performance assessment of photovoltaic systems: …
TRANSCRIPT
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Abstract— This thesis focuses on the study and characterisation
of failures in photovoltaic (PV) modules.
It is made a characterization of the main failures found in
photovoltaic modules in terms of their physical mechanisms. An
analysis of the characteristics of these failures reveals their impact
from an electric point of view in a PV module, allowing their
simulations.
In pursuance of the simulation and study of failures in the
performance of the modules in terms of their currents, voltages
and power, a Simulink model based on the 5-paramater solar cell
model was created, where each one of the solar cell’s parameters
could be changed individually. The analysis of each failure allows
the identification of the most severe failures (open circuits), but
also the intensity levels of other failures in order to cause higher
power losses. It was demonstrated that faulty modules in series
and parallel connections with healthy modules led to a power loss
attenuation that complicates the detection of these failures.
Bypass diode activation was found to be a consequence of most
of the simulated failures. As such it is proposed a method only
dependent on electric measurements to identify how many bypass
diodes are conducting, hence detecting possible module failures.
The method in question was theoretically validated at the
simulation level but was not validated with experimental data.
Index Terms— PV Module Failures, Solar Panel Model, Failure
Detection
I. INTRODUCTION
Over the last few years the world has witnessed an
exponential growth in solar photovoltaics power generation
making this industry one of the fastest growing ones in the
world. In 2016 the installed capacity of solar PV power
increased by 38% representing more than half of all new
renewable power capacity installed in that year [1]. With this
growth, cumulative solar PV capacity reached almost 300 GW
and generated over 310 TWh, representing over 1% of the
global power output [1].
PV systems such as PV power plants or smaller scale PV
applications, rely on continuous operations and maintenance
(O&M) routines to ensure long term up-time, higher system
efficiencies and economic viability. The continuous growth of
this industry enhanced the importance of O&M activities.
Augmented challenges are found in solar PV plants located in
remote places, with difficult access and poor communication
infrastructures. One main O&M issue in the PV industry is the
number of components that need to be inspected in large PV
plants, especially solar panels A study done for grid-connected
systems in Germany in the 1990’s [2] revealed that solar panels,
or PV modules, accounted for 15% of the total system failures,
whereas inverters contributed with 63% and other system
components contributed with 22%. Despite being only 15% of
total system failures, PV modules failures affect the overall
system’s efficiency and can jeopardize the energy production.
Well maintained PV systems present in average 6% higher
performance than poorly maintained ones [3].
Several measurements methods of failure identification on
PV modules already exist such as Visual Inspection,
Thermography, Electroluminescence (EL) imaging, Ultraviolet
(UV) imaging and Signalling Transmission Methods.
The method used in this work to study failures in PV modules
is electrical measurements and I-V (Current-Voltage)
characteristic curves. I-V curves, as the name suggests, show
the relationship between the current flowing through an
electronic device (PV modules in this case) and the applied
voltage across its terminals. Electrical measurements such as
voltage, current and output power are easily obtainable and
require simple equipment such as voltmeters and amperemeters
but also ad hoc devices such as I-V curve tracers. These devices
apply different loads to a PV module and measure its current
and voltage.
This thesis will focus on characterising common failures in
PV modules and understand how they affect the module
performance with the help of simulation tools working at the
solar cell level to calculate the I-V curve. Based on the impact
of the simulated failures, a method for failure detection
exclusively based on electric measurements is proposed.
II. SOLAR CELL CHARACTERISTIC I-V CURVE
The current and voltage (I-V) characteristic curve of a solar
cell is a graphical representation of the relationship between the
current and the voltage produced by a solar cell for a given
irradiation and temperature.
Performance Assessment of photovoltaic
systems: Monitoring their abnormal
operating conditions
Francisco Franco, Instituto Superior Técnico, Lisboa
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From the I-V curve some key parameters can be extracted to
assess the quality of a PV module.
The Open-Circuit Voltage (Voc).is the maximum voltage
available from a PV cell and occurs at zero current. An increase
in the solar cell’s operating temperature will decrease Voc.
