Analysis of Distributed Peak Power Tracking in Photovoltaic Systems
Shahab Poshtkouhi, Jordan Varley, Rahul Popuri, Olivier Trescases
University of Toronto, Department of Electrical and Computer Engineering
10 King’s College Road, Toronto, ON, M5S 3G4, Canada
Abstract— It has been demonstrated that performing localized
maximum peak power tracking (MPPT) on each photovoltaic
(PV) panel, instead of using a single MPPT controller across
the PV string can substantially increase the total harvested
power, since each panel experiences unique illumination and
temperature conditions. In this work, the effect of the dc-dc
converter efficiency on the power savings from distributed MPPT
(DMPPT) is analyzed for a wide range of test cases and different
PV panel parameters. The benefit of DMPPT for a practical
system is shown to be up to 25% for a standard deviation of
σ = 0.2. A set of modular hardware-based PV panel emulators
(ePVs) is presented. The ePVs can be programmed to match the
unique i/v curves of real panels under various conditions and
can therefore be used to optimize future DMPPT systems.
I. I NTRODUCTION
Performing maximum peak power tracking (MPPT) on an
array of series-connected photovoltaic panels (PV) as shown in
Fig. 1(a) has been extensively used to continuously optimize
the total harvested power under time-varying environmental
conditions, such as temperature and lighting fluctuations [1].
It has recently been demonstrated that performing MPPT on
a per-panel basis, instead of using a single MPPT controller
across the PV string can substantially increase the total harvested power, since each panel typically experiences unique
light and temperature conditions [2]–[5]. This is especially
true for installations in urban environments, where complex
time-varying shading patterns appear on the PV array. The
use of dedicated series-connected dc-dc converters for performing localized, or distributed MPPT (DMPPT) is shown
in Fig. 1(b). The dc-dc converter on each panel allows the
PV voltage Vpv to be individually optimized for peak power
harvesting [2]. The dc-dc converters may either operate using
a communication link, or as standalone master-less units [2],
where a four-switch non-inverting buck-boost topology was
demonstrated on a DMPPT system having four panels. Seriesconnected dc-dc converters used for DMPPT are often referred
to as micro-converters, as opposed to micro-inverters, which
are used in parallel connected DMPPT systems. Micro-inverter
systems result in increased the wiring costs, since the lowvoltage AC bus must be wired in parallel to each panel.
The wiring must also be thicker to accommodate a higher
bus current due low-voltage operation. On the other hand,
micro-inverter systems offer more flexibility and scalability
compared to series connected micro-converter systems. Microinverter and micro-converter technology is rapidly evolving, as
a number of startup and established PV companies has raced
to release new products in recent years [6]–[10]. These recent
offerings have generated a significant amount of excitement in
the solar industry, but remain quite expensive due to packaging
and semiconductor costs and have yet to be widely accepted.
In addition to the cost considerations, long-term reliability
concerns are likely to delay the large scale adoption of
such schemes. Manufacturers have responded by eliminating
electrolytic capacitors from their designs and increasing the
level of integration. In at least one-case, an application IC was
(ASIC) was specifically developed for optimizing the DMPPT
performance [10]. Existing micro-inverter systems use powerline communication schemes for harvesting data from each
panel, which eliminates the need for additional wiring.
Today DMPPT is also exclusively intended to be used
at the panel level, however one can envision four separate
levels of granularity. The fourth possible level extends all the
way down to individual PV cell, as shown in Fig. 2. As the
granularity increases, the energy harvesting capability of the
system improves under partial shading, however at this point
in time the total cost of the micro-converters is prohibitive
beyond level 2. This is despite the fact that high-density, lowvoltage dc-dc converter technologies could potentially be used
at the cell level.
PV Module 1
(ePV 1)
+
vpv1
MPPT
+
vstring
PV Module 2
(ePV 2)
+
vpvn
(ePV n)
-
PV Module 1
(ePV 1)
Inverter
(a)
+
vpv1
-
DMPPT
dc-dc
Converter
PV Module 2
dc-dc
(ePV 2)
Converter
(ePV n)
+
vpvn
-
istring
+
vpvm1
+
vstring
Inverter
~ AC
-
ipvn
PV Module n
~ AC
-
PV Module n
ipv1
istring
-
dc-dc
Converter
+
vpvmn
-
(b)
Fig. 1. (a) Standard PV system, where MPPT is performed on the seriesconnected string. (b) DMPPT system with one dc-dc converter per panel.
