THERMAL CHARACTERISTICS OF MICROINVERTERS ON DUAL-AXIS
TRACKERS
by
MOHAMMAD AKRAM HOSSAIN
Submitted in partial fulfillment of the requirements
For the degree of Master of Science
Department of Mechanical and Aerospace Engineering
CASE WESTERN RESERVE UNIVERSITY
May, 2014
Thermal Characteristics of Microinverters on Dual-axis Trackers
Case Western Reserve University
Case School of Graduate Studies
We hereby approve the thesis1 of
MOHAMMAD AKRAM HOSSAIN
for the degree of
Master of Science
Dr. Alexis Abramson
Committee Chair, Adviser
Department of Mechanical and Aerospace Engineering
01/30/2014
Dr. Roger French
Committee Member, Co-Adviser
Department of Materials Science and Engineering
01/30/2014
Dr. Joseph Prahl
Committee Member
Department of Mechanical and Aerospace Engineering
01/30/2014
Dr. Yifan Xu
Committee Member
Department of Epidemiology and Biostatistics
1
01/30/2014
We certify that written approval has been obtained for any proprietary material contained therein.
Thesis defense date: 01/30/2014
Dedicated to science
and the pursuit of progress.
Thermal Characteristics of Microinverters on Dual-axis Trackers
Abstract
by
MOHAMMAD AKRAM HOSSAIN
0.1 Abstract
The thermal characteristics of microinverters on dual-axis trackers operating under
real-world conditions were analyzed using a statistical analytical approach. 24 microinverters connected to 8 different brands of photovoltaic (PV) modules were analyzed
from July through October 2013 at the Solar Durability and Lifetime Extension (SDLE)
SunFarm at Case Western Reserve University (latitude 41.50 , longitude -81.640 ). Exploratory data analysis shows that the microinverters’ temperature is strongly correlated
with ambient temperature and PV module temperature, and moderately correlated with
irradiance and AC power. Ambient temperature is the influencing factor under conditions of low irradiance in morning hours, when the irradiance is below 60 W/m 2 . Noontime data analysis reveals that the microinverters thermal behavior is more strongly influenced by PV module temperature than AC power. Using a Euclidean distance measuring principle and average linkage criteria, a hierarchical clustering technique was also
applied to noontime microinverter temperature data to group the similarly behaved microinverters. Microinverter temperature clustering shows that the clustering groups are
more strongly influenced by PV module temperature than AC power. A linear regression
iv
model was developed to predict the temperature of the microinverters connected to different brands PV modules. The predictive model is a function of ambient temperature,
PV module temperature, irradiance, AC power data, and the interaction between power,
irradiance and module temperature. The difference between actual microinverter and
predicted microinverter temperature lies between 0.40 C to 1.60 C at a 95% confidence
interval.
v
Acknowledgements
I would like to express my sincere gratitude to my co-advisors Dr. Alexis Abramson
and Dr. Roger French for their continuous support, patience, motivation and guidance
for this project. I also would like to thank the rest of my thesis committee: Dr. Joseph
Prahl and Dr. Yifan Xu for their encouragement and insightful comments about this
project. Thanks to Underwriters Laboratories (UL) for providing financial support for
this project.
I would like to especially thank to Dr. Timothy Peshek and Dr. Laura Bruckman for
their insights, valuable comments and opinions while working on this project. Thanks
to all the members in Solar Durability and Lifetime Extension Center for their diligence,
patience and resourcefulness. I owe special thanks to Yang Hu and Zachary Baierl for
assisting me a lot in building the test setup.
Assistance and technical support from researchers from the Medical Informatics Division of EECS, especially Yashwanth Reddy Gunapati and Tarun Jian were extremely
valuable in completing this work.
vi
Table of Contents
Abstract
iv
Acknowledgements
List of Tables
vi
x
List of Figures
xii
Chapter 1. Introduction
1
World Energy Scenario
2
Evolution of PV cell and module
5
PV System
8
Thermal Model for PV System
8
Inverter system
10
Microinverter History and Evolution
12
Microinverter Topology
13
Critical to Lifetime Performance (CLP) Components
14
Power Loss inside Microinverter
16
Reliability of Microinverters
17
Lifetime and Degradation Science
21
Chapter 2.
Experimental Setup
24
SDLE SunFarm
24
Metrology Platform at SDLE SunFarm
27
Data Acquisition System
29
Experimental Setup Overview
30
vii
Chapter 3. Analysis Methods
34
Data validation
34
Exploratory Data Analysis
36
Correlation Coefficient
36
Local Solar Time
37
Normalized Temperature
37
t-Test Statistics
37
Cluster Analysis
38
K-means clustering
38
Linear Regression Model
39
R software
40
Chapter 4. Results and Analysis
41
Exploratory Data Analysis (EDA)
41
Morning Data Analysis
45
Noon Data Analysis
49
Cluster Analysis
62
Linear Regression Model
66
Chapter 5. Discussion
Influence of Irradiance on PV Module and Microinverter Temperature
71
71
Influence of AC Power Output and PV Module Temperature on Microinverter
Temperature
72
5.4 Influence of Ambient Conditions on Microinverter Temperature
74
Clustering Analysis
76
viii
Linear Regression Model
78
Chapter 6. Conclusions
80
Chapter 7. Suggested Future Research
82
Appendix A. Preparation of this document
84
Appendix B. Thermal performances at different power range
85
Appendix. Complete References
90
ix
List of Tables
1.1
List of CLP of components with stressors, common failure modes and
effects on the microinverter
15
4.1
Correlation coefficient for different variables for the Q.t12 systems
43
4.2
Correlation coefficient for different variables for the Q.t12 systems in
the morning time from July through October, 2013
4.3
45
Comparison of PV module temperature, and microinverter
temperature with ambient temperature at different irradiance
zone for the Q.t12 system in the morning from July through October,
2013
4.4
47
Variation of normalized module and microinverter temperature at
different irradiance zone for the Q.t12 system in the morning from
July through October, 2013
4.5
Correlation coefficient for different variables for the Q.t12 systems at
noontime from July 1 through October 30, 2013.
4.6
49
Thermal performances of the P.t.12 systems at different power range
from July 1 through October 30, 2013.
4.7
48
51
Thermal performances of the T.t.14 systems at different power range
from July 1 through October 30, 2013.
52
4.8
Thermal performances of the L.t.6 systems at different power range
53
4.9
The average power and temperature difference between the L.t.6 at
noon time
53
x
4.10
The rise in temperature in the site 12 PV modules and microinverters
during noon time
4.11
54
The coefficient values of different variables for the predictive model
(Equation 4.1)
67
B.1
Thermal performances of O.t.12 modules at different power range
85
B.2
Thermal performances of R.t.14 modules at different power range
86
B.3
Thermal performances of S.t.14 modules at different power range
87
B.4
Thermal performances of K.t.6 modules at different power range
88
B.5
Thermal performances of Q.t.12 modules at different power range
89
xi
List of Figures
1.1
World energy consumption in year 2011 7
1.2
Annual investment in different renewable energy sectors across the
world between 2001-2012
1.3
4
Different type of inverter systems: a) Central /string inverter and b)
microinverter assembly
1.4
3
9
Different type of inverter systems: a) Central /string inverter and b)
microinverter assembly
11
1.5
Circuit diagram of a microinverter
14
1.6
Unscheduled maintenance cost for PV system operation
18
1.7
Failure count for components of a PV system
19
2.1
Top figure: SDLE SunFarm layout, bottom figure: dual axis tracker
with PV modules and sample trays
2.2
a) Thermocouple on the backsheet of the microinverter, b) data
cabinet
2.3
25
28
Baseline DC output power of PV modules measure by SPIRE 4600
solar simulator
30
2.4
Solar irradiance from July 1 through October 30, 2013
32
2.5
AC Power output data for O.t12 systems from July 1 through October
3.1
30, 2013
33
Validation of thermocouple recorded temperature data
35
xii
4.1
Scatter pairs plots for the Q.t12 systems from July 1 through October
30, 2013.
4.2
Ambient Temperature vs. microinverter backsheet TC temperature
for the Q.t12 systems from July through October 2013
4.3
56
Variation of normalized microinverter backsheet temperature for
different modules at different power range
4.11
54
Variation of normalized module backsheet temperature for different
modules at different power range
4.10
50
Normalized module backsheet, microinverter backsheet and
microinverter internal temperature for the T.t14.1 system
4.9
48
Scatter pairs plots for the Q.t12 systems at noontime from July 1
through October 30, 2013.
4.8
46
Irradiance vs normalized module backsheet and microinverter
backsheet TC temperature in the morning for the Q.t12 systems
4.7
45
Scatter pairs plots for the Q.t12 systems in the morning time from July
through October, 2013
4.6
44
Variation in AC power output of microinverters in the Q.t12 systems
for different ambient temperature range
4.5
43
Irradiance vs. AC Power output for the Q.t12 systems from July
through October 2013
4.4
42
57
Variation of normalized module backsheet temperature for power
range 190-210 W
58
xiii
4.12
Variation of normalized microinverter backsheet temperature for
power range 190-210 W
4.13
Variation of normalized module backsheet temperature for power
range above 210 W
4.14
61
Hierarchical cluster analysis of time-series AC Power data at noon
from July 1 through October 30, 2013.
4.16
60
Variation of normalized microinverter backsheet temperature for
power range above 210 W
4.15
59
62
Hierarchical cluster analysis of normalized PV module backsheet
temperature time-series data at noon from July 1 through October 30,
2013.
4.17
63
Hierarchical cluster analysis of normalized microinverter backsheet
temperature time-series data at noon from July 1 through October 30,
2013.
4.18
Normalized microinverter backsheet temperature K-means diagram
for full time-series data set
4.19
64
65
Hierarchical cluster analysis of normalized microinverter backsheet
temperature for the corrected time-series noon time data from July 1
through October 30, 2013.
4.20
Residual Plot: Regression validation for predictive linear regression
model for the L.t6 microinverters
4.21
66
68
Comparison between predicted model with actual temperature for
the L.t6.2 microinverters on 17 th September, 2013
69
xiv
4.22
Comparison between predicted model with actual temperature for
the L.t6.2 microinverters on a cloudy day
70
xv
1
1
Introduction
The growth of solar energy has been remarkable over the past few years. This remarkable growth has been majorly influenced by the declining cost of photovoltaic modules.
With years of research and development, the global average price of photovoltaic (PV)
module is now less than $0.70 / watt 1 . However one of the major concerns for the future of the PV industry is the reliability of the PV system, inclusive of PV modules, interconnects, the inverter system, the grid connection and the mounting systems. Modern
commercial PV module manufacturers typically provide a 25 year warranty and claim
1% power degradation per year. However a system is only as good as its weakest link, and
the reliability of the inverter system in particular is of high concern 2,3 . Although limited
studies have been conducted to date, an understanding of inverter thermal characteristics and behavior would provide critical insight to associated reliability issues. Therefore, the focus of this thesis is to analyze the characteristics of a PV power plant operating at the SDLE center in Cleveland, Ohio to provide insight to the thermal behavior of a
specific class of inverters: microinverters.
Introduction
2
1.1 World Energy Scenario
One of the major concerns in today’s world is global warming. The consequences of
global warming are evident in the global temperature rise, sea level rise, climate change
and frequent extreme weather conditions. Greenhouse gas is the primary contributor
to global warming as more than 80% of the greenhouse gas emission is produced by the
burning of fossil fuels 4 . According to the International Energy Agency (IEA), final energy
consumption reached 8918 MTOE (million tonnes of oil equivalent) in the year 2011 and
caused 31342 Mt (million tons) of carbon dioxide emissions 5 . The Carbon dioxide emission rate has almost doubled since 1973 5 , and the emission rate continues to increase at
an alarming rate as the demand for energy grows. For the first time in several hundred
million years, the carbon dioxide level in the atmosphere exceeded 400 ppm (parts per
million) in May 2013 4 . One of the viable options for reducing carbon dioxide emissions
is to use renewable energy sources instead of fossil fuel sources. According to the IEA,
renewable sources supplied about 11% of the total energy consumption globally in the
year 2011 and contribute 19% towards global electricity generation. Hydro, solar, wind,
biomass, ocean and geothermal energy are commonly considered as viable sources of
renewable energy. Although the total consumption of renewable energy sources is relatively small compared to fossil fuel energy source consumption (figure 1.1), the growth
in the renewable energy sector is very strong (figure 1.2). Dynamic growth has been observed in the solar and wind energy sectors, in particular. In fact, the total worldwide
investment in renewable energy was US $240 billion in 2012, although this was a decrease of 11% compared to the investment made in 2011 6 . Uncertainty in energy policy
and rapidly falling equipment costs of solar and wind energy were the major reasons
cited for the decrease in investment in 2012.
Introduction
3
Figure 1.1. World energy consumption in year 2011 7
Solar energy is the largest source for carbon-neutral energy. Solar energy can be
used either by converting it to electricity using PV cells or by capturing the energy as
heat; known as solar thermal. The development of PV technology has been rapid, and
the corresponding costs have decreased significantly. In 2010, the global PV power generation capacity was 20.9 GW and by the end of 2012, it reached 100 GW capacity 6 . According to IEA estimates, the cumulative global PV capacity will reach around 3000 GW
by 2050 and meet 11% of the demand for global electricity 8 . The European Union is the
leader in the PV market as their cumulative installed capacity is around 69 GW. China
is the emerging figure in the PV market. About 3.7 GW was installed in China in 2012
and their cumulative PV capacity was about 7 GW. These numbers indicate an approximately 600% growth in comparison to 2010. According to National Energy Administration of China, the projected target for 2013 is an additional 10 GW installation. In the
US, 3.3 GW has been installed in 2012, and total cumulative PV capacity reached 7.7 GW,
Introduction
4
Figure 1.2. Annual investment in different renewable energy sectors
across the world between 2001-2012
with 7.2 GW connected to the grid. In terms of funding, the solar energy sector has received the largest amount of investment compared to other renewable energy sectors
for 3 years in a row (figure 1.2). With increased reliability and decreasing price trends of
PV modules, the worldwide PV market is expanding rapidly, and PV power generation
is becoming a competitive option for electricity generation against traditional fossil fuel
Introduction
5
based electricity generation. However, the price and competitiveness of PV systems may
still depend on financial incentives to secure significant growth into the future.
