Piezoelectric-based Broadband Bistable Vibration Energy Harvester and SCE/SSHI-based High-Power Extraction Kanishka Aman Singh (kanishka@iastate.edu), Ratnesh Kumar, Fellow, IEEE (rkumar@iastate.edu), Robert J. Weber, Fellow, IEEE (weber@iastate.edu) Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50014, USA. Abstract This paper presents ambient mechanical vibrations as an alternative source for energy harvesting, especially beneficial where alternatives such as light, wind, biomass and thermal energy are limited, e.g., powering underground sensors. Transduction of ambient kinetic energy, e.g., the vibrations from thunder and field work, into electrical energy using piezoelectric generators has been investigated, utilizing a nonlinear bistable broadband piezoelectric harvester. A new model for the bistable piezoelectric harvester is suggested based on the standard Butterworth van Dyke model and its validity demonstrated through simulations. For efficient extraction of the transduced energy, we employ synchronous charge extraction (SCE) and parallel synchronized switch harvesting on inductor (SSHI). The switching in these circuits is implemented using a fully selfpropelled, low-power electronic breaker circuit, capable of detecting extrema in the input to perform switching. The power outputs from simulation of the bistable harvester have been presented, with the SCE and parallel SSHI providing respective average outputs of 78.5µW and 125µW for a sinusoidal input of 0.326N at 10Hz applied to a 69.1 x 16.8 x 0.64 mm 3 cantilever (piezoelectric dimensions 35.56 x 14.48 x 0.2 mm 3 ). This shows significant gains over the harvested power reported in literature. I. INTRODUCTION: MOTIVATION AND OBJECTIVES ITH the development of wireless sensors for remote Wapplications, such as underground sensing for soil moisture and nutrient content for agricultural purposes, a concern to extend battery life to power these sensors has surfaced. To this end, miniature renewable self-contained power supply units may be used to convert energy in existing forms in the environment into electrical form. For underground applications, light and thermal energy are limited. However, mechanical energy in the form of ambient vibrations, ever present in the environment, and augmented by external factors such as thunder or agricultural work, is a viable option. Harvesting kinetic energy requires its transduction to electrical form [1]. The three most commonly used transduction mechanisms are piezoelectric [2-5], electromechanical [6-8], and electrostatic [9-11]. The maximum power density from the three methods is theoretically comparable [1]. However, sub-millimeter and wafer-scale implementations are difficult for electromagnetic systems, and electrostatic systems require a polarizing charge/voltage, large motion amplitudes, and suffer from parasitic capacitances [12]. Therefore, we focus on This research was supported in part by the National Science Foundation under the grants NSF-ECCS-0801763 and NSF-ECCS-0926029. piezoelectric harvesters, which lend themselves to simple implementations, microengineering, and a variety of material choices, while providing relatively high output voltages. Piezoelectric-based harvester structures may be either linear or nonlinear. In order to maximize the energy harvested from broadband ambient vibrations, this paper focuses on nonlinear harvesters, and makes the following contributions: Presents an improved and more accurate model for a nonlinear bistable harvester based on the standard Butterworth van Dyke piezoelectric model; Combines nonlinear harvesting with optimized energy extraction circuits using electronic breaker switches, to generate power at levels greater than that reported in literature. To the best of our knowledge, this is a first effort reporting the combining of nonlinear harvesting with synchronized extraction; and Provides extensive simulation results to validate the proposed harvester model and the effectiveness of the extraction schemes over the ones reported in literature. II. PIEZOELECTRIC HARVESTING Most piezoelectric harvesters focus on resonant frequency operation in order to maximize the energy harvested, and can be modeled as a second-order linear spring-mass system [1]. However, for wideband ambient vibrations, nonlinear operation