While it is clear that DMPPT has a good potential for
efficiency improvements, determining the actual power savings
of an experimental DMPPT system under realistic conditions
IV.
1. Multipanel
Communication Bus
AC ~ 120V 60 Hz
2. Panel
3. Sub-panel
Emulated PV Array
DMPPT System
LabVIEW GUI
Vstring
0-24V, < 5 A
12V
Isolated
Power
Supply
4. Cell
BuckBoost
Converter
ipv1
+
vpv1
-
dc-dc
1
T1, G1
Opto-isolator
SPI
Istring
Controller
Vpv
Ipv
Emulated PV (ePV)
Fig. 2.
Four possible levels of DMPPT granularity.
is very challenging. A purely software-based approach is a
good starting point, however the results are highly sensitive to
the accuracy of the dc-dc converter modeling. Low dc-dc converter efficiency can easily overshadow the relatively modest
improvement in harvested power resulting from DMPPT. In
addition to evaluating the harvested power, the interaction of
the multiple micro-converters during transient events, faults
and startup must be verified experimentally. A combination
of software modeling and hardware-based proof-of-concept is
clearly the best approach for demonstrating a complex DMPPT
system. A hardware based platform for the DMPPT system
is also useful for evaluating the dynamic performance of the
downstream inverter.
The focus of this paper is two-fold; firstly the impact of
converter efficiency on DMPPT is analyzed and secondly a
flexible hardware platform is developed to test and optimize
future DMPPT architectures. Applying complex time-varying
light and temperature patterns to each PV panel in an array is
not necessarily practical in a lab environment. The approach
proposed in this work is shown in Fig. 3. The real PV panels
in the testbed are replaced by programmable hardware-based
PV emulators (ePV). Each ePV contains a regulated dc-dc
converter that implements the unique I/V characteristic of
each PV panel under specific light and temperature conditions.
The parameters of the emulated PV panel, as well as the
light and temperature conditions can be programmed using
a graphical user interface. The resulting modular system is a
highly scalable and provides a flexible platform for DMPPT
testing. The proposed solution is more flexible then existing
solar emulators [11]–[13] since it provides true hardware
emulation with flexible software control of temperature and
illumination. The approach used in this work does not rely on
analog power amplifiers or light sensors as in [12].
This paper is organized as follows. The simulated power
savings for a representative six-panel PV system with DMPPT
are reported in Section II, both for ideal and non-ideal dc-dc
converters. The implementation of the ePV system is described
in Section III and experimental results are provided in Section
DMPPT
ePV 2
dc-dc
2
ePV n
dc-dc
n
Fig. 3. Emulated PV Architecture for modular testing and evaluating of
DMPPT systems.
II. P OWER SAVINGS USING DMPPT
A standard PV system with DMPPT is shown in Fig. 1(a),
while a DMPPT system having one dc-dc converter per panel
is shown in Fig. 1(b). The net benefit of DMPPT over standard
MPPT is calculated by considering the efficiency of the dcdc converters that must be introduced into the PV array. The
power ratio kp is defined as the ratio between the power
obtained using DMPPT and MPPT
n
Pdmppt
pvi · ipvi )
i=1 max(v
(1)
=
kp =
Pmppt
max(istring · ni=1 vpvi )
Where Pdmppt is the maximum power obtained when each
panel is operated at the peak power point, as illustrated
in Fig. 1(b) and Pmppt is the power obtained when the
power is optimized at the bus-level as shown in Fig. 1(a).
The maximizing function max() is implemented by the PPT
algorithm. The following analysis assumes that the peak power
tracking algorithm is functioning perfectly in all cases.
A. Benefit of DMPPT with Ideal DC-DC Converters
The power ratio kp was evaluated for two representative PV
arrays having the parameters given in Table I. The simulated
PV arrays consists of 6 panels, each having individual illuminations of G1:6 . The ratio kp is calculated for 10k cases
having different randomly distributed combinations of G1:6
ranging from G = 1100 W/m2 to 600 W/m2 . The power
versus voltage curves for the panel #2 is shown in Fig 4.
