Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study
Introduction. Photovoltaic (PV) modules constitute the backbone of renewable energy systems, yet their performance is compromised by degradation mechanisms, particularly potential induced degradation (PID), which causes rapid power losses through ionic migration under high voltage stress, creating p...
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National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2026
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Electrical Engineering & Electromechanics| _version_ | 1869562791633879040 |
|---|---|
| author | Khammassi, Z. Jeridi, A. Khaterchi, H. Zaafouri, A. |
| author_facet | Khammassi, Z. Jeridi, A. Khaterchi, H. Zaafouri, A. |
| author_institution_txt_mv | [
{
"author": "Z. Khammassi",
"institution": "University of Tunis"
},
{
"author": "A. Jeridi",
"institution": "University of Tunis"
},
{
"author": "H. Khaterchi",
"institution": "University of Tunis"
},
{
"author": "A. Zaafouri",
"institution": "University of Tunis"
}
] |
| author_sort | Khammassi, Z. |
| baseUrl_str | http://eie.khpi.edu.ua/oai |
| collection | OJS |
| datestamp_date | 2026-07-01T21:42:56Z |
| description | Introduction. Photovoltaic (PV) modules constitute the backbone of renewable energy systems, yet their performance is compromised by degradation mechanisms, particularly potential induced degradation (PID), which causes rapid power losses through ionic migration under high voltage stress, creating parasitic shunts that reduce shunt resistance Rsh and energy output. Problem. Although the influence of moisture and temperature has been widely investigated, the combined contribution of operational and environmental factors such as dust soiling remains insufficiently clarified. Goal. This work assesses dust as a contributor to potential induced degradation focusing on the combined effects of tilt angle, dust exposure and dust-moisture interaction on insulation integrity and degradation susceptibility. Methodology. A comparative experimental study was conducted on 3 identical crystalline-silicon PV modules without bypass diodes, installed at tilt angles of 20°, 30° and 40°. A controlled and uniform layer of sandy dust (maximum particle size about 150 μm) was deposited on the front surface. Insulation resistance between the frame and the front glass was measured at three locations (bottom, middle and top) under dry conditions and then at relative humidity above 80 %. The modules were subsequently subjected to a DC electrical stress of 1 kV, followed by cleaning. Electrical performance was evaluated under identical irradiance and temperature conditions using current-voltage (I-V) and power-voltage (P-V) characterization to extract the fill factor (FF) and Rsh. Results. Lower tilt angles (20°) promoted non-uniform dust accumulation, reducing insulation resistance and increasing leakage currents. High humidity intensified these effects, creating localized PID-prone regions. Post-cleaning, modules at 20° exhibited significantly lower FF and Rsh compared to 40°, indicating persistent degradation and incomplete recovery. Scientific novelty. This work establishes dust as an active PID initiator rather than merely an optical attenuator, uniquely examining coupled effects of tilt angle and dust-moisture interaction on PID susceptibility through moisture-assisted surface conduction pathways. Practical value. Appropriate tilt-angle selection and cleaning strategies are essential to preserve insulation integrity, limit leakage currents, mitigate degradation risk and maintain PV performance in dusty and humid environments. References 38, tables 6, figures 19. |
| doi_str_mv | 10.20998/2074-272X.2026.4.08 |
| first_indexed | 2026-07-02T01:00:17Z |
| format | Article |
| fulltext |
Electrical Engineering & Electromechanics, 2026, no. 4 55
© Z. Khammassi, A. Jeridi, H. Khaterchi, A. Zaafouri
UDC 621.383.51:621.311.243 https://doi.org/10.20998/2074-272X.2026.4.08
Z. Khammassi, A. Jeridi, H. Khaterchi, A. Zaafouri
Impact of tilt angle, dust deposition, and humidity on potential induced degradation and
electrical performance of crystalline silicon photovoltaic modules: an experimental study
Introduction. Photovoltaic (PV) modules constitute the backbone of renewable energy systems, yet their performance is compromised by
degradation mechanisms, particularly potential induced degradation (PID), which causes rapid power losses through ionic migration under
high voltage stress, creating parasitic shunts that reduce shunt resistance Rsh and energy output. Problem. Although the influence of moisture
and temperature has been widely investigated, the combined contribution of operational and environmental factors such as dust soiling
remains insufficiently clarified. Goal. This work assesses dust as a contributor to potential induced degradation focusing on the combined
effects of tilt angle, dust exposure and dust-moisture interaction on insulation integrity and degradation susceptibility. Methodology. A
comparative experimental study was conducted on 3 identical crystalline-silicon PV modules without bypass diodes, installed at tilt angles of
20°, 30° and 40°. A controlled and uniform layer of sandy dust (maximum particle size about 150 μm) was deposited on the front surface.
Insulation resistance between the frame and the front glass was measured at three locations (bottom, middle and top) under dry conditions and
then at relative humidity above 80 %. The modules were subsequently subjected to a DC electrical stress of 1 kV, followed by cleaning.
Electrical performance was evaluated under identical irradiance and temperature conditions using current-voltage (I-V) and power-voltage
(P-V) characterization to extract the fill factor (FF) and Rsh. Results. Lower tilt angles (20°) promoted non-uniform dust accumulation,
reducing insulation resistance and increasing leakage currents. High humidity intensified these effects, creating localized PID-prone regions.
Post-cleaning, modules at 20° exhibited significantly lower FF and Rsh compared to 40°, indicating persistent degradation and incomplete
recovery. Scientific novelty. This work establishes dust as an active PID initiator rather than merely an optical attenuator, uniquely examining
coupled effects of tilt angle and dust-moisture interaction on PID susceptibility through moisture-assisted surface conduction pathways.
Practical value. Appropriate tilt-angle selection and cleaning strategies are essential to preserve insulation integrity, limit leakage currents,
mitigate degradation risk and maintain PV performance in dusty and humid environments. References 38, tables 6, figures 19.
Key words: photovoltaic performance, potential-induced degradation, tilt angle, dust deposition.
Вступ. Фотоелектричні (PV) модулі є основою систем відновлюваної енергетики, проте їхня ефективність знижується внаслідок
деградаційних процесів, зокрема потенціально-індукованої деградації (PID), яка спричиняє швидкі втрати потужності через
міграцію іонів під дією високовольтного електричного поля, утворення паразитних шунтів, зменшення шунтового опору Rsh та
зниження енергетичної продуктивності. Проблема. Незважаючи на те, що вплив вологи та температури досліджено достатньо
широко, сумарний вплив експлуатаційних і навколишніх факторів, зокрема забруднення пилом, залишається недостатньо вивченим.
Мета. Оцінити вплив пилу як чинника потенціально-індукованої деградації з урахуванням сумісної дії кута нахилу, пилового
забруднення та взаємодії пилу з вологою на цілісність ізоляції та схильність до деградації. Методика. Проведено порівняльне
експериментальне дослідження трьох однакових кремнієвих PV модулів без обвідних діодів, встановлених під кутами нахилу 20°, 30°
та 40°. На фронтальну поверхню наносився контрольований рівномірний шар піщаного пилу з максимальним розміром частинок
близько 150 мкм. Опір ізоляції між рамою та фронтальним склом вимірювали у трьох точках (нижня, середня та верхня частини)
спочатку в сухих умовах, а потім при відносній вологості понад 80 %. Після цього модулі піддавали дії постійної напруги 1 кВ, а далі
виконували очищення поверхні. Електричні характеристики оцінювали за однакових умов освітленості та температури шляхом
аналізу вольт-амперних (I–V) та вольт-потужних (P–V) характеристик із визначенням коефіцієнта заповнення (FF) та шунтового
опору Rsh. Результати. Менші кути нахилу (20°) сприяли нерівномірному накопиченню пилу, що призводило до зниження опору
ізоляції та збільшення струмів витоку. Висока вологість посилювала ці ефекти, формуючи локальні області, схильні до PID. Після
очищення модулі з кутом нахилу 20° демонстрували значно нижчі значення FF та Rsh порівняно з модулями з кутом 40°, що свідчить
про стійку деградацію та неповне відновлення характеристик. Наукова новизна. У роботі пил розглядається не лише як оптичний
послаблювач випромінювання, а як активний чинник ініціювання PID. Уперше детально досліджено сумісний вплив кута нахилу та
взаємодії пилу з вологою на схильність до PID через поверхневі провідні шляхи, утворені за участю вологи. Практична значимість.