The Short-Circuit Current (Isc) is the maximum current when
the voltage across the cell is zero. More irradiation will translate
into a higher value of Isc.
The Maximum Power Point (MPP) is the point where the cell
is at maximum power. Associated with the MPP are the
Maximum Power Current and Maximum Power Voltage (Imp
and Vmp respectively).
The slopes in the I-V curve will be denoted by numbers with
units of resistance. Changes in the slope near the Voc region are
associated with an increase in Rs (Series Resistance), whereas
changes in the slope near the Isc region are due to a decrease in
Rsh (Shunt Resistance). The series resistance represents the
resistance between the metal contacts and the solar cell,
whereas the shunt resistance represents shunt paths through
which the current can flow bypassing the solar cell.
III. FAILURES IN SOLAR PANELS
PV module failures have been registered at different times
during a module life time: early life failures [4], midlife failures
[5] and wear out failures [6]. Altogether, the most common
failures found were burn marks and hot spots, defective cell
interconnects or isolated cell parts (cell cracks), short-circuited
cells, snail tracks, delamination, junction box failures, glass or
frame damage and discoloration of the encapsulant EVA
(ethylene vinyl acetate).
Some of the failures described above have a direct impact on
the solar cells, such as cell cracks and hot spots whom are very
related with each other and ultimately can break a solar cell
resulting in an open circuit. Short-circuited cells are mostly a
consequence of a defect during the manufacturing process but
can also occur if strings or modules establish a connection
between each other or if impurities prevenient from poor cell
isolation lodge themselves on solar cells eventually shunting
them.
Other failures such as discoloration of EVA, module shading
and delamination can have direct optical influences on the
module as less radiation reaches the solar cells. These failures,
alongside cell cracks, result in current mismatches in the
module.
Snail tracks are primarily a visible defect caused by the
discoloration of the silver paste of the front side metallization
of silicon cells. This failure is reported to have no influence on
the performance of a PV module despite enhancing the
development of cell cracks.
Junction box failures and glass or frame breakages can have
immediate catastrophic consequences on a PV module that rend
the modules obsolete and therefore cannot be simulated from
an electric point of view. However, these failures lead to a
moisture ingress in the module, increasing its corrosion.
Delamination also increases the corrosion in a PV module.
This work investigates the characteristics of failures that can
be observed on the system’s electric current and voltage. In that
sense, the focus is on failures that affect primarily the electric
response. Table 1 summarizes the failures and their electrical
repercussions on the modules.
Table 1:Most Important Electric Failures Consequences
Failures Electric
Consequences
Failure causes
Cells in Open Circuit Broken cells resulting of severe
cell cracks and hotspots
Short-Circuited Cells Defects during manufacturing
process
and short circuits between strings
Optical Degradation Solar cells deprived of solar
radiation (shading/soiling,
discoloration of EVA,
delamination)
Bypass Diode Failures Junction box failures (moisture
ingress), overheating
Cell Cracks Hotspots, thermal and mechanical
stress, enhanced by snail tracks
Corrosion Moisture ingress prevenient from
delamination, glass or frame
breakage poor junction box
insulation
IV. FAILURE SIMULATIONS
To simulate the failures described in Table 1, a Simulink
model of a solar panel was created based on the 5-paramater
solar cell model. The model was created so that every cell has
its own model so that all the solar cells can have their
parameters changed individually. This manipulation allows the
study of failures at the solar cell level. In order to obtain the five
parameters of the solar cell model (IL,I0,Rs,Rsh,n) it is necessary
to have reliable measurements of I-V curves under controlled
irradiance and temperature conditions.
Since it shies away from the scope of this thesis to calculate
solar cell’s parameters, the California Energy Commission
(CEC) Performance Model was chosen. This model described
in [7] is based on the 5-parameter solar cell model and uses
parameters commonly found on PV modules datasheets to
derive a set of coefficients that describe the I-V curve shape at
Standard Test Conditions (STC). These coefficients calculation
is described in detail in [8] and takes into consideration the
irradiation and the temperature of the modules. Both the
algorithms of the CEC model as well as the database parameters
for many PV modules are available online in the PV_LIB
Toolbox [9]. This model is validated experimentally in a high
technology dedicated laboratory and provides reliable values
for the 5-parameter model of many PV modules.