helps to increase harvested power. This section discusses the modeling of piezoelectric harvesters. A. Modeling The constitutive equations of a piezoelectric material can be written as (1) below, relating two electrical parameters, the electric displacement D and the electric field strength E, to two mechanical parameters, the stress σ and the strain δ through the electric permittivity of the piezoelectric material at null stress ε σ, the elastic compliance at null electric field strength s E, and the piezoelectric strain constant d eff. Multiplying the upper part of (1) with unit area and the lower with unit length, we get (2), where Q d is the charge separation, u is the displacement, and V p is the voltage developed on the piezoelectric material due to the external force applied, F. C l is the lumped capacitance and k the lumped stiffness constant of the piezoelectric material..... (1)
.... (2) Using (1) and (2), piezoelectric materials can be modeled as in Fig. 1 [13], with the primary side modeling the mechanical behavior and the secondary side the electrical one. Energy is transferred from one domain to another through a transformer. C m = 1/k represents the short-circuit mechanical compliance, ρ = d eff.k the winding ratio of the transformer, and C e = C l - d eff 2.k the blocked electrical capacitance of the material. However, this model does not consider inertia and the inherent losses. The Butterworth van Dyke piezoelectric model [14][15], shown in Fig. 2, provides a more complete dynamic model, with forces modeled as voltages and velocities as currents, the inertial behavior captured by an inductor M m, the mechanical damping of the beam by resistor R m, and dielectric losses by resistor R e. Fig. 1: Equivalent circuit of piezoelectric material assuming no losses. Fig. 3: Bistable system formed by cantilever and two magnets. The cantilever is at one of the equilibrium positions, while the other position is symmetrically opposite, shown in dotted lines. system. Although it serves the purpose, this model is a heuristic one. We propose a more accurate model by adding a correct form of nonlinearity to the standard Butterworth van Dyke (BVD) model, introduced in Fig. 2. Thus, the source voltage F is a sum of the externally applied vibration force, F v, and the nonlinear magnetic force, F m. Accordingly, the model is described by (3) for the primary and (4) for the secondary side:, (3) 1, (4) Fig. 2: Lumped electrical model, or Butterworth van Dyke model, of piezoelectric transducer. B. Broadband Piezoelectric Harvesting Resonant harvesters are not suitable for applications where energy might be distributed over a spectrum of frequencies. However, nonlinear bistable structures are able to operate over a wide band of excitation. They have two equilibrium positions, and can either vibrate at one of these positions, or for a large enough excitation, switch between them, thereby increasing the amplitude, and hence the power converted by the harvester. Fig. 3 shows a simple way of realizing the bistable system with a cantilever and two magnets with the same polarities facing each other, one at the cantilever tip, and the other fixed [16]. Due to the repulsive force between the magnets, for distances between them less than a critical value, the cantilever develops two equilibrium states, symmetrically above and below the horizontal axis. In this condition, for small external excitations, the cantilever vibrates in one of the two equilibrium positions. However, if the excitation is large enough to overcome the magnetic force, the cantilever can snap back and forth between the two equilibrium positions. This effectively increases the vibration amplitude, hence the voltage and power outputs, as compared to linear operation. Also, the spread of the output frequency spectrum reduces as compared to the input, making rectification of the output signal easier. III. PROPOSED BISTABLE SYSTEM MODELING Ferrari [16] modeled the bistable system by adding a nonlinear spring to the linear spring-mass model of the resonant where r is the cantilever length, d is the horizontal distance between the fixed supports, x = (r 2 +d 2-2.r.d.cosθ) 1/2 measures the distance between the two magnets as a function of angular deflection θ; F m = (K.d.sinθ)/x 3 is the normal component of the