Правильний вибір кута нахилу та стратегій очищення є важливими для збереження цілісності ізоляції, обмеження струмів витоку,
зменшення ризику деградації та підтримання ефективної роботи PV модулів у запилених і вологих умовах. Бібл. 38, табл. 6, рис. 19.
Ключові слова: фотоелектричні характеристики, потенціально-індукована деградація, кут нахилу, осадження пилу.
Introduction. The current global energy and
environmental context is characterized by an ever-
increasing demand for primary energy sources. Despite
significant advances in renewable energy deployment,
fossil fuels still account for the majority share of the global
energy portfolio [1]. According to the International Energy
Agency, global energy consumption could increase by up
to 45 % between 2022 and 2030, driven mainly by
population growth and rapid industrialization in developing
countries. This upward trend is expected to further elevate
carbon dioxide (CO2) emissions, the principal greenhouse
gas released from fossil fuel combustion, which is a major
contributor to global warming and climate change. These
environmental impacts directly threaten key sectors such as
agriculture and water resources [2–5]. To mitigate these
challenges, it is imperative to accelerate the transition
towards sustainable, renewable, and economically viable
energy alternatives. Renewable energy systems, including
solar, photovoltaic (PV), wind, hydropower, biomass and
geothermal sources, offer promising pathways to meet this
goal. Among these, PV technology has emerged as one of
the most reliable and cost-effective solutions for sustainable
electricity generation. The global solar PV market is
experiencing rapid growth in support of the energy
transition and the rising demand for clean electricity. As of
2024, global PV capacity has reached 1.6 TW up from
1.2 TW in 2022, with most of it installed over the past
twelve years. China and the USA are leading this
expansion, achieving record growth in 2023. The market is
expected to continue expanding, fueled by high-efficiency
modules, decreasing costs, and emerging applications such
as hydrogen production and water desalination [6–8]. The
main part of a solar system is the module. A good PV
module retains more than 80 % of its power output for
many years, which is why manufacturers guarantee reliable
operation for over 25 years. However, PV systems can lose
performance and lifespan due to defects and environmental
factors. Production, transport, installation and weather
conditions are major causes of damage. Understanding
these issues and improving quality control are key to
ensuring long-term reliability The IEC 61215-1:2021
56 Electrical Engineering & Electromechanics, 2026, no. 4
standard requires accelerated tests to validate the
robustness and long-term reliability of PV modules under
outdoor conditions [9, 10]. Despite their widespread global
adoption as efficient renewable energy sources, PV systems
still face several persistent technical challenges.
Faults may occur at the PV generator level, such as
hot spots and microcracks, as reported in [11], or at the
power-conversion stage (inverter/converter), as discussed
in [12]. In addition, dust accumulation (soiling) reduces the
transmittance of the incident radiation and degrades
conversion efficiency, particularly in arid regions.
Numerous recent studies have investigated the impact of
dust on PV system performance under different climates,
installation configurations, and cleaning approaches,
highlighting the need for advanced predictive models and
optimized maintenance strategies [13]. For instance, in a
year-long study conducted in Jeddah, researchers evaluated
the impact of tilt angle on dust accumulation. Results
showed that, after 6 months without rain, flat panels lost
over 80 % of their power, while panels tilted at 45°
performed best. Over the entire year, a 25° tilt angle offered
the best energy yield, demonstrating the importance of
angle optimization for dusty environments [14]. Another
study focusing on panel layout found that tilt angle, height,
and wind direction influence dust deposition patterns, with
the first row of panels collecting more dust. Adequate
spacing between panels can help mitigate this effect [15].
Similarly, tests in Krakow revealed that low-tilt panels
accumulate more dust. Interestingly, light rain may worsen
dust buildup, whereas heavy rain (>38 mm/h) can
effectively clean the surface [16]. In China, microanalytical
assessments across nine cities confirmed that dust-related
efficiency losses range from 4.5 % to over 7 % annually,
depending on the panel tilt. This study also provided
predictive models to improve cleaning schedules and tilt
optimization [17]. The situation is further illustrated by
field tests in Pakistan, where 6 weeks of dust exposure led
to a 15–25 % drop in panel efficiency, with higher
temperatures and dust densities amplifying losses [18]. In
addition, simulations showed that wind speeds above 5 m/s
help reduce dust buildup, while horizontal surfaces (e.g.,
23° tilt) attract more deposition. Wind direction, however,
had limited influence on the accumulation rate [19]. A
study in Sohar, Oman, examined the composition of dust –
mainly sand (65 %), followed by cement, gypsum, and
industrial ash. The impact of these particles varied: while
some affected voltage more than current, materials like
cement and ash caused the most significant power losses
[20]. From a modeling perspective, another study
confirmed that dust particle size and tilt angle directly
influence accumulation. Particles around 150 μm resulted
in the highest deposition. An empirical model was
developed to predict power loss based on tilt angle,
supporting better design and maintenance [21].
Importantly, dust does not only impact optical properties. It
can also increase the surface conductivity of PV modules—
especially under high temperatures—leading to a rise in
leakage currents and a higher risk of potential induced
degradation (PID). In extreme cases, conductivity rose by
118 %, causing a 3.48 % drop in activation energy and
jeopardizing long-term system reliability [22]. PID has
been identified across all PV technologies and in nearly
every operational climate, although its occurrence remains
relatively infrequent. When it does occur, however, it can
lead to severe performance losses within a short period,
making it a key factor in accelerating degradation,
particularly in newer module generations. PID can cause
severe power losses in P-type silicon PV modules, with up
to 53 % reduction after one year, confirmed by voltage
shifts and imaging. It results mainly from leakage currents,
with power drops reaching 18.7 % in just 96 hours, as
shown by changes in I–V curves and EL images. These
effects pose real challenges for operators and highlight
practical ways to detect PID in the field [23, 24].
Various studies highlight the significant impact of
PID on mono- and multi-crystalline silicon modules, with
power losses reaching nearly 19 % after just 96 h of
continuous stress. These investigations deepen the
understanding of the physical mechanisms involved,
propose evaluation methodologies, identify mitigation
strategies, and explore recovery solutions depending on
environmental conditions [25]. In parallel, other research
[26–28] focuses on common defects found in PV modules,
such as cell cracks and hot spots, whose detection and
monitoring help improve system reliability and extend
service life. In the context of the rapid expansion of large-
scale PV plants, designers seek to maximize profitability
while minimizing investment and operational costs. One
widely adopted approach is to increase the voltage of PV
strings by connecting more modules in series. This
configuration reduces ohmic losses in the wiring and
optimizes costs by decreasing the number of cables,
connectors, junction boxes, and inverters required. As a
result, system voltage levels have gradually increased from
600 V in the 1990s to around 1 kV by 2010, with the
current industry standard trending toward 1.5 kV and
research exploring even higher levels. Since it was first
documented in 2010, PID has been extensively investigated
to clarify its underlying mechanisms and to develop
suitable mitigation measures. Its relevance has grown
considerably in recent years due to its potential to cause
severe module failures under specific conditions [29, 30].
Additional studies [31] have analyzed the recombination
behavior of PID-affected modules and assessed the
mismatch losses caused by performance differences
between degraded and unaffected modules. The shading-
induced mismatch effect, which can amplify such losses, is
addressed in reference [32]. PID has direct implications for
maximum power point (MPP) tracking techniques, as
discussed in [33, 34]. An experimental study compares two
identical PV modules, with one exposed to voltage stress to
observe changes in insulation and leakage resistance. The
results show that higher voltage and humidity accelerate
the decrease in insulation resistance and Rsh, which
increases PID effects and makes maximum power
extraction more difficult [35]. In addition to field
observations, numerical approaches have been used to better
understand and predict soiling behavior. Dust deposition
reduces optical transmittance and, consequently, power
output and module lifetime; discrete element modeling
further indicates that the tilt angle strongly governs particle
accumulation, while wind speeds above 5 m/s tend to
remove deposits, and wind direction has only a minor
influence. The deposited mass also increases with exposure
time, and simulations show good agreement with
transmittance-based measurements, with an average
deviation of about 3.41 % [36]. However, few studies have
analyzed the combined impact of dust, module tilt angle, and
dry or humid environmental conditions on the performance
of PV modules.