The failures electric consequences from Table 1 will be
studied and simulated and their impact on the I-V curves will
be analysed. Every time a fault is introduced a new I-V curve is
simulated with its correspondent new MPP. In order to measure
the impact of the fault ΔVmp, ΔImp and ΔMPP are calculated as
follows:
𝛥𝑉𝑚𝑝 =𝑉𝑚𝑝𝑓𝑎𝑢𝑙𝑡
− 𝑉𝑚𝑝
𝑉𝑚𝑝
(1)
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𝛥𝐼𝑚𝑝 =𝐼𝑚𝑝𝑓𝑎𝑢𝑙𝑡
− 𝐼𝑚𝑝
𝐼𝑚𝑝
(2)
𝛥𝑀𝑃𝑃 =𝑀𝑃𝑃𝑓𝑎𝑢𝑙𝑡 − 𝑀𝑃𝑃
𝑀𝑃𝑃 (3)
In the cases where arrays of modules are being simulated in
series or parallel Vmp, Imp and MPP correspond to a fault free
operation of the entire array.
The failures will be simulated under STC conditions unless
said otherwise.
The solar panel used for the simulations is a Suntech
STP225-20/Wd whose parameters can be found on Table 2 as
well as the CEC parameters on Table 3.
Table 2: Suntech STP225-20/Wd Datasheet Parameters at
STC
Isc 8,15 A
Voc 36,7 V
MPP 225 W
Vmp 29,6 V
Imp 7,61 A
Ns 60
Table 3: Suntech STP225-20/Wd Datasheet CEC Parameters
at STC
IL,STC 8.163 A
I0,STC 1.0602×10-10 A
Rs,panel 0.36 Ω
Rs,cell 0.06 Ω
Rsh,panel 223.87 Ω
Rsh,cell 3.7212 Ω
a 1.4654
Adjust 7%
A. Cells in Open Circuit
Fragile connections between solar cells within the solar panel
may result in open circuits. In an open circuit (OC) the current
no longer has an electrical path to pursue. From a simulation
point of view, an open circuit in a solar cell corresponds to
setting its current to zero because in a perfect open circuit there
can be no current flowing.
The first simulation introduces an open circuit in one cell by
setting its series resistance to 10000Ω, followed by another
open circuit in another string.
Figure 1: I-V curve for Cells in Open Circuit in 1 Panel
Table 4:MPP variation for Cells in Open Circuit in 1 Panel
Number of arrays with
1 OC cell
ΔVmp ΔImp ΔMPP
1 -35,64% 0,39% -35,38%
2 -70,02% -2,64% -70,81%
According to the simulation, a bypass diode will start to
conduct due to an open circuit in just one cell as can be seen
through the slope in the I-V curve. Therefore, instead of how
many cells are in open circuit, the issue is in how many strings
this fault occurs. This is illustrated in Figure 1 above, where just
one cell in open circuit is enough to force the bypass diode to
conduct.
Imp is almost the same since the strings are connected in series
and the bypass diodes offer an alternative path to the current.
The activation of each of the bypass diodes explains the
reduction of Vmp. Each time a bypass diode is activated, the
voltage correspondent to that string is lost. Since one string
corresponds to 1/3 of the panel, losing one string will
approximately decrease Vmp to 1/3, and losing two strings will
decrease it to about 2/3. Because the MPP is the product of Vmp
with Imp and Imp does not change with an open circuit cell, the
variation in the MPP is the same as Vmp.
So far it is clear that an open circuit in a solar cell has a very
big impact in the loss of power. The next simulation was carried
out with the intent of understanding the impact of cells in open
circuit in an array of panels connected in series. The simulation
setup included one defective solar panel (with one or two cells
in open circuit in different strings again) with an increasing
number of healthy solar panels in series.