1.2 Evolution of PV cell and module
PV cells are semiconductor based electrical devices that can convert sunlight to electricity by using the photovoltaic effect. The photovoltaic effect was first reported by French
physicist Edmund Becquerel in 1839 9 . Early solar cells were made of selenium on a thin
gold layer with less than a 1% conversion efficiency. The first silicon based solar cell was
reported by Russel Ohl in 1941 10 . Later, Daryl Chapin, Calvin Fuller and Gerald Pearson from Bell Labs developed a 6% efficient PV cell in 1954 which they improved up
to 10% 11 . This technology was licensed by National Fabricated Products in 1955 who
released the first commercial solar cell product known as a silicon solar cell battery 12 .
Although the widespread commercialization of PV cells was unsuccessful at that time,
PV was integrated in space applications to, for example, power satellites. Later developments in the early 70s included products from Sharp in Japan and RTC (a subsidiary of
Philips) in Europe , and Solar Power Corporation in the US. worked on the development
of terrestrial PV cell in 1960s. At that time, the reported price by Solar Power Corporation was US $ 20/W for 1000 modules 12 . The high price per watt was not competitive
compared to the fossil fuel based electricity generation systems. This was the primary
reason for low growth of PV market in 1970s.
There was no standard PV module qualification test before 1975, and at this time
there were large reliability concerns associated with PV. As a result in 1975-76, the US
government purchased 54 kW of commercially available PV modules from US-based
Introduction
6
manufacturers and studied them to ascertain their lifetime and performance characteristics 12 . These PV modules were exposed in Florida, Puerto Rico, Arizona and Cleveland 13 , and the performance and degradation mechanism of PV modules in different
environmental conditions were studied. Additionally, Telecom Australia Research Department ran accelerated testing on a similar set of commercially available PV modules.
Their study suggested the tested PV modules were not mechanically rugged enough for
outdoor use 14 . As a result of this research, a modified PV product was released by Philips
in 1976 with a 15 year field life specification. The PV modules consisted of 37 cells encapsulated in silicone rubber between two glass sheets with rubber edge sealing. In contrast, Spectrolab also developed a PV module with the cells now laminated to front cover
glass sheets using polyvinyl butyral, and Mylar was used as the backsheet 12 . Aluminum
paste was also employed on the back of the cell and screen printing technology successfully for cell fabrication. The US government again purchased 127 kW of PV modules in
1976 and ran tests consisting of temperature cycling, humidity, cyclic pressure loading,
as well as twist and electrical ground resistance tests 12 . The results showed that the PV
modules developed by Spectrolab were the most resistant against these environmental
stressors 15 . Spectrolab PV modules are considered as the predecessor of modern day PV
modules.
Today the market is dominated by crystalline silicon modules. These modules are
mechanically robust enough to come with a 25 year limited warranty and a guarantee of 1% power degradation per year. Crystalline silicon modules can be categorized
into mono-crystalline and polycrystalline, also referred as multi-crystalline, silicon type
cells. They consist of front surface glass, encapsulant, 60 to 72 interconnected PV cells, a
backsheet and a metal frame. The common front surface glass is a low cost transparent
Introduction
7
tempered low iron glass with self-cleaning properties. This type of glass is strong, stable
under ultraviolet (UV) radiation and water and gas impervious. Ethylene vinyl acetate
(EVA) is commonly used as encapsulant material. It helps to keep the whole module
bonded together. EVA is optically transparent and stable under high temperature and
UV radiation. Generally EVA is placed between front glass surface and PV cell, and between backsheet and PV cell. The backsheet is typically made of Tedlar which provides
protection against moisture and gas ingress. The module frame is typically made of aluminum 16 .
Recent rapid growth of PV systems can be attributed to significantly reduced installation cost of the PV system in recent years. In fact, the price of PV modules dropped
from US $3.4/W to US $1.3/W from 2008 to 2011 17 . By the end of 2012, the PV module
price dropped below US $1/W 6 . However, the total PV system price and installation cost
were also reduced but at a much slower rate than the PV module price reduction rate
alone. In the US, the median installation cost of a residential PV system less than 10 kW
was around US $8.1/W in 2008, and the price dropped to jsut US $6.1/W by 2011 7 . The
installation cost has also varies significantly among countries, which can be attributed
to a number of factors: differences in incentive levels, interconnection standards, labor
costs, and permitting approval costs. The installation cost of small residential PV system
less than 10 kW was US $3.4/W in Germany and US $4/W in Australia 7 . The installation
cost difference can be attributed to a number of factors: difference in incentive levels,
interconnection standards, labor cost, permits and approval cost. The difference of installation cost has significant impact on the growth and market size of PV industry. That
is why the growth and market of PV industry is higher in Germany compared to US.
Introduction
8
1.3 PV System
A complete PV system consists of several sub-systems. The first subsystem is for power
generation, consisting of: PV cells, modules and arrays. PV arrays are created by interconnecting a large number of PV modules with each other. The second sub-system is
the interconnect and PV wire system. Depending upon the inverter system, the interconnect can in series or parallel. The final subsystem is the PV inverter system. The
output of a PV module or array is direct current (DC) power. Therefore, in order to connect to the grid or directly to common household appliances, the DC power must be
converted to utility frequency alternating current (AC) power. This power conversion is
completed via a PV inverter system. Currently, two types of inverter systems are used in
PV systems: string inverters and microinverters, as depicted in Figure 1.4.
1.4 Thermal Model for PV System
A simple thermal model can be employed to give insight to the different parameters and
how they are correlated with each other. In addition, the model can be used to understand the dynamic response of module temperature with the changes of parameters.
PV module temperature is influenced by irradiance, ambient temperature, power output, module material and associated heat transfer coefficients, including radiation and
convection due to the wind. Many researchers have developed models to examine the
thermal behavior of PV modules using an energy balance of convection, conduction,
and radiation heat transfer along with a heat generation term arising from extraneous
heat occurances from power output ineffeciencies 18–26 . Test et al. 26 (1981) and Sharples
et al. 25 (1998) developed their own empirical forced convection heat transfer coefficient
Introduction
9
Figure 1.3. Different type of inverter systems: a) Central /string inverter
and b) microinverter assembly
equations using the data of wind speed measured 1 m and 1.5 m above the PV module
surface respectively, to predict the thermal behavior of the PV modules. Their work indicates that accurately incorporating the effects of wind speed into the thermal model
of the PV system is challenging. The wind flow over the PV modules is turbulent, with
particularly unpredictable fluid flow effects occurring near the roof edges, PV module
edges or at the location of other obstructions.
Introduction
10
1.5 Inverter system
Even though the working principle and topology is similar in both string inverters and
microinverters, there are significant differences between their interconnect systems and
PV system output efficiency. In string inverters, a number of PV modules, electrically
in series with each other, are connected together and the cumulative total DC power
generated by the connected PV modules is supplied to the string inverter (figure 1.4a).
The typical size of string inverters varies from 1 KW to 250 KW. Generally string inverters show high a conversion efficiency, robust design capability and a low cost per watt.
However, the current of all PV modules in an array connected to the string inverters
is governed by the lowest current module as a result of the series connection. Consequently, maximum output can not be guaranteed. Shading of one or more PV modules
within the array, and the resulting power mismatch between the PV modules can lead
to this situation. Particularly, shading is a very concerning issue as it can force other
unshaded modules to operate away from their optimal maximum power point tracking
(MPPT), creating a hotspot in the shaded module, leading either to cracking or damage.
In some extreme cases, this can lead to fire. The other disadvantages with string inverter
system are: a lack of module level monitoring, the required use of a high voltage line and
the potential for a single point of failure.
In a microinverter system, a single microinverter is dedicated to one PV module,
and the AC output from different microinverters’ of an array are in a parallel connection with each other (figure 1.4b). The typical size of microinverters vary from 190 W to
300 W. There are several advantages of microinverters over traditional string inverters.
Each microinverter is available to only one PV module, resulting in an optimized output from each module using panel level MPPT. Every PV module is connected in parallel
Introduction
11
Figure 1.4. Different type of inverter systems: a) Central /string inverter
and b) microinverter assembly
with each other so shading, or a defective panel does not reduce the performance of the
whole array. The microinverter is free from a potential power mismatch, which gives
design flexibility so that one can create an array with different power rating without losing performance. Microinverters are incorporated with panel level monitoring, and as
a result, a module failure can be detected instantaneously and remotely. Furthermore,
the use of a low voltage DC line increases safety. The disadvantages of microinverters
include: a higher cost, lower efficiency compared to string inverters and a greater complexity of installation.
Introduction
12
1.6 Microinverter History and Evolution
Ascension Technology first developed the microinverter in 1991 in the USA and in 1994,
they submitted their device to Sandia Labs for testing 27 . Throughout the 1990s, microinverters with varying attributed were introduced by Ascension Technology, Mastervolt, and OKE Services. OKE microinverters showed highly reliable performance when
subjected to temperature cycling and humidity freezing tests under laboratory conditions. However, under real-world outdoor conditions, a large number of failures were
reported within eighteen months of installation 28 . Due to their poor reliability, cost and
efficiency, first generation microinverters could not compete against traditional string
inverters.
Motivated by the opportunity present in the residential market, Enphase Energy,
founded in 2006, released their first microinverter product in 2008. By 2013, they introduced their fourth generation microinverter. Enphase offers either a 15 or 25 year
warranty on their microinverters, dependent on the specific product class 29 . According
to Enphase, the mean time between failures of their microinverters is 300 years. Their
peak efficiency is around 96.3% 30 . The Enphase microinverters have three connections
wires: one for DC connection and two for AC connections so that the microinverter can
be daisy-chained. The microinverters communicate through the AC connections to a
central collection box, Enphase Enlighten. Enlighten collects data which includes DC
and AC power data, temperature and frequency data from every microinverters and reports it to the web interface in five minute intervals. Enphase uses electrolytic capacitors
and potting to fill the microinverter enclosure. Potting provides component protection
against vibration and helps to improve heat dissipation within microinverter. The price,
Introduction
13
reliability, improved warranty and panel level monitoring makes Enphase very popular for residential PV systems, and by September 2011, Enphase shipped their millionth
microinverter 31
Microinverter market share, in particular Enphase, is rapidly growing in the small
residential PV system market. However, in terms of worldwide PV installation, Enphase
represents only 0.5% of the total PV cumulative capacitys 32 . Enecsys is another popular
microinverter company. Their microinverter is based on thin film capacitor technology 33 , 27and they use a potting-free enclosure. Enecsys launched their second generation microinverter in April 2013 with a peak efficiency at about 96% and a 25 year of
warranty 34,35 . Exeltech and Solar- Bridge are two other popular microinverter brands
available in the market, with 25 year warranties and peak efficiencies of approximately
95-96% 36,37 .
1.7
Microinverter Topology
A simple one stage microinverter topology is shown in figure 1.5. The total circuit can
be divided into two sections: high and low frequency zones. The high frequency zone is
also known as the resonant inverter zone. The DC power from the PV module is fed into
the high frequency side of the microinverter. The current flow towards the transformer
is controlled by the high frequency MOSFET switches. The transformer converts the low
voltage input to the high voltage sinusoidal waveform output at the switching frequency.
This zone converts the high frequency power waveform generated from the resonant
inverter to the much smaller line frequency waveform by using high voltage MOSFETs.
Capacitors act as storage of the input power and filter out the input ripple to supply a
Introduction
14
Figure 1.5. Circuit diagram of a microinverter
constant current. Generally 1:12 (depending upon topology) transformers are used to
match the grid voltage.
1.8 Critical to Lifetime Performance (CLP) Components
MOSFETs and capacitors are considered critical components (Table 1.1) of microinverters 38–40 . The lifetime of the electrolytic capacitor is very much dependent upon the
operation environment, and high operating temperature evaporates the aqueous component electrolytes, leading to an increase in equivalent series resistance (ESR). This introduces more dissipative heat inside the capacitors which in turn accelerates the evaporation rate and reduces the capacitance. Since the ripple current amplitude increases
Introduction
15
Table 1.1. List of CLP of components with stressors, common failure
modes and effects on the microinverter
CLP
Compo- Common failure modes
nent
MOSFET
die attach breakdown,
wire
bond
fatigue,
dopant drift
Diodes
die attach breakdown,
wire
bond
fatigue,
dopant drift
Capacitors
electrolyte evaporation,
dielectric breakdown
Inductor
ferrite cracking
Stressors
System-wide manifestation
Thermal stress, RH, Reduced efficiency, short circuit
Power cycling, voltage
module, excess heat
Thermal stress, RH, Reduced efficiency, short circuit
Power cycling, voltage
module
Thermal stress, RH, Reduced efficiency, increase
Current surge, high ripple amplitude
voltage
Thermal stress, high Reduced efficiency, excess heat
current
RH= Relative humidity
with the reduction of capacitance, a higher ripple current may result, causing greater
Joule heating,and pushing the microinverters towards capacitor dry out failure. Even
more, ripple current is highest at solar noon time when the solar irradiance at its peak,
and this is when the microinverter temperature is also highest. Therefore a time series
study of noon time data can provide important thermal information that can help one
to understand the degradation mechanism of the microinverter better.
MOSFET failure can occur due to rapid heat build up on the die package as observed
in the case of IGBT during the power cycle 41,42 . Heat build up in the die degrades the
die attachments and causes thermal stress that possibly lead other failures such as wire
bond breakage. Additionally a sudden inrush of current through the inductor or a blocking voltage surge in the inductor can induce an avalanche failure of the MOSFET. The
likelihood of avalanche failure is higher at solar noon time due to high power-voltagecurrent conditions.
