Passive multi-source energy harvesting schemes

Abstract

Mobile electronics have continually decreased in size; however, mobile power sources have not had comparable increases in energy density or specific energy. Researchers are considering energy harvesting technologies to reduce dependence on batteries, providing alternate sources of power. Combining multiple energy harvesters onto a single platform is a logical and practical method to increase energy output and system robustness. This study explored the dynamics of two passive, multi-source energy harvesting schemes: disparate sources of piezoelectric and photovoltaic, as well as an array of piezoelectrics. A series and a parallel topology were explored for each scheme. For both the schemes, the series topology lends itself to high-level, low-duty cycle load characteristics as it is able to achieve greater amounts of energy on a storage capacitor. The parallel topology lends itself to low-level, high-duty cycle load characteristics due to increased maximum power levels. Both the parallel and the series topologies of the array of piezoelectrics effectively combine the power from the two harvesters in the absence of differences between the two signals. The series topology is insensitive to amplitude differences, and the parallel topology is insensitive to a phase angle or a frequency difference.

Keywords

Energy harvesting multi-source photovoltaic piezoelectric

Introduction

As electronic systems decrease in size and become more mobile, power source endurance becomes increasingly important. As a power source’s energy capacity is proportional to its mass and volume, there is a trade-off between endurance and size. One approach to this issue is to recharge the batteries without plugging into an existing power grid. This involves storing energy gathered from the environment using transducers, also known as energy harvesting. There are many desirable applications of energy harvesting, such as wireless sensor networks (Morais et al., 2008; Park and Chou, 2006; Park et al., 2007), wildlife tracking (MacCurdy et al., 2008), and personal electronics like cell phones. A significant number of studies have explored the geometric optimization of energy harvesting devices (Dietl and Garcia, 2010). As a result, research has shifted to using complex feedback control circuitry, among other topics.

Many of the schemes focus on power maximization from the harvester (Chao et al., 2007; Guyomar et al., 2005, 2007; Kong et al., 2010; Lallert and Guyomar, 2008; Lefeuvre et al., 2005a, 2005b, 2007; Shu et al., 2007; Wickenheiser and Garcia, 2010; Wu et al., 2009). While the schemes produce significant increases in the maximum instantaneous power produced, they all draw from the stored energy to control the additional circuitry. Guan and Liao (2007) investigate the harvesting efficiency of the impedance adaptation method (Ottman et al., 2002) as compared to a passive harvesting circuit with only a full-bridge rectifier. The results show that the passive method is more efficient at harvesting and storing energy due to the power losses in the components needed for the impedance adaptation method. Also, most of the methods make use of inductors to minimize the power losses resulting from the associated switching. As the inductor voltage decreases, the efficiency of the inductor decreases and the size increases. Therefore, with low-voltage harvesters, these methods result in unfavorable trade-offs between performance and mass (Chapman, 2009). Others focus on the overall power management of the system as well (Kansal et al., 2007; Moser et al., 2007). Regardless of the method, more applications and opportunities for energy harvesting can be realized by increasing the power output of the harvesting system.

Another method for increasing the robustness and versatility of energy harvesting systems is to utilize multiple harvesters simultaneously (Lhermet et al., 2008; MacCurdy et al., 2008; Morais et al., 2008; Park and Chou, 2006; Wickenheiser and Garcia, 2009). The idea of combining multiple systems for stand-alone power generation onto one energy storage unit first appeared with large-scale power generation systems (Borowy and Salameh, 1994; Deshmukh and Deshmukh, 2008; Dufo-Lpez and Bernal-Agustn, 2005; Markvart, 1996; Valenciaga and Puleston, 2005; Wichert, 1997). While these studies focused on stand-alone power generation systems for residential applications, energy harvesting applications present different challenges in terms of power levels, size, and mass. The lower power levels available emphasize the need for a very efficient power management system. Figure 1 illustrates the flow of power in a multi-source system from the different harvesters, through the conditioning circuitry into the energy storage medium, and then to the load. The energy harvesters shown represent the most commonly used methods: piezoelectric and photovoltaic. Any power lost to the control of additional circuitry for the transfer of power is represented.

