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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 201 Maximum Power Transfer Tracking for Ultralow-Power Electromagnetic Energy Harvesters Gyorgy D. Szarka, Stephen G. Burrow, Plamen P. Proynov, and Bernard H. Stark Abstract—This paper describes the design and operation of power conditioning system with maximum power transfer tracking (MPTT) for low-power electromagnetic energy harvesters. The system is fully autonomous, starts up from zero stored energy, and actively rectifies and boosts the harvester voltage. The power conditioning system is able to operate the harvester at the maximum power point against varying excitation and load conditions, resulting in significantly increased power generation when the load current waveform has a high peak-to-mean ratio. First, the paper sets out the argument for MPTT, alongside the discussion on the dynamic effects of varying electrical damping on the mechanical structure. With sources featuring stored energy, such as a resonant harvester, maximum power point control can become unstable in certain conditions, and thus, a method to determine the maximum rate of change of electrical damping is presented. The complete power conditioning circuit is tested with an electromagnetic energy harvester that generates 600 mVrm s ac output at 870 μW under optimum load conditions, at 3.75 m·s−2 excitation. The digital MPTT control circuit is shown to successfully track the optimum operating conditions, responding to changes in both excitation and the load conditions. At 2 Vd c output, the total current consumption of the combined ancillary and control circuits is just 22 μA. The power conditioning system is capable of transferring up to 70% of the potentially extractable power to the energy storage. Index Terms—AC–DC converter, energy harvesting, low power, maximum power tracking, rectification. I. INTRODUCTION HE output of small electromagnetic energy harvesters typically requires rectification and boosting in order to produce an output voltage that falls within the allowable operating range of the load electronics. In some applications, there is also a need to buffer energy in high capacity storage elements, such as supercapacitors, in order to supply loads with a higher peak demand than the harvester output [1]. Several circuit architectures have been reported in published literature, which meet these requirements, including single-stage ac–dc switch-mode power converters [2]. Efficiencies up to 75%–80% at 500 μW T Manuscript received October 11, 2012; revised December 21, 2012 and January 23, 2013; accepted February 19, 2013. Date of current version July 18, 2013. Recommended for publication by Associate Editor S. Y. (Ron) Hui. G. D. Szarka, P. P. Proynov, and B. H. Stark are with the Department of Electrical and Electronic Engineering, University of Bristol, Bristol, BS2 8BB, U.K. (e-mail: [email protected]; [email protected]; [email protected]). S. G. Burrow is with the Department of Aerospace Engineering, University of Bristol, Bristol, BS2 8BB, U.K. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2013.2251427 level have been reported [3]. However, in order to achieve the maximum potential power of an energy harvester, it is important that the power conditioning system provides the optimum load for the generator for the particular input and output conditions. Vibration harvesters have a “peak-power”-type response: power variation with changing load damping is not monotonic, displaying a peak at a damping level determined by harvester parameters [4]. Negative-feedback voltage regulation for switching converters cannot provide a stable operation at the peak power point as the operating conditions required violate Middlebrook’s stability criterion [5]. The optimum damping level of an ideal harvester driven at resonance is independent of excitation amplitude; hence, one solution is to employ a converter emulating a fixed impedance to the harvester, as reported in [5] and [6]. However, fixed input impedance places restrictions on converter design (principally requiring discontinuous conduction), and this is difficult to maintain over the full range of input and output conditions. The challenge for the power converter is then to provide the basic functionality of rectification and voltagelevel shifting, while loading the harvester with the optimum impedance, independently of its input and output conditions. In this paper, the electromagnetic energy harvester is assumed to be operating at its mechanical resonance frequency, making its effective output impedance dominantly resistive [7], and constant over time. By contrast, the apparent input impedance of the power converter depends on the input and output voltage conditions. As these vary over time, dynamic control is required to maintain the desired converter input impedance. Maximum power point tracking (MPPT) schemes employ an algorithm, such as gradient descent, to locate a peak power point for the prevailing operating conditions. They are commonly used to maintain temperature-dependent photovoltaic cells at their peak power point [8], [9], and offer the ability to optimally load an energy harvester, compensating for both variations in optimal load and variations in converter output conditions. However, when used with systems with significant stored energy (like the kinetic energy harvesters investigated here) extra care must be taken to ensure correct operation. The literature on maximum power point tracking solutions for energy harvesting is relatively sparse. Elmes et al. [10] reported a maximum energy harvesting control scheme for an energy harvesting