‫ـ‬Jordan International Energy Conference 2011 – Amman
Design and Simulation of Multiple Input DC-DC Converter for
Piezoelectric Wind Harvesting
Taufik Taufik1,*, Jameson Thornton1, Makbul Anwari2
1
California Polytechnic State University, San Luis Obispo, USA
2
Umm Al-Qura University, Makkah, Saudi Arabia
* Corresponding author. Tel: +1 8057562318, Fax: +1 8057561458, E-mail:taufik@calpoly.edu
Abstract: This paper presents a proposed topology which utilizes multiple inputs for a DC-DC converter. The
new topology is derived from a standard buck topology but allows for sourcing from multiple inputs either
independently or simultaneously. The purpose of this topology is to take advantage of several sources of energy
harvesting from renewable sources, and specifically aimed at piezoelectric wind harvesting. This paper derives
the general transfer function for the new topology and provides simulations for various cases to show proof of
concept. Results from computer simulations demonstrate the potential and benefits that the proposed topology
offers for harvesting wind energy using piezoelectric.
Keywords: multiple input converter, energy harvesting, renewable energy, wind power.
1. Introduction
Over the last decade or so the push for renewable energies has increased dramatically.
California specifically has set a mandate that 20% of electricity generated must come from
renewable sources by 2010, and that this must be increased to 33% by 2020 [1]. Initiatives
like this are providing a necessity for increased research and commercialization of renewable
energy technologies. The two most predominant renewable energy sources are solar power
and wind power. Typically solar power is in the form of photovoltaic which require a
considerable amount of power electronics to regulate voltages as well as convert them from
DC to AC voltages. Wind power is often harnessed from large wind turbines. These also
require power electronics to maintain proper frequency output. An emerging area of interest is
harvesting energy via the piezoelectric effect. Several aspects of this energy harvesting are
from mechanical shock, often vibrations [2], [3]. Much of the research in piezoelectric energy
harvesting is for the purposes of scavenging environmental energy (usually vibrations) to
power small wireless devices [4]. Others, [5], have begun looking into using flexible
piezoelectric to harvest wind energy. The research done in [5] however does not detail any
circuitry after the piezoelectric material itself for which to harvest this energy. Others, [6], [7],
have begun looking into methods to increase the yield for energy harvesting systems in
general. These methods can be applied to energy harvesting for any system, but results from
[8] specifically look into increasing yield from piezoelectric energy harvesting. These results
will be useful for further research into harvesting wind energy on a larger scale. Because
piezoelectric materials are inherently AC sources and because energy harvesting is often
unpredictable we will need power electronics to condition and regulate the power generated
from the sources. Linear Technology introduced a chip in early 2010 specifically designed for
piezoelectric energy harvesting, the LTC3588-1 [9]. This chip has a built in bridge rectifier as
well internal MOSFETs and buck control to regulate a few fixed output voltages up to 3.6V at
a current up to 100mA. For the purposes of larger scale energy harvesting it seems reasonable
to assume that we should simply scale up this process and increase the number of
piezoelectric energy harvesting devices and these associated chips. With such low voltages
however it may be impractical to attempt to boost them up in a single stage to around 170V
for the purposes of converting to AC. The concept of multiple input DC-DC converters is not
‫ـ‬Jordan International Energy Conference 2011 – Amman
an entirely new concept; an early analysis in [10] discusses the theory of such topologies. A
US patent [11] has also been awarded to the same authors as in [10] for a multiple input buckboost topology. We begin to see that this concept is picked up quickly for electric and hybridelectric vehicles who wish to use energy from two different sources, typically a battery and a
fuel cell [12]. Generally this concept has been for a more parallel multiple input fashion, but
because the LTC3588-1 has an inherent buck design the maximum voltage we can hope to
achieve from this is 3.6V. However, because the converter acts like a voltage source we
should be able to add these “sources” in series to add the voltages. The overall idea is that we
should be able to harvest wind energy from many flexible piezoelectric sources tied to several
LTC3588’s. Similar to the way that a single photovoltaic cell produces only a portion of 1V,
each piezo-converter will produce at most 3.6V with this specific design. These must then be
stacked in series to achieve a voltage that can be easily converted to AC to either run a typical
AC load or to supply to the grid.
