^{1}

^{*}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

Most manufacturers of solar modules guarantee the minimum performance of their modules for 20 to 25 years, and 30-year warranties have been introduced. The warranty typically guarantees that the modules will perform to at least 90% capacity in the first 10 years and to at least 80% in the following 10 - 15 years. Early degradation resulting from design flaws, materials or processing issues is often apparent from startup to the first few years in service. Importantly, many module failures and performance losses are the result of gradual accumulated damage resulting from long-term outdoor exposure in harsh environments, referred. Many of these processes occur on relatively long time scales and the various degradation processes may be chemical, electrical, thermal or mechanical in nature. These are either initiated or accelerated by the combined stresses of the service environment, in particular solar radiation, temperature and moisture, and other stresses such as salt air, wind and snow. Accelerated Life Testing (ALT) test methodology is normally predicated on first being able to reproduce a specific degradation or failure mode without altering it (correlation); and, second, to produce that result in less than real-time acceleration. Degradation and failure may result when an applied stress exceeds material or product strength. This may be a one-time catastrophic event, the result of cyclic fatigue, or a gradual decline in requisite properties due to ageing mechanisms. Engineers in the manufacturing industries have used accelerated test (AT) experiments for many decades. The purpose of AT experiments is to acquire reliability information quickly. Test units of a material, component, subsystem or entire systems are subjected to higher-than-usual levels of one or more accelerating variables such as temperature or stress. Then the AT results are used to predict life of the units at use conditions. The extrapolation is typically justified (correctly or incorrectly) on the basis of physically motivated models or a combination of empirical model fitting with a sufficient amount of previous experience in testing similar units. The need to extrapolate in both time and the accelerating variables generally necessitates the use of fully parametric models. Statisticians have made important contributions in the development of appropriate stochastic models for AT data [typically a distribution for the response and regression relationships between the parameters of this distribution and the accelerating variable(s)], statistical methods for AT planning (choice of accelerating variable levels and allocation of available test units to those levels) and methods of estimation of suitable reliability metrics. This paper provides a review of many of the AT models that have been used successfully in this area.

Today’s manufacturers face strong pressure to develop new, higher-technology products in record time, while improving productivity, product field reliability and overall quality. This has motivated the development of me- thods like concurrent engineering and encouraged wider use of designed experiments for product and process improvement. The lack of accurate information about degradation rate increases the financial risk [

However, there is little information on PV modules degradation modes in terms of frequency, speed of evolution and degree of impact on module lifetime and reliability.

Research on photovoltaic modules is rather focused on the race to develop new technologies without sufficient experience feedback on already operational technologies [

For such applications, Accelerated Tests (ATs) are used in manufacturing industries to assess or demonstrate component and subsystem reliability, to certify components, to detect failure modes so that they can be corrected, to compare different manufacturers, and so forth. ATs have become increasingly important because of rapidly changing technologies, more complicated products with more components, higher customer expectations for better reliability and the need for rapid product development. There are difficult practical and statistical issues involved in accelerating the life of a complicated product that can fail in different ways. Generally, information from tests at high levels of one or more accelerating variables (e.g., use rate, temperature, voltage or pressure) is extrapolated, through a physically reasonable statistical model, to obtain estimates of life or long- term performance at lower, normal levels of the accelerating variable(s).

The present article proposes a bibliographic review on the degradation modes of PV modules [

The paper is organized in two parts, the main types of degradation of the PV module identified in the literature are exposed in the first part. A review of models associated with the degradation of the PV modules is presented in the second part.