backpack generating tens of watts of power. In [11], a microcontroller-based power point tracker is reported for a rotational generator producing dc output up to 10 mW; the circuit employs a resistance matching strategy, similar to the approach adapted in [12] for submilliwatt RF energy harvesting. One of the first authors to publish on peak power control in the energy harvesting literature was Ottman; the presented power converter architecture differed from the 0885-8993/$31.00 © 2013 IEEE 202 work here as the rectifier of the two-stage topology fed into a stiff dc link, which itself was controlled to provide the power tracking capability. Additionally, the paper focused on piezoelectric transducers. Low-power solutions offering regulation of the buffered output voltage of the rectification stage for maximum power point operation have been demonstrated in the literature: for piezoelectric harvesters using an off-the-shelf buck converter operated intermittently [14], or for electromagnetic generators using a low-power integrated boost converter [15]. Recently, an integrated maximum power point tracking circuit has been presented in [16] that operates down to sub-100 μW levels, using an approach referred to as power-optimal point of charging for the control of a dc–dc charge-pump. These solutions are designed to maximize the power generated by the harvester without considering the losses of power conversion or the quiescent power overheads of any control and ancillary circuits. Derivatives of the MPPT technique, referred to as maximum power transfer tracking (MPTT) [8], are designed to maximize the power transferred to the load and the energy storage element. Dayal and Parsa [17] proposed a lowpower implementation for an MPTT scheme, but only simulated results are presented for the control circuit. In the reported paper, the output voltage is maximized by varying the duty ratio of the pulse width modulation (PWM) driving signal of a splitcapacitor ac–dc converter. This technique assumes that the load is near constant and purely resistive; otherwise, maximizing the voltage would not yield maximum output power conditions. Also, it requires the energy storage element to be small in order to be able to monitor the effect of varying duty ratio. These assumptions pose impractical limitations on small-scale energy harvesting that is typically characterized by very low generated power levels, large energy storage elements, and load circuits with highly dynamic power consumption. The effects of the stored energy within the mechanical oscillator of the harvester on MPPT are alluded to in [10] and [11], by stating that the control loop has to be slow in order to avoid instability. However, the behavior of the harvester under varying damping and the implications regarding the design of the control circuit has not been discussed in the literature. In this paper, the maximum response rate of the MPTT algorithm resulting in stable operation is investigated and a complete MPTT harvesting system is presented. Section II describes an electromagnetic energy harvester with the governing equations of motion, investigating the harvester’s response to dynamic electrical damping experimentally. Next, an analysis of the harvester’s response to a step change in the damping is described, which enables the derivation of the minimum settling time required between perturbations of the control parameter. Section III provides a description of the power conditioning circuit. Section IV presents the operating principles for the perturb-and-observe algorithm and describes the control circuit. Section V presents experimental results that show the steadystate performance of the MPTT and the behavior under transient load and excitation conditions. Finally, Section VI summarizes the key findings and concludes with suggestions for future work. IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 Fig. 1. Small-scale electromagnetic energy harvester with a 3.4 g NdFeB magnet acting as the moving mass within a coil wound using 600 turns of 100 μm diameter copper wire. The resonant frequency is 43.8 Hz. A piezoelectric thin film is bonded to the top of the cantilever for displacement monitoring. II. ENERGY HARVESTER: STEADY-STATE AND TRANSIENT CHARACTERISTICS A. Electromagnetic Energy Harvester A cantilever-type vibration harvester is used in this paper, shown in Fig. 1. It features a BeCu beam with a 3.4 g NdFeB magnet acting as the tip mass. Energy from the motion is transferred to the electrical domain via the electromagnetic coupling between the moving magnet and a wound coil. The tip mass is large compared to the beam; hence, the generator can be modeled as a base excited, second-order, velocity-damped mass–spring system, where the response to external forcing is described by mz̈ + cż + kz = mω 2 Y sin ωt. (1) The base displacement has an amplitude Y at an angular frequency of ω. The equivalent mass at the tip is given as m, while c denotes the viscous damping within the system that is the combination of the mechanical and the electrical damping. The spring constant of the compliant beam is k, and z refers to the motion of the moving mass relative to the frame. The schematic illustrations of the electromagnetic energy harvester and the lumped element model of the spring-mass-damper system are presented in Fig. 2. The steady-state solution, referring to the condition where the amplitude of the periodic motion is constant, is given as [4] z(t) = Z sin(ωt − ϕ) (2) where the amplitude is given by Z= mω 2 Y (3) (k − ω 2 m)2 + c2 ω 2 and the phase angle between the base and tip displacement is given by ϕ = tan−1 cω . k − ω2 m (4) At the natural