L
S1
V1
D1
S2
V2
Vo
D2
C
V3
S3
D3
Fig. 1. Stacked-buck topology with 3 sources
2. Design and Analysis
2.1. Stacked Buck Converter Topology
The proposed topology is shown in Fig. 1. Each module within the dashed boxes represents a
piezoelectric-converter combination. The output of each individual converter will be a fixed
voltage, and specifically in the case of the LTC3588-1 will be 3.6V. The purpose of utilizing
the stacked-buck topology is twofold. The primary reason for utilizing this topology being
that an already available commercial product, the LTC3588-1, has an inherent buck design
that cannot be altered along with the other desirable components. This product is very small
and compact and already available. The second reason for this topology is to increase the
voltage output level with the final desired result of producing energy for a larger load at 170V
DC, which would result in 120VAC through an inverter. This could be done with a boost
converter, but would require a duty cycle of about 98% which is impractical for many
converters. The approach is to simulate the feasibility of stacking these converters in a series
fashion to achieve a voltage level that can more easily be converted up to about 170V.
2.2. Derivation of Transfer Function
For the purposes of derivation, all components are assumed ideal and lossless. For purposes of
illustration we will use three sources to simplify the length of the math involved, but this can
easily be generalized to N cases.
‫ـ‬Jordan International Energy Conference 2011 – Amman
SW1
D1
SW2
T
2T
T
2T
D2
SW3
D3
τ1 τ2
τ3
τ4
τ5
τ6 T
2T
Fig. 2. Switching signals for 3 sources with arbitrary duty cycles and delays
Table 1 summarizes the relationships of between the time delays τ as depicted in Figure 2.
Table 1. Relationships for time delays in Figure 2
ton1 =D1T =τ1+τ2+τ3
toff1 =(1-D1)T =τ4+τ5+τ6
ton2 =D2T =τ2+τ3+τ4
toff2 =(1-D2)T =τ1+τ5+τ6
ton3 =D3T =τ3+τ4+τ5
toff3 =(1-D3)T =τ1+τ2+τ6
Equation (1) demonstrates the use of Volt Second Balance (VSB) rule which states that the
average voltage across an inductor over a single period must be 0. Applying VSB to arbitrary
switching signals shown in Error! Reference source not found. results in equation (1).
(𝑉1 − 𝑉𝑂 )𝜏1 + (𝑉1 + 𝑉2 − 𝑉𝑂 )𝜏2 + (𝑉1 + 𝑉2 + 𝑉3 − 𝑉𝑂 )𝜏3 +
(𝑉2 + 𝑉3 − 𝑉𝑂 )𝜏4 + (𝑉3 − 𝑉𝑂 )𝜏5 + (−𝑉𝑂 )𝜏6 = 0
(1)
Rearranging and collecting terms with common voltages gives us Equation 2.
𝑉1 (𝜏1 + 𝜏2 + 𝜏3 ) + 𝑉2 (𝜏2 + 𝜏3 + 𝜏4 ) + 𝑉3 ( 𝜏3 + 𝜏4 + 𝜏5 ) −
𝑉𝑂 ( 𝜏1 + 𝜏2 + 𝜏3 + 𝜏4 + 𝜏5 + 𝜏6 ) = 0
(2)
Using Equation 2 and Table 1, the τ terms in parentheses can now be substituted with
corresponding duty ratios. Also notice that ∑61 𝜏𝑖 = 𝑇 so that equation (2) yields Equation (3).
𝑉1 𝐷1 𝑇 + 𝑉2 𝐷2 𝑇 + 𝑉3 𝐷3 𝑇 − 𝑉𝑂 𝑇 = 0
(3)
Cancelling out the switching period and rearranging gives the final equation for the transfer
function as shown in Equation (4).