Introduction
16
1.9 Power Loss inside Microinverter
The power loss inside microinverters falls into two categories: switching loss and inductor loss. Switching loss occur at the MOSFETs in the resonant inverter 43 . Switching
losses occur because the only time that both the drain-source voltage and current are
nonzero is during the ON-OFF transition times. This loss mechanism is reduced with
high speed MOSFETs, with low recovery times, or by using a zero voltage switch topology (ZVS). In ZVS, a resonant condition between the transformer leakage inductance
and output capacitance of the MOSFET allow for the output capacitance to be fully discharged before the MOSFET switches ON. Conduction loss is related to the drain-source
resistance (Rd s ) and RMS current (Iswi t chR M S ) through the MOSFET. The charging-discharging
loss is related to the gate charge (Qg ), gate source voltage (Vg s ) and switching frequency
(fswi t ch ) 43 . The expression for switching power loss (P swi t chl oss ) is:
2
P swi t chl oss = I swi
t chR M S R d s + 2Q g V g s f swi t ch
(1.1)
Inductor loss is comprised of core and winding losses. Core loss can be estimated by
Steinmetz equation 43 for core loss:
β
P cor el oss = Vc k f α B peak
(1.2)
Here Pcor el oss is the loss in the core, Vc is the core volume, f is the inductor current frequency, Bpeak is the amplitude of core flux density and α,β,κ are the Steinmetz parameters.
Winding loss is associated with RMS current (I RM S ) through the inductor and AC
resistance(R L AC ) of the inductor. It can be expressed as:
2
P wi nd i ng l oss = I RM
S R L.AC
(1.3)
Introduction
17
The inductor power loss is larger than switching loss due to the large volume and AC
resistance of inductor. The inductor power loss does not have a significant effect on the
inductor. However, it forces the neighboring components to operate to high temperature environment. The switching loss induce periodic thermal stress on the MOSFETs
and can lead to die degradation.
1.10 Reliability of Microinverters
PV system reliability has always been of critical concern for the industry. One famous
example is the Carrizo Plains disaster, a 5.2 MW PV plant that had to shut down just after four years in operation due to design errors. These errors included poor choice of
PV cells, neglecting UV absorbing glass front sheet and using of fast cured EVA 44 . The
reliability of all components of the entire PV system must be considered to minimize
failure and maintenance and enhance safety. Recently, the National Renewable Energy
Laboratory (NREL) conducted system level performance of the PV system under realworld conditions. According to their study of a PV system managed by Tucson Electric
Power,the inverter system failure(figure 1.6) was the reason for 69% of the unscheduled
maintenance costs 3 . In another study of Sandia National Laboratories, conducted between 2003-2007, the number of string inverter failures was at least 4 times higher (figure 1.7) than the failure of any other component 2 .
As discussed before, various CLP components of microinverters (described in table 1.1) are sensitive to thermal stress. However, the microinverters must withstand high
thermal stress conditions, particularly at the solar noon time when power and ambient
temperature are typically highest. Additional stress may occur when the power output
Introduction
18
Figure 1.6. Unscheduled maintenance cost for PV system operation
of the PV module saturates the microinverters. Morning and afternoon lowlight conditions can put the microinverter into a high frequency turn on and off state, which can
be a potential source of thermal stress and current surge. Since microinverters have to
be installed outdoors, these systems must also endure a wide variety of climate conditions, including hot-dry, hot-humid and, freezing, for example. These conditions can
induce various degradation mechanism. However, the reliability of microinverters has
not studied intensively. As discussed above, microinverters are similar to string inverter
technology although one major difference is the amount of power that each must handle and the boost ratio from DC-AC voltages. Nonetheless, they are both expected to
suffer similar kinds of reliability issue under a real-world working environment. First
generation microinverters exhibited very poor reliability in real-world operation 28 that
was one of the reasons behind their demise.
Introduction
19
Figure 1.7. Failure count for components of a PV system
Researchers across the world have worked on studying and improving the reliability
of the string inverter system. For example, Rohouma et al. 45 (2007) studied and compared the reliability of central, string and module integrated inverters (microinverters)
where they found the average useful life of the microinverters is long compare to the
string and central inverters. Additionally they found that cable losses, and shading and
mismatch losses is lower in microinverters compared to the other configurations. In
their study, the failure rates of PV system components were assumed to be constant. Ristow et al. 46 (2008) proposed a prediction model for string inverters using the subsystem
reliability. For their study, the string inverters were divided into following subsystems:
Introduction
20
storage-capacitor subsystem, power-stage-drive subsystem, cooling subsystem and isolation transformer. They found capacitor failures dominate over other types of subsystem failures. Chan et al. 40 developed a reliability prediction model using the data collected from four PV systems to determine the most vulnerable components within the
PV system. According to the model, the most failure-prone devices are power MOSFETs
and their failure is related to power dissipation. Dhople et al. 47 (2012) studied inverter
reliability using Markov reliability models and integrated with energy yield estimation.
Most of these reliability models are largely based on an approach outlined in the military
handbook MIL-HDBK 217 that assumes a consistent failure rates of all the components
to develop a prediction model. However, the failure rates can be very different in different environmental and operating conditions since the stress development rate and the
total stress vary with environmental and operating conditions.
To understand why consistent failure rates might not be an appropriate assumption,
consider two scenarios in which one is mounted on a roof and another is located on a
dual-axis tracker (on the ground). In a roof setup, the microinverter may not be exposed
to sufficient wind to provide cooling.This is because the distance between PV modules
and microinverters in a roof setup is very small. As a result, the roof surface absorbs radiated heat, becomes hot and can lead to subsequent heating and thermal stress in the
microinverter. For the scenario of the dual-axis tracker, the backside of the PV module
and microinverter is open. There is a larger exposure to wind. and no hot roof present
to cause additional heating. Therefore, the thermal conditions and stresses experienced
by the microinverters in both cases will be very different. This is one reason why constant failure rates recommended by MIL-HDBK-217 can not be assumed. Jais et al. 48
(2013) discussed the limitations, inaccuracy and misleading output of the prediction
Introduction
21
reliability models based on MIL-HDBK-217. In their study, they compared the failure
rate predicted by the methodologies described in MIL-HDBK-217 and found significant
difference between actual and predicted failure rate. In some cases, the ratio between
predicted and actual life is 218:1. Sandia National Laboratories, also working on inverter
reliability, studied the degradation of the individual CLP components: IGBT 49 and bus
capacitors 50 in both ideal and extreme operating conditions. They examined thermal
profiles of IGBT, transformers and capacitors in real-world operating conditions, and
developed an accumulated damage model assuming that the degradation of these components is thermally activated 51 . The ulitmate goal of this realibility program is to develop prognostic and health management techniques for the inverters.
1.11 Lifetime and Degradation Science
Traditional reliability prediction models are based on failure data and consider constant
failure rates for various operating and environmental conditions. As discussed above,
this approach leads to inaccurate lifetime predictions and premature failures are typically observed in devices designed using these prediction models 52 . Indoor accelerated
tests can introduce additional stressors, but it is impossible to attain the unique or precise combination of different stressors’ influence under real-world operating conditions
in the simulated environment. Furthermore, the outcome of accelerated tests based on
Introduction
22
one or several stressors can lead to erroneous assumptions since some stresses have synergistic effects on the systems. In contrast, a prognostic approach, also known as prognostic and systems health management (PHM), allows one to predict a device’s operating state from an analysis based on present and historical data when the device is operating in real-world conditions 52 . PHM is particularly attractive for lifetime and degradation science in that it uses a statistical analysis that incorporates system responses under different stress conditions, level of responses, and different stress modes and rates
to provide a better understanding of the lifetime performance of the system.
Data driven and model based approaches are two common techniques used in PHM.
The model based approach uses physical process and interactions between different
components of the systems to predict the time to failure. Saha et al. 53 (2009) used a
model based approach to develop a battery health monitoring system using a Bayesian
framework to predict the remaining useful life (RUL) of the system. The predicted RUL
showed less uncertainty compared to the predicted RUL using data driven approach.
However, for a successful model based approach PHM, system specific knowledge about
physical processes is required. This is sometimes difficult to ascertain from complex
multiple physical process. The data driven approach uses statistical pattern recognition
and machine learning techniques to learn from data. In situ system monitoring is usually used to learn about trends and anomalies and this knowledge is later employed to
estimate the time to failure of the system. It doest not require system-specific knowledge and this approach can be applicable to complex system. Patil et al. 41 (2012) used
Mahalanobis distance to develop a PHM for an IGBT and employing a particle filter algorithm to predict RUL, with approximately 20% error. The model was developed for
a fixed temperature collector-emitter voltage, VC E (ON ) , which may be the source of this
Introduction
23
huge error. The requirement for high quality training data covering all aspects of realworld operation is the limitations of data driven models.
Researchers in the SDLE center developed a PV module lifetime and degradation
science model (PVM L&DS) 54 to study the operational characteristics of these system.
Using domain knowledge and an unbiased statistical analytical approach, a comprehensive set of degradations pathways were developed in PVM L&DS to assess the lifetime
performance of PV module. Semi-supervised generalized structural equation modeling (semi-gSEM) was used to develop systems of equations to explain the relationships
among variables in the model. Statistically significant relationships were determined
using Akaike information criteria (AIC) and adjusted-R 2 . This way PVM L&DS can also
provide rank ordered degradation modes for different climate zones and stress conditions.
For the work presented herein, real-world time-series power and temperature data
of PV modules and microinverters, along with insolation and environmental data associated with the SDLE SunFarm were analyzed using a lifetime and degradation prognostics approach to investigate the impact of thermal characteristics on lifetime and
performance. The incorporation of various stressors and their corresponding responses
provide a complete picture of the degradation mechanisms of the microinverters in realworld operating conditions. The prognostics approach can be expanded for different
climate zone which will allow us to compare the responses under different climate conditions.
24
2
Experimental Setup
The experimental setup for this study is located in the SDLE SunFarm (latitude 41.50 ,
longitude -81.640 ) in Cleveland, Ohio. The SDLE SunFarm is a part of a global sunfarm
network, which was established nine outdoor PV module test beds throughout the world
which can be used to study PV modules and system’s response under various climate
condtions. The raw data collected from the SunFarm goes through data pre-processing
and a semantic annotation process and is then stored in a NO-SQL Hadoop based informatics structure, known as Common Research Analytics and Data Lifecycle Environment (CRADLE). This structure maps the data into a Hadoop Distributed File System
(HDFS) and provides means for the user to query and interact with the data.
2.1
SDLE SunFarm
2.1.1 Overview
The SDLE SunFarm is a highly instrumented outdoor test facility located on west campus at Case Western Reserve University at Cleveland, Ohio. The total size of the SunFarm
is about one acre and peak power output is 32 kW. The whole SunFarm is divided into 16
electrical sites (figure 2.1). Among these 16 sites, two comprise PV modules on fixed tilt
racking systems, and 14 consist of PV modules and sample trays on high precision dual
Experimental Setup
25
Figure 2.1. Top figure: SDLE SunFarm layout, bottom figure: dual axis
tracker with PV modules and sample trays
Red boxes are dual-axis tracker sites with Enphase microinverters
axis trackers. Two of the dual axis tracking sites (site 9 and site 10) are connected to the
Daystar multi-tracers while the other sites are grid connected (figure 2.1). Among the
grid connected sites, two dual axis tracking sites (site 15 and site 16) are connected to
Experimental Setup
26
the grid via Solectria string inverters and the other sites are connected via microinverters. A total of 148 full sized crystalline silicon PV modules from 24 different manufacturers in sets of either six or eight modules are studied at the SunFarm. 36 PV modules
are mounted on the fixed racks and with the remaining on the dual axis trackers. Of particular note for this study is that 18 fixed rack PV modules and 42 dual axis tracking PV
modules, totaling 60 PV modules are connected to Enphase M215 microinverters.
2.1.2 PV module mounting system
The reason for studying the effects on both the fixed rack and dual-axis trackers is to
ascertain the thermal impact on the microinverters under these different conditions.
A fixed rack is commonly seen in rooftop PV system and utility power plant installation. Typically, the tilt angle of a fixed rack system is set at the average elevation angle
of the sun throughout the year at that location. The tilt angle of the fixed rack system
in the SDLE SunFarm is 22.30 , which is slightly shallower than the average elevation angle of the sun because Cleveland experiences more cloudy days throughout the year
than sunny days. 36 PV modules are mounted on to the fixed rack system and the total
fixed rack system is divided into two identical sites: each containing 18 PV modules. In
contrast, dual axis trackers (Feina Tracker, Spain) are usually seen in concentrated photovoltaic systems. The performance of PV modules can be maximized by putting them
onto the dual axis trackers since these tracker track the sun and keep the module plane
normal to the incident radiation. The tracking system of the tracker is controlled primarily by the GPS unit located in the Master control unit of the trackers. Each tracker
is equipped with a sun sensor as well, which helps it to track on cloudy days. Two DC
motors are located in the tracker head for both horizontal and azimuth direction movement control. Ten flexible unistruts are mounted on every tracker panel to mount the
Experimental Setup
27
PV modules, and microinverters. Currently each tracker panel is capable of holding up
to 12 full size PV modules in landscape orientation.
2.1.3 SDLE SunFarm Electrical Design
All the 16 electrical sites of the SDLE SunFarm are equipped with two electrical cabinets.
One cabinet contains all the power electronics devices and the other is equipped with
datalogging instruments such as Campbell CR 1000 datalogger and multiplexer, battery,
Ethernet switches (figure 2.2(b)). The output power of the Sunfarm is connected to the
grid via a reversing relay.
2.2 Metrology Platform at SDLE SunFarm
2.2.1 Environmental Data
Weather data: The SDLE SunFarm is equipped with a highly instrumented metrology
platform for weather, insolation, temperature and power monitoring. The weather data
is monitored by two Vaisala WXT520 weather stations connected to Campbell CR1000
dataloggers. These stations can monitor ambient temperature, rainfall, humidity, wind
speed and direction and report the data to their respective Campbell CR1000 datalogger
once every minute. An anemometer is connected to the Master control unit of the trackers to monitor the wind load in trackers. This anemometer is located in the center of the
SunFarm and placed on a pole. The anemometer and the weather stations record free
stream wind speed. However the wind profile may be more turbulent or at least different
in at the various tracker platforms due to height variations and obstructions.