resonance frequency, which is described by k (5) ω = ωn = m SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS 203 Fig. 2. (a) Schematic illustration of the electromagnetic energy harvester shown in Fig. 1, and (b) illustration of the lumped elements of the spring– mass–damper system. Fig. 4. Generated output power versus time corresponding to the 0.5, 1, 2, 4, and 8 s load resistance sweep profiles of Fig. 3. Excitation amplitude is actively held at 3.75 m·s−2 and the frequency is 43.8 Hz. Fig. 3. Load resistance profiles with various gradients, resulting in linear load resistance sweeps between 1000 Ω and 100 Ω in 0.5, 1 s, 2, 4, and 8 s. Both (left) decreasing and (right) increasing resistance profiles are considered. (2) simplifies to π mωY sin ωt − . (6) c 2 Depending on the application, both of the excitation frequency ω and amplitude Y can vary over time. Furthermore, damping arising from the interfacing electronics affects the total damping given by [4] z (t) = c = cm + Rcoil θ2 + Rload (7) where cm represents the mechanical damping, θ the electromagnetic coupling coefficient, and Rcoil is the parasitic resistance of the coil. Rload is the load resistance, which is synthesized by the input impedance of the power converter in a practical system. In typical small-scale electromagnetic energy harvesters, the impedance of the parasitic coil inductance at the excitation frequency is several orders of magnitude lower than the combined equivalent mechanical resistive output impedance and ac coil resistance. Therefore, it is assumed that close to the theoretical, maximum power can be extracted using a purely resistive load at resonance. B. Illustration of Response to Dynamic Damping The transient response of the mechanical system is related to the energy stored in the oscillator and the total damping of the system. To illustrate this experimentally, the load applied to the harvester of Fig. 1 is swept from 100 to 1000 Ω at differing rates (see Fig. 3), while the excitation is kept constant. Prior to Fig. 5. Measured generated power profiles of Fig. 4 mapped onto corresponding load resistance sweeps and compared against steady-state measurements. each sweep, the harvester is in steady state. The instantaneous generated power is measured and averaged over one cycle. The resulting output power–time profiles are presented in Fig. 4. The output power mapped onto the corresponding load resistance is shown in Fig. 5, resulting in hysteretic trajectories of output power as the load is swept up and down at a particular rate. The cycle-averaged power recorded under steady-state conditions is also shown for comparison. This reveals that the maximum power that can be sustained by the energy harvester at the optimum resistance of 400 Ω is around 870 μW; however, during a sweep, much higher powers are available if the damping is rapidly increased and much lower powers while the damping is being reduced. This behavior can be understood by considering the energy stored in the mechanical components of the harvester. Most harvesters feature significant amplification of source vibrations, analogous to the quality factor or “Q” of electrical resonant circuits. Q also defines the ratio of energy stored in an oscillator to that dissipated each cycle. Thus, for high-Q systems, a change in the operating point requires significant energy to be either added or dissipated. At high load resistance, corresponding to low 204 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 In the steady-state solution of (6), the amplitude of the tip displacement before the step change is Zo = mωY co (9) and after the step change, the oscillation should settle to the new steady-state solution with a tip displacement amplitude of Zs = mωY . cs (10) The initial conditions for the nonhomogeneous second-order differential equation of (1) are obtained by finding the steadystate displacement and velocity at time t = 0. Hence, the initial displacement is z (0) = −Zo , and velocity is ż (0) = 0. The solution of the differential equation is z (t) = (Zs − Zo ) e−(c s /2m )t cos (ωβt) (Zs − Zo ) cs −(c s /2m )t e sin (ωβt) − Zs cos (ωt) (11) 2mωβ where β is given as 1 − ζ 2 , and the damping ratio ζ is + Fig. 6. (a) Generated rms current and voltage waveforms during the 4 s sweep transients, and (b) current and voltage excursions mapped to the corresponding load resistance. damping, significant energy is stored in the system. Increasing the damping reduces the displacement of the mass, thereby reducing the stored energy, which is seen as transient additional output power. Conversely, reducing the damping leads to an increase in stored energy, which although is supplied by the vibration source, limits the rate at which the new steady state is approached. As the rate of change of the electrical damping is reduced, the measured output power levels converge to the steady-state solution. The generated rms current and voltage transients are illustrated in Fig. 6 for the 4-s sweep case. The curves show that during the increase of the damping, the corresponding transient voltage and current travels are higher than during decreasing damping, as some of the initial kinetic energy of the energy harvester is dissipated. The behavior illustrated here is of great importance when implementing a power tracking scheme. If the controller does not take into account the transient component of the output power by allowing sufficient settling time of the harvester, the system can become unstable. C. Response to Step Change in Damping In this section, a step change in the damping is considered, as might be the case when a digital system steps a control reference signal. The harvester is modeled as a highly underdamped, single-degree-of-freedom mass–spring–damper system, excited at its natural frequency with constant acceleration amplitude. Also, prior to the change, the mechanical structure is assumed to be in steady state. The damping as a function of time can be described as c(t) = co , cs , t≤0 . t>0 (8) c ζ= √ . 