Manufacturer’s guarantees of up to 20 years indicate the quality of bulk silicon PV modules currently being produced. Nevertheless, there are several failure modes and degradation mechanisms which may reduce the power output or cause the module to fail. Nearly all of these mechanisms are related to water ingress or tem- perature stress. Degradation mechanisms may involve either a gradual reduction in the output power of a PV module over time or an overall reduction in power due to failure of an individual solar cell in the module. They can deteriorate or become defective even when they operate on actual site for extended periods [

The degradation of PV modules are caused by static and dynamic mechanical loads, thermal cycling, exposure to radiation, moisture, hail impact (sand) dust accumulation, partial occultation causes found above are responsible for the degradation of the modules, which manifests itself in several ways:

Corrosion of the PV module, the discoloration, delamination, breakage of the front panel (glass) module, Potential Induced Degradation (PID), hot spots (hot spots), Bubbles, dust deposits.

The outdoor exhibition of photovoltaic modules includes several factors (wind, rain, light, heat ....) That causes damage as mentioned above. Thus these factors have a negative effect on the module power output.

To better understand these degradations, called accelerated tests can reproduce they are conducted in climatic chambers in extensive conditions of temperature and pressure to reproduce the degradation in a limited time. But it is also interesting to have a model to simulate numerically the evolution of degradation. Many authors have tried to make the degradation assessment models

Pan [

where a and b are parameters that can be assessed by degradation testing. The parameter a is considered constant regardless of the level of sévérisation and b is variable reflecting its dependence on sévérisation levels. Thanks to this relationship, we can determine when the test must be stopped in order to measure the power of the module.

Wohlgemuth [^{−12}.

Temperatures taken during the tests shall not exceed the technological limit temperature of PV module sequal to 120˚C according to Kern [

The 85C/85% relative humidity exposure is as accelerated as necessary. These conditions probably never happen in the real world as the modules tend to dry out at their highest temperatures, but absorb moisture at lower temperatures. It is difficult to judge what outdoor exposure the 1000 hour exposure at 85/85 represents. In a recent experiment 10 crystalline silicon modules qualified to IEC 61215 were exposed to 1250 hours of 85/85. Only 2 of the 10 types successfully passed the extended test [

The study of Wohlgemuth [^{−12} for a temperature of 85˚C and a relative humidity 85%. The parameter is considered constant whatever the test conditions (temperature and humidity) while the parameter b depends on the test conditions. For the model of Peck, b of the degradation model parameter to a temperature T and relative humidity RH can be determined by the relation

or b_{85°C/85% }is the parameter b of degradation model for a temperature of 358˚K (85˚C) and a relative humidity of 85%. The parameter b of the acceleration model is equal to 1.948 × 10^{−9} for a temperature of 105˚C and a relative humidity of 85%, and equalto1.614 × 10^{−11} for conditions of 85˚C/95%HR.

The constants a and b depend on the degradation mode considered. Thus, Equation (2) and (3) give respec- tively the degradation model due to corrosion and discoloration:

(3)

where a (a corrosion and a discoloration) and b (b corrosion and b discoloration) are the parameters of the degradation model. They are determined from accelerated testing Charki, and Laronde [

where n is the number of degradation modes.

The PV module power measured at a given time follows a Gaussian distribution. According to Reis, Sakamoto and Oshiro [^{ }

where P is the power module, μ is its mean value and σ its standard deviation. Thus, it can be calculated by Osterwald, Marion, Adelstein, and Raghuraman [

where

P_{0} is the average power at t = 0 (i.e. the nominal module power),

A is a parameter which reflects annual decrease of module power,

t is time in years. Of course, validity of Equation (6) is restricted by time (t) lower than P_{0}/A.

Another limitation comes from the assumption according to which A is constant in time.^{ }

A/P_{0} (year^{−1}) is the annual degradation rate. From studies on electronic components degradation, we can consider the assumption according to which degradation rate is exponential [

It is sometimes said that high temperature is the enemy of reliability. Increasing temperature is one of the most commonly used methods to accelerate a failure mechanism.

The Arrhenius relationship is a widely used model to describe the effect that temperature has on the rate of a simple chemical reaction. This relationship can be written as

where R is the reaction rate, and temp˚K = temp ˚C + 273.15 is thermodynamic temperature in kelvin (K), k is either Boltzmann’s constant or the universal gas constant and Ea is the activation energy.