Experimental Setup
28
Figure 2.2. a) Thermocouple on the backsheet of the microinverter, b)
data cabinet
Insolation data: The insolation data is collected by the different insolation sensors installed on the SDLE SunFarrm. Four Kipp & Zonen pyranometers of three different models (CMP6, CMP11, CMP21) are placed on the tracker planes, horizontal planes and tilt
rack planes to record the irradiance on these planes. Direct illumination is also measured by a Kipp & Zonen pyrheliometer (CHP1). Four Apogee SP-212 full spectra irradiation sensors and Apogee SU-100 UV sensors are used to measure the concentrated
solar irradiance. Li-cor Li-200 pyranometers and Apogee SP-212 sensors are employed
to align the trackers’ frame orientation. All of these sensors are connected to their respective sites’ Campbell datalogger. The reporting interval is one minute.
Temperature data: The minute by minute module and microinverter backsheet temperature is collected using T-type thermocouples from Omega Engineering Inc. These
Experimental Setup
29
thermocouples are attached to the backsheet via adhesive tape (figure 2.2(a)). The connector junctions of the thermocouple cables are covered to protect from moisture ingress
or other weather issues. The temperature data obtained by the thermocouples is reported through the Campbell datalogger and multiplexer.
2.2.2 Power data
The PV modules of site 9 and 10 are connected to the Daystar Multitracer and that
records the I-V curves of the connected PV modules at one minute intervals and stores
the data on the ftp server. The PV modules at site 15 and 16 are connected to Solectria
PVI1800 string inverters. The power data of these string inverters is stored at the manufacturers, website. The Enphase microinverters are connected to the Enphase Envoy
device. Enphase Envoy maintains powerline communication with all the microinverters. The power data of the PV modules connected to the Enphase microinverters are
reported to the Envoy device in 5 minute intervals and Envoy stores the data in Enphase
website.
2.3 Data Acquisition System
The SDLE SunFarrm data acquisition system consists of 17 CR1000 dataloggers, where
each datalogger is associated with an AM 16/32 multiplexer to increase the capacity of
the datalogger to 32 differential measurement channels. The Campbell datalogger stores
the thermocouple and sensor output and every 2 hours, the raw data is transferred to a
primary storage system. Power data stored in the Daystar ftp server and solectria website
are automatically downloaded via a shell script and Enphase power data is downloaded
using a web browser automation technique provided in a Java Selenium package.
Experimental Setup
30
Figure 2.3. Baseline DC output power of PV modules measure by SPIRE
4600 solar simulator
2.4 Experimental Setup Overview
2.4.1 PV modules and Microinverters
A total of 24 Enphase M215 microinverters connected to 8 different bradns of PV modules from different manufacturers have been selected for the analysis. Figure 2.3 represents the baseline DC power output of the selected 8 different brands of PV modules
for the study. The baseline DC power output was measured by SPIRE 4600 solar simulator. In the naming of the system, the letters "P", "O", "T", "R","S", "L", "K" and "Q"
represents the different PV module brands and t# corresponds to which tracking site on
which they are located. So, L.t6 means the L brand PV module is located on tracker no.
Experimental Setup
31
6. The nameplate AC power output of the microinverters is 215 W, and a minimum of
224 W(DC) PV module is required to saturate the microinverter. In figure 2.3, the black
horizontal line represents the saturation 224 W(DC) line. The baseline power for the
Q.t12 PV modules is 212.75 W(DC) and the microinverters connected to this brands of
modules did not reach the saturation region.
2.4.2
Duration of the Study
To investigate the microinverter performance, the power, insolation, temperature and
environmental raw data are first analyzed to reveal information about thermal behavior.
For this study, the selected data range is from July through October 30, 2013. Figure 2.4
shows the irradiance data from July through October 30, 2013, and figure 2.5 shows the
power data at the same period. Due to programming and technical faults, the power
data between October09, 2013 and October 23, 2013 is missing ( figure 2.5). The analyzed
insolation data was measured by a Kipp & Zonen CMP11 pyranometer, environmental
data was measured by Vaisala WXT520 weather stations, and the PV module and microinverter backsheet temperature data were measured by T-type thermocouples (TC).
The power data which includes DC voltage-current, AC voltage-power, microinverter
internal temperature and frequency were collected from the Enphase website.
2.4.3 Remarks on Data collection
Several issues arose with respect to the actual data collection. The first major issue was
the difference in time stamp of the data from the various data sources since they all use
their own time stamp protocol. The Campbell datalogger reports according to the clock
of the connected computer or network system and Enphase Enlighten system reports
according to their own clock. Moreover the data reporting frequency is also different for
Experimental Setup
32
Figure 2.4. Solar irradiance from July 1 through October 30, 2013
these two sources. Furthermore, during July 1 to October 30,2013, the power data was
reporting using Eastern Standard Time (EST) instead of Eastern Daylight Time (EDT),
and actual lagging between the power data and the Campbell datalogger reported data
was 6 min. Another issue can be any web page format changes that arise during data
collection. For example, in downloading the power data in an automated way from the
web page, a change in web page format interrupts the automation techniques, leading to errors. Additionally, the date format must be checked by looking for NA or NAN
value in the date columns of the reported data. Even more, units must be considered
such as those used to designate data formats (e.g. dates) or temperature (e.g. Celsius vs.
Fahrenheit). A final concern with the data was related to thermocouple faults. The TCs
are attached to the backsheet of the PV modules and microinverters by using adhesive
Experimental Setup
33
Figure 2.5. AC Power output data for O.t12 systems from July 1 through
October 30, 2013
tape. However, field studies show that some the TCs routinely fall off from their backsheets. As a result, whenever any data is taken for analysis, it has to go through a process
of data slewing and data validation.
34
3
Analysis Methods
3.1 Data validation
The collected raw data from the various sources must undergo a set of data validation
processes before analysis as discussed above. For this study, the power data was slewed 1
hour 6 minutes back to match the irradiance data. The TC reported microinverter backsheet temperature was validated by plotting it on the same graph alongside weather station reported ambient temperature data and the Enphase Enligthen reported microinverter internal temperature data. The validation plotting is performed using an R script.
If the temperature reported by the TC connected to the backsheet of the microinverter
approximately follows the temperature reported by the Enphase Enlighten, the TC is assumed to be well attached on the backsheet of microinverter. Erroneous TC data is assumed when it approximately follows the ambient temperature fluctuations. Figure 3.1
shows the temperature of three site 12 microinverters. Both the O.t12.1 and Q.t12.1 temperature follow approximately the same trend as ambient temperature in the morning,
but then reach values higher than ambient at noon and in the afternoon. However, the
O.t12.3 microinverter temperature follows ambient temperature and even sometimes
lower than ambient. It can be concluded that the TC attached to this microinverter
Analysis Methods
35
Figure 3.1. Validation of thermocouple recorded temperature data
has fallen off the backsheet, which was also confirmed by field investigation. A similar validation check is also conducted for the PV modules. Additionally, all the TC data
is plotted together for further inspection.
The Enphase reported microinverter temperature was compared with ambient temperature in the morning time when the AC power output was less than 2 W for the
dataset. The difference between these temperature is typically greater than 20 C, whereas
the difference between the TC reported temperature and ambient temperature is less
than 10 C. It is expected that these two temperatures be similar after the microinverter
has been inoperable for many hours, and perhaps the Enphase internal temperature
Analysis Methods
36
sensor is recording artificially high values. For this reason, the Enphase reported internal temperature is not used in the analysis and instead the TC data is employed.
3.2 Exploratory Data Analysis
An Exploratory Data Analysis (EDA) can detect outliers, check the preliminary assumptions, find patterns and trends, and generate hypotheses. The four types of EDA are: 1)
Univariate non-graphical , 2) multivariate non-graphical, 3) uni-variate graphical and
4) multivariate graphical. For our analysis, pairs scatter plots of multivariate graphical
EDA were generated. First, the NA values were removed from the validated, slewed and
compiled raw data. Then pairs scatter plots were plotted for every variable, and the correlation coefficients were calculated.
3.3 Correlation Coefficient
The correlation coefficient is the measure of linear dependence between two variables.
The value of the coefficient correlation varies from -1 to 1, where -1 indicates strongly
inversely correlated, 0 means no correlation, and 1 indicates strong positive correlation.
A correlation coefficient is used in this study to measure the linear correlation between
the variables which can provide the initial insights about the relationship among the
variables. Note that, if a nonlinear relationship exists between the variables, the correlation coefficient value will be smaller or can be zero. That is why it is advisable to check
the correlation coefficient and EDA plots together.
Analysis Methods
37
3.4 Local Solar Time
While an analysis of the full dataset is insightful, segregating the data into distinct sets
corresponding to specific time ranges can reveal other important information about the
thermal behavior of the microinverters. As a result, we have taken the compiled data
and transformed it into local solar time and into two subsample data sets:, morning
and noon time. These two subsamples were created to isolate and observe the thermal
characteristics under low and high irradiance conditions. Morning time is defined as
local solar time from 05:00 to 06:30, and the noon time dataset is defined between local
solar time from 11:00 to 13:00. The conversion of time format is done using an R script.
3.5 Normalized Temperature
In order to investigate and isolate thermal behavior, the module and microinverter backsheet temperature were normalized with respect to ambient temperature such that:
Normalized temperature= Backsheet TC temperature/Ambient temperature
3.6 t-Test Statistics
t-tests were utilized for comparisons of subsets, or to find the mean of subsets in this
study. A paired t-test is employed for a one to one comparison between the data points
from the same time stamp. This is more insightful than a comparison between means
of two subsets.
Analysis Methods
38
3.7 Cluster Analysis
Clustering is considered the process of organizing a collection of unlabeled data into
groups or clusters according to their similarity. The similarity of data points are measured by using the various distance measure techniques. Euclidean distance, Manhattan distance, and Power distance are some of the more popular techniques available. A
Euclidean distance approach is used to measure distances between data points in this
study. Clustering can also be classified depending on the clustering algorithms used. A
hierarchical clustering algorithm builds a hierarchy of clusters using the relations and
similarities shown by the data of the variables. A hierarchical clustering algorithm is
performed on the variables including: AC power, normalized module backsheet temperature and normalized microinverter backsheet temperature collected during local
solar time between 11:00 to 13:00. A hierarchical clustering algorithm is employed by
using the "hclust" function and an "average" agglomeration (bottom-up) method from
the package "stat" from the R software.
3.8 K-means clustering
To determine the optimum number of clustering, a K-means clustering algorithm with
an elbow method is used in this study. Plotting the sum of the squares versus the number
of clusters and finding the bending or elbow point of the curve gives the optimal number
of clusters for that data set. The elbow point is the point above which the change within
groups sums of squares is very small.
Analysis Methods
39
3.9 Linear Regression Model
Linear regression is an approach used to model the relationship between two or more
explanatory variables and a response or dependent variable by fitting a linear equation to the observed data. Using linear regression analysis, a predictive model for the
backsheet temperature of microinverters, connected to any of the studied 8 PV module
brands, was developed in this study. As a first step towards the development of a predictive model, the data set was randomly subsetted into two: the test data and the predicted
data set. The test data set was used to develop the predictive model, and the predicted
data set was used to determine the prediction accuracy of the prediction model. Various linear regression models were formulated using different variables with all possible
combinations with and without interactions among the variables. Then, the akaike information criterion (AIC) value was determined for the models to select the most appropriate model for prediction. AIC provides a relative estimate of the information lost between the models. Therefore, the preferred model will have the lowest AIC value among
the compared models. The residual plot of the selected model was then checked for
appropriateness and degree of validation of the model. Residual is the difference between the observed value and the predicted value and a residual plot provides a visual
assessment how much every observation is deviated from the fitted line. A residual plot
is a good tool for finding the appropriateness of the model. It also provides us insights
about the model parameters, variance and outliers. For an appropriate linear regression
model, the residual plot should be comprised of random scattering of points without
any pattern.
Analysis Methods
40
3.10 R software
R is an open source software programming language and software environment for statistical computing , data analysis, and graphics. In this study, data analysis and statistical
computing is done by using R software version 3.0.2.
41
4
Results and Analysis
4.1 Exploratory Data Analysis (EDA)
The data for the EDA includes all the average time-series data points available for PV
modules and microinverters, including those days where no power was produced due to
technical faults at high irradiance. It also includes data from the time when the trackers
were offline for tracker maintenance work or during sample loading. For proper analysis, the technical fault, and maintenance data were removed from the final dataset. The
EDA pairs plot is a great tool for identifying these unusual data sets Figure 4.1 shows the
scattered pairs plot for the average data of the Q.t12 systems from July through October,
2013. Table 4.1 is presents the correlation coefficients among different variables for the
Q.t12 systems. The Q.t12 systems contain three Q.t12 PV modules and three Enphase
M215 microinverters connected to these PV modules. The pairs plots in figure 4.1 are arranged into three different colors depending on their correlation coefficients. Pink represents a correlation between variables where correlation coefficients are greater than
0.7, blue indicates a moderate correlation where correlation is between 0.35 to 0.69 and
yellow refers to very small correlation coefficients less than 0.34.
From figure 4.1and table 4.1, it is evident that the microinverter temperature is primarily influenced by ambient temperature and module temperature. In addition, power,
Results and Analysis
42
Figure 4.1. Scatter pairs plots for the Q.t12 systems from July 1 through
October 30, 2013.
Pink plot: Correlation coefficients are greater than 0.7; Blue plot: Correlation coefficients
between 0.35 to 0.69; Yellow plot: Correlation coefficients less than 0.34. Absolute correlation
coefficient values are used to determine the colors.
current and irradiance are the moderately correlated with microinverter temperature,
and interestingly there is no correlation of wind speed with any other variables. The relationship among variables will be discussed further in the following discussion chapter.
