearly100% of single sine component voltage(~8 V at 58.3 Hz and 3.5 V at 124.5 Hz) March, 2013 43
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Expanded Vibration TestingSOR – Multiple Sinusoidal Components (cont’d) Inclusion of more sine components in the transducer bandwidth amplifies effects Average harvested power and amplitude beating both increase As number of sinusoidal components increases, responses approaches that of random vibration with high spectral density Test three 0.3 g sine components supplied to the bare transducerMarch, 2013 44
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Expanded Vibration TestingVoltage Fluctuations Interactions between frequencies induce fluctuations in voltage delivered to the load DC electronics are typically, designed to utilize a constant voltage supply Even slight voltage fluctuations cause electronic devices to drop out of regulation, affect sensor readings and damage the components No found studies discussed implications of voltage fluctuations Sinusoidal vibrations provide nearly constant voltage to the load See the left plot on slide 18 (the capacitor voltage is the voltage supplied to the load) Random vibrations induce significant voltage supply fluctuations SOR vibrations can result in quite complicated vibration interactions and voltage supply waveformsMarch, 2013 Sigma Xi - Student Resarch Showcase 45
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Expanded Vibration Testing Voltage Fluctuations (cont’d) Load supply voltage fluctuations scale with amplitude Multiple sinusoidal components and random vibrations alter waveformSample time responses for 500 Hz bandwidthrandom signals supplied to a transducer tunedto 58.3 Hz at varying spectral densitiesPeak to peak:0.36 V at 2.5e-4 g2/Hz and3.61 V at 5e-3 g2/Hz Input power within the transducer natural frequency scales average power (i.e. including a single sinusoidal component, as in slide 39, translates waveform vertically but does not increase fluctuation intensity) March, 2013 46
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Discussion and DesignImplicationsMarch, 2013 Sigma Xi - Student Resarch Showcase 47
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Discussion and Design Implications Steady state, sinusoidal vibration is the most ideal form of input vibration Only requires design for natural frequency and optimal impedance Lower frequencies harvest more power for similar amplitudes No significant voltage fluctuations No time dependencies Rarely seen application Random vibration is the least ideal form of input vibration Only requires design for natural frequency and optimal impedance Significantly less efficient than sinusoidal In order to harvest significant power spectral densities, more than 1e-3 g2/Hz are typically needed Usually only 1e-6 to 1e-4 g2/Hz in application [2,8,32] Overshadowed by voltage fluctuations, requires additional charge control circuitryMarch, 2013 Sigma Xi - Student Resarch Showcase 48
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Discussion and Design Implications Designing a harvester for use with complex vibration sources requires acknowledgement of more characteristic factors than sinusoidal or random vibration Sinusoidal frequencies, number of sinusoidal components, separation between sinusoidal components, random spectral density profile, determination of optimal impedance Ignoring random content or nearby sinusoidal content gives a poor representation of harvested power and load voltage Ignoring random content gives incorrect optimal impedance Harvested power gains from additional random component or multiple sinusoidal components are overshadowed by induced voltage fluctuations Improper source vibration and harvester response representation during development hurts application Lowers power harvesting ability and efficiency Omitting necessary voltage control and processing circuitry can bring about unexpected consequences such as inaccurate sensor readings, poor circuit functionality and possible damage to target electronicsMarch, 2013 Sigma Xi - Student Resarch Showcase 49
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Conclusion Idealized sinusoidal and random vibration studies are NOT sufficient for general harvester development Environments with sufficiently low noise or random vibration levels and sufficiently spread dominant frequencies may suffice Theoretical and numerical predictions hinge upon exact knowledge of transducer mechanical and electrical properties This cannot be assumed in general Internal transducer electrical and mechanical properties are unknown unless custom developed by applicant Sine on random vibration testing and experimental validation is an essential tool in harvester development SOR testing can recreate almost any vibration environment SOR control can provide accurate quantitative results when harvesting from complex vibrational sourcesMarch, 2013 Sigma Xi - Student Resarch Showcase 50
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Acknowledgements Brian Hatchell for mentoring me through this experimental process and providing the inspiration for the project Emiliano Santiago-Rojas for applying electrical expertise and making this cross discipline application possible Karen Wieda for advising and aiding my assimilating into the PNNL research environmentA special thanks to:Department of Energy – Office of Science and the U.S. Army for makingthis research project possible51
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