2 mk (12) In a highly underdamped system (ζ < 0.1), such as typical small-scale electromagnetic energy harvesters, β is assumed to be 1. This simplifies the solution to −z (t) = Zs + (Zo − Zs ) e−(c s /2m )t cos (ωt) (Zo − Zs ) cs −(c s /2m )t e sin (ωt) . (13) 2mω This equation shows that the underlying sinusoidal oscillation with initial amplitude of Zo decays exponentially to a sinusoidal oscillation with amplitude of Zs , with a rate that is determined by the total damping and the moving mass. This time-domain solution is validated (see Fig. 7) using measured output power for several step changes in the load resistance. The measurement results show a good correlation with the calculated waveforms. The second exponential term of (13) can be considered negligible in a highly underdamped system, where the damping coefficient is very small, as the denominator of multiplying fraction is typically greater than 1, and the product of (Zo − Zs ) cs is small, in the order of 10−5 . Hence, the amplitude of the sinusoidal oscillation is dominated by + |z| ∼ = Zs + (Zo − Zs ) e−(c s /2m )t (14) an exponential decay to the new tip displacement amplitude. Differentiating this solution yields the approximate solution for the velocity cs −(c s /2m )t e cos (ωt) v (t) = Zs ω sin (ωt) + (Zo − Zs ) 2m + (Zo − Zs ) ωe−(c s /2m )t sin (ωt) . (15) Considering that the velocity amplitude in the steady-state solution is given as V̂ = Zω and that ω c/2m, the velocity SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS 205 where Is and Io are given according to I= θmω 2 Y c (Rcoil + Rload2 ) (20) with c=cs and c=co , respectively. The instantaneous generated power dissipated in the load resistance is given as P (t) = i2 (t) · Rload2 . (21) Defining a common factor as A= θ 2 m2 ω 4 Y 2 Rload2 (Rcoil + Rload2 )2 allows us to write the current and power amplitudes as 1 1 A 1 −(c s /2m )t |I| = + − e Rload2 cs co cs Fig. 7. Calculated, based on (13), and measured average output power during the transient response of the system that occurred after a step change in the load resistance. Initial load resistances are shown on the right; after the step change, the resistance is constant at 400 Ω. Excitation is a constant 3.75 m·s−2 acceleration at 43.8 Hz. amplitude during the transient response can be approximated with great fidelity in a highly underdamped systems as (16) |v| = V̂s + V̂o − V̂s e−(c s /2m )t . and 1 1 2 1 + − e−(c s /2m )t c2s cs co cs 2 1 1 −(c s /m )t + − e . co cs U (t) = Blv(t) = θv(t) where B is the magnetic field strength and l is the effective length of the conductor within the magnetic field. Thus, the amplitude of the induced sinusoidal voltage is the coupling coefficient θ times the velocity amplitude given in (16). The steady-state instantaneous current is dependent on the total load resistance of the circuit and is equal to i(t) = U (t) Rcoil + Rload2 (18) where Rload2 denotes the load resistance after the step change, and during the settling time. During the settling time, the amplitude of the generated current will decay exponentially toward the steady-state value I (t) = Is + (Io − Is ) e−(c s /2m )t (19) (24) According to the definition of the settling time, at t = ts the amplitude of the power for increasing damping should be |P | = Ps (1 + ε) (17) (23) |P | = A D. Minimum Settling Time Selection The assumption is made that in order to avoid instability from any system condition, a digital control system should initiate a step change in damping c only once the system has settled. The settling time in this paper is defined as the time required for the output power to reach within 1% of its final value. In a typical MPPT system, adjusting of the control parameter varies the apparent input resistance of the interfacing power electronics, resulting in discrete step perturbation of the generator damping. Considering these steps, a harvester settling time can be defined and used as the lower limit on the time period between adjustments. The counterelectromotive force induced in the coil is proportional to the velocity of the moving magnet according to (22) (25) where Ps = A/c2s , and the error ε is 0.01. Substituting (25) into (24), then dividing both sides by A and rearranging to one side yields 1 2 1 1 − e−(c s /2m )t s −ε 2 + cs cs co cs 2 1 1 + − e−(c s /m )t s = 0 (26) co cs cs Multiplying both sides by e m ts c2s co / (cs − co ) gives a quadratic equation in the form of ε co cs − co x2 − 2x − =0 cs − co co (27) where x = exp[(cs /m)ts ]. Only the positive root of the quadratic equation yields a real solution √ 1+ 1+ε (c s /2m )t s (28) = e εco /(cs − c0 ) Isolating the settling time ts gives √ 2m 1 + 1 + ε ts = ln |cs − co | . cs εco (29) Equation (29) gives a conservative estimate that typically falls within 0.5% of the exact solution derived numerically from (13). Therefore, this formula provides a convenient means of estimating the minimum interval between perturbations in digital maximum power tracking control systems. It also shows the dependence on harvester parameters and tolerances. 