Electrical Engineering & Electromechanics, 2026, no. 4 57
Goal. This work assesses dust as a contributor to
potential induced degradation, focusing on the combined
effects of tilt angle, dust exposure, and dust–moisture
interaction on insulation integrity and degradation
susceptibility.
For this reason, an experimental methodology was
designed to evaluate PID in PV modules subjected to dust
deposition under controlled conditions representative of
real outdoor environments. Three identical PV modules,
installed at tilt angles of 20°, 30° and 40° and without
bypass diodes, were selected to investigate the combined
effects of inclination and soiling on Rsh Dust samples
were collected from a desert area near PV installations in
Tunisia. The collected material, characterized by an
average particle size of approximately 150 µm, was
applied using a controlled-deposition system to ensure a
uniform dust layer across each module surface. Two
environmental conditions were considered: dry and
humid. Insulation resistance measurements were
performed at constant temperature by applying a DC
voltage up to 1 kV using an insulation tester. The same
voltage levels were used to impose a controlled electrical
stress on the modules in order to reproduce high-potential
PID-inducing conditions. Following the stress application,
the I–V characteristics of each module were recorded, and
the corresponding Rsh values were extracted for
comparative analysis.
Methods. Modeling of PV string elements. A PV cell
is the elementary building block of a solar module. It
intercepts solar irradiance and converts it into electrical
energy via the PV effect, behaving essentially like a current
source. Under illumination, the cell can deliver a relatively
high current – depending on its size and format (M2, M4,
G1, M6 or half-cell) – but only a small voltage, typically
about 0.4–0.6 V, which limits the power of a single cell. To
obtain practical power levels, many cells are interconnected
in series and/or in parallel and then encapsulated together to
form a PV module. Among the various PV cell architectures,
passivated emitter and rear cell (PERC) technology has taken
the lead in recent years, progressively replacing the older
back surface field (BSF) design. Regarding PV cell
technologies, the BSF cell (Fig. 1), was the standard
industrial solution up to around 2015. It is based on p-type
crystalline silicon and features a highly doped rear side, most
commonly realized with aluminum (Al-BSF), to limit
charge-carrier recombination. A thin aluminum layer is
deposited by screen printing and then fired so that part of the
aluminum diffuses into the silicon, forming a p+ region that
creates an internal electric field. This field pushes minority
carriers (electrons) away from the rear surface, reduces
recombination losses, and enhances the open-circuit voltage,
enabling typical efficiencies of about 17 % in mass
production and up to roughly 19 % in laboratory cells.
Despite its robustness and straightforward fabrication, BSF
technology has been overtaken by more advanced concepts
such as PERC, HJT and TOPCon, which achieve higher
efficiencies and superior outdoor performance.
N‐Doped Silicon
P‐Doped Silicon
Dopé p+ (Al‐BSF)1E
2E
11 23
4
5
6
23
4
5
6
A
A
Section A‐A
P‐Type Cell C ‐ Si
Back Surface Field (BSF) cell
1 - Front Contact
2 - Anti-Reflextion Passivation layer SiNx
3 - N-Type Silicon layer (emitter)
4 - P-type silicon bulk
5 - Back surface field
6 - Rear Contact by Al
Fig. 1. Architectural model of a BSF solar cell
Since around 2015, PERC technology (Fig. 2) has
progressively replaced traditional BSF cells thanks to its
more efficient rear-side passivation and resulting gain in
efficiency. Still relying on crystalline silicon (mono- or
multicrystalline), a PERC cell maintains a strongly doped
aluminum rear surface, but adds one or more passivation
layers together with a back reflector to further suppress
carrier recombination and improve light trapping.
Localized rear contacts are used to optimize the extraction
of charge carriers. This architecture effectively reduces
electrical losses and delivers higher conversion
efficiencies, with a particular advantage under low
irradiance or elevated operating temperatures, where
standard cells typically suffer from increased rear-side
heating. The passivation layers, most commonly
aluminum oxide (Al2O3), silicon nitride (SiNx), or
combinations of dielectric films, serve to protect the
silicon surface, limit defect-related recombination, and
support stable performance over the module’s lifetime.
3E
A
A
B
B 11 23
4
5
6
2E
7
8
Section A‐A
Dopé N (P)
Dopé P (B)
4
6
7
8
23
Section B‐B
Dopé N (P)
Dopé P (B)
Dopé p+ (Al‐BSF)1E
2E 4
5
6
23
P‐Type Cell C ‐ Si
Passivated Emitter Rear Contact (PERC) cell
1 - Front Contact
2 - Anti-Reflextion Passivation layer
3 - N-Type Silicon layer
4 - P-type silicon bulk
5 – Local Back surface field
6 – Aluminium Rear Contact
7 – Al₂O₃ Passivating layer
8 – SiNx Capping layer
Fig. 2. Architectural model of a PERC solar cell
Al2O3 is widely used in PERC cells to passivate the
rear side: it neutralizes surface defects (chemical
passivation) and creates an internal electric field that repels
electrons, reducing recombination and increasing the open-
circuit voltage (Voc) and short-circuit current (Isc). A SiNx
layer is often added on top to serve as an anti-reflective
coating, an additional passivation layer, and a protective
barrier, further improving the module’s efficiency,
durability and light reflectivity. In this work, with reference
to the previously discussed technologies, which rely on the
presence of 2 junctions each generating a distinct electric
field, we have chosen to adopt a two-diode mathematical
model to more accurately reflect the real operating
behavior of these cells. This more advanced approach,
compared to the single-diode model, uses 7 parameters to
describe their electrical performance in detail. These
include the photocurrent (Iph), which is generated by
incident irradiance (G, W/m2), directly proportional to light
intensity and affected by temperature (T, K), as well as 2
saturation currents (I01 and I02) that account for
recombination losses in the main junction and in the quasi-
neutral regions, respectively. The ideality factors (n1, n2)
characterize the dominant transport mechanisms for each
diode. Additionally, the model includes a series resistance
(Rs), which accounts for ohmic losses occurring in the
contacts, metal fingers, the metal-semiconductor interface,
as well as the interconnections between multiple PV cells;
and a Rsh that models leakage currents resulting from
defects or irregularities within the cell.
Rs
RshD2D1
Iph ID2 IshID1
G : Solar
Irradiation Ipv
Vpv
Load
Fig. 3. Mathematical model of a PV cell
58 Electrical Engineering & Electromechanics, 2026, no. 4
The current (Ipv) and voltage (Vpv) delivered by the
cell depend on the characteristics of the connected load.
Referring to the equivalent model (Fig. 3) and applying
Kirchhoff’s current law, the equation describing the (I-V)
relationship of the PV cell can be written as:
shDDphpv IIIII 21 , (1)
where Ipv is the output current of the double diode model;
Iph is the photocurrent.
Equations (2) – (4) respectively define the currents
through the 2 diodes, ID1 and ID2, and the current flowing
through the shunt resistor Ish:
1exp
1
011
t
pvspv
D Vn
IRV
II ; (2)
1exp
2
022
t
pvspv
D Vn
IRV
II ; (3)
shpvspvsh RIRVI ; (4)
qkTVt , (5)
where the thermal voltage Vt of the diode is determined
using the Boltzmann constant k; q is the electron charge;
T is the operating temperature of the cell.