Initial prototypes of adaptive, multi-source energy harvesting systems exist in the literature (Morais et al., 2008; Park and Chou, 2006). They use active control systems to isolate the harvesters and combine the energy onto a single power source for wireless sensor nodes. Park and Chou (2006) combine solar and wind energies onto a lithium-polymer battery using a supercapacitor array charged through direct current DC–DC boost regulators by the harvesters. The DC–DC boost regulators are part of a closed-loop maximum power point tracking (MPPT) technique to transfer power to the capacitors. This system uses only analog components for the control and consumes less than 1.65 mW. Morais et al. (2008) charge a nickel–metal hydride battery with a solar cell, a wind generator, and a hydroelectric turbine. The energy on separate buffer capacitors is transferred to the battery using DC–DC boost converters as switches, which are controlled using a microcontroller.

This study explores passive multi-source energy harvesting schemes for combining power from multiple harvesters onto a single storage capacitor. These schemes do not suffer from additional power losses or complexity from active switching power management systems and can be used as a baseline for comparison with more complex methods. Also, due to the passive nature of the schemes, they do not need to be designed or adjusted to the excitation frequency. This attribute makes them a practical comparison for baseline purposes and an option for stochastic or widely varying excitation frequencies. Two cases are explored: one using a piezoelectric and a photovoltaic harvester and the other using an array of piezoelectric harvesters. Both series and parallel topologies are considered. Circuit simulations (LTspice IV, Linear Technology) provide a fast and repeatable method for characterizing the dynamics of these circuit topologies while using accepted piezoelectric and photovoltaic circuit models. The results and techniques presented should not be thought limited to the aeroelastic energy harvesters or the solar cells reported, but the circuits applicable to any multi-source energy harvesting system using either a piezoelectric and a solar harvester or an array of piezoelectric harvesters.

Multi-source scheme analysis

This section explains the methods used to analyze the results of the simulations. The maximum instantaneous power flow is used to evaluate the capabilities of the harvester when it is operating at its peak performance levels. Power here refers to the instantaneous power of the storage capacitor, $P_{CL}$ , (equation (1)). Also, unless otherwise noted, the voltage, power, energy, and charge time variables all refer to the storage capacitor, $C_{L}$ , for each topology. Since the piezoelectric harvester’s signal is alternating current (AC), much of the data oscillate at the rectified piezoelectric frequency of $2 \times f_{P} = 10 Hz$ . Connecting the maximums or minimums of each oscillation cycle creates smoothed data sets, which represent the upper or lower envelopes of the data, respectively. Viewing the data in this manner allowed for a clearer interpretation of the behavior of the system by eliminating the 10 Hz oscillation from the plots. Figure 2 shows the upper envelope of an example set of data.

P_{C L} (t) = V_{C L} (t) I_{C L} (t) = (C_{L} {\dot{V}}_{C L} (t)) V_{C L} (t)

(1)

Average power, $P_{avg}$ (equation (2)), calculations examined the effectiveness of the topology at storing the harvested energy over the entire charge cycle. The charging time, $t_{f}$ , is defined as the time it took for the capacitor voltage to be within 2% of its final value for the multi-source topology being analyzed. The initial time, $t_{o}$ , represents the start of the charging cycle or zero in this case. Examining the average power avoids dealing with the dependence of the energy level and charge time metrics on the storage capacitance during the analysis

P_{avg} = \frac{1}{t_{f} - t_{o}} \int_{t_{o}}^{t_{f}} P_{CL} (t) dt

(2)

Piezoelectric circuit model

The Thévenin equivalent circuit model shown in Figure 3(b) exhibits the same impedance behavior as lead zirconate titanate (PZT) (Park, 2001). It represents the piezoelectric cantilever harvester shown in Figure 3(a) for systems with low electromechanical coupling. This model is built on many assumptions, such as that the beam is always excited at resonance and that the excitation amplitude is constant. Wickenheiser et al. (2010) experimentally proved that the assumption of constant excitation amplitude is valid for piezoelectric energy harvesters with low electromechanical coupling. Harvesters with low electromechanical coupling are preferable for the low-amplitude vibration sources commonly seen in desired energy harvesting applications. The simulations reported herein use the ideal Thévenin equivalent circuit with $Z_{C} = C_{P}$ .