𝑉𝑂 = 𝑉1 𝐷1 + 𝑉2 𝐷2 + 𝑉3 𝐷3
(4)
In general, Equation (4) can be extended to N different voltage inputs with N duty cycles
𝑉𝑂 = 𝑉1 𝐷1 + 𝑉2 𝐷2 + 𝑉3 𝐷3 … = ∑𝑁
𝑖=1 𝑉𝑖 𝐷𝑖
(5)
‫ـ‬Jordan International Energy Conference 2011 – Amman
Equation (5) is a linear addition of weighted voltage inputs. This makes sense since if
additional voltage sources were neglected or if sources were never turned on the associated
switch then this term would become zero and the equation reduces to the original transfer
function for a simple buck.
2.3. Circuit Analysis
The brief explanation on circuit analysis presented here is merely to illustrate a few points
that may be important to consider when implementing this design. In addition, the analysis
herein is aimed to show the different cases that the topology may operate in order to gain a
better understanding of the demands on the components.
Error! Reference source not found.(a) shows the current path when all switches are
conducting at the same time. It is apparent that the output current for this time frame is shared
by all switches conducting. For the case where all switches have the same duty cycle and
starting time we can see that the average current for these switches will be the same as that for
a typical buck converter.
Figure 3(b) depicts another case where all switches are not conducting but all diodes are
conducting. In this case all diodes share the same current that is the output current for that
moment. If all switches have the same conducting time, and thus all diodes share a conduction
time, then the average diode currents will be similar to a standard buck.
Figure 3(c) illustrates the case where switches are conducting at different times. This allows
us to see that at certain times during the period a switch current and a diode current may
actually be the same. This begins to show that the average current for a component may no
longer be found from a standard buck derivation but will have to be considered further.
L
L
S1
S1
S1
V1
V1
V1
D1
D1
Vo
S2
D1
Vo
S2
V2
V2
S3
D2
C
V3
D3
Vo
S2
V2
D2
D2
C
V3
L
(a)
S3
C
V3
D3
(b)
S3
D3
(c)
Fig. 3. Current flow when (a) all switches are conducting (b) all switches are off (c) switches 1
and 3 are conducting with switch 2 off
Figure 4 takes this point a bit further to show that because switches may be conducting for
different portions of the switching period they may have different current levels, even if they
conduct for the same amount of time (i.e. have the same duty cycle). This makes component
sizing for average forward currents more complex than for a typical buck. A designer may
‫ـ‬Jordan International Energy Conference 2011 – Amman
need to plan for a worst case scenario. A very conservative approach may be to use
components whose current ratings are the same as the expected average output current. If the
device conducted 100% of the time it would be the same as the average output current, though
we expect each device to turn off for at least some portion of the period so its average current
should be less than this.
S2
S3
S1
Fig. 4. Currents in switches compared to inductor current for a switching period
3. Simulation Results
Three source voltages were used to demonstrate the operation of the proposed topology as
shown in Figure 1. The software used to simulate is LTSpice which is free to download from
Linear Technology website. The following lists the parameters used in the simulation:
Output inductance: 100µH, no series resistance
Output capacitance: 100µF, no series resistance
Load resistance: a 5Ω static load unless otherwise stated.
All diodes: Diodes inc. model DFLS220L with IS=25µA and RS=47mΩ
Switches: Custom model with Ron=1nΩ and Roff = 100MΩ.
3.1. Same Duty Cycle, No Delays
Figure 5 shows waveforms for the case where all input voltages are the same and equal to
10V, the switches all start at the same time and all have the same duty cycle of 0.5. This is the
simplest case and is almost like having three identical buck converters in parallel. The
important difference is that the unfiltered output voltages are actually in series. The switching
waveform is black and is labeled as V(n003). We can see that the waveform has a 50% duty
cycle and switches between approximately 0 volts and 30 volts. The red waveform is the
inductor current, labeled I(L3) showing the very familiar triangular shape that is typical of a
regular buck converter. The blue line through the center is the output voltage and is
approximately 14.3V. From the derived ideal transfer function, the output voltage should be
15 volts. This slight difference is reasonable due to non-ideality of switches and diodes. The
results here are nearly identical to what would be expected from a single buck converter
whose input voltage was 30V (which is the sum of the three input voltages) with a duty cycle
of 50%.