The parameters Ea and ^{−5} = 1/11605 in units of electron-volt per kelvin (eV/K) is commonly used and in this case, Ea has units of electron-volt (eV).

In most accelerated test applications, it would be more appropriate to refer to Ea in Equation (9) as a quasi- activation energy.

The Arrhenius acceleration factor is

When

When temp_{U} and Ea are understood to be, respectively, product use temperature and reaction-specific quasi activation energy,

The Arrhenius-based model presents some limits. Indeed, the Arrhenius equation can be used to quantify the effect of varying temperature and irradiance on the rate of a property change. However it cannot provide a complete picture of the long-term degradation of PV modules, as other stress factors or combination of stresses are involved. These include moisture (inducing physical and chemical processes and generating mechanical stress in combination with temperature), temperature cycling (generating thermomechanical stress), electricity production (inducing electrical and electrochemical stresses), and other externally applied stresses (wind, hail, airborne pollutants.

The Arrhenius relationship Equation (9) was discovered by Svante Arrhenius through empirical observation in the late 1800s. Eyring [

The Eyring relationship is:

where A(temp) is a function of temperature depending on the specifics of the reaction dynamics and 0 and Ea are constants Weston and Schwarz, provides more detail [^{m} with a fixed value of m ranging between m = 0 [

where

Humidity is another commonly used accelerating variable, particularly for failure mechanisms involving corrosion and certain kinds of chemical degradation.

Vapor density measures the amount of water vapor in a volume of air in units of mass per unit volume.

Partial vapor pressure (sometimes simply referred to as “vapor pressure”) is closely related and measures that part of the total air pressure exerted by the water molecules in the air. Partial vapor pressure is approximately proportional to vapor density.

The partial vapor pressure at which molecules are evaporating and condensing from the surface of water at the same rate is the saturation vapor pressure.

For a fixed amount of moisture in the air, saturation vapor pressure increases with temperature.

Relative humidity is usually defined as and is commonly expressed as a percent. For most failure mechanisms, physical/chemical theory suggests that RH is the appropriate scale in which to relate reaction rate to humidity especially if temperature is also to be used as an accelerating variable [

A variety of different humidity models (mostly empirical but a few with some physical basis) have been suggested for different kinds of failure mechanisms.

Much of this work has been motivated by concerns about the effect of environmental humidity on plastic- packaged electronic devices. Humidity is also an important factor in the service-life distribution of paints and coatings. In most test applications where humidity is used as an accelerating variable, it is used in conjunction with temperature.

Peck [

They suggest ALT models based on the physics of failure. Nelson [

The Eyring/Arrhenius temperature-humidity acceleration relationship in the form of Equation (33) uses x_{1} = 11605/temp K, x_{2} = log (RH) and x_{3} = x_{1}x_{2} where RH is relative humidity, expressed as a proportion.

An alternative humidity relationship suggested by Klinger [_{2} = log [RH/(1−RH)] (a logistic transformation) instead.

In most applications where it is used as an accelerating variable, higher humidity increases degradation rates and leads to earlier failures. In applications where drying is the failure mechanism, however, an artificial environment with lower humidity can be used to accelerate a test.

Many organic compounds degrade chemically when exposed to ultraviolet (UV) radiation. Such degradation is known as photodegradation. This section describes models that have been used to study photodegradation and that are useful when analyzing data from accelerated photodegradation tests. Many of the ideas in this section originated from early research into the effects of light on photographic emulsions [

Important applications include prediction of service life of products exposed to UV radiation (outdoor weathering) and fiber-optic systems.

It is clear that UV radiation is a major degradation factor for photovoltaic modules especially in their discoloration [

where I_{sc}(E) is the short-circuit current of the PV module and E the dose of ultra-violet (UV). Zimmerman [

where _{min}, k_{max}], the transmittance can be written:

where a_{cmx} and b_{cmx} are parameters of material used for PV cell [

The relationship between UV dose E and exposure time t in the solar spectrum P(k) is:

The integral extends up to 400 nm that represents a practical limit to UV photodegradation.