The aforementioned aeroelastic flutter wind energy harvester served as the baseline for the piezoelectric circuit model. A pair of MIDE Quickpack QP10n (Midé Corp.) piezoelectric patches is adhered to the base of the beam in a bimorph configuration (Bryant and Garcia, 2011). Unless otherwise stated, the simulation parameters are $A_{P} = 30 V$ , $f_{P} = 5 Hz$ , and $C_{P} = 110 nF$ to match the experimentally obtained 2 mW maximum power output of the aeroelastic flutter wind energy harvesters across a 263 kΩ load. Here, $A_{P}$ represents the amplitude of the AC piezoelectric voltage signal and $f_{P}$ the oscillation frequency. This wind energy harvester was chosen due to its high voltage level, an oscillation frequency in the range of many environmental vibration sources, and its low electromechanical coupling. Figure 4 shows the typical piezoelectric energy harvesting circuit used with a storage capacitor and a full-bridge rectifier. For the simulations, the LTspice IV model for the On Semiconductor MBR0520L Schottky diodes (Fairchild Semiconductor) was used to reduce the effects of diode voltage drops. The model for the TDK C575OX5ROJI07M (TDK), 100-µF storage capacitor was chosen to sufficiently reduce the ripple in the rectified signal.

Photovoltaic circuit model

The photovoltaic circuit model assumes an ideal cell, with ideal I–V characteristics (Figure 5) (Sze, 1981). It is composed of a constant current source, $I_{L}$ , in parallel with a diode, $D_{PV}$ . Here, $I_{L}$ represents the photogenerated current and $D_{PV}$ the pn junction of the cell. The current output of the photovoltaic cell is defined by equation (3), where $I_{S}$ is the diode saturation current, $q$ is the charge of an electron, $T$ is the diode temperature, and $k$ is Boltzmann constant.

I = I_{L} - I_{S} (e^{\frac{qV}{kT}} - 1)

(3)

To create the model for the diode, the emission coefficient, $n$ , is inserted into the junction current equation as per the Shockley ideal diode equation (equation (4)). Here, $I_{D, PV}$ is the pn junction diode current. Rearranging to solve for the emission coefficient, as shown in equation (5), the diode model for the junction is defined by the saturation current and the emission coefficient. A constant solar radiation is assumed for the simulations reported herein. Therefore, the maximum specifications for current and voltage for the photovoltaic replaced the diode current and voltage ( $I_{D, PV} = I_{PV, \max}$ and $V_{D, PV} = V_{PV, \max}$ ) as given in equation (6) (Sennewald, 2011).

I_{D, PV} = I_{S} (e^{\frac{q V_{D, PV}}{nkT}} - 1)

(4)

\ln (\frac{I_{D, PV}}{I_{S}} + 1) = \frac{q V_{D, PV}}{nkT} \Rightarrow n = \frac{q V_{D, PV}}{\ln (\frac{I_{D, PV}}{I_{S}} + 1) kT}

(5)

n \approx \frac{q V_{PV, \max}}{\ln (\frac{I_{PV, \max}}{I_{S}}) kT}, for I_{PV, \max} >> I_{S}

(6)

For the photovoltaic harvesters, a thin film panel from Silicon Solar, Inc., served as the baseline for the photovoltaic model: $V_{PV, \max} = 6 V$ and $I_{PV, \max} = 50 mA$ . To produce theoretical maximum power outputs other than 300 mW, $I_{PV, \max}$ varies while $V_{PV, \max}$ stays constant. A 10 pA saturation current and room temperature ( $T = 300 K$ ) are assumed. To protect the photovoltaic, two diodes separate it from the storage capacitor, as shown in Figure 6. The first diode, $D$ , an ON Semiconductor 1N5819 Schottky diode model, prevents current from flowing from the storage capacitor into the photovoltaic. The second diode, $D_{Z}$ , an ON Semiconductor BZX84C6V2L Zener diode model, limits the voltage over the solar cell to below the maximum 6 V specified by the manufacturers. Since the simulations use an ideal photovoltaic model, there is no impedance for the harvester and the maximum power level does not vary with the load capacitance.

Multi-source: solar and piezo

For this section, the addition of a subscript $P$ denotes the piezoelectric harvester only, $S$ the solar harvester only, $SPS$ the solar and piezoelectric harvesters in the series topology, and $SPP$ the solar and piezoelectric harvesters in the parallel topology. Solar harvesters possess a much higher energy density than piezoelectrics and are commonly the first method considered; therefore, the results in this section are presented as changes with regard to a solar harvester. Also, $r$ (equation (7)) gives the ratio of the solar harvester’s power output to the piezoelectric’s power output. When $r$ varies, the solar harvester’s power output also varies and the piezoelectric’s power output remains constant

r = \frac{P_{S, \max}}{P_{P, \max}}

(7)

Solar and piezo — series SPS topology

The rectified piezoelectric harvester is placed in series with the solar harvester (Figure 7). The Zener diode, $D_{Z}$ , prevents the voltage seen by the solar cell from exceeding its maximum allowable level of 6 V. These components are then placed in series with an ideal storage capacitor, $C_{L}$ .