206 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 Fig. 8. System-level block diagram showing the main power electronics blocks and the power definitions within the main power flow of the system. III. POWER CONVERTER AND ANCILLARY CIRCUITRY The power conditioning system architecture is shown in Fig. 8. It builds on the low-power system reported by Szarka et al. [6], with the addition of low-power measurement and control circuits for the MPTT control, and a modified low-power gate drive circuit design. The output voltage across the supercapacitor varies, thereby allowing the stored energy to be maximized; at the same time it is kept within the allowable dc supply voltage range of the load electronics, which avoids the losses of additional voltage regulation. Zero-energy start-up is provided by a passive voltage multiplier circuit that is automatically disconnected when the active power converter circuit becomes operational. The main power converter is a nonsynchronous full-wave boost rectifier, as shown in Fig. 9, which provides rectification and voltage boosting in a single stage. The parasitic coil impedance, although considered to be negligible at the mechanical resonance frequency, is significant at the switching frequency of the power converter and can be used to eliminate the need for an additional boost inductor. The MPTT control circuit adjusts the duty ratio δ of the PWM gate drive signals. This controls the apparent input impedance of the converter, preserving maximum output power Pstore. Consequently, near-optimum damping conditions for the energy harvester are maintained independently of variations in the output voltage, the conduction mode, and the excitation magnitude; all of which are time-varying factors that influence the apparent input impedance of the power converter. The particular converter topology selected here does not support bidirectional power flow, thus restricting the control to resistive impedance matching only. This approach may be suboptimal when the generator is excited off resonance; however, it offers Fig. 9. Circuit schematic of a nonsynchronous, full-wave boost rectifier that uses the parasitic coil inductance as the boost inductor. The semiconductor devices used are M1/M2—PMF-280UN and D1/D2— 1PS79SB30. high utilization when the source excitation is at the mechanical resonance frequency [3]. An example of typical input current and voltage waveforms are shown in Fig. 10. The gate drive circuit generates two-variable duty ratio PWM signals for the two low-side transistors. The switching frequency is constant 32.768 kHz, determined by the output of the lowpower oscillator chip (OV-7604), as shown in Fig. 11. Polarity of the input voltage is sensed by a thin-film piezoelectric sensor bonded to the cantilever beam. A saw-tooth signal is created using a one-shot circuit and a modified RC filter that provides a slow discharge of the 15 pF capacitor. The duty ratio is determined by the “Reference” input, which is the common interface to the control circuits. The logic output stage, which directly drives the gates of the MOSFETS, receives polarity information from the detection circuit. At any moment in time, only one of the outputs is toggled at the switching frequency, while the other PWM signal is kept high. The only exception to this is during a blanking period around the zero-crossing of the generator’s output voltage, when both outputs are low. SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS 207 Fig. 10. Measured typical input current Iin and voltage V in waveforms. A period of 100 μs at 5 ms point is shown on the right for increased resolution. The duty ratio of the converter is 67% and the output voltage is 3.2 V. The energy harvester is excited with 43.8 Hz, 3 m·s−2 acceleration, producing a little over 450 μW. The printed circuit board implementation of the power conditioning system is shown in Fig. 12, corresponding to the block diagram presented in Fig. 12. IV. CURRENT-SHUNT-BASED MAXIMUM POWER TRANSFER TRACKING A. Operating Principles and Measurement A typical low-power energy harvesting system requires large capacity storage in order to be able to supply the high peak-tomean ratio power demand required by load electronics such as wireless sensor nodes. The combination of low output power and large storage capacitance results in slow charge up of the supercapacitor. This enables the MPTT control to rely solely on output current measurement. The reference signal that sets the duty ratio of the boost rectifier is perturbed, and the effect of this on the power transferred to the supercapacitor is observed by measuring the output current while the output voltage is assumed to be near constant. This implementation requires the rate of change of the output voltage to remain low enough to ensure a near-constant voltage between successive measurements. In the presented system, this limits the minimum capacitor size to 20 mF, when the worst-case voltage increase between measurements is 5 mV. The measurement circuit is an operational amplifier based circuit (see Fig. 13) that is designed to measure the voltage drop across a 150 Ω precision shunt resistor. The current ripple, both at the switching and at the excitation frequency, must be minimized to ensure correct measurement. This is achieved by a combination of parallel capacitance introduced before the shunt resistor in the circuit, and an active low-pass Sallen–Key [18] architecture employed in the design of the amplifier circuit. The 30 μF capacitor smoothes the switching frequency current ripple without adding any significant delay to the response of the system to the perturbation. Fig. 11. Gate drive circuit generating 32.768 kHz output PWM signals. “Pos,” “Neg,” and “Blank” are digital signals from the polarity detection circuit [6]. “Reference” is an analogue signal from the control circuit to set the duty ratio. Fig. 12. Printed circuit board implementation