The saturation current is influenced by temperature,
the surface area of the diode (and thus the PV cell), and
the properties of the junction. It varies exponentially with
temperature and can be represented as:
opref
g
ref
op
sc TTkn
qE
T
T
II
11
exp
1
3
01 ; (6)
opref
g
ref
op
sc TTkn
qE
T
T
II
11
exp
2
3
02 ; (7)
0G
G
TTkII refopiscph , (8)
where Isc is the PV cell’s short-circuit current; T
represents its actual operating temperature; Tref is the
reference temperature used for performance comparison;
Eg is the optical bandgap of the cell material; n1, n2 are the
diode ideality factors, which generally lies between 1 and 2;
Top is the absolute temperature; I01, I02 are the diode’s
saturation currents; ki is the temperature coefficient
related to the short-circuit current; G0 is the irradiance
under standard test conditions (STC), whereas G is the
actual irradiance under real operating conditions [37].
PV module is a device designed to capture solar
radiation and convert it into electrical energy through the
PV effect; his based characteristics as shown in Table 1. It
is one of the key components of a PV system. The module
is composed of an array of identical PV cells,
interconnected in series and/or in parallel in order to
achieve the desired electrical characteristics: voltage,
current and fill factor (FF). To obtain a sufficiently high
voltage at the module terminals, the cells are generally
connected in series, which increases the overall voltage
and reduces ohmic losses. However, when the number of
series-connected cells is large, partial or total shading of a
single cell, or any change in its electrical characteristics,
leads to a reduction in the current it can deliver. The
affected cell then becomes reverse-biased, causing local
overheating and the formation of hot spots, which may
damage the cells and degrade the operation of the module.
The integration of bypass diodes is therefore essential to
mitigate these phenomena. Moreover, PV cells represent
only one part of the laminated structure of the module.
This structure also includes the packaging (protective
glass, encapsulant and backsheet), the internal circuitry
(electrodes, ribbons and interconnections), bypass diodes,
junction boxes, the mechanical frame, as well as cables
and connectors. All of these elements contribute to the
overall reliability and durability of the PV module.
Table 1
Example of characteristics of a PV module
Characteristics Value
Maximum power Pmax, W 165
Open-circuit voltage Voc, V 23.45
Short-circuit current Isc, A 8.8
Voltage at maximum power Vmpp, V 19.4
Current at maximum power Impp, A 8.51
Maximum system voltage V, V 1000
Temperature coefficient for power Pmax, % –0.45
Number of cells connected in series Ns, cellules 36
Diode quality factor 1.3
Series resistance Rs, Ω 0.15
Parallel resistance Rsh, Ω 120
Optical band gap of the material Eg, eV 1.1
PID in PV systems. In PV systems, modules are
typically connected in series to reach the voltage range
required by the inverter, which results in high voltage
levels within the DC string. Under these conditions, the
DC-side configuration (grounding scheme, insulation level
and protection devices), as well as correct, standards-
compliant grounding, become critical parameters to ensure
safe and stable operation of the installation. Grounding all
accessible metallic parts, especially PV module frames, is
essential to dissipate leakage currents, reduce the risk of
electric shock and insulation faults, and lower the
likelihood of degradation phenomena such as transient
overvoltage or certain accelerated aging mechanisms,
thereby directly improving the long-term reliability of the
system. Moreover, depending on the inverter technology
(with or without an isolation transformer) and the selected
grounding scheme, a significant potential difference may
develop between the metallic frame and the PV cells. This
electrical stress promotes PID, which accelerates array
aging and leads to performance losses.
Transformerless inverters, which provide no galvanic
isolation between the DC and AC sides, commonly operate
with a floating DC grounding scheme. This approach is
cost-effective and widely used, particularly in humid
climates; however, the lack of a defined reference potential
can allow a negative bias to build up along the PV string.
This bias drives PID through the gradual accumulation of
charges at the cell surface and within the encapsulant,
disturbing the internal electric field and causing a
progressive, and sometimes irreversible, reduction in
conversion efficiency and energy yield. By contrast,
positive pole grounding using a transformer-based inverter
provides galvanic isolation, but it is seldom adopted
because it can worsen PID by imposing a high negative
voltage on the modules located at the end of the string,
increasing their vulnerability. Finally, negative pole
grounding (also with a transformer-based inverter), as
shown in Fig. 4, keeps the PV cells at a positive potential
with respect to the frame, thereby mitigating PID-related
stress and enhancing long-term module reliability.
Nevertheless, the sustained positive bias can increase
Electrical Engineering & Electromechanics, 2026, no. 4 59
susceptibility to corrosion in coastal or highly humid
environments, which is why this configuration is generally
preferred in dry or moderately humid sites.
DC
AC
GRID
CONNECTED
Isolated InverterPV array Transformer
Pv+
Pv‐
Fig. 4. Grounding topology for the negative pole of the PV string
The main cause of PID is the high voltage between the
solar cells and the glass surface at the front of the module.
PID directly impacts the core of power generation, the PV
cells, by increasing the leakage current. In this context,
leakage current is defined as the portion of the current that
flows from the base to the emitter while bypassing the
external load. This mechanism is illustrated in Fig. 5, 6,
which shows the various leakage paths within the module as
functions of its tilt (or incidence) angle and the thickness of
the dust layer accumulated on its surface. For analytical
purposes, the total leakage current can be decomposed into
five distinct components. First, the current may escape
through the sodalime glass and the water molecules present
on its surface (I1). Second, it may flow through the dust layer
deposited on the module (I5). Third, leakage can occur due
to electrons or ions located on the front surface of the cell
(I2). Fourth, the current can pass through the ethylene-vinyl
acetate (EVA) encapsulation layer (I3). Finally, fifth, part of
the current may leak through the rear contact, thereby
completing the circuit (I4).
Fig. 5. Leakage current caused by the PID effect
SiNx (Anti-reflective coatin)
Cell
N-Doped Silicon
P-Doped Silicon
Dopé p+ (Al-BSF)
Rear contact by Al
4
4
Detail 1
Grounding systemVPID
VCell
1
dust deposition
3
VPV
Fig. 6. Cross-sectional modeling of a PV module
To analyze PID at both the cell and module levels
for a tilted PV generator (defined by its incidence angle)
exposed to dust soiling, a voltage-divider circuit is
employed. The underlying assumption is that the
magnitude of the electric field within the SiNx layer plays
a decisive role in the initiation and progression of PID. As
shown in Fig. 6, four resistors are connected in series to
represent the main leakage-current path: the dust layer
(1), the glass (2), the encapsulation sheet (3), and the
SiNx anti-reflection coating on the solar cell (4). The
voltage drop across the SiNx layer can then be estimated
using the model shown in Fig. 7:
PID
SolingGlassPolySiNx
SiNx
SiNx V
RRRR
R
V
, (9)
where VPID is the potential difference between the front
glass of the module and the surface of the encapsulated
silicon cells; VSiNx is the voltage across the SiNx passivation
layer; RSiNx, RPoly, RGlass, Rsoiling are the resistances of the
SiNx layer, the polymer encapsulant (EVA), the glass and
any deposited dust layer, respectively.
Glass and polymer layers exhibit high bulk
resistivity, whereas the SiNx film is comparatively more
conductive. This stack configuration redistributes the
electric field and limits the voltage drop across the SiNx
layer, thereby reducing the susceptibility to PID. The
encapsulation materials surrounding the PV cells provide
thermal stability, protection against moisture, resistance to
UV-induced aging, and electrical insulation between
internal components. An increase in the overall resistive
path decreases the leakage current for a given applied
potential, which in turn limits the surface potential of the
solar cells and mitigates PID effects. Consequently, the
resistance measured between the PV cell and the module
frame constitutes a key diagnostic parameter for PID in
PV systems, as deviations from nominal values indicate
insulation degradation and emerging faults.
VPID
N‐Doped Silicon
RGla ss
RPolymer foil
R SiNx Ant i-
refle ct ive c oating
IL
IL
VSiNx
VPoly
VGla ss
Rsoil ing VSoil ing
Fig. 7. Model representing the voltage drop in the SiNx
passivation layer
PID modeling. Several studies have investigated the
impact of PID on PV modules operated at different bias
voltages (750 V, 500 V and 250 V) under fixed
environmental conditions of 70 °C and 100 g/m3 humidity.