Results and Analysis
43
Table 4.1. Correlation coefficient for different variables for the Q.t12 systems
Irradiance
Ambient.T
Wind
Mod.T
Micro.T
Current
Power
Micro I.T
Irradiance Ambient.T Wind Mod.T Micro.T. Current Power Micro I.T
1.00
0.27 0.06
0.78
0.60
0.81
0.83
0.66
0.27
1.00 -0.24
0.65
0.89
0.22
0.21
0.85
0.06
-0.24 1.00
-0.19
-0.23
-0.05 -0.05
-0.22
0.78
0.65 -0.19
1.00
0.90
0.80
0.81
0.93
0.60
0.89 -0.23
0.90
1.00
0.55
0.55
0.99
0.81
0.22 -0.05
0.80
0.55
1.00
0.96
0.63
0.83
0.21 -0.05
0.81
0.55
0.96
1.00
0.63
0.66
0.85 -0.22
0.93
0.99
0.63
0.63
1.00
Ambient T: Ambient Temperature, Wind: 5 point moving average wind speed, Mod.T=Q.t12
average PV module temperature, Micro.T= Average TC reported Q.t12 microinverters backsheet temperature, Current= Average DC current input to Q.t12 microinverters, Power= Average AC power at the output of the Q.t12 microinverters, Micro. I.T=Enphase reported Q.t12
microinverters internal temperature
Figure 4.2. Ambient Temperature vs. microinverter backsheet TC temperature for the Q.t12 systems from July through October 2013
Figure 4.2 represents the pairs plot between ambient temperature and PV module
temperature. The data points, shown in green circle, indicate a higher temperature trend
Results and Analysis
44
Figure 4.3. Irradiance vs. AC Power output for the Q.t12 systems from July
through October 2013
due to non-power generating periods for technical faults. From the Figure 4.2, different
data trends corresponding to a different temperature range can also be examined. The
red arrow indicates a data set when temperature is above 300 C; the brown arrow indicates when the temperature is between 20 and 300 C; and violet indicates low temperature behavior when when temperature is less than 150 C.
Figure 4.3 represents the pairs plot for irradiance versus AC power. Here, unusual
data trends and hidden data trends can be easily identified. Green circles represent data
sets when the tracker is offline for tracker maintenance work and red circles depict when
the power output of the PV module is zero due to technical faults on a bright sunny day.
Blue and violet arrows indicate cloudy day and sunny day output of the PV module,
respectively. The influence of ambient temperature on AC power output can be seen in
Results and Analysis
45
Figure 4.4. Variation in AC power output of microinverters in the Q.t12
systems for different ambient temperature range
figure 4.4. Approximately 10 W power loss observed in Q.t12 PV modules when ambient
temperature increases from 10-150 C to 300 C
4.2 Morning Data Analysis
Table 4.2. Correlation coefficient for different variables for the Q.t12 systems in the morning time from July through October, 2013
Irradiance
Ambient. T
wind
Mod.T
Micro.T
Current
Power
Micro I.T
Irradiance Ambient.T Wind Mod.T Micro.T. Current Power Micro I.T
1.00
0.12 -0.10
0.72
0.34
0.84
0.87
0.44
0.12
1.00 0.02
0.70
0.97
-0.01 -0.02
0.93
-0.10
0.02 1.00
-0.06
-0.01
-0.09 -0.10
-0.02
0.72
0.70 -0.06
1.00
0.85
0.62
0.63
0.90
0.34
0.97 -0.01
0.85
1.00
0.20
0.19
0.99
0.84
-0.01 -0.09
0.62
0.20
1.00
0.98
0.31
0.87
-0.02 -0.10
0.63
0.19
0.98
1.00
0.31
0.44
0.93 -0.02
0.90
0.99
0.31
0.31
1.00
Results and Analysis
46
Figure 4.5. Scatter pairs plots for the Q.t12 systems in the morning time
from July through October, 2013
Pink plot: Correlation coefficients are greater than 0.7; Blue plot: Correlation coefficients
between 0.35 to 0.69; Yellow plot: Correlation coefficients less than 0.34. Absolute correlation
coefficient values are used to determine the colors.
Figure 4.5 presents the EDA pairs plots of the Q.t12 systems in the morning time and
table 4.2 presents the corresponding correlation coefficients. Here we delve into greater
detail on the analysis of the morning time behavior by specifically examining the data at
Results and Analysis
47
different irradiance levels. As shown in figure 4.5, the microinverter backsheet temperature is very strongly correlated with the ambient temperature as shown by correlation
coefficient of 0.97 (table 4.2). Results from a simple t-test and paired t-test was employed
to determine the relationship between the microinverter backsheet and ambient temperatures. Table 4.3 shows the differences of PV module temperature, and microinverter
temperature with ambient temperature at a 95% confidence interval for the Q.t12 systems in the morning. Figure 4.6 show a plot of normalized module and microinverter
temperature as a function of irradiance and Table 4.4 gives the summary of the variation
in normalized module and microinverter temperature at different irradiance zones in
the morning. The blue circles contain those data points when ambient temperature is
below 100 C, and the green circle contains data from September 06, when technical issues caused the microinverter to not deliver any power output to the grid from morning
unitl 10AM.
Table 4.3. Comparison of PV module temperature, and microinverter
temperature with ambient temperature at different irradiance zone for
the Q.t12 system in the morning from July through October, 2013
Irradiance
W /m 2
0-60
Above 60
Difference between
Ambient.T and
Mod. T (0C )
Low.Lim Up.Lim
0.88
1.12
-5.38
-7.35
Difference between
Ambient.T and
Micro. T (0C )
Low.Lim Up.Lim
0.31
0.39
-1.23
-1.60
Up.Lim= Upper limit of 95% confidence interval, Low.Lim= Lower limit of 95% confidence
interval
Results and Analysis
48
Figure 4.6. Irradiance vs normalized module backsheet and microinverter backsheet TC temperature in the morning for the Q.t12 systems
Table 4.4. Variation of normalized module and microinverter temperature at different irradiance zone for the Q.t12 system in the morning from
July through October, 2013
Irradiance
W /m 2
0-60
Above 60
Norm.
Norm.
Mod. T
Micro. T
Low.Lim Up.Lim Low.Lim Up.Lim
0.92
0.93
0.97
0.98
1.31
1.40
1.06
1.08
Norm.Mod.T=Normalized module temperature, Norm.Micro.T= Normalized microinverter
temperature
Results and Analysis
49
4.3 Noon Data Analysis
At noon time, the microinverter TC temperature is primarily correlated with ambient
temperature and module backsheet temperature (figure 4.7 table 4.5). Irradiance, AC
power and DC current are also moderately and similarly correlated with microinverter
backsheet temperature during noon time conditions. In the pairs plots of power and irradiance at noon time (figure 4.7), the cloudy days data show high power output in low
irradiance similar to the behavior observed under morning conditions. Also from these
plots it is observed that microinverter and PV module backsheet temperature maintains
an inverse correlation with the wind speed. The correlation between wind, and PV module temperature as well as with and microinverter backsheet temperature is higher at
noon time than in the morning, albeit the difference in not significant (Table 4.5).
Table 4.5. Correlation coefficient for different variables for the Q.t12 systems at noontime from July 1 through October 30, 2013.
Irradiance
Ambient.T
wind
Mod.T
Micro.T
Current
Power
Micro I.T
Irradiance Ambient.T Wind Mod.T Micro.T. Current Power Micro I.T
1.00
0.30 -0.13
0.79
0.60
0.82
0.84
0.64
0.30
1.00 -0.24
0.69
0.90
0.28
0.26
0.87
-0.13
-0.24 1.00
-0.31
-0.32
-0.21 -0.22
-0.31
0.79
0.69 -0.31
1.00
0.92
0.77
0.77
0.94
0.60
0.90 -0.32
0.92
1.00
0.58
0.58
0.99
0.82
0.28 -0.21
0.77
0.58
1.00
0.95
0.64
0.84
0.26 -0.22
0.77
0.58
0.95
1.00
0.65
0.64
0.87 -0.31
0.94
0.99
0.64
0.65
1.00
A more detailed noon time analysis was also conducted to determine the parameters that influence microinverter thermal characteristics at high irradiance. The compiled noon time data consists of data between solar time 11:00 to 13:00, which includes
all sunny and cloudy days, non-tracking and tracking days and days where no power
Results and Analysis
50
Figure 4.7. Scatter pairs plots for the Q.t12 systems at noontime from July
1 through October 30, 2013.
Pink plot: Correlation coefficients are greater than 0.7; Blue plot: Correlation coefficients
between 0.35 to 0.69; Yellow plot: Correlation coefficients less than 0.34. Absolute correlation
coefficient values are used to determine the colors.
was produced due to technical faults. In order to analyze only the sunny day performance without technical faults, first the compiled data was subsetted for irradiance values above 600 W /m 2 and a power over 100 W. A paired t-test was applied between ambient temperature and module backsheet temperature, ambient temperature and microinverter backsheet TC temperature, and ambient temperature and Enphase reported
microinverter internal temperature.
Results and Analysis
51
Table 4.6. Thermal performances of the P.t.12 systems at different power
range from July 1 through October 30, 2013.
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: P.t.12.1; Baseline power 231.73 W
688.53
5.82
158.97
1.76
643.17-733.83 5.39-6.25 157.66-160.33 1.70-181
754.73
6.86
181.01
1.78
721.55-787.91 6.55-7.17 180.03-182.00 1.74-1.83
861.87
7.68
200.9
1.97
852.33-871.42 7.61-7.75 200.31-200.50 1.95-1.99
839.32
8.01
215.57
2.22
820.28-858.36 7.90-8.12 215.03-216.47 2.17-2.22
Module: P.t.12.2; Baseline power 231.73 W
808.71
5.79
161.93
1.912
782.02-835.40 5.61-5.98 161.03-162.82 1.88-1.96
867.46
6.22
177.27
1.96
852.98-881.93 6.1-6.35 176.72-177.83 1.93-1.99
810.23
7.38
199.54
2.06
784.84-835.62 7.01-7.65 198.02-201.07 2.00-2.12
816.64
7.995
215.31
2.33
805.12-828.16 7.9-8.08 214.45-216.17 2.28-2.38
Norm.
Micro.T
Norm.
Micro.I.T
1.31
1.29-1.33
1.32
1.31-1.34
1.41
1.40-1.42
1.47
1.45-1.49
1.28
1.26-1.31
1.31
1.30-1.33
1.4
1.39-1.41
1.48
1.46-1.50
1.359
1.34-1.37
1.37
1.36-1.38
1.41
1.39-1.44
1.53
1.50-1.55
1.33
1.32-1.35
1.35
1.34-1.36
1.4
1.38-1.43
1.54
1.51-1.56
Norm.Mod.T=Normalized module temperature, Norm.Micro.T= Normalized microinverter
backsheet temperature, Norm. Micro. I.T= Normalized Enphase reported microinverter internal temperature, 95%CI=95% confidence interval.
To investigate variability of thermal performance within the same brands of PV modules and to observe the saturation thermal characteristics of the microinverters, an analysis is conducted on individual PV modules as a function of power range: 150-170 W,
170-190W, 190-210 W and above 210 W. Table 4.6 shows the thermal performance of the
P.t12 modules for the noon time data at these power output ranges. From Table 4.6, it
can be observed that both of the P.t12 PV modules produce the same power but at different irradiance levels, and the temperature in the Pt12.2 system is higher than the P.t12.1
system. In fact, in the month of July and August, the P.t12.2 PV module required greater
irradiance to obtain same power. For example, 202 W of AC power was produced at an
Results and Analysis
52
Table 4.7. Thermal performances of the T.t.14 systems at different power
range from July 1 through October 30, 2013.
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: T.t.14.1; Baseline power 232.07 W
668.25
5.85
159.92
1.8
622.18-714.32 5.43-6.26 158.69-161.14 1.73-1.86
743..97
6.61
181.51
1.89
713.72-724.22 6.34-6.89 180.61-182.40 1.84-1.95
813.22
7.55
200.87
2.12
797.51-828.93 7.47-7.64 200.27-201.47 2.08-2.17
823.66
7.91
215.21
2.25
809.33-838.00 7.83-7.99 214.64-215.78 2.22-2.29
Module: T.t.14.2; Baseline power 232.07 W
682
5.73
159.05
1.76
632.47-731.52 5.39-6.18 157.76-160.34 1.69-1.83
725.31
6.6
180.46
1.88
691.25-759.38 6.29-6.92 180.35-181.39 1.82-19.4
814.103
7.55
201.11
2.1
800.10-828.10 7.48-7.63 200.47-201.74 2.06-2.14
818.79
7.95
215.55
2.21
803.83-833.74 7.87-8.02 215.03-216.08 2.27-2.24
Module: T.t.14.3; Baseline power 232.07 W
674.52
6.24
160.24
1.78
624.59-724.46 5.84-6.64 159.10-161.40 1.71-1.84
731.34
6.65
181.57
1.86
698.12-764.55 6.34-6.97 180.65-182.49 1.79-1.92
811.33
7.76
201.11
2.11
797.41-826.06 7.68-7.85 200.49-201.74 2.06-2.13
826.66
8.17
215.06
2.25
810.81-842.52 8.12-8.22 214.52-215.60 2.21-2.28
Norm.
Micro.T
Norm.
Micro.I.T
1.33
1.31-1.35
1.37
1.34-1.39
1.46
1.44-1.48
1.48
1.46-1.49
1.31
1.29-1.33
1.36
1.34-1.38
1.46
1.44-1.48
1.48
1.47-1.49
1.31
1.28-1.33
1.35
1.33-1.37
1.445
1.42-1.46
1.455
1.44-1.46
1.29
1.27-1.31
1.34
1.32-1.36
1.438
1.42-1.45
1.456
1.44-1.46
1.32
1.29-1.34
1.35
1.32-1.37
1.458
1.44-1.47
1.47
1.46-1.49
1.3
1.28-1.32
1.34
1.32-1.36
1.458
1.44-1.47
1.49
1.47-1.50
irradiance of 1079 W/m 2 in July and August whereas in September the same PV module
can produce 224 W AC power at an 874 W/m 2 irradiance level. If we analyze further in
the power range 170-190 W, it can be found that the mean normalized module backsheet
temperature for the month of July and August was 2.01, but in September it reached only
1.88. These difference in AC power output will be discussed in details in the next chapter.
Results and Analysis
53
Table 4.8. Thermal performances of the L.t.6 systems at different power range
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: L.t.6.1; Baseline power 230.92 W
750.44
5.45
162.39
1.89
714.18-786.69 5.11-5.78 161.38-163.41 1.85-1.93
834.55
6.34
181.66
2.05
818.72-850.38 6.2-6.48 181.00-182.33 2.02-2.07
808.21
6.59
195.94
2.29
782.54-833.87 6.36-6.83 195.10-196.77 2.24-2.34
Module: L.t.6.2; Baseline power 230.92 W
773.72
5.59
161.7
1.9
746.31-701.13 5.34-5.83 160.93-162.48 1.86-1.93
843.3
6.17
179.73
2.1
829.48-857.11 6.06-6.28 179.20-180.26 2.07-2.13
859.98
5.73
195
2.28
797.27-922.69 4.87-6.58 193.21-196.78 2.17-2.40
Module: L.t.6.3; Baseline power 230.92 W
743.65
6.29
160.76
1.84
709020-778.00 5.93-6.66 159.62-161.92 1.79-1.89
789.98
6.92
182.51
1.95
771.17-808.79 6.72-7.12 181.80-183.23 1.93-1.98
867.07
7.37
196.4
2.08
849.06-885.08 7.17-7.57 195.73-197.08 2.05-2.11
Norm.