of the main power conditioning system blocks, corresponding to Fig. 12. The second-order Butterworth filter has a cutoff frequency of 20 Hz, approximately half the excitation frequency, in order to provide a close to dc current measurement at the output of the amplifier. The micropower operational amplifier MCP6031 is selected because of its low input offset voltage that is typically 208 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 Fig. 13. Shunt-resistor-based current-sense amplifier using a low-pass Sallen– Key architecture [18]. Fig. 15. Steady-state characterization of power conditioning system in openloop configuration. Voltage reference is stepped using an external signal at >5 s intervals. Excitation is held at 3.75 m·s−2 and 43.8 Hz. Output voltage is regulated using a shunt regulator circuit as a load (LM4041). Fig. 14. Digital MPTT circuit using a low-power MSP430 microcontroller that samples the output current using a 10-b ADC and controls the reference voltage of the duty ratio by an 8-bit 0–450 mV output R–2R ladder. The sample readings are synchronized to the generator’s displacement cycle using the output of the piezoelectric displacement sensor. The reference voltage is therefore changed in discrete steps of 1.75 mV, corresponding to a 0.6% change in the duty ratio. The worst-case minimum time required between perturbations, using (29), is approximately 350 ms, roughly 15 displacement cycles. The output of a level-crossing detection circuit that monitors the piezoelectric sensor output is used as a nonmaskable interrupt (NMI) that wakes the microcontroller up from “sleep mode.” This approach not only circumvents the need for a power hungry timer circuit but also ensures that the sample readings are synchronized to the displacement, which was shown to improve the control circuit’s stability [10]. Under this configuration, the microcontroller is active for a total of 90 μs, plus an additional 25 μs when only the internal ADC is ON, in every 342.5 ms period. This results in an average power consumption of approximately 750 nW. V. EXPERIMENTAL RESULTS around 150 μV [19], its low current consumption, and rail-torail input/output signal support. The gain of 30 V/V is selected, in order to maintain a sufficient signal-to-noise ratio. B. Digital Implementation of MPTT The well-known perturb-and-observe algorithm is implemented on a MSP430F1132 microcontroller: the PWM duty ratio of the boost converter is altered and the consequent change in the output power is measured when the mechanical structure has settled. Based on the measured outcome, the direction of the subsequent alteration is determined and the process repeated. The controller’s CPU is clocked at 5 MHz frequency in order to minimize the power hungry on-time. The 10-b onboard analogue-to-digital converter (ADC) converts the current amplifier’s output, and the reference voltage for the duty ratio is set by an R–2R ladder, shown in Fig. 14. The top two bits of the ladder are connected to ground, while the remaining eight bits are controlled via a full output port of the controller. This provides a 1.75 mV resolution with a maximum output of 450 mV. A. Steady-State Performance In order to evaluate the effectiveness of the MPTT circuitry, the power Pstore as a function of the duty ratio is measured. This is the useful output power after subtracting losses incurred due to nonideal loading of the generator, during the power conversion process, and the quiescent power overheads of the ancillary and control circuits. In this test, the output voltage is kept constant using a micropower shunt regulator (LM4041) and the reference voltage is stepped using an external source in 5 s intervals to create quasi-steady-state measurements. During all of the tests presented in this section, a 68 mF supercapacitor is used as the main energy storage element. The combined current consumption of the ancillary circuits and the leakage current drawn by the start-up circuits is 19 μA at 2 V output voltage and increases to 22 μA at 4.5 V output. The digital control circuit adds an additional 3 μA, amounting to a total of 44 μW of minimum quiescent power loss. Fig. 15 presents the results measured at 3.75 m·s−2 excitation magnitude, corresponding to a maximum extractable power of SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS Fig. 16. Measured duty ratio samples and their modal values compared with the range of duty ratios (shaded region) that correspond to over 99% of the maximum useful output power based on the measurements of Fig. 15. 870 μW under optimum load conditions. The maximum transferred power is 615 μW at 2 V at the optimum duty ratio. This corresponds to a power conversion efficiency of 78.5%, and an overall system efficiency of 70.7%, where 100% is the maximum extractable power from the energy harvester. As the output voltage is increased, the optimum duty ratio is also increased. The maximum useful power is, however, reduced due to the increased power overheads of the power conditioning circuits. It is worth noting that a small dip in the power level can be observed in the 4.5 V line around 80% duty ratio, creating two local maxima that could result in the failure of a perturb-andobserve MPTT algorithm. During normal operation however, this situation would not arise, as the output voltage rises slowly across the large capacity storage element, allowing the algorithm to track the correct peak. Starting the tracking at high duty ratios would also reduce the risk of finding the wrong local maximum. Fig. 16 shows duty ratio at discrete output voltages, held constant by the adjustable shunt regulator circuit. As the duty ratio is