‫ـ‬Jordan International Energy Conference 2011 – Amman
Fig. 5. V1=V2=V3=10V, D1=D2=D3=0.5, 𝜏1 = 𝜏2 = 0.
3.2. Different Duty Cycles, No Delays
Figure 6 shows results with all input voltages at 10V, with all switches having the same turn
on time, but different turn off times. The duty cycles are 40%, 30%, and 10%. With these duty
cycles we expect the output voltage to be 8V, the simulated output voltage is 7.2V. Again this
result is not far off and the discrepancy can be attributed to lossy components. We can see that
the unfiltered node voltage, labeled V(n003), has a descending step type of shape. The steps
are at 30V, 20V, 10V, and 0V. This corresponds to the addition of the input voltages with
30V being the sum of the three, 20V for two, 10V for a single, and 0V when all switches are
off. The interesting event occurring at this stage is that the inductor current waveform is
becoming significantly different from the typical triangular shape of a standard buck
converter.
When all three switches are conducting the inductor current has the steepest slope with the
voltage across the inductor being the sum of the inputs minus the average output voltage.
Thus we see that for the case where all switches begin to conduct at the same time with
different duty cycles that as each switch turns off the slope of the inductor current gradually
decreases. When all the switches are off the inductor current has only –VO across it so that it
begins to discharge.
Because the waveform is not typical of a standard buck converter this may cause difficulties
when choosing component sizing. Such component sizing as critical inductance to maintain
continuous conduction mode, or the approximate average output current or ripple voltage
which may depend on this inductance value as well. The detailed analysis of this waveform
are not discussed in this paper, but are briefly introduced with some discussion. Further
detailed analysis and discussion will be presented at a later date in another paper.
‫ـ‬Jordan International Energy Conference 2011 – Amman
Fig. 6. V1=V2=V3=10V, D1=0.4, D2=0.3, D3=0.1, 𝜏1 = 𝜏2 = 0.
3.3. Different Duty Cycles, Arbitrary Delays
Error! Reference source not found. 7 shows a more arbitrary case of duty cycles with the
three source voltages still the same 10V but with duty cycles of 80%, 50%, and 30%. These
switching cycles have the following respective delays; 0, 2us, and 4us. The theoretical output
voltage is 16V. The simulated output voltage is approximately 15.3V again due to lossy
components.
Error! Reference source not found. shows a similar step pattern as the previous case, but
the inductor current is actually declining with a single switch conducting. In a regular buck
converter this would never happen because the source voltage is always higher than the output
voltage. However, because the output voltages are stacked then the resulting voltage could be
higher than a single input. This allows for a case where the average output voltage is actually
higher than a single input. In this particular case, the output of 15.3V with an input of 10V is
obtained. This results in a declining inductor current in two places during the switching
period.
‫ـ‬Jordan International Energy Conference 2011 – Amman
Fig. 7. V1=V2=V3=10V, D1=0.8, D2=0.5, D3=0.3, 𝜏1 = 0, 𝜏2 = 2𝜇𝑠, 𝜏3 = 4𝜇𝑠.
4. Conclusion
In this paper, computer simulation was used to demonstrate the ability of the proposed
stacked buck converter for harvesting energy from the wind using piezoelectric material. The
proposed topology is capable of taking in multiple sources which represent several
piezoelectric cells which will be feeding the converter. Eventually thousands of piezo electric
cells will be connected several of these converters to produce a small-scale wind power
generation without the use turbines. Such application will be best suited for urban
environment or for small power applications in remote or isolated areas. Hardware
implementation of the proposed converter has been built and will be presented in a future
paper.
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