December 11, 2014
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EE356 Project: Φ2 Boost MPPT
Max Praglin
Abstract—A class Φ2 DC-DC converter is proposed for maximum power point tracking in a weight- and space-sensitive
application. The solar converters on the Solar Impulse plane
are examined as an application of this topology. Presented
here is a 275W maximum power point tracking (MPPT) boost
converter based around the Φ2 topology achieving more than
87% efficiency in simulation. Conventional switch-mode boost
converters for both solar powered vehicles and terrestrial PV
installations are compared.
I. I NTRODUCTION
R
ESONANT power converters are attractive for applications in which space or weight are valued at a premium.
The possibility of high switching frequency (and therefore aircore inductors) means that a resonant power converter could
replace a heavier switching regulator in a weight-sensitive
application. The high switching frequency also enables higher
volumetric power density. In this paper, a design is proposed
for the maximum power point tracker (MPPT) electronics
onboard the Solar Impulse plane. A class Φ2 boost converter’s
power stage, semiconductor devices, and magnetics are selected and evaluated over the operating conditions seen in the
application.
Fig. 1.
flight.
Fig. 2. The MPPT electronics deliver power to the high-voltage bus, on
which the battery pack acts as a buffer for night time or cloudy weather.
From [8].
high voltage battery bus onto which MPPT electronics deliver
power (see Figure 2). Peak solar output power is greater than
average motor power; therefore, batteries generally charge
during the day and discharge during the night.
Pending confirmation from Solar Impulse regarding specifications of the MPPT modules currently employed, terrestrial MPPT technologies suggest that the MPPT subsystem
accounts for approximately 80kg, or 5% of the plane’s mass.
A conservative estimate of mass can be derived from specifications of the Photon MPPT developed for solar car racing
(in which low weight and high efficiency are also paramount).
At the power density of the Photon MPPT, these electronics
account for approximately 1% of the plane’s mass. See Figure
18 in the Appendix for benchmarks of modern PV MPPT DCDC converters.
Conventional PV MPPT DC-DC converters operate at lower
Solar Impulse, a Swiss-built solar plane built for long endurance
A. Solar Impulse
Solar Impulse is the first manned solar-powered plane (see
Figure 1) to fly over a 24-hour cycle and is scheduled to
make an around-the-world flight in 2015. It is a single-seater
plane with 1600kg mass, 6kW of motor power (30kW peak),
86kW h Li-Ion battery capacity, and 10kW of peak solar array
output [7][8][9]. The desire to operate at night, when there
is zero usable solar power, leads to an architecture with a
Fig. 3. I-V curve of the SunPower C60 mono-crystalline solar cell from the
C60 datasheet.
December 11, 2014
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frequencies than their resonant counterparts, and are therefore
likely to be larger and heavier. Topologies other than the Φ2
were investigated. Series resonant converters were ruled out
because of the need for both high- and low-side gate drive
circuits. The Class-E topology was considered but not used
due to of its higher switch stress than the Φ2 . This is not the
first paper studying the use of resonant topolgies for MPPT
applications [11].
Fig. 4. The Φ2 inverter topology is the starting point for the MPPT boost
converter.
B. Converter Specifications
Solar Impulse carries 11,628 solar cells [7]. Photos of Solar
Impulse and involvement from SunPower suggest the wings
are covered with C60 cells, a mono-crystalline silicon solar
cell whose I-V characteristics are shown in Figure 3.
From publicly available data, certain aspects of the MPPT
system can be inferred. There are 36 solar strings and MPPT
channels, there are an average of 81 cells in each string,
and the battery pack has 72 Li-Ion cells in series. A 1%
ripple specification is imposed in order to operate at the
maximum power point of the solar panels. It is estimated that
the specifications of the existing MPPT system are:
Input Voltage
Output Voltage
Output Power
Settling Time1
Input Current Ripple
Min.
40V
175V
–
–
–
Nom.
45V
270V
–
–
Max
55V
290V
275W
3.6µs
5%IM P P
The output voltage ripple is ignored because a converter
supplying a battery will have a theoretically constant output
voltage. The assumed large capacity of the load (a battery)
means that overshoot in output power due to the start-up
transient of the converter will not be damaging to the constant
voltage load.
nearly independent of solar panel input power because when
on, the converter operates at its most efficient point. This
is a reasonable assumption since the turn-on transient of the
converter will be fast compared to the pulse length. The reader
is referred to references [3] [5] for discussions of resonant DCDC control.
