In a PV module, the relative humidity (rh) of a front encapsulant is different from that of a backside encapsulant (rhback). In this study, the effective humidity (rheff) in a PV module was investigated to study the effects of moisture variation on the degradation rate (). rheff represents uniform humidity in a PV module when it is exposed to certain damp heat conditions. Five types of accelerated tests were conducted to derive the relation between rheff and rhback. rheff showed a linear relationship with rhback at constant temperature. Two types of models, namely, Eyring and Peck models, were used for predicting the of PV modules, and their results were compared. The of PV modules was thermally activated at 0.49 eV. Furthermore, the temperature and rheff history of PV modules over one year were determined at two locations: Miami (FL, USA) and Phoenix (AZ, USA). The accumulated values based on the temperature and rheff of the modules were calculated by summing the hourly degradation amounts over the time history.

1. Introduction

Moisture can diffuse into photovoltaic (PV) modules through their breathable back sheets or their ethylene vinyl acetate (EVA) sheets [1]. When in service in hot and humid climates, PV modules experience changes in the moisture content, the overall history of which is correlated with the degradation of the module performance [1]. If moisture begins to penetrate the polymer and reaches the solar cell, it can weaken the interfacial adhesive bonds, resulting in delamination [2] and increased numbers of ingress paths, loss of passivation [3], and corrosion of solder joints [4, 5]. Of these possibilities, the occurrence of corrosion has one of the highest frequencies in outdoor-exposed PV modules [6]. Significant losses in PV module performance are caused by the corrosion of the cell, that is, the SiNx antireflection coating, or the corrosion of metallic materials, that is, solder bonds and Ag fingers [7, 8]. Corrosion is defined as the destructive chemical or electrochemical reaction of a metal with its environment. The moisture from the environment may lead to electrochemical reactions that can result in corrosion. For the electrochemical reaction of metals with their environment, an aqueous, ion-conduction enabling environment is necessary; moreover, at high temperatures, gas-metal reactions are possible [9]. The International Electrotechnical Commission (IEC) 61215 test defines a damp heat (DH) test in 10.13. The DH test is conducted for determining the effect of long-term penetration of humidity on materials. Therefore, many researchers have studied the reliability of PV modules on the basis of IEC 61215. Laronde et al. [10] have employed DH testing to study the degradation of PV modules subjected to corrosion. Peike et al. [11] have reported that grid corrosion or reduced conductivity between the emitter and grid is the most likely cause of DH-induced degradation. They have also shown that high temperatures accelerate water vapor permeation into the module and the subsequent degradation reactions. Furthermore, it has been reported that loss of adhesion strength is exacerbated by exposure to high humidity environments [2] and facilitates the delamination of EVA from the cell [3], which results in grid corrosion [12]. Therefore, in order to understand the effect of grid corrosion on the degradation of PV modules, one needs to comprehend how the surrounding environment affects the module temperature () and moisture content of the module. Kempe [1] has suggested that analytical equations can be used to determine timescales for moisture ingress with breathable back sheets. Koehl et al. [13] have showed that the maximum moisture concentration in front of a cell was not reached after 1,000 h under DH conditions at 85°C and 85% rh because of the long path to the back sheet. They have also documented that the humidity in front of the cell is not directly influenced by ambient fluctuations in actual weather conditions.

As mentioned above, PV modules are degraded by ambient temperature and humidity; moreover, these factors can accelerate the degradation. This degradation is mainly caused by corrosion [4, 5, 7, 8, 10, 11]. It can be assumed that the temperature of a PV module is uniform; however, moisture concentration in a PV module is not uniform. Therefore, it is difficult to predict moisture-induced degradation.

Therefore, in this study, effective humidity (rheff) in a PV module was investigated to study the effect of moisture variation in a PV module. rheff represents uniform humidity in a PV module when it is exposed to certain DH conditions. This paper documents the relation of rheff with ambient temperature and humidity. Moreover, the resultant module degradation rate () for various rheff values is also reported in this paper. These data allow the prediction of real-world thermal- and moisture-induced values of PV modules and enable the computation of acceleration factor (AF) for the DH test.

2. Experiments

Six-inch multicrystalline Si (m-Si) solar cells were used in this study. The typical characteristics of the cells at a light intensity of 1 sun were approximately as follows: open-circuit voltage (), 0.60 V; short-circuit current density (), 33.9 mA/cm2; fill factor (FF), 0.72; and conversion efficiency, 16.8%.