The results indicate that the temporal evolution of
degradation can be described by an exponential law: the
loss in performance is initially rapid, then progressively
slows down. After a certain exposure time, the PID-
induced degradation rate becomes very small, approaching
a quasi-steady state. This behavior can be modeled as
]1[)( tePIDtPID
, (10)
where PIDPID
t
lim , (11)
where t is the PID stress duration; PID∞ is the asymptotic
(maximum) degradation level reached by a PV module for
very long exposure times; τ is the corresponding time
constant.
60 Electrical Engineering & Electromechanics, 2026, no. 4
The quantity PID∞ increases with the applied bias
voltage (e.g., 250 V, 500 V, 750 V). The parameter τ the
rate at which the degradation approaches this limit and is
governed by both the intrinsic PID robustness of the
module materials and the prevailing environmental
conditions. A PID-resistant module is associated with a
larger τ and therefore requires longer stress duration to
reach PID∞, whereas a PID-sensitive module exhibits a
smaller τ and attains PID∞ over a shorter time.
On the basis of extensive experimental data, a compact
predictive model was derived to quantify the influence of
operating and environmental parameters on PID. The
leakage current was shown to scale with the square of the
operating voltage (module-to-ground potential) and to be
proportional to the square of both the module service time
and the relative humidity. In addition, the leakage current
follows an Arrhenius-type temperature dependence with an
activation energy of 0.94 eV. In the equivalent PV cell
circuit, this leakage path is represented by the Rsh, whose
evolution is fitted by the relation given in (12) [38]:
2226
deg
90700
exp107
1
t
RT
RHV
R
avg
op
sh,
, (12)
where Rsh,deg is the degraded Rsh value; Vop is the operating
voltage of the panel (panel-to-ground voltage); RH is the
relative humidity; R is the gas constant; Tavg is the average
temperature; t is the time.
The degraded Rsh is influenced not only by the cell
location relative to the metallic frame, where PID becomes
more severe near the frame, especially at the module
corners, but also, to a large extent, by dust soiling. The
module tilt angle governs how much dust settles on the
front surface; at certain inclinations, deposits can become
heavier and more uneven, creating locally more conductive
regions and additional leakage pathways. This non-uniform
soiling can intensify leakage currents and the electric-field
stress at critical interfaces, thereby increasing both the
likelihood and the severity of PID and accelerating the
overall performance loss of the PV module (Fig. 8).
Fig. 8. Representation of dust deposition and its distribution on a
PV module
The dust accumulation on the front surface of a PV
module is modeled by a surface density of deposited
particles σd(t, φ) [g/m2], which depends on the exposure
time t and the module tilt angle φ
d(t, ) = rd0f()t, (13)
where rd0 is the nominal dust deposition rate on a
horizontal surface (gꞏm−2ꞏday−1); f(φ) is the angle-
dependent correction factor. Assuming that dust particles
fall vertically under gravity, the effective collecting area
is the projection of the module on a horizontal plane. If S0
denotes the actual area of the module, the projected area
Sproj on which dust accumulates is
Sproj = S0cos. (14)
Under this assumption, a first-order approximation
for the angular correction factor is therefore
f() cos. (15)
At the bottom of the PV module, the impact of PID
is most pronounced due to dust accumulation, which is
promoted by the tilt angle: particles slide along the
surface and pile up at the lower frame bar, where they
accumulate. This impact gradually decreases toward the
top of the PV module. Accordingly, the following
equation defines a normalization factor that weights the
severity of PID as a function of the position of a PV cell
in the module with respect to its lower edge.
L and l denote the width and the height of the PV
module, respectively. The horizontal coordinate x [0, L]
is measured from the left edge, and the vertical coordinate
y [0, l] is measured from the bottom edge. Since dust
accumulation and PID effects are more pronounced near
the lower corners of the module, where particles tend to
pile up along the frame edges, the spatial dependence of
the PID severity can be modeled by a two-dimensional,
dimensionless normalization factor F(x, y, θ) defined as:
L
x
eyxF l
y
ky
2
).(
cos1,, , (16)
where ky > 0 controls the vertical decay of the PID impact
and 0 1 enhances the contribution of the lateral
edges. In this formulation, F(x, y, θ) attains its maximum
value at the lower corners (x, y) = (0, 0) and (L, 0), while
it decreases both toward the top of the module and toward
the central region along the bottom edge. The local PID
can be expressed as:
D(x, y) = DmaxF(x, y, θ), (17)
where Dmax is the maximum degradation level at the lower
corners of the PV module.
Rsh,deg(x, y) = Rsh,degF(x, y, θ). (17)
Experimental study. This experimental study
focuses on comparing the performance of three identical
small-scale PV modules mounted on the same supporting
structure, each tilted at a different angle of 20°, 30° and 40°
(Fig. 9), to ensure the reliability of the results and minimize
the influence of environmental factors, all measurements
are carried out under stable weather conditions, with
uniform irradiance and a constant temperature.
P3
P1
P2
P3
P1
P2
P3
P1
P2
Module 1Module 2Module 3
C
CC
Fig. 9 Structure comprising 3 small-scale PV modules mounted
at respective inclination angles of 20°, 30° and 40°
The modules were carefully selected because they are
not equipped with bypass diodes. This specific design
feature makes their electrical behavior comparable to that of
a single PV cell, thereby enabling a more accurate and direct
investigation of internal phenomena, particularly those
associated with the shunt (parallel) resistance. In order to
evaluate the Rsh and establish a correlation between the
experimental conditions (tilt angle and degree of soiling)
and the observed variations in electrical performance, a
uniform layer of fine sand dust was deposited on the glass
surface of the modules using a horizontal deposition
apparatus designed to ensure an even distribution over the
horizontal surface normal to the vertical (Fig. 10).
Electrical Engineering & Electromechanics, 2026, no. 4 61
This procedure is intended to reproduce realistic
environmental soiling conditions, which may affect the
electrical characteristics and the conversion efficiency of
the modules as a function of their tilt angle. After the sand
dust deposition (Fig. 11), it was observed that the PV
module tilted at 20° had the highest amount of deposited
dust, followed by the one at 30°. In contrast, the module
tilted at 40° showed a significantly lower dust
accumulation compared to the other two.
Device designed to uniformly deposit sand dust on the
modules, which are exposed at different tilt angles.
Megohmmeter: A measuring instrument used to
determine insulation resistance.
A computer, equipped with
dedicated software,
enables the extraction of
measurement reports.
Fig. 10. An experimental test bench (a vertical dust deposition
device was used to uniformly distribute fine sand particles over
the front surface of the PV modules)
Fig. 11. Distribution of fine sand deposits on 3 PV modules
tilted at 20°, 30° and 40°
To ensure a consistent and representative
comparison, Fig. 12 depicts the experimental setup
adopted for insulation-resistance measurements.
Junction box
Aluminum frame
P1
P2
P3
R1
R
R2
Fig. 12. Selected measurement points on the module (P1, P2, P3)
and insulation resistances to be measured (R1, R2, R)
Three measurement locations (P1, P2, P3) are selected
on the front glass surface of each module along a vertical
axis, corresponding to the lower, central and upper regions to
capture potential spatial non-uniformities associated with
dust deposition and moisture. Point P1, located near the
lower frame, represents the area most susceptible to
gravitational accumulation of contaminants, whereas P2 and
P3 correspond to generally less soiled regions. The lower-
right corner of the metallic frame is used as the common
reference for all frame-related measurements to ensure data
consistency. Using an insulation tester at different applied
voltages, three resistances are determined: R1 – between the
positive terminal (representing the front surface of the PV
cells) and the aluminum frame; R2 – between the frame and
each surface point Pi; and R – between the positive terminal
and each of the 3 points P1, P2, P3. This methodology
enables quantification of the spatial distribution of insulation
performance and assessment of the combined effects of tilt
angle, environmental conditions (dry versus humid), and
imposed electrical stress, particularly with respect to PID-
like phenomena and shunt-resistance degradation.