The inverter is designed for a 6.75Ω load resistor in order
to deliver 300W at 45V. Using Equation (1) in [1], the components Lr and Cr are first selected. Next, the network composed
of Lf , Cf , Lmr , and Cmr is selected based upon Equation
(2) in [1]. This process requires selection of Cf , which is
informed by the output capacitance of the switch we intend
to use. Based on the availability of GaN devices that might
work at this power level, a starting value of Cr = 500pF is
selected. The impedance of the input Φ2 network and reactive
components Lr and Cr , as well as their parallel combination
(notated Zds ), are shown in Figure 5. Note that the value of Lf
has been tuned such that Zds appears inductive at 13.56MHz,
a switching frequency selected such that any radiated EMI will
fall in an ISM frequency band. Other noteworthy components
of the Zds plot are the notch at the second harmonic of the
switching frequency and the peaking at the third harmonic.
II. Φ2 C ONVERTER D ESIGN
The inverter and rectifier are designed independently. The
operation of a Φ2 DC-DC converter is not discussed here; the
reader is referred to [1][2][3][6] for in-depth explanation of
this converter, especially the DC-DC boost variety. The Φ2
inverter topology, the design with which we begin, is shown
in Figure 4. Simulations were performed with LTSpice.
A. Φ2 Inverter
The power output of the boost converter is selected as 300W
such that there is margin in applying pulse density modulation
(PDM) or hysteretic control to modulate average output power
to 275W. Thus, maximum power point tracking is possible at
any level of solar insolation. Hysteretic or PDM control of
the power stage will enable the converter’s efficiency to be
Fig. 5.
1 A 2.75µs settling time for output power is somewhat arbitrarily chosen.
If we track the maximum power point with a perturb-and-observe (P&O)
algorithm, for example, a 1ms period between perturbations would be fast in
the context of most MPPTs. Should power be controlled using pulse density
modulation, and 1W increments of power are desired, the step response of
the converter’s output power should settle within 1% of its final value within
1W
10−3 s · 275W
= 3.6µs.
This impedance shape, characteristic of the Φ2 converter,
yields a waveform at the drain of the switch such as that of
Figure 6. The components might be adjusted to lower the peak
voltage closer to two times the input voltage, allowing for the
use of a lower voltage switch.
Impedances of the Φ2 converter
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C. Including Device Models
Fig. 6.
VDS waveform of the Φ2 converter.
B. Rectifier Design
The rectifier’s topology is shown in Figure 7, having the
benefit of a DC path between the input and output. The rectifier
design is based upon strategies suggested in [4][6]. The
rectifier can be tuned to appear resistive (at the fundamental
of the VDS waveform) by creating an intermediate circuit
in SPICE: a behavioral voltage source copies the DS node’s
waveform and passes it through a LCR circuit tuned for high
Q at the switching frequency, yielding the fundamental of the
VDS waveform. Another behavioral voltage source can copy
the fundamental and drive the rectifier, as in Figure 7. The
values Lr and Cr are then adjusted such that the current and
voltage entering the rectifier are in phase and the correct power
is delivered to the load.
The simulation pictured in Figure 9 adds manufacturerprovided SPICE models to the previous simulation. The Cf
capacitor has been reduced now that a realistic model including device capacitance is present. As a simple approximation,
inductors are modeled with series resistance giving them a
certain Q-factor at the fundamental frequency. The EPC 2010
was selected because of its low-inductance packaging, 200V
VDS rating, 12A continuous / 60A pulsed current rating, and
25mΩ RDS,On rating. The C4D10120D was chosen because
of its surface-mount D2PAK package, 1200V VR rating, and
14A IF rating. A RF-specific diode may be a better choice,
but the simulation indicates that the losses in the SiC diode
are on the order of 2-3 W.
The converter’s values, including the duty cycle of the
switch, were tuned to reduce losses while staying above 300W
output power and reducing input current ripple. This crude
method does not consider that weight, volume, form factor,
loss breakdown, etc. may be important to the end application.
In manually tuning the values of the Φ2 DC-DC, tradeoffs were discovered. For example: as Lf was increased (with
all other quantities remaining the same), efficiency suffered
but the input ripple improved. The Q of the inductors also
changed the extent to which the values of Lf and LR matter.
Yet another consideration would be the trade-off in volume
between adding input capacitance and increasing Lf to meet
an input ripple specification; this would be an interesting study,
but it is not investigated here.