A significant advantage of the $SPS$ topology is a higher available voltage. This is desirable for multiple reasons. First, the electronic components energy harvesting systems typically power have a minimum voltage necessary to operate, normally around 2.2–3.6 V. As solar cells are low-voltage harvesters, the addition of a piezoelectric harvester can help meet these voltage requirements. Second, the higher the voltage, the more energy stored in the capacitor for use by the electronic components (equation (8)).

E_{CL} (t) = \frac{1}{2} C_{L} V_{CL} (t)^{2}

(8)

Solar and piezo — parallel SPP topology

The rectified piezoelectric harvester is placed in parallel with the solar harvester (Figure 8). The Zener diode, $D_{Z}$ , prevents the solar cell from seeing too high of a voltage just as in the $SPS$ topology. The diode, $D$ , prevents any backward current from flowing through the solar cell as it is no longer in the same current loop as the full-bridge rectifier. These components are placed in parallel with an ideal storage capacitor, $C_{L}$ .

An advantage of the $SPP$ topology is that the currents from the two systems are summed, not the voltage. For high-voltage harvesters, this topology would not result in voltage levels which would be more difficult to regulate to the range of 2.2–3.6 V.

Solar and piezo — $r ≊ 1$

One of the significant advantages of the $SPS$ topology is that it allows for higher storage capacitor voltages and therefore higher amounts of stored energy. Figure 9 shows the storage capacitor energy curves during the charging cycles for both of the multi-source topologies and the separate piezo and solar harvesters. Due to the summation of the piezoelectric and solar voltage levels, the $SPS$ topology’s stored energy curve settles to a significantly higher value. The amount of energy stored due to the solar cell, shown in Figure 9(b), is actually quite small in comparison to the other topologies. However, a caveat of the higher available voltages and stored energy is the amount of time it takes to charge up to the higher levels.

Examining the results shown in Figure 9 as well as in Table 1, the $SPS$ topology stores approximately 37 times more energy than the solar cell, $S$ . However, it takes approximately 90 times longer to store that energy. This relationship is represented much more cleanly by examining the average power of the energy charging cycles for the different topologies. Table 1 shows that the solar harvester has an average power of 0.89 mW, while the $SPS$ topology is only at 0.36 mW. The $SPP$ topology’s average power is lower, equal to that of the piezoelectric harvester, $P$ , at 0.25 mW. The average power for the $P$ topology is lower than that of the $S$ topology even though $P_{P,; m a x} ≊ P_{S, m a x}$ because the oscillations of the rectified piezoelectric’s AC signal prevent the steady flow of current into the capacitor that occurs with the solar harvester.

Table 1.

Charging statistics for energy harvesting circuits.

	$S$	$P$	$SPS$	$SPP$
Final voltage, $V_{f}$ (V)	5.8	29	35	29
Final stored energy, $E_{f}$ (mJ)	1.7	43	61	42
Charge time, $t_{f}$ (s)	1.9	178	171	167
Average power, $P_{avg}$ (mW)	0.89	0.24	0.36	0.25
Maximum power, $P_{\max}$ (mW)	1.5	2.0	2.5	2.0

The addition of the piezoelectric to the solar harvester in either the $SPS$ or $SPP$ topology negatively affects the average power of the systems while providing higher voltages and stored energy. The capacitor power versus voltage curves (Figure 10) illustrate the cause of the significant effect of adding the piezoelectric. Recall that $V_{PV, \max} = 6 V$ . After this voltage, the solar cell is no longer able to contribute, and all of the photogenerated current, $I_{L}$ , dissipates over the pn junction of the cell, $D_{PV}$ . Figure 10(a) shows that just before the maximum solar voltage level, the multi-source topologies switch from closely following the charging curve of the solar harvester to following the charging curve of the piezoelectric harvester. This can be described as the charging curve being separated into a “solar-dominant” and a “piezo-dominant” region for $SPS$ and $SPP$ topologies. Note that the upper envelope is used to represent the power of the $SPP$ and $SPS$ topologies for $V_{CL} > 6 V$ . The upper envelope is used for the entire range of voltages for the $P$ topology. Therefore, for the multi-source topologies, the high average power solar cell is only contributing power for a small fraction (1%) of the entire charging time. The rest of the charging is dominated by the low-average power piezoelectric harvester.