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Figure 2: ΔMPP for Cells in Open Circuit in Series Array
Configuration
Each time a healthy panel is added in series the power that is
lost is attenuated. With five healthy panels in series with one
panel with one cell in open circuit, the power loss is 5.89%.
Initially, with just one panel alone it was about -35%. If two
cells in different strings are in open circuit the fault is more
severe but is also attenuated to the point where five healthy
panels in series with the faulted panel, make the power loss to
be 11.79% when compared to -71% with just one faulty panel.
In a series connection of solar modules there is a nonlinear
power attenuation as more panels are added in series.
One cell in open circuit has a catastrophic impact regarding
power loss for just one panel. In a series connection however,
this power loss is attenuated as more healthy panels are added
in series. This next simulation setup includes an array with one
damaged panel and several other healthy panels in series in
parallel with other healthy arrays of the same size. Two
simulations were carried out, one for an array size of five panels
and another for an array size of three panels. For these two
simulations, more arrays were added in parallel up to a
maximum number of four. This simulation allows the study of
the impact of just one cell in open circuit in a series and parallel
array configuration.
Figure 3: ΔMPP for Cells in Open Circuit in Series/Parallel
Array Configuration
In the previous simulation it was clear that the more healthy
panels are added in series the more the power loss is attenuated.
This series connection power loss attenuation is present in this
situation, where the system with the five panels array always
shows less relative power lost when compared to the three
panels array system. Besides that, every time an array is added
in parallel, a power loss attenuation is also visible.
B. Short-Circuited Cell
To simulate a short circuit (SC), the resistances in the
equivalent electric circuit of the solar cell model are set to zero,
both Rs and Rsh. In the first simulation the number of short-
circuited cells was increased by two until an entire string is
short-circuited.
Figure 4: I-V Curve for Short-Circuited Cells in 1 Panel
Table 5: MPP variation for Short-Circuited Cells in 1 Panel
Number of short-
circuited cells
ΔVmp ΔImp ΔMPP
2 -2,96% -0,41% -3,36%
4 -7,19% 0,55% -6,68%
6 -10,13% 0,14% -10,00%
8 -13,08% -0,30% -13,35%
10 -17,32% 0,76% -16,70%
12 -20,25% 0,32% -20,00%
14 -23,20% -0,17% -23,34%
16 -26,17% -0,73% -26,71%
18 -30,39% 0,54% -30,01%
20 -33,33% -0,01% -33,33%
As more cells are short-circuited the less voltage the system
will have. Voc keeps decreasing as the number of short-circuited
cells increases. It is worth pointing out that the shape of the I-V
curve remains similar which is why that only Vmp will change
significantly with the number of short-circuited cells. No
inflexion points are observed because there is no current
mismatch and no bypass diode is forced to conduct.
Since Imp remains unaffected, the power lost is directly
proportional with the number of short-circuited cells as can be
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verified by the linear regression with the R-squared value of 1
as shown in Figure 5.
Figure 5: ΔMPP per Short-Circuited Cell
Following the same logic as for the open circuit simulations,
a faulty panel with short-circuited cells is simulated in an array
with other healthy solar panels in series. Four simulations were
carried out, each with a different number of short-circuited cells
in the faulty panel.
Figure 6: ΔMPP for Short-Circuited Cells in Series Array
Configuration
The results show that just one short-circuited cell has
negligible effects on the system and therefore is practically
impossible to detect. For this fault to be noticed the number of
short-circuited cells must be high. As more healthy panels are
added in series the power lost keeps getting attenuated.
This next simulation setup includes an array with one panel
with short-circuited cells and four other healthy panels in series
(five panels in total) in parallel with other arrays of also five
modules in series. Three simulations were carried out where the
faulty panel had one, ten and twenty short-circuited cells. For
these three simulations, arrays were added in parallel up to a
maximum number of four. This simulation allows the study of
the impact one and multiple short-circuited cells in a series and
parallel array configuration.
Figure 7: ΔMPP for Short-Circuited Cells for Series/Parallel
Array Configuration
C. Homogeneous Shading / Soiling
To simulate homogeneous shading, the value of G (solar
irradiance) is reduced on the shaded cells, reducing the IL
parameter but increasing Rsh. The reduction of G simulates the
increase of the simulated shadow which is defined by 1 −𝐺
𝐺𝑆𝑇𝐶.