Combining Equation (15) and (17) and using the mean value theorem, Equation (18) obtained to estimate the UV degradation of PV module is given by:

Avec

This model presents a major constraint. In fact, its use requires knowledge of the intrinsic characteristics of the materials used for the production of PV cells such as a_{cmx}, b_{cmx},

As described in Martin et al. [_{Tot}. Intuitively, this total effective dosage can be thought of as the cumulative number of photons absorbed into the degrading material and that cause chemical change. The total effective UV dosage at real time t can be expressed as

where the instantaneous effective UV dosage at real time

Here _{0} and A in the integrand of Equation (20) can either be measured directly or estimated from data and the function

The integrals over wavelength, like that in Equation (20), are typically taken over the UV-B band (290 nm to 14,320 nm), as this is the range of wavelengths over which both

Degradation (or damage) D(t) at time t depends on environmental variables like UV, temp and RH, that may vary over time, say according to a multivariable profile ξ(t) = [UV, temp, RH, ×××]. Laboratory tests are conducted in well-controlled environments, usually holding these variables constant (although sometimes such variables are purposely changed during an experiment, as in step-stress accelerated tests). Interest often centers, however, on life in a variable environment. These sample paths might be modeled by a given functional form,

where z is scaled time and g(z) would usually be suggested by knowledge of the kinetic model (e.g., linear for zeroth-order kinetics and exponential for first-order kinetics), although empirical curve fitting may be adequate for purposes where the amount of extrapolation in the time dimension is not large. As in SAFT models, μ can be modeled as a function of explanatory variables like temperature and humidity when these variables affect the degradation rate.

The inverse power relationship is frequently used to describe the effect that stresses like voltage and pressure have on lifetime. Voltage is used in the following discussion. When the thickness of a dielectric material or insulation is constant, the voltage stress is proportional to the square of the voltage. Let volt denote voltage and let volt_{U} be the voltage at use conditions. The lifetime at stress level volt is given by

where

If T(volt_{U}) has a log-location-scale distribution with parameters μ_{U} and σ, then T(volt) also has a log location- scale distribution with_{U} = log(volt_{U}), x = log(volt),

The inverse power relationship is widely used to model life as a function of pressure-like accelerating variables (e.g., stress, pressure, voltage stress).

This relationship is generally considered to be an empirical model because it has no formal basis from knowledge of the physics/chemistry of the modeled failure modes. It is commonly used because engineers have found, over time, that it often provides a useful description of certain kinds of AT data.

Analytically, suppose that degrading dielectric strength at age t can be expressed as

Then the acceleration factor for volt versus volt_{U} is

which is an inverse power relationship, as in Equation (24). To extend this model, suppose that higher voltage also leads to an increase in the degradation rate and that this increase is described with the degradation model:

where

Then equating D(t) to volt and solving for failure time t gives the failure time

Then the ratio of failure times at volt_{U} versus volt is the acceleration factor

which is again an inverse power relationship with b_{1} = 1 − 2. This motivation for the inverse power relationship described here is not based on any fundamental understanding of what happens to the insulating material at the molecular level over time.

The generalized Eyring relationship extends the Eyring relationship in Section 3.3.3, allowing for one or more nonthermal accelerating variables (such as humidity or voltage). For one additional nonthermal accelerating variable X, the model, in terms of reaction rate, can be written as

where X is a function of the non-thermal stress. The parameters

In the following sections, following common practice, we set (tempK)^{m} = 1, using what is essentially the Arrhenius temperature-acceleration relationship.