Figure 10 also illustrates a significant difference between the $SPS$ and $SPP$ topology power behavior while $V_{CL} < 6 V$ . The $SPP$ topology curve shows visible oscillations at the rectified piezoelectric frequency constructively added onto the $S$ topology curve. Therefore, during the “solar-dominant” section of the charging curve for the $SPP$ topology, both the solar cell and the piezoelectric are contributing comparable amounts of power, resulting in a power increase over just the $S$ topology itself. The same behavior is not seen during the “solar-dominant” section of the $SPS$ charging curve.

The advantages of the $SPP$ topology can be seen by examining the results of the schemes when only the period where the photovoltaic can contribute is considered (Table 2). These results would occur if the storage capacitor is discharged by the load such that $V_{CL} < 6$ always. As the table shows, in this situation, the average power, maximum power, and charge time results are better for the $SPP$ topology than the $S$ topology.

Table 2.

Charging statistics for energy harvesting circuits for $V_{CL} < 6 V$ .

	$S$	$P$	$SPS$	$SPP$
Final voltage, $V_{f}$ (V)	5.9	5.9	5.9	5.9
Final stored energy, $E_{f}$ (mJ)	1.7	1.7	1.7	1.7
Charge time, $t_{f}$ (s)	1.9	10	2.4	1.8
Average power, $P_{avg}$ (mW)	0.89	0.17	0.72	0.96
Maximum power, $P_{\max}$ (mW)	1.5	0.61	1.3	2.0

From these results, it can be said that the choice between the multi-source topologies depends on the characteristics of the load. For a high-power, low-duty cycle load, the $SPS$ topology would prove effective due to its ability to store significant amounts of energy at once. An example would be wireless sensor node communication. The data transmission power requirements for the integrated radio frequency (RF) transmitter in the MSP-CC430 (Texas Instruments, Inc.) microcontroller are 37.5 mW for receiving and 24–43.5 mW for transmitting. For energy harvesting solutions with maximum power levels not in this range, energy storage solutions are necessary. The high-energy storage capabilities of the $SPS$ topology will allow the system to better provide the short bursts of power necessary. For a low-power, low-duty cycle load, the $SPP$ topology would prove effective due to its higher instantaneous power characteristics when $V_{CL} < 6 V$ . This will allow for the energy harvesting system to directly power the load, store energy, and significantly reduce the overall system mass by decreasing the size of the battery.

Solar and piezo — $r ≅ 1$

For multi-source energy harvesting systems, the power outputs of the two systems will not always be approximately equal to one another. As the solar cell will be subject to diurnal cycles as well as weather patterns, the output will vary significantly over the course of just a day. Figure 11 shows the maximum power of the multi-source topologies for the storage capacitor as the power ratio, $r$ , given by equation (7), varies. Specifically, the piezoelectric parameters stay constant to produce the 2 mW maximum power output and the solar parameters vary. As $r$ increases beyond one, the maximum power for the $SPP$ topology is consistently greater than that of the $SPS$ topology. This is a result of the additional piezoelectric power added on top of the $SPP$ topology during the “solar-dominant” section of the charging curve. This plot also shows that for $r > 1.75$ , the maximum power of both systems increases linearly with the solar cell. This means that there are no negative effects of having the solar cell at a significantly higher power output level that are not present for the case of $r ≊ 1$ .

Two other cases of interest are when one of the harvesters is not producing any power output. These instances can be equated to nighttime for the solar cell and periods of calm winds or no vibrations for the piezoelectric. As Figure 12(a) shows, when the solar cell is not producing any power, the charging curves for both of the multi-source topologies closely match that of the $P$ topology. Figure 12(b) shows that the same is true when the piezoelectric is not producing any power. These results show that the circuit architectures for the $SPS$ and $SPP$ successfully isolate the harvesters from one another, preventing power from dissipating over one or the other. This characteristic is a key for a multi-source topology as part of the advantage of this type of system stems from the ability of the two energy sources to complement one another.

Multi-source: array of piezoelectrics

In the case of an array of piezoelectrics, both harvesters use the same method of transduction. However, differences between the signals can arise due to small differences between the harvesters. As illustrated by the set of equations representing the AC signals of the two harvesters (equation (9)), a phase angle, $φ$ , a difference in frequency, $Δ f$ , and a difference in amplitude, $Δ A$ , can occur. The nature of the differences depends highly on the method of excitation. For fluid flow excitation, frequency and phase differences would be expected more often than for mechanical vibrations. However, for all cases, amplitude differences would be a major concern due to the difficulty in manufacturing multiple piezoelectric harvesters with the exact same natural frequency.

\begin{matrix} V_{P 1} = A_{P 1} \sin (f_{P 1} * t) \\ V_{P 2} = A_{P 2} \sin (f_{P 2} * t + φ) \end{matrix}

(9)

A standard piezoelectric harvesting system served as the control for comparison (Figure 4) to evaluate the performance of the multi-source circuit topologies. This control harvester was always at the baseline presented in section “Piezoelectric circuit model.”All of the component characteristics for the multi-source topologies are detailed in that section as well. Throughout the analysis, a subscript $PPS$ denotes the series and a $PPP$ the parallel multi-source harvesting topologies.