Figure 8: I-V Curve for Homogeneous Shading in 1 Panel
Table 6: MPP variation for Homogeneous Shading in 1 Panel
Shade ΔVmp ΔImp ΔMPP
0% 0% 0% 0%
5% 0% -5% -5%
10% 1% -11% -10%
15% 0% -15% -15%
20% 0% -20% -20%
30% 1% -31% -31%
40% 1% -41% -41%
50% 0% -52% -52%
60% 0% -63% -63%
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Homogeneous shading has an exclusive impact on Imp. Since
all the cells receive the same irradiation there is no risk of
current mismatch and bypass diodes will not conduct, hence
there are no inflexion points in the I-V curve. Furthermore, the
loss of power is directly proportional to the shading percentage.
D. Partial Shading / Hot Spot
Partial Shading occurs whenever the panel is covered by a
non-uniform shade. As less radiation reaches a solar cell the less
current it generates. Therefore, partial shading will cause a
current mismatch between the shaded cells and the remaining
ones. This occurrence can lead to the formation of hot spots
where there is a high dissipation of power increasing the shaded
solar cells temperature, which then contributes to the
degradation of the module.
The following simulation pretends to show how severe the
shading in just one cell must be so that the power loss is
noticeable. The value of G is gradually reduced for just one cell
in order to observe the effect on the I-V curve and generated
power.
Figure 9: - I-V Curve for Partial Shading in 1 Panel
Table 7: MPP Variation for Partial Shading in 1 Panel
Shade ΔVmp ΔImp ΔMPP
0% 0% 0% 0%
10% 4% -6% -2%
20% 7% -15% -9%
30% 10% -26% -18%
40% 13% -36% -28%
50% -36% 0% -35%
60% -36% 0% -35%
70% -36% 0% -35%
As the shading intensity increases the current mismatch is
more accentuated and eventually the bypass diode starts to
conduct, which happens at around 40% to 50% shade. For lower
shading intensities (0% to 20%) the most noticeable change will
be in the Imp parameter. The more intense the shade gets the
decrease in Vmp gets more visible until finally the bypass diode
starts to conduct and Vmp as well as Imp don’t change anymore.
When the bypass diode starts to conduct the entire module loses
35% of its maximum output power which roughly corresponds
to losing 1/3 of the module due to the activation of the bypass
diode.
E. Short-Circuited Bypass Diode
Junction box failures with moisture ingress may result in a
short circuit of the bypass diode terminals. In a short-circuited
string of cells, the voltage is forced to zero. From a simulation
point of view, a short circuit in a bypass diode corresponds to
substitute it for a null resistance. In this simulation the number
of short-circuited bypass diodes is increased.
Figure 10: I-V Curve for Short-Circuited Bypass Diodes
Table 8: MPP variation for Short-Circuited Bypass Diodes
Short-Circuited
Bypass Diodes
ΔVmp ΔImp ΔMPP ΔVoc
1 -33% 0% -33% -33%
2 -67% 0% -67% -67%
As already seen from previous simulations, when a bypass
diode conducts it short-circuits a string of 20 cells, resulting in
a voltage drop of 1/3 per bypass diode activated. This voltage
drop is reflected on Vmp and Voc.
F. Open Circuit in Bypass Diode
A bypass diode can become ineffective at bypassing the
current if it overheats. In this simulation a partial shading of an
entire string of 20 cells is simulated. These 20 cells receive 50%
less radiation which is enough to force the bypass diode to
conduct as seen in the partial shading simulations. The first
simulation occurs under normal operating conditions of the
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bypass diode whereas in the second simulation the bypass diode
fails to conduct.