A copper ribbon wire, which was plated with 62Sn36Pb2Ag solder, was used for cell interconnection. The dimensions of the ribbon wire were 0.15 mm × 1.5 mm. The samples were divided into two groups on the basis of lamination conditions. Type 1 was arranged with EVA, cell, and EVA. Type 2 was laminated with low-iron glass of area 180 mm × 180 mm and thickness 3.2 mm, an EVA of thickness 0.35 mm, a cell, an EVA, and a TPT back sheet of thickness 0.35 mm, as shown in Figures 1(a), 1(b), and 1(c). The solar cells were laminated with EVA by heating them up to 150°C for 12 min. After encapsulation, the samples were divided into five groups and exposed to accelerated stresses, as shown in Table 1. Five kinds of test conditions were selected: 85°C, 85% rh (8585), 65°C, 85% rh (6585), and 45°C, 85% rh (4585) for temperature acceleration and 65°C, 75% rh (6575), and 65°C, 65% rh (6565) for humidity acceleration. A total of five cases, each with ten samples, were tested. DH conditions were obtained in an environmental chamber (Hygros340C, ACS Co., Massa Martaba, Italy).

The electrical performance of each sample was measured every 200 h using a solar simulation system (K202 Lab200, Mac Science, Seoul, South Korea). The standard test conditions were (a) irradiance: 1000 W/m2, (b) cell temperature: 25°C, and (c) spectral distribution of irradiance: AM 1.5 G (IEC 60904-3).

Accelerated tests (ATs) were conducted for 4,500 h for 8585, 6585, and 4585 and for 3,200 h for 6575 and 6565. The maximum power of all samples decreased by over 5% after the ATs. Using the results, the average for each condition was calculated.

3. Prediction Models and Effective Humidity

data can be postulated with an empirical kinetic model by assuming that the rate of degradation is proportional to the concentration of water in PV modules, and that the rate constant has Arrhenius temperature dependence.

Escobar and Meeker [14] has proposed two degradation models: variations of Eyring and Peck models, which are used for operating conditions when temperature and humidity are the accelerated stresses in a test. The degradation rate based on the Eyring model () is given by where is the thermal activation energy of the degradation process (eV), is the Boltzmann constant ( eV/K), is the temperature (°K), and rh is the relative humidity (%). and are two constants dependent on the failure mode. (%/h) is the inverse of the mean time to failure (MTTF) at a given condition. In order to obtain , we determined the time to 5% reduction in the initial maximum power () at all samples. The life distributions were determined with ALTA 7 software. Using the results, the MTTF was calculated.

The other degradation model based on the Peck model () is expressed as follows: where and are two constants dependent on the failure mode.

In order to obtain , in (1) and , in (2), the equations can be represented on a logarithmic scale by a straight line, using the following equations:

A plot of the left-hand side of (3) versus (°K) gives an Arrhenius plot with a slope and an intercept .

versus (°K) gives an Arrhenius plot with a slope and intercepts and .

The in PV modules depends on their ambient climate, material (encapsulant, back sheet) properties, and the operation conditions. If all information is available, moisture concentration in the backside encapsulant can be calculated using the diffusion model [1]. However, the moisture concentration in the front encapsulant is different from that at the back of the cell because of the long path from the back sheet [13]. In a 85°C, 85% rh test, the maximum moisture content in the backside encapsulant was reached quickly; however, the maximum moisture content of the front encapsulant was not reached even after 1,000 h of exposure time [13]. Therefore, rheff of a PV module was considered to determine the uniform moisture content in the module.

In order to derive the effect of uniform humidity in a PV module on its degradation, PV modules with a EVA/cell/EVA structure (Type 1) were used as shown in Figure 1(a). This is because the cell and EVA layer structure allow water vapor to permeate the surface of the cell within minutes during the DH test [15].

In case of Type 1, it can be assumed that the rh in the PV module is uniform. If and constants (, , etc.) are determined, the degradation rate of Type 1 () can be predicted with However, in case of glass/EVA/cell/EVA/back sheet structure (Type 2), rh is not uniform in the PV module. Therefore, it is difficult to fix the rh in the PV module. If is known, is expressed with the right-hand side of (4), and rheff is as follows: where and other parameters (, , , and ) can be determined by ATs as shown in Table 1. Using (5), rheff is rearranged as follows:

4. Results

4.1. Results of Accelerated Tests

The changes in average normalized of the modules in Type 1 as a function of time are plotted in Figure 2. The figure shows that decreases linearly over time. The results correspond well with those found in earlier studies [6, 16]. Several authors [17, 18] argue that the limited experimental evidence available is not enough to take the linear for granted and suggest that an exponential degradation rate could be a more suitable trend as is the case in some optoelectronic devices. However, it should be noted that both trends exhibit very similar evolution during the first 10–15 years; if similar initial annual degradation rates are assumed, then the linear degradation rate is a more pessimistic estimate [19].

In order to keep the discussions simple, we will not consider the exponential degradation rate here.

Using AT results of Type 1 samples, the was determined for each set of conditions.

is obtained by fitting the data in (1) and (2) for three values of temperature. and other constants were calculated as summarized in Table 2.

of the modules was also determined for each set of conditions. The values (%/h) of 8585, 6585, 4585, 6575, and 6565 were 0.00611, 0.00208, 0.00087, 0.00132, and 0.00079, respectively.