The resulting power ratio kp versus standard deviation σ in
G1:6 is shown in Fig. 5, where each point represents one test
case. The simulation data was obtained for the two sets of PV
parameters as listed in Table I. In this section, the efficiency
of the dc-dc converters is assumed to be 100 %, which results
TABLE I
PV PANEL S PECIFICATIONS
Parameter
Short Circuit Current, Isc
Open Circuit Voltage, Voc
Current at Max. Power, Imp
Voltage at Max. Power, Vmp
Max. Power, Pmax
Temp. Coefficient of Isc , Ki
Temp. Coefficient of Voc , Kv
Diode Constant, a
Number of series cells
PV Sys.#1
[14]
3.35
18
3.15
14.6
45.99
3.18
-0.123
1.3
54
PV Sys. #2
[15]
5.99
48.7
5.61
41
230.01
3.5
-0.1235
1.3
72
Units
A
V
A
V
W
mA/K
V/K
120
0.5603 kW/m^2
0.534 kW/m^2
100
Power (W)
0.507 kW/m^2
0.479 kW/m^2
80
0.450 kW/m^2
60
0.45 kW/m2
40
20
0
0
5
Fig. 4.
10
15
20
Voltage VPV (V)
25
30
35
P/V characteristics of panel #2.
B. Benefit of DMPPT with Non-ideal DC-DC Converters
The four-switch non-inverting buck-boost converter shown
in Fig. 6 is the most flexible choice of topology for MPPT
applications, since it allows both vpvm > vpv and vpvm < vpv
1.35
1.3
PV System # 2
PV System # 1
1.25
1.2
Power Ratio, kp
in kp ≥ 1. The kp is unity for all test cases where the 6
panels have identical G, regardless of the value. These test
cases correspond to σ = 0, where DMPPT has no benefit over
MPPT. Secondly, while kp is correlated to σ as expected, the
spread in kp increases with σ. Interestingly, the results show
that DMPPT does not necessarily lead to large power benefits
even for large σ. For the PV system #1, a maximum kp of
1.31 was obtained, corresponding to a 31 % improvement in
harvested power for σ = 0.2. The maximum benefit is 35 %
for the second PV system. The maximum value, as well as the
spread of kp is clearly dependent on the panel parameters. The
maximum kp is generally obtained for cases where the large
σ comes from a single panel operating at a large deviation
from the others, which forces all panels to operate far from
the individual peak power points with the MPPT approach.
This analysis is useful for determining an upper bound on the
potential benefits of DMPPT, since the efficiency of the dc-dc
converters was neglected. Predicting the actual energy benefits
of DMPPT requires knowing the time profile of G1:6 and kp ,
which is highly dependent on the geographic location of the
array.
1.15
1.1
DMPPT has a benefit
1.05
1
0.95
0.9
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Standard deviation in lighting, σ
Fig. 5. Power ratio versus standard deviation in G for two PV systems,
assuming ideal dc-dc converter.
[2]. The topology of Fig. 6 is rarely operated as a true buckboost converter, where all four transistors are switched at the
switching frequency fs . This is primarily due to high switching
losses and poor efficiency. Instead, the converter is operated in
either buck, boost or pass-through mode according to Table II
[2]. The dc-dc converter is designed to regulate and maximize
the input power coming from the PV panel Ppv = ipv × vpv .
As a result, the output voltage of each dc-dc converter vpvm
fluctuates according to the local peak-power point, while the
output current istring is common to all the series-connected
dc-dc converters. As suggested by [2], the string current istring
can be regulated by the inverter to maintain a constant bus
voltage vbus . The buck-boost converter has higher conduction
losses compared to the standard boost and buck topologies due
to the additional switch in series with the current path. Using
a buck or boost converter reduces the system cost, however it
constrains the operating range of the string current istring as
shown in Fig. 7. For the buck topology, the string current must
be kept above istring,crit , which is determined by the panel
operating at the highest illumination and corresponding power
P2 . The duty cycle saturates to D = 1 for istring < istring,crit ,
as shown in Fig. 7(a). Similarly, the duty cycle saturates to D
= 0 for istring > istring,crit for the boost converter. In this
case, istring,crit is determined by the panel that operates at the
lowest illumination and corresponding power P1 , as shown in
Fig. 7(b).