Figure 11: I-V Curve for Bypass diode in Open Circuit
Table 9: MPP variation for Bypass diode in Open Circuit
Bypass Diode ΔVmp ΔImp ΔMPP
Normal Operation -36% 0% -35%
Open Circuit 9% -48% -43%
When the bypass diode fails to conduct the entire current of
the module will be conditioned by the fault current. This results
in a shift of the MPP to a point with more voltage but with much
less current, resulting in an additional 8% power loss. If the
shade or the mismatch in current, would be more severe, the
module would have been subjected to an even lower current
aggravating even more the power loss. This simulation
illustrates the importance of bypass diodes.
G. Cell Cracks
Cracking in solar cells although invisible to the naked eye,
are an important factor in terms of power loss in PV modules as
they can lead to electrically inactive cell areas, reducing the
power output of the module [10]. The decrease in the Short-
Circuit current of a solar cell due to cracking is directly
proportional to the increase of the inactive cell area [10], [11].
Furthermore, experimental results have also shown an increase
of 7% in the series resistance of a cracked cell [10].
The first simulation analyses the impact of just one cracked
cell as the inactive area of the cell increases. Following a similar
approach than [11], as the active cell area decreases, the IL and
I0 current parameters shall decrease as well according to the
following equations:
𝐼𝐿 = 𝐼𝐿𝑟𝑒𝑓× 𝐴𝑎𝑐𝑡𝑖𝑣𝑒 (4)
𝐼0 = 𝐼0𝑟𝑒𝑓× 𝐴𝑎𝑐𝑡𝑖𝑣𝑒 (5)
In this simulation the series resistance of the cracked cell is
also increased by 7%.
Figure 12: I-V Curve for Cell Crack in 1 Panel
As the active cell area decreases the current produced by the
cracked cell decreases as well. As the crack gets more severe
and the current mismatch increases the bypass diode is forced
to conduct when the active area of the cell is around 50%. This
can be seen in Figure 13 where the power lost is plotted as a
function of the inactive cell area. At around 50% inactive cell
area the bypass diode starts to conduct and a consequence the
power lost stagnates even though the inactive cell area
increases. A very strong cell crack is therefore required in order
to force the bypass diode to conduct.
Figure 13: Power Loss per Inactive Cell Area
Not just one cell is expected to be cracked in one solar panel.
The next simulation will increase the number of cracked cells
for a constant amount of inactive cell area. Several simulation
corresponding to different inactive areas were done and the
results can be seen in Figure 14.
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Figure 14: Multiple Cell Cracks Power Loss
As expected, the losses in power are greater for larger
inactive cell areas as last simulation suggested. However, it is
worth noticing that for a given inactive cell area, many other
cells need to be cracked so that power loss is more significant.
H. Corrosion
Corrosion of the cell’s metallisation is caused by moisture
ingress. Moisture ingress is a consequence of other failures such
as frame or glass breakage and delamination. From an electrical
point of view, corrosion will correspond to an increase in the
series resistance of each solar cell. In the next simulation the
series resistance of all solar cells in the module are increased.
Figure 15:- I-V Curve for PV module Corrosion
Table 10: MPP Variation for PV Module Corrosion
ΔRs ΔVmp ΔImp ΔMPP
0% 0% 0% 0%
150% -4% -1% -5%
200% -8% -1% -9%
250% -12% -2% -14%
300% -15% -3% -18%
400% -22% -5% -27%
500% -28% -9% -34%
The increase in Rs has very little impact on Imp. The slope
around Voc increases as expected. The increased slope will
reduce Vmp as the series resistance increases. A 250% increase
in Rs is required to have a 14% power loss.
V. FAILURE DETECTION
The greatest power losses were observed when the failures
simulated forced a bypass diode to conduct, or when the bypass
diode itself was short-circuited. Both have similar
consequences to the PV module: a large voltage drop. This
section presents a method to detect the bypass diode activation
without the need to disconnect the panels from the inverter and
using only the measurements of the operation voltage and
current at the MPP.
A. Bypass Diode Activation Detection
A study [12] proposed a method for automatic fault detection
in grid connected PV systems based exclusively on current and
voltage indicators. These indicators only depend on the PV
system array configuration. In this section the same method will
be adapted to detect when a bypass diode starts to conduct
instead of an entire PV module being bypassed in a series PV
array configuration.