Measurements and results. Three curves in Fig. 13–15
show an excerpt of the measurements carried out on Module 1,
tilted at 20°, under dry conditions. They correspond to the
insulation resistance measured between the module frame and
the selected surface points, denoted respectively P1, P2, P3.
V
R
R, M V, V
Fig. 13. Dry-state insulation resistance (frame-front surface)
at P1 of Module 1 tilted at 20°, under 1000 VDC
V
R
R, M V, V
Fig. 14. Dry-state insulation resistance (frame-front surface)
at P2 of Module 1 tilted at 20°, under 1000 VDC
V
R
R, M V, V
Fig. 15. Dry-state insulation resistance (frame-front surface)
at P3 of Module 1 tilted at 20°, under 1000 VDC
Figure 16 shows that the insulation resistance measured
between the frame and the lower point on the front surface
P1 is significantly lower than the value obtained at the central
point P2. A decrease in resistance is also observed at the
upper point P3, which can be explained by its proximity to
the frame in the upper part of the module. In addition, the
low tilt angle promotes dust deposition over a large portion
of the surface, thereby further accentuating the overall
reduction in insulation resistance.
Table 2 summarizes dry-state insulation resistance
measurements (GΩ) between the module frame and the
glass-surface points Pi (P1, P2, P3) for 3 PV modules tilted
at 20°, 30° and 40° and tested at 500 V and 1000 V,
revealing a clear dependence on both tilt angle and surface
62 Electrical Engineering & Electromechanics, 2026, no. 4
condition: the 20° module M1 exhibits consistently very
low resistances (≈ 0.017–0.08 GΩ), indicative of severely
degraded insulation, whereas the 30° module M2 shows
intermediate values (≈ 0.3–0.9 GΩ) and the 40° module M3
reaches very high levels exceeding 40 GΩ, reflecting a
substantially improved insulation state at higher tilt.
Fig. 16. Dry-state insulation resistance (frame-front surface)
at P1, P2, P3 of Module 1 tilted at 20°, under 500 V and 1000 V
This behavior is consistent with enhanced dust
retention at low tilt angles, which limits natural particle
removal, promotes surface leakage paths, and leads to non-
uniform contamination characterized by heavier deposition
near the lower frame and a progressively cleaner upper
region, as evidenced by the spatial trend where P1 (most
soiled area) systematically yields the lowest resistance,
P2 intermediate values, and P3 the highest (up to 45 GΩ for
M3 at 500 V); additionally, increasing the test voltage from
500 V to 1000 V produces a slight reduction in measured
resistance, most noticeable for M3, consistent with field-
enhanced surface conduction, although this voltage effect
remains secondary compared with the dominant influence
of tilt angle and contamination distribution.
Table 2
Isolation resistance values under dry conditions measured
between the module frame and each Pi point on the glass surface
Insulation resistance, GΩ
Dry environment
Voltage, V Pi M1 θ=20° M2 θ=30° M3 θ=40°
P1 0.032 0.3 1.34
P2 0.019 0.7 27.36 500
P3 0.08 0.9 45
P1 0.035 0.3 0.92
P2 0.017 0.7 22.75 1000
P3 0.07 0.8 40
Measurements could not be extended above 100 V
because the insulation resistance dropped to very low
levels, leading to saturation of the measuring instrument.
As shown in Table 3, the wet-condition insulation
resistance (GΩ) measured between the module frame and
the glass-surface points P1, P2, P3 for modules tilted at
20°, 30° and 40° is substantially lower than that obtained
under dry conditions, confirming the strong influence of
moisture on surface leakage. At P1, the resistance
evolution remains broadly comparable to the dry-case
behavior, which can be attributed to heavy soiling in the
lower part of the module caused by gravitational dust
accumulation, whereas at locations with lower deposit
density, humidity becomes the dominant factor by
facilitating leakage pathways and further degrading
insulation integrity. Among the tested configurations, the
20° module M1 exhibits the most severe degradation, with
resistances collapsing to approximately 0.001 GΩ at P2
and P3, suggesting the formation of quasi-continuous
conductive films on the glass; the 30° module M2 shows
higher yet still strongly reduced values, particularly at P2
(0.01 GΩ), indicating increased sensitivity to locally
contaminated regions. In contrast, the 40° module M3
maintains the highest insulation levels (about 1.1–1.2 GΩ
at P1 and P3), although a noticeable decrease persists at P2
(0.03 GΩ), and the overall spatial pattern highlights
pronounced non-uniformity under humid conditions, with
P2 and P3 emerging as the most critical zones, likely due
to localized moisture retention combined with deposits
(dust/salts) that enhance water adsorption and ionic
conduction; nevertheless, increasing tilt remains
beneficial by limiting water stagnation and improving
natural drainage, which explains the comparatively better
performance of the 40° module.
Table 3
Isolation resistance values under dump conditions measured
between the module frame and each Pi point on the glass surface
Insulation resistance, GΩ
Dry environment
Voltage, V Pi M1 θ=20° M2 θ=30° M3 θ=40°
P1 0.085 0.46 1.2
P2 0.001 0.01 0.03 100
P3 0.001 0.81 1.1
After applying an identical PID-type electrical stress
imposed by the measuring instrument and cleaning the
front surfaces, electrical measurements were carried out
under controlled laboratory conditions: the modules were
installed at a uniform tilt angle of 30°, exposed to the same
irradiance level, and maintained at a stabilized temperature
of 30 °C; their I–V and P–V characteristics were then
recorded, as shown in the following figures. The tests were
performed on modules whose specifications are
summarized in Table 4.
Table 4
Specifications of the test modules employed in the experiments
Pmax, W 10 Voc, V 20.5
Tolerance, % 5 Isc, A 0.59
Vmp, V 18 Vmax, V 750
Imp, A 0.55 Size, cm 34518018
Test condition 1000 W/m2 AM1.5 25°C
Figure 17 shows that the relatively pronounced slope of
the I–V curve and the MPP location suggest increased
internal losses (higher series resistance and/or degraded Rsh,
which is consistent with performance degradation potentially
associated with soiling and/or PID-type electrical stress.
Ipv, mA Ppv, W
Vpv, V
Fig. 17. I–V and P–V characteristics of module 1 (pre-inclined at
θ=20°), measured after cleaning and reinstallation at 30° under
uniform irradiance and temperature conditions
Figure 18 indicates that the low-voltage region of
the I–V curve exhibits reduced leakage, pointing to a
higher Rsh compared with the 20°-tilted module. The lack
of an early current roll-off and the more nearly
rectangular I–V shape are consistent with fewer parasitic
Electrical Engineering & Electromechanics, 2026, no. 4 63
conductive pathways. This trend agrees with the 30° tilt
configuration, which limits dust accumulation, thereby
lowering surface conduction and mitigating PID-related
stress, ultimately leading to a higher maximum power and
improved operational stability.
Ipv, mA Ppv, W
Vpv, V
Fig. 18. I–V and P–V characteristics of module 2 (pre-inclined at
θ=30°), measured after cleaning and reinstallation at 30° under
uniform irradiance and temperature conditions
Figure 19 shows that the very smooth I–V profile at
low voltages reflects minimized leakage currents,
suggesting a high Rsh with limited degradation compared
with the 20° and 30° modules. The absence of an early
current drop and the reduced slope near the origin confirm
that parasitic conductive paths on the module surface are
strongly mitigated. This improvement is consistent with a
40° tilt angle, which promotes natural self-cleaning of the
glass, limits dust accumulation, and reduces surface
conduction and PID-type effects. Consequently, the
module achieves a higher maximum power and exhibits
more stable and better overall electrical performance.
Ipv, mA Ppv, W
Vpv, V
Fig. 19. I–V and P–V characteristics of module 3 (pre-inclined at
θ=20°), measured after cleaning and reinstallation at 40° under
uniform irradiance and temperature conditions
Experimental performance evaluation of the
three modules: characterization and comparison. To
experimentally evaluate these 3 identical PV modules, we
first determine the degradation rate and corresponding Rsh
for each module. Table 5 indicates that the FF is a
sensitive indicator of module degradation, increasing
from 30.5 % for M1 (20°) to 45 % for M2 (30°) and 57 %
for M3 (40°), while remaining far below the STC
reference value (76 %), which reflects increased internal
losses and a more pronounced shunt-resistance
deterioration, particularly at low tilt angles. In this study,
degradation is assessed relative to the FF value.