Micro.T
Norm.
Micro.I.T
1.34
1.32-1.35
1.4
1.39-1.40
1.46
1.44-1.48
1.33
1.31-1.34
1.409
1.399-1.419
1.47
1.45-1.49
1.38
1.36-1.39
1.45
1.44-1.46
1.51
1.45-1.56
1.34
1.32-1.36
1.42
1.43-1.44
1.47
1.41-1.53
1.305
1.28-1.32
1.36
1.35-1.37
1.4
1.39-1.41
1.46
1.43-1.49
1.57
1.55-1.59
1.63
1.60-1.65
Table 4.9. The average power and temperature difference between the
L.t.6 at noon time
AC Power (W)
Norm. Mod.T
Norm. Micro.T
Difference between
L.t6.1 and L.t6.2
7.77
0.04
- 0.02
Difference between
L.t6.2 and L.t6.3
-11.62
0.04
0.05
Difference between
L.t6.1 and L.t6.3
-3.9
0.08
0.03
Table 4.7 and Figure 4.8 show the T.t.14 PV modules’ and microinverters’ thermal
performance under different power ranges at noon time. Table 4.8 shows the show
the T.t.14 PV modules’ and microinverters’ thermal performance under different power
ranges at noon time. The average power and temperature difference between the L.t.6
Results and Analysis
54
Table 4.10. The rise in temperature in the site 12 PV modules and microinverters during noon time
Maximum
Power
(W)
AC Power (W)
Difference between
Mod.T and Amb. T
(0 )C
Difference between
Micro.T and Amb. T
(0 )C
P.t12.2
225
P.t12.1
225
O.t12.1
225
O.t12.1
225
Q.t12.3
220
Q.t12.2
222
Q.t12.1
223
182.7
23.23
200.23
22.32
202.07
23.29
202.92
23.1
177.44
24.5
179.81
24.13
179.58
22.93
9.06
9.23
9.62
11.2
9.24
9.69
9.06
Figure 4.8. Normalized module backsheet, microinverter backsheet and
microinverter internal temperature for the T.t14.1 system
modules and microinverters are listed in table 4.9 The PV modules’ and microinverters’ thermal performance under different power ranges at noon time for the other 5 PV
Results and Analysis
55
manufacturer brands are presented in Appendix B. Table 4.10 shows the PV module and
microinverter temperature rise above the ambient temperature, and the average power
output of different PV modules in site 12 during noon time. Interestingly the rise in temperature in the Q.t12 microinverters is very similar to the other microinverters at site 12
although the power output of the Q.t12 PV modules is significantly lower. Additionally,
the microinverter internal temperature is very close to its surface temperature measured
via the thermocouple when operating above the 190 W range and at saturation level,
with the exception of the T.t14.3 system.
Figure 4.9 and 4.10 show the bar plot of all the PV modules and microinverters backsheet temperature at different power range. The Q.t12 PV modules’ baseline power is
212.75 W(DC). Therefore, there are no data points for the Q.t12 PV modules at above
210 W(AC) range. The reported baseline power of the L.t6 modules is 230.92 W(DC), but
the data does not include a significant number of points (only 3-4 data points) at values
above the 210 W range (table 4.8). The rise in the normalized PV module temperature
for the R.t12.R.t14.2, R.t14.3 and S.t14 modules is very small between 190-210 W, and
above 210 W, or saturation range.A significant rise (0.20 and above) can be observed in
the K.t6.2, P.t12 and O.t12 modules.
The increase in normalized microinverter backsheet temperature is comparatively
smaller than the normalized PV module backsheet temperature. From figure 4.10, all
the tracker 14 microinverters, except the S.t14.2 microinverter, show the largest increase
when in the 170-190 W and 190-210 W range where a significant rise was also observed in
the respective PV modules. The problem with the S.t14.2 microinverter will be discussed
in next chapter.
Results and Analysis
56
Figure 4.9. Variation of normalized module backsheet temperature for
different modules at different power range
Figure 4.11 and 4.12 show the variation of normalized PV module and microinverter
backsheet temperature for all the brands of PV modules in the 190-210 W power range.
The normalized module backsheet temperature for the L.t6 and and Q.t12 modules is
Results and Analysis
57
Figure 4.10. Variation of normalized microinverter backsheet temperature for different modules at different power range
comparatively higher than the others. For the K.t6, O.t12, R.t14, S.t14 and T.t14 PV modules, the variation of normalized PV module temperature within the same brands is very
small. From Figure 4.12, for the Q.t12, P.t12, R.t14, T.t14 and S.t14 (except S.t14.2), the
variation of normalized microinverter backsheet temperature within the same brands is
Results and Analysis
58
Figure 4.11. Variation of normalized module backsheet temperature for
power range 190-210 W
very small. The normalized backsheet temperature of the microinverters connected to
the K.t6, L.t6 and O.t12 modules varies significantly within the brands.
Figures 4.13 and 4.14 show the variation of the normalized module and microinverter backsheet temperature for all the brands of PV modules at above 210 W. There is
not much variation in the O.t12, S.t14 ans T.t14 PV module temperatures. For T.t14 and
S.t14 (except S.t14.2), the variation of normalized microinverter backsheet temperature
within the same brand is very small. Although the K.t6.2 PV module power output is
higher than the K.t6.1, the module temperature of K.t6.2 is higher than the K.t6.1. The
thermocouple attached to the backsheet of the K.t6.1 module sometimes reports a very
small temperature at high irradiance. We will encounter this issue again in the cluster
analysis of he PV module backsheet temperature.
Results and Analysis
Figure 4.12. Variation of normalized microinverter backsheet temperature for power range 190-210 W
59
Results and Analysis
Figure 4.13. Variation of normalized module backsheet temperature for
power range above 210 W
60
Results and Analysis
Figure 4.14. Variation of normalized microinverter backsheet temperature for power range above 210 W
61
Results and Analysis
62
Figure 4.15. Hierarchical cluster analysis of time-series AC Power data at
noon from July 1 through October 30, 2013.
4.4 Cluster Analysis
4.4.1 Power Cluster
Figure 4.15 represents the AC power cluster of all the PV modules. The power time-series
data was taken between a local solar time 11:00 to 13:00 for an irradiance level above
600 W/m 2 and power output over 150 W. In the clustering dendrogram, all the PV modules can be separated into 5 clusters (shown by red boxes in the diagram). This clustering dendrogram is organized according to brands of the PV modules and performance
based on baseline power. The details of the clustering dendrogram will be discussed in
next chapter.
Results and Analysis
63
Figure 4.16. Hierarchical cluster analysis of normalized PV module backsheet temperature time-series data at noon from July 1 through October
30, 2013.
4.4.2 Normalized PV Module Backsheet Temperature Cluster
The normalized PV module backsheet temperature cluster in figure 4.16 can also be defined in 5 clusters. The K.t6.1 PV module backsheet temperatures form its own cluster
due to anomalous temperature readings under high irradiance conditions. The R.t14 PV
modules appear in one cluster, and the S.t14 and T.t14 PV modules form another cluster
with the Q.t12.1 and L.t6.3 PV modules. In addition the Q.t12.1, Q.t12.2 and L.t6.1 PV
modules backsheet temperatures are clustered together.
Results and Analysis
64
Figure 4.17. Hierarchical cluster analysis of normalized microinverter
backsheet temperature time-series data at noon from July 1 through October 30, 2013.
4.4.3 Normalized Microinverter Backsheet Temperature Cluster
Figure 4.17 depicts the normalized microinverter backsheet temperature clustering dendrogram. Figure ( 4.18) shows the plotting of the sum of squares versus the number of
clusters determined by employing K-means clustering algorithm in the normalized microinverter backsheet temperature. This clustering also divides into 5 (determined from
the elbow point of figure 4.18). The right most cluster contains the R.t14.3, O.t12.1,L.t6.2,
Q.t12.1, K.t6 and P.t.12 microinverters. This cluster contains mostly high power modules
such as K.t6,P.t12 and O.t12.1 and as well as various low power modules such as L.t6.2
and Q.t12.1. The T.t14 microinverters also appear in a similar clustering as that of the AC
Results and Analysis
65
Figure 4.18. Normalized microinverter backsheet temperature K-means
diagram for full time-series data set
power and PV module backsheet clusters. Similarly, L.t6.1, Q.t12.1 and Q.t12.2 are also
clustered together for all three of the clustering procedures. The S.t14.2 forms a cluster
of its own due to TC anamolies. The data collected from the TC attached to the backsheet of S.t14.2 microinverter was analyzed, and it was concluded that no anomalies
existed until 2013-09-04. After this time, the TC appears to have been reporting lower
than expected temperatures. After visual inspection, it was concluded that the S.t14.2
microinverter’s backsheet thermocouple became unattached from the backsheet of the
Results and Analysis
66
Figure 4.19. Hierarchical cluster analysis of normalized microinverter
backsheet temperature for the corrected time-series noon time data from
July 1 through October 30, 2013.
microinverter. As a result, this data set was subsetted to include only data up to 2013-0904 and clustering was rerun. Figure 4.19 represents the new clustering dendrogram, and
now the S.t.14.2 microinverter falls in the same data set as other S.t14 microinverters.
4.5 Linear Regression Model
Equation 4.1 represents the predictive model used to predict the microinverter backsheet temperature connected to any of the studied 8 PV module brands. The equation
was developed using the following parameters as a function of time:
• Average PV module backsheet temperature
• Average AC power output from every brands of modules
Results and Analysis
67
• Irradiance
• Ambient temperature
• The interactions between PV module backsheet temperature and AC power; irradiance and power; module backsheet temperature; irradiance and power
such that:
Mi cr o.Ti =
P8
j =1 β0 j x i j
+(
P8
j =1 β1 j x i j )Ambi ent .Ti
+(
P8
j =1 β2 j x i j )Mod ul e.Ti
P
P
+( 8j =1 β3 j x i j )I r r ad i ance i + ( 8j =1 β4 j x i j )Power i
+(
P8
j =1 β5 j x i j )(Mod ul e.Ti
∗ I r r ad i ance i ) + (
P8
j =1 β6 j x i j )(I r r ad i ance i
∗ Power i )
P
+( 8j =1 β7 j x i j )(Mod ul e.Ti ∗ I r r ad i ance i ∗ Power i ) + ε
(4.1)
Table 4.11. The coefficient values of different variables for the predictive
model (Equation 4.1)
Brands
R.t14
S.t14
T.t14
L.t6
K.t6
P.t12
O.t12
Q.t12
Int. Amb.T Mod.T
Irr
Pow
Mod.T*Irr Irr*Pow Mod.T*Irr*Pow
β0
β1
β2
β3
β4
β5
β6
β7
-0.35 0.65
0.39
1.1e-2 -1.25e-2 -2.85e-4 -5.22e-5
1.54e-6
-0.81 0.74
0.31
9.1e-3 -8.2e-3
-1.65e-4 -6.73e-5
1.58e-6
-0.51 0.66
0.39
9.6e-3 -1.01e-2 -2.14e-4
-4.8e-5
1.25e-6
-0.63 0.67
0.38 7.78e-3 -1.01e-2 -1.87e-4 -3.57e-5
1.04e-6
-1.13 0.68
0.40
8.1e-3 -1.72e-3 -2.18e-4
-4.5e-5
1.19e-6
-0.33 0.63
0.43 1.22e-2 -1.2e-3
-2.89e-4
-7.0e-5
1.87e-6
-0.48 0.67
0.38 1.04e-2 -8.34e-3 -2.38e-4
-4.7e-5
1.28e-6
-0.39 0.68
0.36 8.83e-3 -1.39e-2 -1.64e-4
-4.1e-5
1.03e-6
Int.= Intercepts, Amb.T:Ambient Temperature, Pow=AC power output of the module, Irr.=
Irradiance, Mod.T*Irr= interaction between PV module backsheet temperature and irradiance, Irr.*Pow= interaction between irradiance and AC power,Mod.T*Irr.*Pow= interaction
between PV module backsheet temperature, irradiance and AC power.
where ε represents the error terms in the equation 4.1.
Results and Analysis
68
Figure 4.20. Residual Plot: Regression validation for predictive linear regression model for the L.t6 microinverters
The coefficients of variables for the predicted model are listed in the table 4.11. i=1
to 8 represents the 8 different brands of PV modules. x i j represents the coefficients
positions in Table 4.11. β0 represents the intercepts, β1 represents the coefficients for
ambient temperature, β2 represents the coefficients for PV module backsheet temperature, β3 represents the coefficients for irradiance, β4 represents the coefficients for AC
power output, β5 represents the coefficients for interaction between PV module backsheet temperature and irradiance , β6 represents the coefficients for interaction between
Results and Analysis
69
Figure 4.21. Comparison between predicted model with actual temperature for the L.t6.2 microinverters on 17 th September, 2013
irradiance and AC power, and β7 represents the coefficients for interaction between PV
module backsheet temperature, irradiance and AC power.
The AIC value of the predictive model is 14276.67. The lowest AIC value obtained in
a model was 14113.98. Since the difference in AIC is not significant, the model presented
by equation 4.1 is chosen to reduce the complexity.