constantly changing, even in these steady-state conditions, 100 recordings of the duty ratio are plotted, as dots, for each voltage, showing a range of around ±2.5%. The solid black line is fitted over the statistical modal value of each group of 100 samples, representing the most frequent duty ratio. The shaded region in Fig. 16 represents the duty ratio range over which in excess of 99% of the maximum transferred power is obtained. This region widens toward the low output voltage levels, as can also be seen in Fig. 15. The modes of the duty ratio measurements fall within the 99% power region for most of the output voltage points, which shows that the control circuit can effectively track the optimum power point. During the measurements of the duty ratio samples, the energy harvester’s generated power, the transferred power, and the quiescent power overhead of the power conditioning system were also recorded. The 100 measurement points were averaged, to take into account that the duty ratio ranges around an optimum value. These values are plotted in Fig. 17 against output volt- 209 Fig. 17. Average power obtained from 100 measurements per output voltage. Output voltage is regulated by an adjustable shunt regulator. Constant frame acceleration of 3.75 m·s−2 at 43.8 Hz. P m a x is the maximum extractable harvester power under optimum load conditions. age, along with the maximum extractable power from the energy harvester under optimum load conditions for comparison. The difference between the measured generated power and the transferred power are due to a combination of three major loss mechanisms: 1) a nonideal power conversion process; 2) quiescent power overheads of the control and ancillary circuits; and 3) the conduction loss in the shunt resistor used for the monitoring of the output current. The ratio between the generated power of the nonideally loaded harvester and the maximum potentially extractable power under optimum load conditions is referred to as the utilization factor. The utilization of the energy harvester peaks above 89% at 1.8 V output, and remains over 86% over the entire output voltage range. Less than 100% utilization is primarily due to the increased conduction losses within the coil that result from switching frequency current ripple. The power conversion efficiency is calculated as the ratio of the useful output power (Pstore ) of the converter to the generated power of the harvester, while the overall system effectiveness is defined as the useful output power normalized to the maximum extractable power from the energy harvester under optimum load conditions. The conversion efficiency is at its maximum of 76.5% at low voltage levels where the quiescent power overhead is at its minimum, dropping down to 66% at 4.5 V. The peak overall effectiveness reaches almost 70%, which when compared against the maximum of 70.7% recorded under the steady-state characterization (see Fig. 15) shows a highly effective control. B. Transient Response to Step Change in Excitation and Output Voltage The dynamic performance and stability is evaluated by recording the transient behavior of the power conditioning circuit, monitored by the duty ratio of the converter, in response to a step change in the frame excitation magnitude and in the output voltage under the worst-case considerations. 210 Fig. 18. Output current and duty ratio in response to a step change in excitation magnitude from 3 to 4 m·s−2 at a constant 2.5 V output. The frequency is constant at 43.8 Hz. The current is inferred from the output of the current-sense amplifier circuit. First, a step change in the acceleration magnitude from 3 to 4 m·s−2 is considered (see Fig. 18) potentially providing twice the generated power. The output voltage is maintained at a constant 2.5 V for the test. The increase in excitation amplitude results in increased generated power and voltage, which, in turn, affects the emulated resistance of the power converter. The control adjusts the duty ratio of the rectifier, and is seen to reestablish optimum damping conditions within around 4.5 s. At the instant of the step change in the frame acceleration magnitude (just before the 2 s mark), the available generated power and thus the useful output power increases at a rate that is dominated by the mechanical response of the energy harvester, i.e., the time required by the tip mass to build up its momentum. The duty ratio of the power converter, as a means of monitoring the control trajectory of the algorithm, is also presented in Fig. 18. The results show the clearly distinguishable duty ratio steps that characterize the digital implementation of the perturb-and-observe algorithm, and the tracking around a new “optimum” point. A worst-case step change in the load conditions is also considered in this study: a rapid discharge of the energy storage element from its maximum rated output voltage of 4.5 to 2 V, as shown in Fig. 19. This situation mimics the burst release of energy from the storage that may occur as a result of the execution of a power hungry task by the load electronics. Small dynamic variations in the power consumption of the load do not affect the output power performance of the power conditioning circuit as the 68 mF supercapacitor provides a buffer between the load and the power converter that smoothes these changes. The output current waveform is also presented in Fig. 19. During the discharge of the output capacitor, the output of the current-sense amplifier is saturated, and then the current starts to increase as a result of the changing duty ratio of the power converter. The duty ratio drops from around 84% to below 70% and converges to a