In a fault free operation of a PV array, the output voltage is
the product between Vmp of a single module and the number of
modules in series (Ns). Using these two values plus Voc of a
single module, a base ratio voltage indicator is established:
𝑅𝑣𝑟𝑒𝑓=
𝑉𝑚𝑝1𝑝𝑎𝑛𝑒𝑙∙ 𝑁𝑠
𝑉𝑜𝑐1𝑝𝑎𝑛𝑒𝑙
(6)
If one or more panels are entirely bypassed the indicator is
calculated in the same way, however, the number of bypassed
modules (Nb) must be subtracted to Ns:
𝑅𝑣𝑏 =𝑉𝑚𝑝1𝑝𝑎𝑛𝑒𝑙
∙ (𝑁𝑠 − 𝑁𝑏)
𝑉𝑜𝑐1𝑝𝑎𝑛𝑒𝑙
(7)
The relationship between equations (6) and (7) is given by β:
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𝛽 =𝑅𝑣𝑏
𝑅𝑣𝑟𝑒𝑓
(8)
𝛽 = 1 −𝑁𝑏
𝑁𝑠
(9)
The expression obtained for 𝛽 shows that it only depends on
the number of modules in series. Depending on the size of the
array, several values for 𝛽 (up to a maximum of Ns) can be
calculated for each number of bypassed solar panels.
Using Rvref from equation (6) a threshold is calculated for every
value of 𝛽:
𝑇𝛽 = 1.02 ∙ 𝑅𝑣𝑟𝑒𝑓∙ 𝛽 (10)
Rvb is a theoretical ratio created to calculate 𝛽 and establish
a threshold for every module that is bypassed. In practise for a
given PV array, one has access to the Vmp and the total Voc of
the entire array (whether it is by simulation or multiplying Voc
of one panel with Ns). The value that is going to be compared
with the several thresholds is then calculated using these two
variables of the entire array and not just one panel:
𝑅𝑣 =𝑉𝑚𝑝𝑎𝑟𝑟𝑎𝑦
∙ 𝑁𝑠
𝑉𝑜𝑐𝑎𝑟𝑟𝑎𝑦
(11)
When Rv is smaller than a certain threshold, the method
detects how many modules were bypassed. The way the ratios
are calculated can be changed so that the method now detects
when a bypass diode starts to conduct instead of an entire
module being bypassed.
Equations (6) and (7) can be recalculated but using the total
number of bypass diodes as well as those that are conducting.
Nb now stands for the number of active bypass diodes and Ns is
replaced with the total number of bypass diodes in the
array (3𝑁𝑠). Assuming each solar panel has three bypass
diodes, the new ratio voltage-based indicator is now:
𝑅𝑣𝑟𝑒𝑓=
𝑉𝑚𝑝1𝑝𝑎𝑛𝑒𝑙∙ 3𝑁𝑠
𝑉𝑜𝑐1𝑝𝑎𝑛𝑒𝑙
(12)
And Rvb is then calculated using the following expression:
𝑅𝑣𝑏 =𝑉𝑚𝑝1𝑝𝑎𝑛𝑒𝑙
∙ (3𝑁𝑠 − 𝑁𝑏)
𝑉𝑜𝑐1𝑝𝑎𝑛𝑒𝑙
(13)
By doing so the final expression for 𝛽 is:
𝛽 = 1 −𝑁𝑏
3𝑁𝑠
(14)
As expected, β still only depends on the size of the array but
is now expressed in terms of the number of bypass diodes,
allowing the threshold to be relative to the numbers of active
bypass diodes and not bypassed modules.
Equation (11) also needs to be adjusted according to the total
number of active bypass diodes in the array:
𝑅𝑣 =𝑉𝑚𝑝𝑎𝑟𝑟𝑎𝑦
∙ 3𝑁𝑠
𝑉𝑜𝑐 𝑎𝑟𝑟𝑎𝑦
(15)
In order to test this method a system of three solar panels in
series was simulated and the bypass diodes were forced to
conduct due to an induced open circuit in the strings. The
theoretical values for Rvb, β and the threshold Tβ, were
calculated according to the equations (13), (14) and (10)
respectively. Table 11 summarizes the threshold values
calculated.
