Reliability and Cost Evaluation of PV Module Subject to Degradation ...

International Journal of Performability Engineering, Vol. 10, No. 01, 2014, pp.95-104. © RAMS Consultants Printed in India

Reliability and Cost Evaluation of PV Module Subject to Degradation Processes RAFIK MEDJOUDJ1*, RABAH MEDJOUDJ1 and DJAMIL AISSANI2 1

Bejaia University, Targa-ouzemour, Bejaia, ALGERIA LAMOS laboratory of Bejaia University, Targa-ouzemour, Bejaia, ALGERIA

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(Received on September 18, 2012, revised on May 31, and September 04, 2013) Abstract: This paper develops a new degradation model of the PV module performance based on two degradation processes. The first is the initial photon degradation related to physical process in the solar cell itself, where the function of the performance loss caused by this mechanism is exponentially distributed. The second is the continuous degradation process; it is related to the long term weathering and to the degradation of the module package resulting in a degradation of the module performance. In this case, the function of the performance loss caused by this mechanism follows the Weibull distribution. The obtained results by simulation are discussed and corroborated by mathematical analysis of a simpler equivalent model. The analysis covers lifetime energy loss, Cumulative loss of energy (kWh, %), annual cost of energy loss, and the total cost of energy loss. Finally, the objective reached is the reliability evaluation of the PV module. Keywords: Reliability, Photovoltaic module, Degradation mechanisms, Degradation models.

1.

Introduction

Reliability modeling is of major concern in photovoltaic energy system. Its evaluation can be done using either deterministic or stochastic processes. Deterministic methods cannot recognize the random behavior of the system. So they cannot be directly applied to renewable energy systems. Probabilistic methods will interpret a single numerical risk index. These two methods are applied to identify the different degradation processes and data analysis. Various mechanisms have been discussed as the source of the degradation, namely: the initial photon degradation related to a physical process in the solar cell itself [1]. This effect is normally observed in the first hours of operation. Other effects are related to long term weathering and degradation of the module package resulting in a degradation of the module performance [2]. To understand the effect and relevance of each of these mechanisms on the total energy production of a PV module over its lifetime, we have required the identification of associated degradation rates for each process. Many recent published works have developed the issue of mechanism failures and degradation models of photovoltaic modules such as degradation in field-aged modules based on observations. In this latter it was included degradation of packaging materials, adhesional loss, and degradation of interconnects, degradation due to moisture intrusion, and semiconductor device degradation [3]. However, others have modeled the degradation of modules using some assumptions, such as the constant degradation rate (i.e., the loss of energy life is given by 0.7 per annum for all its lifetime). In this paper the degradation model of the PV module is established, based on two degradation processes developed initially. The novelty introduced in this work corresponds to the degradation modelling using the mixed Weibull distribution to evaluate ____________________________________________ *Communicating author’s email: [email protected]

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Rafik Medjoudj, Rabah Medjoudj and Djamil Aissani

the reliability of the module. The rest of the paper is organized as follows: After the introduction of some useful notations, section 2 is devoted to the degradation mechanism explanation. The data analysis is of great interest to evaluate the probability distribution parameters; it is done in section 3. Section 4 is dealing with the modelling and the mixed Weibull distribution is introduced. Section 5 is devoted to the case study application and the discussion of the obtained results. The conclusion is given in section 6. Notation NREL LEEE-TISO JRC

National Renewable Energy Laboratory Laboratory of energy, ecology and economy / Ticino Solar Joint Research Centre

OE PV PVUSA PTC C 0 to, C 4 I sc

Outdoor exposure Photovoltaic Module Photovoltaic for Utility Scale Applications PVUSA test conditions Regressed coefficients Short circuit current Shape parameters

β i ,η i , γ i λ ρ Pdf Cdf 2.

Degradation rate Degradation fraction Probability density function Cumulative density function

Degradation Mechanism

The degradations observed in fielded systems are gathered into five categories that ultimately drive performance loss and possibly failure. These are: 1) degradation of packaging materials, 2) loss of adhesion, 3) degradation of cell/module interconnects, 4) degradation caused by moisture intrusion, and 5) degradation of the semiconductor device [4].Some of these mechanisms are developed as follows: 2.1

Semi-conductor degradation

Degradation of the semi-conductor material itself can contribute to performance loss in field-aged modules. Crystalline silicon modules now have a long track record of performance stability in the field. This stability, in part, is due to the stability of the semiconductor material used to make the cells. Package degradation can cause module performance failures, which can lead to system level issues like array performance failure, safety hazards, and/or failure of a supplemental function. It occurs when the laminate package is damaged or packaging materials degrade during normal service, affecting the function and/or integrity of the module. Examples of packaging degradation include glass breakage, dielectric breakdown, bypass diode failure, encapsulant discoloration, and backsheet cracking and/or delamination [5]. 2.2