In order to derive the relationship between rheff and rh in the backside encapsulant, in (4) was replaced with values. Figure 3 shows a plot of rheff versus rh in the backside encapsulant at a constant temperature and constant humidity. In both models, rheff versus rh has a linear relation at a constant temperature, and rheff decreases linearly with temperature at constant humidity (inset in Figure 3). Therefore, rheff is expressed as follows:

Using rheff values at AT conditions, predicted of (5) are plotted as a function of time in Figure 4. It shows that the predicted is almost identical to the measured data.

4.2. Acceleration Factor

AF is defined as the ratio between the at a given temperature, rheff and at a reference temperature, and rheff (in our case 25°C, 50% ) [20]. AF is expressed as where and rh0 are the reference temperature and reference humidity, respectively.

Figure 5 shows the AF contours on plots of rheff versus module-temperature data. Estimated AFs for the 8585 condition versus 25°C, 50% rh range from 190× to 250× for the Peck and Eyring models, respectively. However, in real-world operation, a constant temperature and rh are not realistic. To project field at a specific location, it was characterized by the annual module temperature and rh of the backside encapsulant.

5. in Two Benchmark Climates

Two benchmark climates (BMCs) were selected to quantify the stress: Miami (FL, USA) and Phoenix (AZ, USA). The module-temperature history exposed to the two BMCs was derived from meteorological data [21]. Meteorological data for Miami, FL, for 2005 and Phoenix, AZ, for 2002 were obtained from the National Climatic Data Center.

The rh of the backside encapsulant was calculated using the model of moisture ingress [1]. We determined the activation energy for encapsulant solubility in a previous research [22]. for maximum water vapor transmission rate of back sheets was evaluated. The transient WVTR was measured using a WVTR instrument (Permatran-W3/33, Mocon, Minneapolis, MN, USA) at 25°C, 37.8°C, and 50°C. Assuming an Arrhenius equation between and temperature, can be described by Parameters and were obtained from a curve fit of a plot of of versus . The and values are  g/m2/day and 0.367 eV, respectively.

The accumulated based on the module temperature and rheff can be calculated by summing the hourly degradation amounts over the time history, as given by

Thermal and history of a PV module over one year were calculated at two BMCs as shown in Figure 6. Compared with Miami, the module temperature at Phoenix is shifted more than 10°C higher and the rheff has a relatively low distribution.

Accumulated in the two BMCs is calculated using (12), which are based on the module temperature and rheff of Figure 6.

The normalized and of the PV module exposed to two BMCs are plotted over one year in Figure 7(a). The accumulated was 3.0% greater than in Miami. The conditions of 8585 are normally used for DH tests as IEC 61215. Therefore, the accumulated exposed to 8585 was evaluated and compared to the accumulated in the Miami. The accumulated and for exposure to 8585 were about 23.7 and 23.1 times greater than those in Miami, as shown in Figure 7(b). Koehl et al. [13] have reported that AF of 8585 is about 23 for a tropical site (Serpong, Indonesia), 40 for an arid site (Sede Boqer, Israel), and 106 for an alpine site (Zugspitze, Germany) for a degradation process with an activation energy of 0.416 eV.

In case of 6585, the values according to Eyring and Peck models are 9.5 and 9.3 times greater than those in Miami. Therefore, it can be supposed that the Peck model is a slightly conservative estimation for prediction.

6. Conclusions

The objectives of this study were to investigate the relation of ambient temperature and humidity with the rheff of a PV module and to use the rheff values to predict the values under actual weather conditions.

The degradation of PV modules is accelerated by temperature and humidity [1, 4, 5, 10, 11]. It can be assumed that the temperature in a PV module is uniform. However, the moisture concentration is not uniform [13]. Therefore, we used a Type 1 module with a EVA/cell/EVA structure for uniform humidity in the module.

Two types of models, namely, Eyring and Peck models, were used for prediction, and their results were compared with each other. Five types of ATs were conducted to determine and humidity dependence. The of PV modules were thermally activated at 0.49 eV.

The moisture content in a PV module is dependent on material properties such as back sheets and EVA. Therefore, we determined the relation between the rh of the backside encapsulant and rheff. rh of the backside encapsulant was calculated using the moisture ingress model. Thermal and rheff history of a PV module over one year were calculated in two BMCs. For exposure to 8585, the accumulated and values at Phoenix were, respectively, about 23.7 and 23.1 times greater than those at Miami.


AF:Acceleration factor
AT:Accelerated tests
BMC:Benchmark climate
DH:Damp heat
EVA:Ethylene vinyl acetate
FF:Fill factor
IEC:International Electrotechnical Commission
:Short-circuit current density
MTTF:Mean time to failure
:Degradation rate
:Degradation rate based on the Eyring model
:Degradation rate based on the Peck model
rh:Relative humidity
rhback:Relative humidity of a backside encapsulant
rheff:Effective humidity
:Module temperature
:Open-circuit voltage.


This work was supported by the New and Renewable Energy of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grant funded by the Ministry of Trade, Industry and Energy (MOTIE) (no. 2012T100100605). Furthermore, this work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grant funded by the Korea Governments Ministry of Knowledge Economy (no. 20104010100640).