Component values are given below:
Component
Lf
Lmr
Cmr
Cf
Lr
Cr
D
Q
Value
500nH
80nH
445pF
50pF
300nH
350pF
43%
150
Fig. 7. The rectifier is tuned by applying the fundamental of the VDS
waveform and attaining resistive operation.
A new circuit simulation (see Figure 8) is made by replacing
the right-hand side of the original Φ2 circuit (the reactive
elements of the inverter) with the rectifier of Figure 7. The
capacitor Cr has been moved to be parallel to the diode in
order to absorb the capacitance of the diode. This placement
is equivalent at AC frequencies.
Fig. 9.
The Φ2 DC-DC with manufacturer-provided device models.
D. Magnetics
Fig. 8.
Combination of the Φ2 inverter and resonant rectifier.
In order to investigate the feasibility of the required magnetics (in both volume and Q factor), off-the-shelf components
and the magnetics in papers discussing resonant converters
were used as a benchmark. West Coast Magnetics 202 Series
December 11, 2014
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RF inductors (in the range of hundreds of nanohenries) list
Q factors that are reasonable in the context of the inductors
in [1]. A round number of Q = 150 was used while tuning
the converter and reporting efficiencies. Because higher Q
inductors could conceivably be made, such as those in [10],
efficiency was measured while sweeping Q. The results of
changing the Q factor are illustrated in Figure 17. Efficiency
is greater than 90% with Q > 200
III. Φ2 C ONVERTER P ERFORMANCE
Figures 13-16, showing converter efficiency and output
power versus operating parameters, can be found in the
Appendix. The converter achieves 87.0% efficiency at nominal
input and output voltage and at full output power. The transient
response of the converter is remarkable; the settling time
requirement of 3.6µs is easily met (see Figure 10).
Fig. 11. Input current of a single Φ − 2 converter. Two converters operating
180◦ out of phase decrease the ripple current.
180◦ out of phase from each other can cancel much of the
ripple and double its frequency. This strategy would reduce the
components to the order of 33µH and 100µF ; these values
are used to create a physical model of the converter in the
next section.
B. Converter Size
In Figure 12, analysis of the converter’s size and weight
is performed using the aforementioned West Coast Magnetics
202 Series RF inductors, a Coilcraft XAL1510 Series input
filter inductor, and a film input capacitor. Two sets of Φ2
power stage components are included to achieve input ripple
cancellation; the size of components could be smaller than
pictured below because the power level would be divided by
two.
Fig. 10.
Turn-on transient of input current.
The as-presented converter is unable to deliver full output
power to a battery pack that is at zero state-of-charge (see
Figure 15). This may be acceptable: the voltage-capacity
characteristics of Li-Ion cells will cause the cell voltage to
quickly rise as the cell is charged. Thus, the output voltage of
the converter will stay near 270V for the majority of operating
conditions. For example, the Panasonic NCR18650B’s opencircuit voltage will rise by more than 20% after the first 10%
of capacity is replenished.
The output power capability of the converter does fall below
the specified 275W when the cell voltage is below 45V (see
Figure 16), corresponding to the VM P P of the SunPower
C60 cell. This is acceptable because the solar string’s power
capability will fall quickly with falling VM P P .
The input current (see Figure 11) exhibits a ripple of
0.4 · IM P P , which is unacceptable for forcing the solar panel
to operate at its maximum power point. An input filter is
discussed briefly in the next section.
IV. P RACTICAL C ONSIDERATIONS
A. Input Filtering
The input current ripple can be kept within the 5% specification with LC filter components on the order of 33µH and
680µF . Thorough analysis of this filter is not performed in this
paper; the required capacitance is prohibitively large. Instead
of using this input filter, two half-power converters operating
Fig. 12. Mock-up of Φ2 power stage components. Two half-power converters
and an input filter are shown.
The volume is 91cm3 and weight is estimated at approxW
imately 100g. This yields 3000 W
kg and 3.3 cm3 , exceeding
the characteristics of the converters listed in Figure 18. This
estimate does not include gate drive circuitry, control circuitry,
output capacitance, connectors, or heat sinking (which could
all be minimized during packaging 36 of these converters together for Solar Impulse). To reduce control circuitry overhead
December 11, 2014
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A PPENDIX
on each power converter, a centralized control architecture
could be implemented.
C. Thermal Management
With 87% efficiency, at most 36W must be dissipated,
which is feasible with air cooling. A concern with the
EPC2010 is its small package size and hence potential difficulty to cool; however, less than 4W are dissipated in the
K
. It would be
device, and the datasheet lists Rth,jb = 16 W
feasible to cool the device with copper planes coupled to a
heatsink under the PCB.