magnetic force K/x 2 ; V p /ρ is the secondary voltage reflected on the primary through the transduction factor (or turns ratio) ρ; rdθ/dt is the angular velocity of the cantilever, and (r/ρ)dθ/dt is this velocity reflected on the secondary side. In the absence of external force F v, the beam rests at one of its equilibrium states θ 0, under the action of the magnetic force F m balanced by the restoring spring force rθ/c m. Thus, the derivatives of θ and the output voltage in (3) reduce to zero, leading to the equilibrium equation (5), solving which, we get the initial deflection θ 0 :.. sin 2...cos To validate our model, the above equations were simulated in Matlab Simulink (Mathworks Inc.) [17], for a sinusoid input excitation of 1.63N, 10Hz, and parameter values of Table 1, taken for a real piezoelectric cantilever harvester Volture V21B by Midé [18], measuring 69.1 x 16.8 x 0.64 mm 3 (piezoelectric dimensions 35.56 x 14.48 x 0.2 mm 3 ). Fig. 4 shows the plots for monostable operation with no magnets used, and Fig. 5 for bistable operation with the magnets. The plots show about 30% increases in vibration amplitude and open circuit voltage for bistable operation. Fig. 6 shows the output under the same bistable operating conditions of Fig. 5, but employing a PSpice based circuit-model of Fig. 2, modified to include the nonlinear magnetic force in the form of a nonlinear capacitor. These plots are almost identical to those from simulation of our proposed mathematical model (see Fig. 5), thereby validating our model. (5)
Table 1: Values of parameters used. C m (m/n) R m (N.s/m) M m (kg) C e (nf) R e (MΩ) 5.865*10-4 4.8*10-3 3.26*10-3 4.0 106.1 r (mm) d (mm) K (N.m 2 ) d eff (m/v) ρ=c m/d eff (V/N) 35.56 36.5 9.33*10-7 3.165*10-7 1852.536 Since the harvested energy is required to charge a battery, all circuits analyzed have a battery as the load. Also, since the ambient vibrations are random in nature, the piezoelectric harvester produces alternating voltage, necessitating the use of a rectification step to be able to charge a battery. Fig. 4: Displacement (radians) and output voltage (Volts) plots for monostable operation, as obtained from simulating Equations (3)-(5) in Matlab Simulink. A. Standard Extraction Circuit The standard extraction circuit uses only a rectifier [19-21]. In the standard circuit of Fig. 7, the piezoelectric voltage V p is fed through the bridge rectifier formed by diodes D 1 -D 4 to the battery with voltage V b. As the mechanical input F increases, charge builds up on C e till V p is able to overcome the voltage drop V D across diodes and charge the battery. The energy flowing into the battery at any instant is given by (6) below. Locating the point where the diodes begin to conduct, the average power into the battery is given by (7) for a sinusoidal input. This can be maximized to P max (8) by setting the battery voltage to half that of the maximum open circuit piezoelectric voltage, V pm, reduced by the voltage drop across the diodes, as in (9). Here, ω represents the frequency of input vibration. Fig. 7: Standard energy extraction circuit. Fig. 5: Displacement (radians) and output voltage (Volts) plots for bistable operation, as obtained from simulating Equations (3)-(5) in Matlab Simulink. 1 2 2, 2 0, (6) 2 2 2 (7) (8) 1 2 2 (9) It is to be noted here that the nonlinear operation increases the vibration amplitude, thus V p and V pm, nonlinearly, resulting in more harvested power than the linear harvesters reported in literature [20]. The operation of the bistable harvester is shown in the plots of Fig. 8 for a sinusoidal input of 0.326N, 10Hz. Fig. 6: Displacement (radians) and output voltage (Volts) for bistable operation, as obtained from simulating the proposed BVD-based model in PSpice. IV. POWER EXTRACTION CIRCUITS This section explores ways of optimizing power extraction from our nonlinear bistable harvester, and compares them to a standard harvesting circuit comprising an AC to DC converter. B. Synchronous Charge Extraction The synchronous charge extraction (SCE) circuit [20][21] allows charge to build up on the clamped electrical capacitance C e until it reaches a maximum, corresponding to the maximum displacement of the cantilever. At this point, all the charge is extracted from the capacitor and transferred to the battery.