These sections describe some important special-case applications of this more general model. If the underlying model relating the degradation process to failure is a SAFT model, the generalized Eyring relationship can be used to describe the relationship between times at different sets of conditions temp and X. In particular, the acceleration factor relative to use conditions temp_{U} and X_{U} is

Suppose that T(temp_{U}) (time at use or some other baseline temperature) has a log location scale distribution with parameters μ_{U} and σ. Then T(temp) has the same log-location-scale distribution with

where

Many different models have been used to describe the effect of the combination of temperature and voltage on acceleration. For instance, Meeker and Escobar [

Again, failure occurs when the dielectric strength crosses the applied voltage stress, that is, D(t) = volt. This occurs at time

From this, one computes

where

Relative humidity is another environmental variable that can be combined with temperature to accelerate corrosion or other chemical reactions.

Gillen and Mead [

The extended Arrhenius relationship Equation (31) applied to ALTs with temperature and humidity uses x_{1} = 11605/tempK, x_{2} = log(RH) and x_{3} = x_{1}x_{2} where RH is a proportion denoting relative humidity. The case when

Klinger [_{2} = log[RH/(1−RH)] instead of log(RH). This alternative relationship is based on a kinetic model for corrosion.

The acceleration model with the capacity to take into account temperature (T) and relative humidity (RH) is the Peck model [

According to Charki et al. [

In this case, x_{1} and x_{2} correspond respectively to relative humidity (RH) and module temperature (T); ^{0}) and temperature (T^{0}) in the reference conditions.

The acceleration factor is expressed as [

where

We consider that

where

If the acceleration factor is defined by relation Equation (37), it is possible to estimate an equivalent temperature, T_{eq}, which represents the degradation that would have occurred if the module had been aged for the same length of time but at a constant temperature. The equivalent temperature T_{eq} can be calculated using the following relation [

where t is time, T_{module(t)} is the time-dependent module temperature, and t_{1} and t_{2} are the integration start and end times.

Using the same methodology below, the equivalent of relative humidity H_{eq} can be estimated as

where t is time, H(t) is the time-dependent environmental relative humidity, and t_{1} and t_{2 }are the integration start and end times.

The module temperature T_{module(t)} and the relative humidity H(t) are simulated hour by hour for a period of 50 years, for at four cities: Paris (France), Oslo (Norway), Madrid (Spain) and Tamanrasset (Algeria). The equivalent temperature T_{eq} and the equivalent relative humidity H_{eq} obtained versus Ea and n respectively using relations Equations (39) and (40) are plotted in

When modeling photodegradation, it is often necessary to account for the effect of temperature and humidity. The Arrhenius rate reaction model Equation (9) can be used to scale time (or dosage) in the usual manner. Humidity is also known to affect photodegradation rate. Sometimes the rate of degradation will be directly affected by moisture content of the degrading material. In this case one can use a model such as described in Burch, Martin and Van Landingham [

Combining these model terms with the log of total effective UV dosage from Equation (19) gives

where temp K is temperature in kelvin, MC(RH) is a model prediction of moisture content, as a function of rela- tive humidity, k is Boltzmann’s constant, E_{a} is a quasi-activation energy, and

Accelerated test programs often start with simple experiments to understand the failure modes that can occur and the behavior of mechanisms that can cause failures.

Use of methods for designed experiments is important for these tests. In addition, there may be special features of accelerated tests that require special test planning methods, providing expertise in the analysis of data arising from preliminary studies and the accelerated tests themselves. Features such as censoring, multiple failure modes and models that are nonlinear in the parameters are common. Methods for detecting model departures are particularly important. The work presented in this paper has underlined the degradation modes and factors to consider in experiments over long periods. Development of models associated with different degradation modes of PV modules is an interesting research field to improve the knowledge of photovoltaic modules behavior during their life cycle.

Research in the development of accelerated test models is a multidisciplinary activity.

FatouDia,NacireMbengue,Omar NgallaSarr,MoulayeDiagne,Omar A.Niasse,AwaDieye,MorNiang,BassirouBa,CheikhSene, (2016) Model Associated with the Study of the Degradation Based on the Accelerated Test: A Literature Review. Open Journal of Applied Sciences,06,49-63. doi: 10.4236/ojapps.2016.61006