Furthermore, to simplify the analysis of thermal
influence, it is assumed that the temperature coefficients
associated with voltages are identical, βVoc ≈ βVmpp, and
similarly, that the temperature coefficients associated with
currents are identical, αIsc ≈ αImpp. This assumption allows
for estimating variations in maximum power point
parameters using the conventional coefficients provided
for Voc and Isc, while maintaining consistency with the
manufacturer’s specifications.
Table 5
Comparative analysis of electrical performance following stress
application using FF as a degradation indicator
M1, θ=20° M2, θ=30° M3, θ=40° Factory status STC
Voc, V 21.3 20.6 20.7 20.5
Isc, A 0.37 0.374 0.397 0.59
Pmax, W 2.41 3.58 4.747 10
Pth.max, W 7.88 7.70 8.22 12.1
FF, % 30.5 45 57 76
Thus, the degradation of modules 1, 2 and 3 relative
to the reference module, denoted respectively as D1/R, D2/R
and D3/R, can be defined as:
%1001
max
max
RM
iM
FF
FF
iD , (19)
where i = (1/R, 2/R, 3/R). So D1/R = 25 %, D2/R = 40 %
and D3/R = 59 %. The results confirm that increasing the
tilt angle mitigates soiling, reduces leakage currents and
PID-related effects, and therefore helps preserve the
module’s electrical performance.
The degradation of a PV module can be quantified by
comparing its measured electrical parameters with the
reference values provided by the manufacturer under STC,
particularly the FF. In this study, degradation is assessed
relative to FF value. Furthermore, to simplify the analysis of
thermal influence, it is assumed that the temperature
coefficients associated with voltages are identical, βVoc ≈ βVmpp,
and similarly, that the temperature coefficients associated
with currents are identical, αIsc ≈ αImpp. This assumption
allows for estimating variations in maximum power point
parameters using the conventional coefficients provided for
Voc and Isc, while maintaining consistency with the
manufacturer’s specifications.
Therefore, the degradation of modules 1, 2 and 3
relative to the reference module can be defined by the
equations denoted as D1/R, D2/R and D3/R, respectively.
By identification, the Rsh is associated with the slope
of the I–V characteristic of the module in the region to the
left of the maximum power point (low-voltage region). It
can therefore be estimated from the derivative dI/dV
evaluated in this domain, as indicated as:
I Isc – V / Rsh. (20)
As shown in Table 6, Rsh of module M1 (θ = 20°),
which was subjected to the highest level of sand-dust
deposition, is Rsh1 ≈ 121 Ω. This value is significantly lower
than those of the other modules: Rsh2 = 337 Ω for module M2
(θ = 30°) and Rsh3 = 733 Ω for module M3 (θ = 40°). Since
Rsh represents the resistance of the parallel paths through
which leakage current can flow when a voltage is applied
between the module frame and the PV cell, this reduction
in Rsh confirms that the amount of dust deposited on the
modules is a key factor promoting PID. Furthermore, the
data shows that the severity of this degradation is
inversely proportional to the tilt angle of each module
during the soiling exposure.
Table 6
Determination of the Rsh of PV modules through analysis
of their I–V characteristic curves
M1, θ=20° M2, θ=30° M3, θ=40°
Isc, A (I, V) Isc, A (I, V) Isc, A (I, V)
0.37 (0.338, 3.9) 0.374 (0.358, 5.4) 0.397 (0.391, 4.4)
Rsh = 121 Ω Rsh = 337 Ω Rsh = 733 Ω
64 Electrical Engineering & Electromechanics, 2026, no. 4
Discussion. The objective of this experimental work
was to analyze the influence of the tilt angle on the initial
dust accumulation and its consequences on the electrical
integrity of PV modules subjected to potential-induced
voltage bias stress. More specifically, this work investigates
how differential particle deposition, governed by module
inclination, modulates the severity of performance
degradation induced by applying an electrical potential
between the frame and the output terminals. The
methodology was based on the use of three identical PV
modules, initially positioned at distinct tilt angles (20°, 30°,
40°) before being subjected to a controlled, vertical
deposition of sand dust. An insulation resistance test,
applying a voltage from 100 V to 1 kV, was subsequently
used to impose identical electrical stress on each sample.
Following a thorough cleaning, I–V characterization was
performed under standardized laboratory conditions (30°
tilt, uniform irradiance and temperature) to evaluate the
residual impact on performance. The main results reveal a
clear differential degradation. The module pre-inclined at
20° exhibited the most degraded FF and the highest power
loss. Conversely, the module initially at 40° showed the
least degradation and an FF closest to its original condition,
while the module at 30° occupied an intermediate position.
This systematic correlation between a lower initial tilt angle
and increased degradation suggests a multi-step causal
mechanism. Interpretation of these observations leads to the
following proposed scenario. First, the tilt angle during
deposition directly conditions the mass and adhesion of the
dust layer. A shallow angle (20°) maximizes the capture
surface for vertically sedimenting particles, leading to
greater accumulation. A steeper angle (40°) conversely
promotes particle shedding and reduces retention. Second,
this contamination layer, potentially conductive in the
presence of residual humidity, compromises the surface
insulation properties. It establishes parasitic conduction
paths between the active cells and the grounded frame.
Consequently, the most soiled module (20°) likely presented
the lowest insulation resistance prior to the high-voltage
test. During this test, the leakage current density and the
local electric field intensity across the contaminant layer
were therefore maximal for this sample. This amplified
electrical stress likely caused irreversible degradation of the
dielectric materials (encapsulant, backsheet) and critical
interfaces. Third, this degradation subsequently manifests as
a permanent reduction in the FF after cleaning. The
decrease in FF is a characteristic indicator of altered internal
electrical parameters, primarily a drop in Rsh due to the
creation of internal micro-shunts. The complete causal chain
can therefore be summarized as follows: a low initial angle
leads to increased dust accumulation, which reduces surface
insulation resistance, a condition that amplifies the electrical
stress during the HV test; this stress, in turn, causes
permanent internal degradation (such as a decrease in Rsh
and a reduction in FF. In conclusion, this study
demonstrates that the tilt angle of a PV module not only
modulates the temporary optical losses due to soiling but
also critically influences its susceptibility to permanent
electrical degradation. A shallow tilt angle, by promoting
heavier dust accumulation, can precipitate a reduction in
surface insulation. When coupled with high-voltage events,
such as during testing, under storm conditions, or in humid
environments, this can lead to irreversible performance
deterioration. These findings underscore the importance, for
the long-term durability of installations in dusty
environments, of considering steeper tilt angles where
feasible and adopting proactive cleaning strategies. Such
measures are essential to mitigate both immediate energy
yield losses and the long-term risk of performance failure.
Conclusions. This study shows that the initial tilt
angle of a PV module affects not only soiling-related
optical losses, but also its susceptibility to long-term
electrical degradation (PID), especially under humid
conditions and high-voltage stress.
Tests on 3 identical modules (20°, 30°, 40°) with
controlled dust deposition, insulation-resistance mapping
(dry/humid), and DC stress up to 1 kV, followed by
standardized I–V and P–V measurements, revealed a clear
tilt dependence: the 20° module suffered the strongest
degradation (FF and Rsh drop), the 40° module the
weakest, and the 30° module an intermediate response.
This trend is explained by higher and more uneven
dust accumulation at low tilt, which lowers surface
insulation, increases leakage, and intensifies local electric
stress, leading to irreversible dielectric damage and shunt-
path formation.
Results indicate that the glass–frame region is a
critical leakage pathway due to the coupling between the
front glass, the grounded metallic frame, and the dust layer
(potentially made more conductive by moisture), which can
exacerbate PID severity, especially at low tilt angles.