Table 11:Rvb, β and Tβ values for 3 Modules in Series
Number of Active Bypass Diodes
0 1 2 3 4 5
Rvb 7,27 6,46 5,65 4,85 4,04 3,23
β 1,00 0,89 0,78 0,67 0,56 0,44
Tβ 7,42 6,59 5,77 4,94 4,12 3,30
The system was then simulated increasing the number of
active bypass diodes up to five This was achieved by inducing
open circuits in different strings. The Vmp and Voc of the whole
array system were extracted and used to calculate Rv according
to equation (15). Table 12 contains the Vmp as well as the Rv
values calculated for every bypass diode activated due to an
open circuit.
Table 12:Simulation results and Rv values for 3 Modules in
Series
Number of Active Bypass Diodes
0 1 2 3 4 5
Vmp [V] 88,93 78,37 67,80 57,62 47,05 36,49
Rv 7,27 6,41 5,54 4,71 3,85 2,98
By comparing the values obtained for Rv in Table 12 with the
calculated Tβ values in Table 11, it is clear that for a
hypothetical number of active bypass diodes Rv is always
smaller than all the previous threshold values. For example, the
simulation results showed a Rv value of 5.54 when there two
active bypass diodes. This value is smaller than the threshold
corresponding to two active bypass diodes (5.77) but bigger
than the threshold for three active bypass diodes (4.94).
Therefore, the conclusion is that there are in fact two active
bypass diodes.
VI. CONCLUSIONS
In this work a series of PV module failures were presented,
characterised and simulated. Most of these failures occur at the
10
solar cell level, hence the importance of developing a model
that allowed the simulation of PV modules where the solar cells
parameters can be changed.
The Simulink model created was based on the 5-parameter
solar cell model. This model is widely established and allows
the manipulation of five parameters that can influence a PV
modules performance. The CEC model provides reliable values
for the 5-parameter model of many PV modules available on
today’s market, allowing an accurate simulation of many
commercially available PV modules including the one used in
this work.
Cells in open circuit revealed to be the most severe since it
only takes one cell to be in open circuit to lose 1/3 of the
module’s power due to the activation of a bypass diode. On the
other hand, short-circuited cells have a smaller impact on the
module and the power loss is directly proportional with the
number of short-circuited cells. Short-circuited cells location
within the module is not relevant because they will not trigger
a bypass diode unlike an open circuit cell.
Both cells in open circuit and short-circuited cells cause
power losses on the module. However, faulty panels in a series
connection with healthy panels reveal that that power loss is
attenuated. One cell in open circuit cell can still have noticeable
effects on the power loss of the entire array. With five healthy
panels in series the impact of one cell in open circuit in the
maximum power is roughly -5% whereas one short-circuited
cell is imperceptible. This power attenuation is even more
severe when more arrays are connected in parallel. This reveals
a monitoring problem because these failures become impossible
to detect as the system grows. How many sensors and where to
put them in order to maximize the chances of failure detection
is a challenge that was not addressed in this work but is of the
upmost importance.
Other mismatch faults were simulated such as
shading/module soiling. Homogeneous shading is not really a
mismatch fault because theoretically all cells are under the same
shadow and produce the same current. One shaded cell has a
very small impact on the I-V curve and the power generated
unless the shade reaches around 50% where the mismatch is
enough to activate the bypass diode. Cell cracks were also
simulated. Their impact was related with the inactive cell area.
Very small inactive cell areas (5%) are not enough the cause an
impact on the I-V curve and power generated. That is why cell
cracks can go unnoticed and not only because they can be
invisible to the human eye.
The role of the bypass diode is of the most importance. It is
the modules defence mechanism against severe mismatch
faults. A method exclusively based on voltage measurements
and the size of an array was proposed to detect how many
bypass diodes are conducting and therefore signalling possible
severe mismatch faults. With this method there is no need to
disconnect the modules. The method worked simulation wise
but lacks experimental results to be proper validated.
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