D. Gate Drive
Gate drive circuits have been ignored because the output
power is so much higher than the value of 21 QV fs . The gate
charge of the EPC2010 is at most 7.5nC (yielding a gate drive
power of approximately 0.25W ). The 275W output power of
the converter eclipses the gate drive power, so hard switching
at 13.56M Hz would be acceptable. Nonetheless, interesting
alternatives to a hard-switched gate drive are discussed in [2].
Fig. 13.
Efficiency vs. Input Voltage.
Fig. 14.
Efficiency vs. Output Voltage.
Fig. 15.
Output Power vs. Output Voltage.
V. C ONCLUSION
A class Φ2 resonant DC-DC converter is proposed for use in
the MPPT subsystem of the Solar Impulse plane. The design
achieves an efficiency of 87% under nominal conditions,
and efficiency can be improved to over 90% with higher Q
magnetics. An inverter and rectifier are designed, combined,
and evaluated in a LTSpice simulation with realistic device
models. Real components are selected for estimation of the
size and mass of the converter. The converter presented here
is expected to exceed the figures of merit of traditional MPPT
designs.
December 11, 2014
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R EFERENCES
Fig. 16.
Output Power vs. Input Voltage.
Fig. 17.
Converter efficiency vs. Inductor Q.
Design
Photon 2
M250 3
Pantheon II 4
P400 5
Φ2 Boost MPPT
6
Volume [cm3 ]
640
888
973
681
91
[1] Rivas, J.M.; Han, Y.; Leitermann, O.; Sagneri, A.; Perreault, D.J., ”A
High-Frequency Resonant Inverter Topology with Low Voltage Stress,”
Power Electronics Specialists Conference, 2007. PESC 2007.
[2] Rivas, J.M.; Leitermann, O.; Han, Y.; Perreault, D.J., ”A Very High
Frequency DCDC Converter Based on a Class Φ2 Resonant Inverter,”
Power Electronics, IEEE Transactions on, vol.26, no.10, pp.2980,2992,
Oct. 2011.
[3] Pilawa-Podgurski, R.C.N.; Sagneri, A.D.; Rivas, J.M.; Anderson, D.I.;
Perreault, D.J., ”Very High Frequency Resonant Boost Converters,” Power
Electronics Specialists Conference, 2007.
[4] Burkhart, J. M.; Korsunsky, R.; Perreault, D. J., ”Design Methodology for
a Very High Frequency Resonant Boost Converter,” Power Electronics,
IEEE Transactions on, vol.28, no.4, pp.1929,1937, April 2013
[5] Rivas, J.M.; Wahby, R.S.; Shafran, J.S.; Perreault, D.J., ”New architectures for radio-frequency DC/DC power conversion,” Power Electronics
Specialists Conference, 2004.
[6] Sagneri, A.D., ”Design of a Very High Frequency dc-dc boost converter,”
Massachusetts Institute of Technology, 2007.
[7] Solar Impulse, “Inventing the Future.”
[8] Ross, H. “Solar Powered Aircraft: The True ALL Electric Aircraft.” 2009.
[9] Dugdale, A. “Solar Impulse: Around the World in a 100% Sun-powered
Airplane.” Gizmodo, 2007.
[10] Sullivan, C.R.; Li, Weidong; Prabhakaran, S.; Shanshan Lu, ”Design and
Fabrication of Low-Loss Toroidal Air-Core Inductors,” Power Electronics
Specialists Conference, 2007.
[11] Simeonov, G. “Resonant Boost Converter for Distributed Maximum
Power Point Tracking in Grid-Connected Photovoltaic Systems.” University of Toronto, 2010.
Mass [kg]
0.546
2.0
3.6
0.930
0.1
Efficiency[%]
95
96.5
95
98.8
87
Fig. 18. Comparison of terrestrial MPPT models. Note that these MPPT
models do not necessarily operate up to 300V output. Efficiencies and power
outputs are a best estimate for the converters at comparable operating points.
2 Made
by Dilithium Power Systems for solar car racing.
by Enphase.
4 Made by Solarbridge.
5 Made by Solar Edge. Used in Solar City installations.
6 The converter designed in this paper. Does not include packaging, heat
sinking, control, etc. in the estimates.
3 Made
Output Power [W ]
300
250
250
400
300
Power/Mass [ W
kg ]
550
125
69
430
3000
W
Power/Volume [ cm
3]
0.47
0.28
0.26
0.59
3.3