From a practical standpoint, these findings support
the adoption of steeper installation angles where feasible
and preventive cleaning strategies to preserve insulation
integrity, limit leakage, mitigate PID risk, and enhance
the long-term durability of PV systems operating in dusty
(and humid) environments.
The study will be extended to additional tilt angles,
soiling levels, and exposure durations to identify critical
thresholds and strengthen the relationships between
soiling, insulation integrity, and electrical losses (FF, Rsh).
Field campaigns under real operating conditions,
incorporating climatic cycles (temperature, dew,
wind/rain, salinity), will enable a more accurate
quantification of PID kinetics and its reversibility.
Conflict of interest. The authors declare that they
have no conflicts of interest.
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Received 04.01.2026
Accepted 12.03.2026
Published 02.07.2026
Z. Khammassi 1, PhD,
A. Jeridi 1, PhD,
H. Khaterchi 1, PhD,
A. Zaafouri 1, Professor,
1 University of Tunis,
Higher National Engineering School of Tunis,
Industrial Systems Engineering and Renewable Energies
Research Laboratory, Tunisia,
e-mail: ziedkhammassi@yahoo.fr (Corresponding Author)
How to cite this article:
Khammassi Z., Jeridi A., Khaterchi H., Zaafouri A. Impact of tilt angle, dust deposition, and humidity on potential induced degradation
and electrical performance of crystalline silicon photovoltaic modules: an experimental study. Electrical Engineering &
Electromechanics, 2026, no. 3, pp. 55-65. doi: https://doi.org/10.20998/2074-272X.2026.4.08
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| id | eiekhpieduua-article-349346 |
| institution | Electrical Engineering & Electromechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-02T01:00:17Z |
| publishDate | 2026 |
| publisher | National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | eiekhpieduua/16/69e9de5ae50d46730bcb0b0005662916.pdf |
| spelling | eiekhpieduua-article-3493462026-07-01T21:42:56Z Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study Khammassi, Z. Jeridi, A. Khaterchi, H. Zaafouri, A. photovoltaic performance potential-induced degradation tilt angle dust deposition фотоелектричні характеристики потенціально-індукована деградація кут нахилу осадження пилу Introduction. Photovoltaic (PV) modules constitute the backbone of renewable energy systems, yet their performance is compromised by degradation mechanisms, particularly potential induced degradation (PID), which causes rapid power losses through ionic migration under high voltage stress, creating parasitic shunts that reduce shunt resistance Rsh and energy output. Problem. Although the influence of moisture and temperature has been widely investigated, the combined contribution of operational and environmental factors such as dust soiling remains insufficiently clarified. Goal. This work assesses dust as a contributor to potential induced degradation focusing on the combined effects of tilt angle, dust exposure and dust-moisture interaction on insulation integrity and degradation susceptibility. Methodology. A comparative experimental study was conducted on 3 identical crystalline-silicon PV modules without bypass diodes, installed at tilt angles of 20°, 30° and 40°. A controlled and uniform layer of sandy dust (maximum particle size about 150 μm) was deposited on the front surface. Insulation resistance between the frame and the front glass was measured at three locations (bottom, middle and top) under dry conditions and then at relative humidity above 80 %. The modules were subsequently subjected to a DC electrical stress of 1 kV, followed by cleaning. Electrical performance was evaluated under identical irradiance and temperature conditions using current-voltage (I-V) and power-voltage (P-V) characterization to extract the fill factor (FF) and Rsh. Results. Lower tilt angles (20°) promoted non-uniform dust accumulation, reducing insulation resistance and increasing leakage currents. High humidity intensified these effects, creating localized PID-prone regions. Post-cleaning, modules at 20° exhibited significantly lower FF and Rsh compared to 40°, indicating persistent degradation and incomplete recovery. Scientific novelty. This work establishes dust as an active PID initiator rather than merely an optical attenuator, uniquely examining coupled effects of tilt angle and dust-moisture interaction on PID susceptibility through moisture-assisted surface conduction pathways. Practical value. Appropriate tilt-angle selection and cleaning strategies are essential to preserve insulation integrity, limit leakage currents, mitigate degradation risk and maintain PV performance in dusty and humid environments. References 38, tables 6, figures 19. Вступ. Фотоелектричні (PV) модулі є основою систем відновлюваної енергетики, проте їхня ефективність знижується внаслідок деградаційних процесів, зокрема потенціально-індукованої деградації (PID), яка спричиняє швидкі втрати потужності через міграцію іонів під дією високовольтного електричного поля, утворення паразитних шунтів, зменшення шунтового опору Rsh та зниження енергетичної продуктивності. Проблема. Незважаючи на те, що вплив вологи та температури досліджено достатньо широко, сумарний вплив експлуатаційних і навколишніх факторів, зокрема забруднення пилом, залишається недостатньо вивченим. Мета. Оцінити вплив пилу як чинника потенціально-індукованої деградації з урахуванням сумісної дії кута нахилу, пилового забруднення та взаємодії пилу з вологою на цілісність ізоляції та схильність до деградації. Методика. Проведено порівняльне експериментальне дослідження трьох однакових кремнієвих PV модулів без обвідних діодів, встановлених під кутами нахилу 20°, 30° та 40°. На фронтальну поверхню наносився контрольований рівномірний шар піщаного пилу з максимальним розміром частинок близько 150 мкм. Опір ізоляції між рамою та фронтальним склом вимірювали у трьох точках (нижня, середня та верхня частини) спочатку в сухих умовах, а потім при відносній вологості понад 80 %. Після цього модулі піддавали дії постійної напруги 1 кВ, а далі виконували очищення поверхні. Електричні характеристики оцінювали за однакових умов освітленості та температури шляхом аналізу вольт-амперних (I–V) та вольт-потужних (P–V) характеристик із визначенням коефіцієнта заповнення (FF) та шунтового опору Rsh. Результати. Менші кути нахилу (20°) сприяли нерівномірному накопиченню пилу, що призводило до зниження опору ізоляції та збільшення струмів витоку. Висока вологість посилювала ці ефекти, формуючи локальні області, схильні до PID. Після очищення модулі з кутом нахилу 20° демонстрували значно нижчі значення FF та Rsh порівняно з модулями з кутом 40°, що свідчить про стійку деградацію та неповне відновлення характеристик. Наукова новизна. У роботі пил розглядається не лише як оптичний послаблювач випромінювання, а як активний чинник ініціювання PID. Уперше детально досліджено сумісний вплив кута нахилу та взаємодії пилу з вологою на схильність до PID через поверхневі провідні шляхи, утворені за участю вологи. Практична значимість. Правильний вибір кута нахилу та стратегій очищення є важливими для збереження цілісності ізоляції, обмеження струмів витоку, зменшення ризику деградації та підтримання ефективної роботи PV модулів у запилених і вологих умовах. Бібл. 38, табл. 6, рис. 19. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2026-07-02 Article Article application/pdf https://eie.khpi.edu.ua/article/view/349346 10.20998/2074-272X.2026.4.08 Electrical Engineering & Electromechanics; No. 4 (2026); 55-65 Электротехника и Электромеханика; № 4 (2026); 55-65 Електротехніка і Електромеханіка; № 4 (2026); 55-65 2309-3404 2074-272X en https://eie.khpi.edu.ua/article/view/349346/351645 Copyright (c) 2026 Z. Khammassi, A. Jeridi, H. Khaterchi, A. Zaafouri http://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | photovoltaic performance potential-induced degradation tilt angle dust deposition Khammassi, Z. Jeridi, A. Khaterchi, H. Zaafouri, A. Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_alt | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_full | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_fullStr | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_full_unstemmed | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_short | Impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| title_sort | impact of tilt angle, dust deposition, and humidity on potential induced degradation and electrical performance of crystalline silicon photovoltaic modules: an experimental study |
| topic | photovoltaic performance potential-induced degradation tilt angle dust deposition |
| topic_facet | photovoltaic performance potential-induced degradation tilt angle dust deposition фотоелектричні характеристики потенціально-індукована деградація кут нахилу осадження пилу |
| url | https://eie.khpi.edu.ua/article/view/349346 |
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