Figure 4.20 represents the fitted vs. residual plot for L.t6 microinverters using the
linear regression prediction model (equation 4.1). and Figure 4.21 shows the comparison between actual and predicted microinverter temperature on a select bright sunny
Results and Analysis
70
Figure 4.22. Comparison between predicted model with actual temperature for the L.t6.2 microinverters on a cloudy day
day. The comparison between predicted microinverter temperature and actual microinverter temperature on a cloudy day is shown in Figure 4.22. From Figure 4.21, the maximum difference between actual and predicted values is 3.04 0 C for the L.t6.2 microinverter backsheet temperature. The 95% confidence interval for the difference between
actual and predicted temperature of corresponds to a temperature differential between
0.40 C and 1.60 C for all the microinverters connected to the 8 different PV modules.
71
5
Discussion
The Results and Analysis chapter presented the requisite data and information relevant to the work described herein. Here we discuss important observations of these
results, including a more in-depth examination of the factors that influence microinverter temperature.
5.1 Influence of Irradiance on PV Module and Microinverter
Temperature
Irradiance is the source of energy for the PV modules, and therefore the PV modules
backsheet temperature is strongly correlated with irradiance as shown throughout the
various figures in Chapter 4. However, irradiance does not directly interact with the
microinverters as they are shaded by the PV modules themselves. We see this in Figure 4.1and Table 4.1, which demonstrate that irradiance is only moderately correlated
with microinverter temperature. From the morning analysis ( Table 4.2) , the correlation
coefficients of microinverter temperature with AC power, irradiance and current fall below 0.4. These low values are largely because the irradiance in the morning is typically
very low , leading to low power output and therefore temperature of the PV modules.
This is because the amount of radiated energy received by the microinverter from the
Discussion
72
PV modules’ backsheet is therefore also small. In fact, the difference between ambient temperature and PV module backsheet temperature is about 0.880 C to 1.12 0 C, and
the difference between ambient temperature and PV module backsheet temperature is
about 0.310 C to 0.39 0 C in the morning (from Table 4.3). As a result, the contributions
of PV module backsheet temperature, irradiance, power and current are not significant
enough in comparison with the influence of ambient temperature during these morning
hours. As the irradiance increases throughout the morning, the power output becomes
larger, and a sharp increase in PV module backsheet temperature is observed since the
PV module is receiving the irradiance directly (table 4.3, 4.4 and figure 4.6). Again the
corresponding increase in microinverter backsheet temperature is not as significant as
the PV module backsheet since the microinverter is not receiving the irradiance directly.
It should be noted that, in the pairs scatter plots of power and irradiance figure 4.5,
some data points are observed where higher power output was reported at low irradiance. These are data points from partly cloudy days. Since the location of the irradiance
sensor and trackers is not exactly the same, it may appear that irradiance is low when in
fact the PV module may be in a direct path of the sunlight.
5.2 Influence of AC Power Output and PV Module Temperature
on Microinverter Temperature
The PV module plays an important role in influencing the microinverter temperature,
and here we consider both the direct effect of power output and module temperature.
Figure 4.4 shows the variation in power output from the microinverters at two ambient
temperature ranges: 10-150 C and above 300 C. Here, we see the power output is lower
when the ambient temperature is higher (above 300 C). This is because the power output
Discussion
73
of the microinverters correlates well to the power output of the PV modules, which also
demonstrate similar behavior. This inverse relationship occurs because at higher operating temperatures, the open circuit voltage and fill factor decrease significantly with a
slight increase in short circuit current 55 . As a result, the maximum power output from
the PV module typically decreases with an increase in PV module temperature. Taking the O.t12 PV modules and microinverters as an example, the temperature difference
among the O.t12 PV modules between 150-170 W and 170-190 W region is very small.
But there is a significant temperature difference at the higher powers (Figure 4.9 ). For
the microinverters in the same family, a similar temperature trend is observed albeit
smaller in magnitude (Figure 4.10 ). This corresponding behavior demonstrates that the
PV module temperature plays a significant role in influencing the microinverter temperature. Similar PV module and microinverter temperature trends are also observed in
other families except for the T.t14 PV modules and microinverters. In the T.t14 system,
no significant rise in microinverter temperature is observed in above 210 W although a
significant rise is observed in PV module temperatures. The reason for this one anomaly
is unknown.
Both the L.t6 and Q.t12 PV modules are low performing PV modules and their highest
range of operation occurs at 190-210 W (Figure 4.10 ). Therefore, both the L.t6 and Q.t12
PV modules show higher temperature in Figure 4.11 compared to other PV modules.
Interestingly, the L.t6.3 PV module’s output is 3.9 W and 11.62 W higher, on average,
during noon time as compared to the L.t6.1 and L.t6.2 PV modules, respectively. The
temperature rise of the L.t6 module is, however, comparatively small (Table 4.9), and its
corresponding microinverter temperature is lower ( figure 4.12).This also shows how the
PV module temperature influences the microinverter temperature.
Discussion
74
Table 4.10 also shows the influence of both AC power output and PV module temperature on microinverter temperature. The output power of the Q.t12 PV modules is
at least 20 W less than the other PV modules (O.t12 and P.t12) at site 12, but the temperature rise in Q.t12 PV modules is higher than its counterparts. As a result, although
the power loss inside Q.t12 microinverters is comparatively small, the temperature rise
in Q.t12 microinverters is very similar to the P.t12 and O.t12 microinverters due to the
higher Q.t12 PV module temperature.
This relationship is also evident when a PV module is not generating power at sufficient irradiance such that all the irradiance received by the PV module converts to heat.
Therefore, the temperature of the PV module becomes higher than the power generating
conditions of the PV module. The points in the green circle in Figure 4.2 correspond to
the non-power generating state of the system due to the technical faults. Since the PV
module backsheet temperature is a heat source for the microinverter, similar high temperature trends are also observed during microinverter backsheet temperature at non
power generating periods.
5.3 5.4 Influence of Ambient Conditions on Microinverter Temperature
As discussed above, the microinverters do not receive direct irradiance from the sun.
They do, nonetheless, transfer heat with the surroundings (ambient conditions) and
with the PV modules themselves. This can be seen from the fact that the correlation between microinverter temperature and irradiance is lower than the correlation between
PV module backsheet temperature and irradiance (Table 4.1). In the morning at low
irradiance (irradiance below 60 W /m 2 ), the microinverter temperature is almost equal
Discussion
75
to the ambient temperature (Table 4.3). A significant temperature rise is then observed
in PV module and microinverter temperature during noon time (Table 4.10). The radiant energy received from the PV module backsheet and energy loss during DC to AC
conversion are the main two contributors to the additional temperature rise of the microinverter at noon time. These three parameters are therefore critical factors for the
predictive model as discussed in more detail below.
Wind speed is the variable that determines the magnitude of the convection heat
transfer rate to/from the PV module and microinverter backsheet. One might expect
then a strong correlation between wind speed and microinverter temperature. For this
analysis, a 5 point moving average wind speed was employed. From the Figure 4.1 and
Table 4.1, the correlations between wind and PV module and microinverter backsheet
temperature are not significant. This may be a real phenomenon or may be due to the
disparity in height between the tracker platform and where the wind measurement pole
is located. A more robust analysis with anemometers at the exact location of each tracker
may be required to confirm the relationship.
A final note about microinverter temperature is that one can observe that from Table
4.7 and Figure 4.8, the Enphase reported microinverter internal temperature is smaller
in the 150-170 W and 170-190 W range than the TC reported microinverter backsheet
temperature. We also notice that in the 190-210 W range and above 210 W, the Enphase
reported temperature is generally equal to or larger than the TC temperature (Appendix
B). The conclusion here is that the temporal rise in internal temperature (i.e. the Enphase reported temperature) occurs more quickly than that of the surface temperature
Discussion
76
(i.e. the TC temperature) with an increase in AC power output. This likely occurs because within the microinverter, the high current induces winding and switch losses inside, generating heat internally. As a result, the internal temperature response is quicker.
5.4 Clustering Analysis
5.4.1 Power Cluster Discussion
In Figure 4.15, the dendrogram is organized according to the baseline power of the PV
modules with the exception of the P.t12.2 and L.t6.3 PV modules. All the high performing
modules brands: R.t14, S.t14, T.t14, O.t12 and P.t12.1, appear in one central cluster. All
of these brands’ baseline power fall above 230 W(DC)) whereas the others do not. When
further broken into sub-clusters it can be observed that the R.t14.2 module does not fall
in the same sub-cluster with the other R.t14 PV modules, which means that the power
output of R.t14.2 is slightly different than R.t14.1 and R.t14.3. The right most cluster contains the low performing brand Q.t12, and the L.t6.1 and L.t6.2 PV modules. Even though
their baseline power is 230.92 W(DC), the L.t6.1 and L.t6.2 PV modules performed poorly
as reflected in the clustering dendrogram, and as a result they clustered with the Q.t12
PV modules baseline power of only 212.75 W. The P.t12.2 and L.t6.3 PV modules form
their own individual clusters. This is likely because the P.t12.2 PV module behaves differently in the months of July-August and September-October. The AC power output of
the L.t6.3 PV module is higher than the other two L.t6 PV modules power output (Table 4.9) although, between values associated with other PV modules. As a result, it forms
its own cluster.
Discussion
77
5.4.2 Normalized Module Temperature Cluster
Due to the low conversion efficiency, the amount of residual energy will be greater in the
low performing PV modules, accompanied by additional heat generation. Therefore, the
Q.t12.1, Q.t12.2 and L.t6.1 PV modules backsheet temperature are clustered together
(Figure 4.16). In addition, the O.t12 and P.t12 PV modules’ backsheet temperature are
clustered together along with the high power output PV module K.t6.2 and the low power
output PV module L.t6.2. The O.t12 and P.t12 modules are in the same cluster because
their AC power output are similar. The actual cause behind K.t6.2 and L.t6.2 module
clustering together requires more investigation.
5.4.3
Normalized Microinverter Temperature Cluster
The normalized microinverter temperature cluster (Figure 4.17 and 4.19) is highly influenced by PV module temperature cluster (Figure 4.16). The AC power output of L.t6.2 is
much lower than the K.t6.2, P.t12 and O.t12 modules ( Figure 4.15), however, the L.t6.2
microinverter is located in the same cluster with K.t6.2, P.t12 and O.t12 microinverters
since their PV module temperature is similar (Figure 4.16). All the R.t14 modules fall under the same cluster for AC power and normalized PV module backsheet temperature,
but for the microinverter temperature cluster, R.t14.3 is located on a different cluster.
This is occurred because R.t14.3 is in a different sub-branch in the module backsheet
temperature clustering dendrogram. On the other hand , although the R.t14.2 is located
in different sub-branch in the AC power cluster, it is located in the same cluster with
R.t14.1 in normalized module , and microinverter temperature. Similarly, L.t6.2 and
K.t6.2 modules and microinverter exhibit a similar trend. This similarity suggests that
Discussion
78
the thermal behavior of microinverters is more strongly influenced by the PV module
temperature than AC power.
The O.t12 modules are located in the same cluster for both AC power and normalized module backsheet temperature. However, for normalized microinverter backsheet
temperature,O.t12.2 forms a cluster of its own. The O.t12.2 microinverter is connected
to O.t12.2 PV module that produce more power than any other. As a result, heat generation is at a maximum and the microinverter reaches saturation more frequently. This
is why this particular microinverter exhibits different temperature characteristics than
others.
5.5 Linear Regression Model
Equation 4.1 represents the predictive regression model for the microinverter temperature as a function of ambient temperature, PV module backsheet temperature, irradiance, AC power and the interactions between PV module backsheet temperature and
AC power; irradiance and power; and module backsheet temperature, irradiance and
power. The AIC value of the predicted model is 14276.67, and if we include the the interaction between AC power and backsheet temperature, the AIC value does not improve.
The model that includes the interaction of ambient temperature with other variables
produces the lowest AIC value, 14113.98 , but at the expense of simplicity since the resulting model contains 15 variables. The difference between the AIC value of the predicted model and lowest AIC value is very small, about 162.69. As a result, the model
represented by equation 4.1 was chosen.
Discussion
79
Interestingly, the coefficients of AC power are negative in every case. This is because
higher AC power output indicates low residual energy in the PV modules. Thus PV module temperature rise is small when AC power output is high, and the corresponding
microinverter temperature increase is small since microinverter temperature is more
strongly correlated with PV module temperature than AC power.
Figure 4.20 represents the fitted vs. residual plot for L.t6 microinverters. Figure 4.20
do not show any specific pattern since all the residual values are scattered randomly.
This indicates the accuracy of the predictive model is good. Figure 4.21 shows that on
a sunny day, the model under predicts in the noon time. On a cloudy day (Figure 4.22),
the difference between actual and predicted temperature is large when there is a sharp
temperature change. This is because the regression prediction model is based on the
summer time data where the number of cloudy days is very limited, and as a result, the
regression model does not predict well when there a sharp change of irradiance occurs.
Furthermore, under prediction is observed also in the afternoon for both sunny and
cloudy days. The accuracy of the predictive model can be improved if we create separate
models that predict the isolated effects of morning and afternoon. This could be a topic
for future work.
80
6
Conclusions
A data analytics procedure has been developed to identify the thermal characteristics of microinverters on dual-axis trackers operating under real-world conditions. This
work analyzed the climate, insolation, temperature and power time-series data of a PV
power plant from July 1 to October 30,2013. The test set consisted of 24 microinverters
connected to 8 different brands of PV modules located on the SDLE SunFarm- a highly
instrumented outdoor facility designed to study degradation mechanisms and pathways
of PV materials and systems. The collected time-series data were preprocessed, cleaned,
aligned, slewed, cross checked and validated before proceeding with the analysis. Pairs
scatter plots were employed to examine the raw data and present significant correlations among variables. Pairs scatter plots also reveal outliers or any anomalies in data.
Correlation coefficients were determined to quantify the correlation between the variables. For further analysis, the data set was divided into two segments: morning and
noon using local solar time. tThe largest correlation coefficient associated with the microinverter temperature was ambient temperature, followed by PV module backsheet
temperature, AC power output and finally irradiance.