Array of piezoelectrics — series PPS topology

The two piezoelectric energy harvesters are placed in series after rectification for the passive series circuit topology (Figure 13). The potential advantages of this topology are the same as in the $SPS$ topology, namely higher storage capacitor voltages and energy levels through the summation of $A_{P 1} and A_{P 2}$ .

In the absence of differences between the two signals, the charge time and the final voltage are both twice that of the $P$ topology. However, since the final stored energy is four times that of the $P$ topology, the average power doubles. The maximum power is double that of the $P$ topology as well. Therefore, in the absence of differences between the two signals, the $PPS$ topology constructively combines the power from the two systems very effectively.

Array of piezoelectrics — parallel PPP topology

In the parallel topology, the piezoelectric harvesters are placed in parallel after rectification (Figure 14). This topology has the same potential advantages as the $SPP$ topology, namely constructive current interference.

In the absence of differences between the two signals, the final voltage and stored energy level are equal to that of the $P$ topology. However, the charge time is half that of the $P$ topology, resulting in double the average power. The maximum power is double that of the $P$ topology as well. As with the $PPS$ topology, in the absence of differences between the two signals, the $PPP$ topology constructively combines the power from the two systems very effectively.

Array of piezoelectrics — phase angle, $φ$

When a phase angle is introduced between the two harvesters in the multi-source topologies, the results of the simulations show that the storage capacitor charging is significantly affected. Figure 15 shows the effects of a varying phase angle on the capacitor final stored energy and average power. For the $PPS$ topology, the capacitor final voltage level, final stored energy, and average power all decrease as the phase angle increases. The $PPP$ topology remains unaffected. This can be explained by considering that for the individual piezoelectric harvesters to send current to the storage capacitor in the $PPS$ topology, its rectified voltage must be higher than the sum of the storage capacitor voltage and the rectified voltage from the other piezoelectric harvester. When the two harvesters are out of phase, the rectified voltage from one of the piezoelectrics reaches its peaks before the other, creating periods of time where one of the harvester’s voltage level is too low to conduct current. This does not occur in the $PPP$ topology because the two piezoelectrics and the storage capacitor must all be at the same voltage level at all times.

Figure 16 shows how the instantaneous storage capacitor power is affected for both of the topologies. For the $PPS$ topology (Figure 16(a)), the maximum power level decreases along a quartic curve with respect to the capacitor voltage level. For the $PPP$ topology (Figure 16(b)), it decreases linearly until about 80°, at which point it starts increasing again. This means that as the phase between the two signals varies, the capacitor voltage at which the harvester system’s peak performance occurs varies. It has been reported that a piezoelectric harvester charging a capacitor through a full-bridge rectifier experiences its maximum power levels, or peak performance, at half of the final charged voltage of the capacitor (Wu et al., 2009). Since the final charged voltage of the capacitor is changing in the $PPS$ topology, the capacitor voltage associated with the peak performance changes as well. For the $PPP$ topology, the variation in the peak performance capacitor voltage is caused by the variations in destructive and constructive interferences between the harvester rectified voltages mentioned earlier.

The performance of the passive multi-source topologies is significantly affected by a phase angle between the two harvester signals. The $PPP$ topology performs more reliably than the $PPS$ topology as only the maximum power level is affected with a phase angle. For the $PPS$ topology, the final stored energy and average power levels are affected as well. The choice between the two topologies depends on the nature of the excitation signals. With machine vibrations, the response will be relatively predictable and the choice much simpler. However, with a stochastic excitation such as wind energy, knowing whether the phase angle between the two signals varies with any consistency or is stochastic itself will dictate which topology will perform better in this regard.

Array of piezoelectrics — frequency difference, $Δ$ f

A frequency difference, $Δ f$ , between the two harvesters causes the phase angle between the two signals to vary at a rate directly related to the frequency difference. This interaction creates a ripple in the charging curve for the $PPS$ topology (Figure 17). As the frequency difference between the two harvesters increases, the charging curve converges to a lower level. However, for the $PPP$ topology, the charging curve remains constant for $Δ f \neq 0$ .