In this section, the benefit of DMPPT is analyzed for the
same range of incident light levels as in previous section, with
the exception that the efficiency of the dc-dc converter η is
included in the calculation of the power ratio kp
n
η(ipvi , vpvi ) · max(vpvi · ipvi )
Pdmppt
n
kp =
= i=1
(2)
Pmppt
max(istring · i=1 vpvi )
The converter efficiency η depends on the mode of operation,
which is determined by the relationship between istring and
ipv according to Table II. The DMPPT analysis for the 6panel PV system #1 was repeated with the same 10k test
cases as Fig. 5, but using (2) for a more accurate evaluation
of DMPPT. For each test case, the istring was adjusted to
TABLE II
O PERATING M ODE OF F OUR -S WITCH B UCK -B OOST C ONVERTER
Condition
istring > ipv
istring > ipv
istring ≈ ipv
Mode
Buck
Boost
Pass
through
M1
pwm
on
on
M2
pwm
off
off
M3
on
pwm
on
M4
off
pwm
off
M (D)
D
1/D 1
Ipv
Ipv1
M1
+
vpv
Buck DMPPT
D=1:
PV does not operate at
peak power: limitation of
buck
P1
Istring1
Istring,crit
Vpv
Vpv1 Vpv2
Vpvm1 Vpvm2
Vpv1 Vpv2
Vpvm
(a)
Ipv
Istring
PV Characteristic
Ipv2
Ipv1
Boost DMPPT
Istring,crit
P2
D=0:
PV does not operate at
peak power: limitation of
boost
P1
P2
Istring1
P1
Vpv
Vpv1 Vpv2
Vpv1
Vpvm
Vpvm2
Vpv2 Vpvm1
(b)
Fig. 7. Limited operating range for DMPPT when using the (a) buck and
(b) boost converter.
1
0.98
0.96
0.94
0.92
Buck
Mode
Boost
Mode
Passïthrough
Mode
0.9
0.88
0.86
G=1000 W/m2, T=50C
2
G=800 W/m , T=25C
0.84
0.8
0
istring
P2
P1
P2
0.82
ipv
Istring
PV Characteristic
Ipv2
DCïDC Converter Efficiency (%)
achieve a constant bus voltage of vbus = 160 V. The dc-dc
converter parameters used in the efficiency calculations are
given in Table III. The dc-dc converter efficiency versus istring
is shown in Fig. 8 for different G. The calculated efficiency
includes the switching losses, gate-drive losses and conduction
losses in all components. For each test case, the mode and
resulting efficiency η was calculated for each of the 6 panels
according to the incident light G1:6 . The kp is plotted in
Fig. 9. The result shows that kp < 1 for small deviations
in G16 since the benefit of DMPPT is outweighed by the
power lost in the dc-dc converter. This clearly shows the need
for having an extremely high-quality power-stage in the dc-dc
converters, resulting in a significant cost overhead. This cost
overhead needs to be carefully considered in the context of
potential power savings due to DMPPT and the incremental
cost of additional PV panels. The maximum kp is significantly
reduced from 1.31 for the system #1 in Fig. 5 to 1.25 in Fig. 9.
This is a conservative number since in reality the DMPPT
system will avoid the need to have an additional MPPT stage
in the central inverter. It is important to state that the actual
kWh savings in a DMPPT savings is clearly dependent on the
time distribution of the light across the PV array. If only a
relatively small amount of time is spent with a large value of
σ, then the benefit of DMPPT is expected to be negligible or
even negative. Further work is required to determine realistic
time distributions of G across PV arrays through experimental
measurements.
2
G=600 W/m , T=15C
G=400 W/m2,T=15C
1
2
3
4
Istring (A)
5
6
7
8
Fig. 8. Efficiency of the multi-mode dc-dc converter for different levels of
incident light G.
M3
+
L
C vpvm
-
M2
Fig. 6.
M4
Four-switch non-inverting buck-boost converter.
III. E MULATED PV I MPLEMENTATION
The implementation of the hardware PV emulator (ePV)
of Fig. 3 is shown in Fig. 10. The system parameters are
listed in Table III. For each ePV, an isolated off-the-shelf
AC-DC power supply provides a 12 V input voltage to the
dc-dc converter, which is implemented using the same noninverting buck-boost topology as Fig. 6. Digital voltage-mode
control is implemented in an FPGA using a digital PID (DPID)
compensator. The voltage reference Vref is generated by the
I/V lookup table (LUT) that is stored in a RAM memory module. The LUT contains the pre-calculated I/V characteristic
of the ePV for a particular combination of incident light G
and junction temperature T . This configuration operates well
beyond the peak power point, for vpv > Vmp , since the PV cell
operate more like a constant voltage source in this region. The
system can also be re-configured to operate in average current
mode, where vpv is sensed to generate a reference current in
the lookup table. This provide superior stability in the region
vpv < Vmp , where the PV cell operates essentially as a current
source. The ePVs are linked together using an opticallyisolated serial communication bus, which is managed by a
ipv
1.35
1.3
Power Ratio, kp
1.25
1.2
1.15
1.1
M1
+
12 V
-
DMPPT has a benefit
M3
+
vpv
-
C
L
M2
1.05
M4
1
0.95
0.9
0
Hsense
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Vpv
0.2
Standard Deviation in Lighting, σ
Fig. 9.