Conclusions
81
The morning data analysis showed the characteristics of microinverter temperature
at low irradiance, and also revealed the effects of irradiance increase on PV module temperature and microinverter temperature. The noon time data analysis revealed the thermal behavior response at high irradiance conditions. These studies showed that the PV
module backsheet temperature is generally higher for lower power producing PV module brands. Additionally, the PV module temperature generally determines the temperature rise of the microinverter at noon time. However, if the temperature of PV modules are similar, AC power output effects on the microinverter temperature become important. Even more, hierarchical clustering techniques applied to the noon time data
revealed interesting patterns in backsheet temperature of the microinverters. For example, clustering also showed that the influence of module backsheet temperature is
stronger than the influence of AC power on microinverter temperature.
A simple linear regression predictive model for the microinverter backsheet temperature connected to different PV module brands was developed as a function of ambient
temperature, module backsheet temperature, irradiance and power, and the interactions between these variables. For the model development, the entire data set were randomly subdivided into two data sets: Test data and Predicted data. A number of models
were developed first using the test data, and the best predictive model was selected using AIC value of these models . The predictive model was validated by analyzing the
residual plots. Then using the predicted data set, the confidence interval of the difference between actual microinverters’ and predicted microinverters’ has been estimated,
and the difference between actual microinverter temperature and predicted temperature lies between 0.40 C and 1.60 C at a 95% confidence interval.
82
7
Suggested Future Research
All of the analysis in this thesis was conducted on the data collected between July
1 to October 30, 2013. Data collection will continue in the same manner in the winter
months to evaluate the performance and thermal characteristics under cold/freezing
conditions. Further analysis will be conducted on the data in future summer months
as well to explore differences in the correlations of the significant parameters. The microinverter backsheet temperature data and other environmental time-series data from
the other SunFarms that are part of the global SunFarm network will also be collected
and analyzed in the future. This will provide insight to the thermal characteristics of the
microinverters located in different climate regions and allow us to compare results of
devices under different operating conditions.
For future analyses, it is also important to conduct studies on real-world fixed rack
systems in addition to the dual-axis trackers employed for this work. This is because in
small scale utility power plants, the use of fixed rack systems is very common as is the
case, for residential systems where PV modules are installed on the rooftop. One may
expect thermal behavior to be different on a roof mounted system than on a dual-axis
tracker, since the gap between roof surface and PV module backsheet is about 10 inches
and microinverters are installed halfway in the gap. In the dual-axis system, the backside
Suggested Future Research
83
to PV module is open and therefore radiated heat will be lost into the open surroundings.
This would not be the case for the roof mounted systems, thereby trapping some of the
heat within the small enclosure between roof and PV module. Furthermore, due to the
small gap between PV module and roof, the wind access will be less compared to the the
dual-axis tracking system. Thus convective heat loss from the backsheet will be reduced
in this scenario. As a result, microinverters will have to operate at higher temperature
than those studied herein, and critical components will endure greater thermal stress.
This will likely affect the lifetime and reliability of the microinverters. Future work will
explore this alternative setup.
Appendix
84
Appendix A
Preparation of this document
This document was prepared using pdfLATEX. The (free) programs and versions implemented are as follows (links to the current versions are included):
• LATEX implementation: TeXworks
https://www.tug.org/texworks/
• Bibliographical database: Zotero version 4.0.19
https://www.zotero.org/
Appendix
85
Appendix B
Thermal performances at different power range
Table B.1. Thermal performances of O.t.12 modules at different power range
Power
Range
150-170
Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170
Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: O.t.12.1; Baseline power 240.96 W
814.15
5.79
159.87
1.90
778.41-849.90 5.27-6.32 158.40-161.35 1.82-1.97
806.88
6.90
182.53
1.83
783.72-830.04 6.57-7.24 181.33-183.72 1.78-1.89
865.11
7.74
201.85
2.01
857.48-872.74 7.63-7.84 201.23-202.47 1.99-2.03
841.64
8.19
215.72
2.23
856.484-871.33 8.14-8.23 215.07-216.37 2.18-2.29
Module: O.t.12.2; Baseline power 240.96 W
807.42
5.79
160.18
1.85
765.85-848.99 5.21-6.31 158.68-161.68 1.77-1.92
807.64
6.83
182.52
1.835
786.21-829.07 6.47-7.19 180.65-181.40 1.78-1.89
860.29
7.86
201.34
2.00
857.73-868.29 7.77-7.95 200.65-202.02 1.98-2.02
861.51
8.24
216.18
2.2
848.21-874.81 8.19-8.29 215.57-217.79 2.15-2.25
Norm.
Micro.T
Norm.
Micro.I.T
1.37
1.34-1.40
1.339
1.31-1.36
1.42
1.41-1.43
1.5
1.47-1.52
1.32
1.30-1.35
1.309
1.28-1.33
1.407
1.39-1.41
1.48
1.46-1.50
1.42
1.38-1.45
1.39
1.36-1.41
1.49
1.48-1.50
1.57
1.55-1.59
1.37
1.34-1.40
1.36
1.33-1.38
1.47
1.46-1.48
1.56
1.53-1.58
Appendix
86
Table B.2. Thermal performances of R.t.14 modules at different power range
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: R.t.14.1; Baseline power 231.35 W
671.2
5.85
159.39
1.67
625.30-717.27 5.42-6.29 158.35-160.78 1.62-173
756.04
6.89
182.85
1.88
735.29-776.79 6.71-7.07 182.15-183.54 1.83-1.92
826.12
7.57
200.34
2.02
814.8-837.44 7.50-764 199.85-200.83 1.99-2.05
881.45
7.92
215.45
2.14
834.46-928.73 7.55-8.3 214.09-216.81 2.05-2.23
Module: R.t.14.2; Baseline power 231.35 W
662.61
6.23
159.46
1.7
616.35-708.87 5.82-6.64 158.19-160.74 1.64-1.76
735.69
7.07
182.15
1.83
708.61-762.77 6.82-7.33 181.35-183.00 1.78-1.88
816.84
7.91
200.16
2.05
804.01-829.67 7.84-7.99 200.13-201.19 2.01-2.08
843.98
8.22
214.56
2.06
820.28-867.67 8.1-8.34 213.71-215.40 2.00-2.12
Module: R.t.14.3; Baseline power 231.35 W
679.07
6.19
159.65
1.71
628.79-729.35 5.75-6.63 158.37-160.92 1.65-1.77
756.08
7.15
182.42
1.88
734.68-777.48 6.95-7.36 181.67-183.16 1.82-1.92
814.63
7.92
200.08
2.08
801.69-827.57 7.84-7.99 199.60-200.57 2.05-2.11
882.65
8.07
214.81
2.14
844.00-921.31 7.58-8.56 213.69-216.14 2.03-2.25
Norm.
Micro.T
Norm.
Micro.I.T
1.29
1.27-1.31
1.37
1.35-1.39
1.43
1.42-1.44
1.46
1.42-1.550
1.27
1.25-1.29
1.36
1.34-1.38
1.43
1.42-1.44
1.47
1.44-1.51
1.29
1.26-1.31
1.32
1.30-1.34
1.42
1.40-1.43
1.41
1.38-1.43
1.28
1.26-1.30
1.33
1.31-1.35
1.44
1.42-1.45
1.44
1.42-1.46
1.3
1.28-1.33
1.369
1.34-1.38
1.458
1.44-1.47
1.47
1.43-1.52
1.29
1.27-1.31
1.368
1.34-1.38
1.467
1.45-1.48
1.5
1.46-1.47
Appendix
87
Table B.3. Thermal performances of S.t.14 modules at different power range
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: S.t.14.1; Baseline power 230.85 W
677.96
6.48
160.47
1.76
629.68-726.23 6.07-6.89 159.11-161.83 1.69-1.82
758.95
7.07
182.04
1.93
738.05-779.85 6.87-7.27 181.32-182.77 1.88-1.98
823.18
7.9
200.17
2.09
810.72-835.65 7.84-7.96 199.6-200.68 2.06-2.12
872.65
8.31
215.22
2.13
840.25-905.05 8.23-8.38 214.04-216.40 2.05-2.21
Module: S.t.14.2; Baseline power 230.85 W
679.48
6.32
159.56
1.74
628.03-729.02 5.94-6.79 158.21-160.92 1.68-1.80
756.76
7.05
182.12
1.93
734.51-779.00 6.83-7.26 181.39-182.85 1.88-1.99
820.06
7.92
201.76
2.1
806.78-833.21 7.86-7.97 200.22-201.22 2.07-2.14
847.42
8.26
215.2
2.14
818.19-876.66 8.21-8.31 214.21-216.19 2.07-2.21
Module: S.t.14.3; Baseline power 230.85 W
697.38
6.18
159.92
1.74
649.40-745.35 5.76-6.59 158.60-161.24 1.68-1.81
754.48
7.1
182.06
1.91
731.90-777.06 6.90-7.31 181.26-182.85 1.86-1.96
816.77
7.84
200.53
2.09
803.35-830.15 7.76-7.92 200.01-200.50 2.06-2.12
856.16
8.06
214.95
2.12
829.74-882.63 7.88-8.24 214.01-215.89 2.05-2.19
Norm.
Micro.T
Norm.
Micro.I.T
1.298
1.27-1.32
1.36
1.34-1.38
1.42
1.41-1.46
1.43
1.40-1.46
1.301
1.277-1.325
1.384
1.36-1.40
1.46
1.45-1.47
1.49
1.46-1.52
1.249
1.21-1.26
1.248
1.23-1.26
1.27
1.26-2.28
1.21
1.18-1.23
1.31
1.29-1.33
1.4
1.37-1.42
1.47
1.46-1.49
1.48
1.45-1.50
1.305
1.28-1.325
1.355
1.336-1.37
1.429
1.417-1.442
1.425
1.40-1.43
1.271
1.25-1.28
1.333
1.315-1.352
1.416
1.40-1.429
1.422
1.40-1.44
Appendix
88
Table B.4. Thermal performances of K.t.6 modules at different power range
Power
Range
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
150-170 Mean
95% CI
170-190 Mean
95% CI
190-210 Mean
95% CI
>210 Mean
95% CI
Irradiance
Current
Power
Norm.
Mod.T
Module: K.t.6.1; Baseline power 225.19 W
739.77
5.51
160.25
1.77
690.57-739.77 5.00–6.02 158.95-161.54 1.72-1.83
761.94
6.45
180.97
1.81
729.23-794.64 6.07-6.83 179.93-182.01 1.76-1.86
835.27
7.57
200.82
1.91
820.35-850.20 7.43-7.71 200.11-201.52 1.88-1.94
837.84
7.71
214.5
2.07
816.7-858.99 7.42-8.00 213.70-215.29 2.01-2.14
Module: K.t.6.2; Baseline power 225.19 W
691.18
5.68
160.3
1.74
640.19-742.16 5.13-6.22 158.58–161.68 1.69-1.79
754.19
6.52
181.29
1.82
719.46-790.12 6.12-6.92 180.22-182.36 1.77-1.88
826.85
7.51
201.52
1.94
808.33-845.36 7.32-7.70 200.78-202.27 1.92-1.96
847.24
7.91
215.48
2.14
833.82-860.66 7.74-8.08 214.90-216.07 2.09-2.19
Norm.
Micro.T
Norm.
Micro.I.T
1.36
1.33-1.38
1.346
1.32-1.368
1.439
1.42-1.45
1.489
1.46-1.51
1.35
1.32-1.38
1.348
1.32-1.37
1.48
1.46-1.49
1.53
1.507-1.56
1.31
1.29-1.33
1.33
1.31-1.35
1.4
1.39-1.41
1.469
1.449-1.488
1.29
1.27-1.31
1.32
1.29-1.34
1.42
1.41-1.43
1.49
1.47-1.51
Appendix
89
Table B.5. Thermal performances of Q.t.12 modules at different power range
Power
Range
Irradiance
Current
Power
Norm.
Mod.T
Module: Q.t.12.1; Baseline power 212.75 W
150-170 Mean 764.9
6.53
162.36
1.84
95% CI 736.80-793.00 6.27-6.78 161.46-163.26 1.80-1.88
170-190 Mean 852.71
7.32
181.43
2.04
95% CI 742.22-763.20 7.24-7.41 180.84-182.01 2.01-2.06
190-210 Mean 834.69
7.78
195.27
2.16
95% CI 813.76-853.61 7.71-7.88 194.30-196.25 2.10-2.21
>210 Mean
95% CI
Module: Q.t.12.2; Baseline power 212.75 W
150-170 Mean 747.47
6.42
161.71
1.87
95% CI 716.57-778.37 6.14-670 160.85-162.58 1.83-1.92
170-190 Mean 856.65
7.27
181.37
2.08
95% CI 846.30-866.99 7.19-7.36 180.83-181.90 2.06-2.10
190-210 Mean 840.8
7.69
195.8
2.24
95% CI 816.81-864.79 7.56-7.82 194.69-196.92 2.17-2.31
>210 Mean
95% CI
Module: Q.t.12.3; Baseline power 212.75 W
150-170 Mean 780.45
6.68
162.22
1.91
95% CI 854.74-806.16 6.43-6.93 161.39-163.02 1.87-1.95
170-190 Mean 855.19
7.41
180.38
2.12
95% CI 845.47-864.91 7.33-7.49 179.86-180.89 2.10-2.15
190-210 Mean 857.51
7.68
196.5
2.28
95% CI 810.70-904.32 7.22-7.13 194.86-198.13 2.18-2.37
>210 Mean
95% CI
Norm.
Micro.T
Norm.
Micro.I.T
1.334
1.31-1.349
1.41
1.40-1.419
1.48
1.46-1.50
1.322
1.30-1.33
1.388
1.380-1.396
1.42
1.40-1.44
1.36
1.34-1.37
1.434
1.42-1.44
1.475
1.44-1.50
1.358
1.34-1.37
1.437
1.429-1.44
1.493
1.46-1.51
1.348
1.33-1.36
1.423
1.41-1.43
1.47
1.433-1.506
1.32
1.30-1.33
1.391
1.38-1.40
1.45
1.42-1.48
Bibliography
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