The reason for the ripple in only the $PPS$ topology can be explained by looking at the voltage and power curves of the storage capacitor simultaneously with respect to time (Figure 18). For a $Δ f = 0 Hz$ (Figure 18(a)), both the capacitor voltage and power are smooth; however, when a $Δ f = 0.001 Hz$ (Figure 18(b)) is introduced, significant changes occur in the power curve. The power curve changes from the normal smooth curve for piezoelectric energy harvesting to a series of pulses; power is no longer flowing in a consistent manner, causing the capacitor to charge in bursts. As mentioned in the previous section, when the signals are out of phase, they reach their peak voltages at different times and sum to a lower amplitude than if the phase angle was zero. With a frequency difference, the phase angle is constantly varying, and most of the time, the signals are not summing to their maximum amplitude. This causes significant periods where the harvester voltages are too low to charge the capacitor and results in the pulses of power shown in Figure 18(b).

The effect that a frequency difference has on the upper envelope of the instantaneous power curves is shown in Figure 19. While the voltage curve for the $PPP$ topology is not adversely affected by the $Δ f$ , the power is. It creates significant oscillations between constructive and destructive interferences, causing these erratic ripple patterns for both the $PPP$ (Figure 19(b)) and $PPS$ (Figure 19(a)) topologies. This behavior would complicate power management systems controlling the capacitor charging to maintain operations in the maximum power range, as the system could easily slip from a high-power region to a low-power region even if limited to a small capacitor voltage range. However, if any frequency difference is expected between the two harvesters, the $PPP$ topology is less affected.

Array of piezoelectrics — amplitude difference, $Δ$ A

Another possible difference between the two harvesters is the amplitude of the piezoelectric voltage, $Δ A$ . When varying $Δ A$ , the first expected result is that the final stored energy for the $PPS$ topology decreases linearly with an increasing $Δ A$ (Figure 20). As the voltage signal from one of the harvesters decreases in amplitude, the sum of the amplitudes decreases, causing a decrease in the final charged voltage of the capacitor. Also, the final stored energy for the $PPP$ topology should not change as the voltages of the two harvesters are not summed. However, it was mentioned earlier that the voltages of the rectified outputs from the two harvesters and the storage capacitor must be equal at all times as they are all in parallel. In this instance, when the voltage of one harvester exceeds that of the other, the lower voltage harvester stops contributing power when $V_{CL} > A_{P}$ , and the difference between the two is taken up as blocking voltages by the full-bridge rectifier. The full-bridge rectifiers successfully isolate the harvesters from one another in the $PPP$ topology and allow the storage capacitor to charge to the voltage of the higher piezoelectric harvester.

The lower voltage harvester no longer contributing when $V_{CL} > A_{P}$ significantly affects the average power of the $PPP$ topology. Figure 21 shows the average power for both topologies as $Δ A$ increases. While the $PPS$ topology shows a linear decrease in the average power corresponding with the decrease in the final capacitor voltage, the $PPP$ topology exhibits an exponentially decaying average power down to an asymptote. This can be understood as the amount of power contributed by the lower power harvester becomes negligible as the $Δ A$ increases, and the average power converges to the average power of a single harvester, $0.25$ mW. The fact that this is an exponential decrease and not a linear one shows that even small $Δ A$ values have significant affects on the performance of the $PPP$ topology.

These trends are exhibited as well in the upper envelopes of the instantaneous power for the storage capacitors (Figure 22). For the $PPS$ topology, the maximum capacitor voltage decreases linearly, and the capacitor voltage at the maximum power decreases linearly at the same rate. For the $PPP$ topology, there is a clear drop-off in the power levels following along a line starting from $V_{CL} = 30 V$ at $Δ A = 0 V$ and intersecting with $V_{CL} = 0 V$ at $Δ A = 30 V$ . This line represents the point in the charging curve at which the lower voltage harvester ceases to contribute power to the capacitor charging. As a result, the $PPS$ topology is insensitive to performance degradations from a $Δ A$ not caused by the different overall voltage levels. However, the $PPP$ topology is affected by voltage incompatibilities between the lower voltage harvester and the storage capacitor, significantly affecting the topology’s average power and maximum power levels.