transistor Q 1, and a switch with NPN transistor Q 2. The signal at the envelope detector charges C s to the envelope voltage. Q 1 remains blocked while this envelope at its emitter is less than the signal voltage at its base, thus blocking Q 2. When the signal voltage falls below the envelope voltage after an extremum, Q 1 turns on, allowing C s to discharge and turn on Q 2 in the process; thus turning on the switch. When the current through Q 2 falls to zero, the diode D 8 prevents reversal of current direction, turning the switch off, thus providing automatic control of switch ontime; this is necessary in this architecture in order to maximize the energy harvested. Fig. 11 shows a breaker in an SCE circuit. Fig. 8: Simulation plot for standard extraction circuit, showing the displacement (qualitatively) and the corresponding voltages (V), current (µa) and power flowing into the battery (µw) for a sinusoidal input of 0.326N, 10Hz to the nonlinear bistable harvester. Average harvested power is about 40µW. In the SCE circuit of Fig. 9, switch S remains open normally while electrostatic energy builds up on C e. S is closed at the displacement extrema, transferring the energy stored in C e to the primary winding L 1 of the coupled inductor as magnetic energy. When the transfer is complete, the capacitor voltage drops to zero, typically in a quarter of the time period of the oscillator L 1 -C e. At this point, S is turned off again, transferring energy in the coupled inductor to the battery through diode D 5. Fig. 10: Electronic breaker circuit for switching on at maxima displacement. Fig. 9: Synchronous charge extraction (SCE) circuit. For sinusoidal F, the piezoelectric open circuit voltage has amplitude V pm. However, with the SCE circuit, the piezoelectric voltage V p goes to zero at the displacement extrema, and rises from zero as the cantilever moves in the opposite direction; so, for the same sinusoid input, V p oscillates between +2V pm and -2V pm. The electrostatic energy stored on C e at the extrema is given by (10) below, and the power flowing into the battery by (11), where T is the input excitation time period. The extracted power in (11) is independent of the battery voltage and always maximized; hence SCE is a self-optimized circuit. However, non-idealities, such as quality factor of the inductor and diode voltage drops, effect some changes in the extracted power [21]. Fig. 11: SCE circuit with the electronic breaker. The operation of the SCE circuit is shown in the plots of Fig. 12 for a sinusoidal input of 0.326N, 10Hz. The current and power flowing into the battery appear as pulses at the instant the switch is turned on. The slight delay in turning the switch on at an extremum is due to the transistor threshold voltage. Fig. 13 shows the voltages and currents in the coupled inductor and the power into the battery at the time the switch is turned on. 1 2 2 2 (10) 2 2 (11) In order to realize a self-propelled, low-power switch S that triggers at displacement extrema, the electronic breaker circuit [22] was used. As SCE architecture requires rectification prior to extrema detection, only maxima needs to be detected. The corresponding switching circuit of Fig. 10 includes an envelope detector with a storage capacitor C s, a comparator with the PNP Fig. 12: Simulation plot for SCE circuit, showing the displacement (qualitatively) and the corresponding voltages (V), current (ma) and power flowing into the battery (mw) for a sinusoidal input of 0.326N, 10Hz to the nonlinear bistable harvester. Average harvested power is about 80µW.
Fig. 14: Parallel synchronized switch harvesting on inductor (SSHI) circuit. 1 (17) Fig. 13: A zoomed-in view of the voltages, currents and power transferred at the instant the switch is turned on. C. Parallel Synchronized Switch Harvesting on Inductor The parallel synchronized switch harvesting on inductor (SSHI) circuit [20][21], similar to SCE, involves switching at displacement extrema. However, unlike SCE, the switch is turned on at extrema to invert charge polarity on the clamped capacitor, while the battery charges during rest of the operation. In the parallel SSHI circuit of Fig. 14, switch S remains open normally, and the battery charges while V p is greater than V b. At a displacement extremum, S is closed to form an L-C e oscillator with a time-period much smaller than that of input vibration. S is kept on for half the L-C e time-period to let the voltage on C e, clamped at V b, invert in polarity through the inductor L. During this inversion, the bridge diodes remain reverse biased, and the battery is not charged. Once S is opened, C e is charged again in the opposite direction to a magnitude of V b, when the bridge diodes start conducting, resuming charging the battery. Ideally, the polarity inversion on C e would be perfect, and the voltage would flip between +V b and V b, charging the battery for the full duration the switch is off. However, due to the finite quality factor Q of the inductor, the inversion is not perfect, and is determined by (12), where V inv and V init are the voltages after and before inversion. Some charge Q c is needed to raise V p to V b before charging of the battery starts, as in (13). Hence, for a sinusoidal input, energy E flowing into the battery over half the period of input vibration, T/2, is given by (14) and the power P by (15). The optimum battery voltage V b-opt for maximum power transfer P max can be calculated to be (16), leading to (17). V pm refers to the open circuit piezoelectric voltage amplitude. The electronic breaker is used again for switching. Here, as the switch is placed before the rectifier, detection of both maxima and minima is required. The electronic breaker for minima switching control is obtained from the maxima breaker by inverting the polarities of diodes and transistors in Fig. 10. In the parallel SSHI circuit with electronic breakers of Fig. 15, after displacement maxima (minima), V p falls below the envelope voltage on C s1 (C s2 ), hence Q 1 (Q 4 ) starts conducting, turning on Q 2 (Q 3 ). After polarity inversion on C e, the reversal of current direction in the oscillator L-C e is prevented by diodes D 8 (D 9 ), turning the switch off automatically. The parallel SSHI operation is shown in the plots of Fig. 16 for a sinusoidal input of 0.326N, 10Hz. At displacement extrema, the reversal of piezoelectric voltage on C e is not perfect; some charge is required to raise V p up to the battery voltage V b, during which no power flows into the battery. At V b, the rectifier diodes begin to conduct, charging the battery. The delay in turning the switch on after reaching the extrema is due to the transistor threshold voltage. Fig. 15: Parallel SSHI circuit with maxima and minima electronic breakers. 1 (12) (13) 2 1 (14) 2 2 1 1 (15) (16) Fig. 16: Simulation plot for SSHI circuit, showing the displacement (qualitatively) and the corresponding voltages (V), current (µa) and power flowing into the battery (µw) for a sinusoidal input of 0.326N, 10Hz to the nonlinear bistable harvester. Average harvested power is about 125µW.
D. Results The simulated powers harvested from each circuit discussed above have been compared in Table 2. A sinusoid vibration of 0.326N, 10Hz was used for all simulations. We note that (a) nonlinearity increases the power output, and (b) SCE and SSHI circuits increase power extraction over the standard circuit. Table 3 compares some outputs reported in literature to the simulated output from our parallel SSHI-based nonlinear bistable harvester for the same vibrational input. The cantilever used in the bistable harvester measured 69.1 x 16.8 x 0.64 mm 3 (piezoelectric element of 35.56 x 14.48 x 0.2 mm 3 ). The final column of Table 3 shows the Gain in harvested power. Table 2: Comparison of harvested power from different extraction circuits. Type Output (µw) Gain over Standard Linear Standard Linear 26.5 - Standard Nonlinear 41.5 1.57 SCE Linear 40 1.51 SCE Nonlinear 78.5 2.96 SSHI Linear 60 2.26 SSHI Nonlinear 125 4.72 Table 3: Performance comparison of Parallel SSHI (P-SSHI) Bistable Harvester with reported outputs. Reference Badel [20] Badel [20] Badel [20] Lallart [23] Type P-SSHI (Single crystal piezo) P-SSHI (piezo ceramic) SCE (piezo ceramic) SSHI with Electronic Breaker Acceleration (km/s 2 ) Frequency (Hz) Output (mw) 3.2 900 1.8 3.2 900 0.09 3.2 900 0.04 1mm displ. 106.1 0.05 Size (mm 3 ) 40x7 x1 40x7 x1 40x7 x1 40 mm long P-SSHI Bistable Harvester Output Gain 7.5mW 3.17 7.5mW 82.3 7.5mW 166 14mW 149 V. CONCLUSION AND FUTURE WORK This paper discusses energy harvesting for underground sensors from wideband ambient vibrations, e.g. thunder and field work. Based on the Butterworth van Dyke piezoelectric model, an improved model of a nonlinear bistable harvester has been presented, with the nonlinear input force modeled by a nonlinear capacitor. The nonlinearity of the harvester, achieved through the use of two magnets, results in increase of vibration amplitude. Hence, voltage and harvested power are increased. This nonlinear bistable harvester was then used with SCE and parallel SSHI extraction circuits to get significantly high power outputs. The electronic breaker was used as a selfpropelled, low powered switch to detect extrema in the input and turn on and off automatically as required. For a sinusoidal vibration input of 0.326N at 10Hz, using a 69.1 x 16.8 x 0.64 mm 3 cantilever (piezoelectric dimensions 35.56 x 14.48 x 0.2 mm 3 ) provided by Midé, the simulated harvested power from SCE and parallel SSHI circuits were respectively, 78.5µW and 125µW, with respective gains of 2.96 and 4.72 over the standard linear harvester. 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