Power ratio versus standard deviation for 10k test cases.
d[n]
Digital
Compensator
DPWM
TABLE III
mode
vpv[n]
e[n] -
Ipv
ADC
+
Vref [n]
SPI
Receiver
DC-DC C ONVERTER PARAMETERS FOR EFFICIENCY ANALYSIS
Parameter
On Resistance of MOSFETs, Ron
Switching Frequency, fs
Inductance, L
Inductor DCR, Rl
Capacitance, C
Value
15.4
234
22
10
50
Units
mΩ
kHz
µH
mΩ
µF
PC USB interface. The PC acts as the master and uploads the
individual I/V characteristics to each ePV, based on interrupts
from the user input. The individual I/V characteristics are precalculated in the PC, based on the input from a LabVIEW
graphical user interface (GUI). The calculation is based on
the modeling approach of [16] using the parameters of the PV
system #1 panel [14]. The GUI allows the user to enter the
PV parameters listed in Table I, as well as the temperature
and illumination conditions for each ePV. The current GUI
is configured for a 4 ePV system, as shown in Fig. 11. The
ePV operates in one of two possible modes depending on the
PV parameters selected by the user in the GUI. If the opencircuit voltage Voc is below the 12 V output of the off-the-shelf
AC-DC converter, the ePV operates in buck mode. If Voc >
12 V the ePV is programmed to operate in buck-boost mode
to cover the full range of the I/V curve. Efficiency is not a
major concern in the epV, therefore it is operated strictly in
buck-boost mode to simplify the controller and avoid having
to dynamically changing modes during operation.
Fig. 10.
RAM
Architecture of the emulated PV prototype.
Fig. 11.
LabVIEW GUI for the 4 ePV system.
peak power point, where the dv/di in the i/v curve is low. The
mismatch in the experimental data is primarily due to accuracy
limitations in the current and voltage sensing hardware, as well
as the finite precision of the i/v curve stored in the RAM. The
platform provides a flexible platform for testing future DMPPT
controllers.
V. C ONCLUSION
IV. E XPERIMENTAL R ESULTS
One of the fabricated ePVs is shown in Fig. 12. The
measured ipv /vpv and ppv /vpv characteristics of the fabricated
ePVs are shown in Fig. 13(a) and (b) respectively, for four
different combinations of T and G . The solid lines correspond
to the ideal values calculated inside the PC. The ePV voltageloop compensation is optimized for high stability near the peak
power point, where the DMPPT system is intended to operate.
The ePVs are unable to regulate voltages below 300 mV due
to duty-cycle saturation. The voltage mode controller used for
the experimental work is inherently more stable beyond the
It was shown that DMPPT can result in up to 25 %
power savings compared to standard MPPT, depending on the
standard deviation in incident light. Further work is required
to determine the actual time distribution of the illumination.
Nonetheless, the efficiency of the local DMPPT block must be
carefully considered, since it was shown that the benefits of
DMPPT can be outweighed by losses in the dc-dc converter
for near-uniform lighting conditions on the array. The PV
panel emulator achieves a close matching with programmed i/v
characteristics and provides a flexible platform for optimizing
future DMPPT systems.
Buck-boost
power stage
[3]
[4]
RAM (stores
dynamic I/V
table)
[5]
[6]
CPLD
(non
volatile)
[7]
[8]
[9]
[10]
[11]
Fig. 12.
Emulated PV panel prototype.
[12]
4
G=1000 W/m2, T=25C
G=950 W/m2, T=23C
3.5
[13]
2.5
PV Current, I
pv
(A)
3
2
[14]
G=850 W/m , T=40C
2
2
G=900 W/m , T=50C
[15]
1.5
[16]
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
12
14
16
18
20
PV Voltage, vv (V)
(a)
40
35
G=1000W/m2,T=25C
2
G=950W/m , T=23C
PV Power, Ppv, (W)
30
2
G=900W/m ,T=50C
G=850W/m2,T=40C
25
20
15
10
5
0
0
2
4
6
8
10
PV Voltage, vpv (V)
(b)
Fig. 13. (a) Measured I/V and (b) P/V characteristics for the ePV under 4
conditions.
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