Conclusion

Two, passive multi-source energy harvesting systems were explored as possible methods to vastly increase the robustness and effectiveness over single harvester systems. The piezoelectric circuit model used is an ideal model applicable to piezoelectric harvesters with low electromechanical coupling. Further examinations of specific instances of these schemes will utilize a more complex piezoelectric circuit model, such as the one presented by Elvin and Elvin (2009). This will allow for the isolation of the effects of the ideal signal interaction observed here and the electromechanical coupling, providing a thorough understanding of the schemes.

The first was the combination of a piezoelectric and a photovoltaic into both a parallel ( $SPP$ ) and a series ( $SPS$ ) topologies. When the capacitor was allowed to fully charge, the $SPS$ topology exhibited higher final stored energy levels than would normally be available with either the piezoelectric harvester ( $P$ ) or the solar harvester ( $S$ ). The higher stored energy levels lend the $SPS$ topology toward high-load, low-duty cycle applications where the bursts of power needed are significantly above that either the solar or the piezoelectric is capable of providing. Both the $SPS$ and $SPP$ topologies exhibited “piezo-dominant” and “solar-dominant” charging periods, as the solar harvester provided high power levels below its maximum voltage and the piezoelectric charged the storage capacitor up to its higher voltage level. The $SPP$ topology showed increases in the maximum power during the “solar-dominant” period as the power from the two harvesters summed. Therefore, the $SPP$ topology lends itself toward low-load, high-duty cycle applications as the storage capacitor voltage can be discharged below the solar maximum voltage level to maintain the topology harvesting in the high-power region. When the power output from the two harvesters are not equal, the advantages exhibited by each respective topology were not significantly affected. Also, the circuit architecture was shown to effectively isolate the two harvesters from one another such that when one harvester is not producing any power, the other harvester charging the capacitor unimpeded.

For small, low-power piezoelectric energy harvesters, array configurations present a significant design tool for developing energy harvesting systems. An array of piezoelectrics, multi-source harvesting scheme was explored in both a series ( $PPS$ ) and a parallel ( $PPP$ ) topologies. Both the series and the parallel topologies doubled the instantaneous maximum power available from a single harvester. Also, the series topology provided the advantage of a higher available voltage level and final stored energy levels. However, the introduction of differences between the two harvesters significantly degraded the performance of these topologies. The series topology proved to be highly sensitive to phase angles and frequency differences between the harvesters. On the other hand, the parallel topology was significantly affected by an amplitude difference. Also, the maximum instantaneous power levels were affected by phase angles and frequency differences for the parallel topology, while the average capacitor charging rate was unaffected. Both systems also exhibited beat phenomena in their instantaneous power curves with respect to the voltage levels of the capacitors in the presence of a frequency difference. However, given an array of piezoelectric harvesters where few differences are expected, the passive multi-source topologies effectively harvest the available energy while minimizing the necessary control and the number of components.

Future considerations of these schemes for specific instances will examine the use of the power optimization methods mentioned in the ``Introduction’’ section. Specifically, the question of whether a single power optimization technique could be applied to the passive multi-source schemes presented here as opposed to separate techniques for each harvester will be addressed. This will allow for harvesting significantly more power while only suffering from the overhead of a single power optimization technique.

Footnotes

Appendix 1 Acknowledgements

The authors would like to recognize the help of Matthew Bryant of Cornell University for providing access to his aeroelastic piezoelectric energy harvesters.

Funding

This work was performed with the guidance and support of Hyungjae Shin and the Samsung Synergistic Modalities for Energy Harvesting in Personal Electronic Devices project.

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Passive multi-source energy harvesting schemes

Abstract

Keywords

Introduction

Multi-source scheme analysis

Piezoelectric circuit model

Photovoltaic circuit model

Multi-source: solar and piezo

Solar and piezo — series SPS topology

Solar and piezo — parallel SPP topology

Solar and piezo — r ≊ 1

Solar and piezo — r ≅ 1

Multi-source: array of piezoelectrics

Array of piezoelectrics — series PPS topology

Array of piezoelectrics — parallel PPP topology

Array of piezoelectrics — phase angle, φ

Array of piezoelectrics — frequency difference, Δ f

Array of piezoelectrics — amplitude difference, Δ A

Conclusion

Footnotes

Appendix 1

Acknowledgements

Funding

References

Solar and piezo — $r ≊ 1$

Solar and piezo — $r ≅ 1$

Array of piezoelectrics — phase angle, $φ$

Array of piezoelectrics — frequency difference, $Δ$ f

Array of piezoelectrics — amplitude difference, $Δ$ A