new optimum condition in approximately 8.5 s after the start of the discharge. IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 Fig. 19. Rapid discharge of the 68 mF supercapacitor from its maximum rated voltage of 4.5 to 2 V via an adjustable shunt regulator (LM4041), thus mimicking a burst release of the stored energy for the load application. Fig. 20. Charging of a 68-mF supercapacitor over 500 s, showing zero-energy start-up and active MPTT. The overall system efficiency is normalized to the maximum extractable power of 870 μW. Measurements were taken at constant frame acceleration of 3.75 m·s−2 at 43.8 Hz. This reaction time represents the worst-case scenario as it corresponds to the largest optimum duty ratio difference that can occur under normal operation conditions and is a function of the maximum rate of change of the duty ratio of the control circuit and, thus, of the calculated settling time. An energy harvesting system with smaller tip mass, for example, would have a smaller settling time and the control could be set to react more quickly to rapid changes in the environmental conditions or in the power drawn by the load electronics. C. Overall System The last test is aimed to present the capability of the power conditioning system to start-up from zero-energy conditions and then track the maximum power transfer point actively while charging a 68 mF supercapacitor. At a constant excitation of 3.75 m·s−2 , the charging of the supercapacitor is recorded over 500 s (see Fig. 20) along with SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS 211 TABLE I KEY SYSTEM METRICS Fig. 21. Comparison of charge up times of a 68 mF supercapacitor using: 1) passive voltage quadrupler circuit; 2) full-wave boost rectifier in an open-loop with constant duty ratio of δ = 0.67; and 3) full-wave boost rectifier with MPTT control. Excitation is regulated to be 3.75 m·s−2 at 43.8 Hz. the duty ratio (inferred from the reference voltage of the control circuit). The measured output voltage and useful output current of the power converter are used to calculate the transferred power. The ratio of this to the maximum extractable power under optimum load conditions provides the overall system efficiency ηover (see Fig. 20). The passive quadrupler circuit provides zero-energy startup, charging the supercapacitor to 1.85 V at which point the active boost rectifier circuit starts to operate. The duty ratio, starting from a high initial value, quickly finds and tracks the optimum power transfer point over the charging of the capacitor. The overall efficiency is highest at low output voltages with an average value of close to 70%, as presented in Section V-A. The recorded instantaneous efficiency may exceed this due to the inertial effects of the mechanical structure resulting in short burst of power when the damping is increased. Fig. 21 presents the transient accumulation of energy in the 68 mF supercapacitor when charged by differing power conditioning solutions: 1) passive voltage quadrupler; 2) the full-wave nonsynchronous boost rectifier in open loop with a constant duty ratio of δ = 0.67; and 3) full-wave boost rectifier with MPTT control. The start-up phase is common for all approaches, provided by the passive voltage multiplier circuit, during which the capacitor is charged from 0 to 1.85 V. The results illustrate that the overall output power gain of the system when MPTT control is employed: The total charge-up time, corresponding to 0.5 J of energy stored, is reduced by 26.5% and by 8.6% as compared to the passive circuit and the open-loop systems, respectively. A summary of the key system metrics is presented in Table I. VI. CONCLUSION The work presented in this paper aimed to address the challenges that arise from implementing MPTT for low-power, kinetic electromagnetic energy harvesters. The transient response of the single-degree-of-freedom mechanical system is presented and discussed using experimental results and analytical derivations. A method that aids the design of perturb-and-observe algorithm-based control with discrete perturbations of the control parameter is presented: the minimum time required between perturbations in order to allow the mechanical structure to settle is calculated for highly underdamped mass–spring–damper systems under the assumption of a constant, sinusoidal, nondirect excitation that occurs at the natural resonance frequency of the mechanical structure. A complete power conditioning circuit for a low voltage, submilliwatt electromagnetic energy harvester has been presented that requires no external power and is capable of self-starting from zero-energy conditions. In contrast with previous work, the transferred power is maximized instead of the generated power, thus accounting for the losses suffered during the power conversion process and the due to the quiescent power overheads. Good peak power tracking effectiveness is demonstrated despite of the lack of accurate regulation of the apparent input impedance of the boost rectifier, thus allowing the use of a slow feedback control, and consequently, a reduced quiescent power implementation. The total power consumption of the power conditioning system is 44 μW at 2 V output. Steady-state and transient measurements show that the system is stable and capable of tracking the maximum power transfer point by optimizing the duty ratio of the PWM signals of the boost converter over the entire output voltage range. A harvester utilization of up to 89% is achieved. Overall system effectiveness up to 70% is recorded, corresponding to approximately 600 μW of useful output power. 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