Delamination

Module delamination, resulting from loss of adhesion between the encapsulant on other module layers, it is also a failure mechanism that needs to be addressed for manufacturers

Reliability and Cost Evaluation of PV Module subject to Degradation Processes

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to achieve 30-year product lifetimes. Most of the delamination observed in the field has occurred at the interface between the encapsulant and the front surface of the solar cells in the module [6]. A common observation has shown that delamination is more frequent and more severe in hot and humid climates, sometimes occurring after less than 5 years of exposure. Delamination causes a performance loss due to optical de-coupling of the encapsulant from the cells. Great concern from a module lifetime perspective is the likelihood that the void resulting from the delamination will provide a preferential location for moisture accumulation, greatly increasing the possibility of corrosion failures in metallic contacts [7]. 2.3

Interconnect degradation

Interconnect degradation in modules occurs when the joined cell-to-ribbon or ribbon-toribbon area changes in structure or geometry. Changes in solder-joint geometry caused by thermo-mechanical fatigue reduce the number of redundant solder-joints in a module causing decreased performance. These changes occur due to cracks that develop at high stress concentrations, such as voids and thread-like joints. 2.4

Moisture intrusion

Moisture permeation through the module backsheet or through edges of module laminates causes corrosion and increases leakage currents. Corrosion attacks cell metallization in modules and semiconductor layers in thin-film modules, causing loss of electrical performance. 3.

Data Analysis

Exhaustive studies of PV modules degradation have been reported in the past. For example, studies carried out by the NREL show module performance losses of 1-2% per year in systems tested over ten-year period and the LEEE-TISO has measured losses ranging from 0.7 and 8.2% respect nominal power after first 15 month of exposure. In general, these of investigations have been carried out with short amount of samples. LEEE-TISO, for instance, have measured power degradation on 98 c-Si modules between 0% and 5% after first exposure (initial degradation) with respect to the initial power and 1.2% during the first year. Data from a multi-crystalline module continuously exposed outdoors in open circuit configuration for eight years at Sandia laboratory shows about 0.5% per year performance loss [7]. The array was installed in March 1982, and a sample set of 18 modules were measured at JRC in October 1982. The average deviation of the measured power from the declared power was 3.9%. At this time, one cannot state that this percentage is due to photon degradation, but considering the outdoor exposure (OE) data it is possible to estimate 2.6% photon degradation and 1.3% deviation from declared power. Over the 19 years of operation, this would correspond to a compound equivalent degradation of 0.27% per annum excluding the initial degradation due to Photon effects. If we include photon degradation as constant factor we would have degradation rate of 0.4% per annum. This is less than reported for other sources, but may be attributed to the high level of maintenance and replacement of components as stated by Quintana [8]. The degradation rate for a PV array installed in 1991 indicates a degradation of 4.39% in 11 years or 0.4% per annum [9]. This degradation rate is inclusive of the initial photon degradation. As demonstrated above, initial degradation of 2.6 % in the initial power is

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typical for all silicon PV modules while the continuous degradation of the performance can typically reach 5.5% over the 20 year warranty lifetime [10]. A recent study at the National Renewable Energy Laboratory (NREL) suggests that performance of both single and multi-crystalline field aged modules degrades about 0.7% per year, primarily due to I sc losses caused by UV absorption around the top of the silicon surface [11]. Finally, data from the LEEE- TISO, CH-Testing Centre for Photovoltaic Modules reports power degradation rates on c-Si modules ranging from 0.7%-9.8% in the first year of exposure and 0.7% to 4.9% in the second year of exposure. 4.

Degradation Models of PV Module Performance

The degradation of a PV module is the case of the slow degradation model. 4.1

Wiener and Gamma Model

Degradation module can be modeled by different processes, for example by Wiener or gamma processes. Wiener process of the degradation is supposed to take place gradually over time in a sequence of tiny increments [12, 13]. It is used for modeling degradation processes where the degradation increases linearly in time with random noise. The rate of degradation is characterized by the drift coefficient. In general, a Wiener-process-based degradation model can be represented as (1) W (t ) = λt + σB(t ) where, λ is the drift coefficient, σ > 0 is the diffusion coefficient, and B (t ) is the standard Brownian motion representing the stochastic dynamics of the degradation process. The increments are noted ∆W (t ij ) where i=1…n is the degradation index and j=1…q i is the time index

Figure 1: Definition of Increased Degradation The Wiener process W (t ij ), t i , j > 0 has the following properties: -

W ( 0) = 0

-

Increments ∆W (t ij ) = W (t ij ) − W (t i ( j −1) )

In the case of linear degradation, ∆W (t ij ) follows a normal distribution with mean

m∆t ij and variance σ 2 ∆t ij . In the case of non-linear degradation, ∆W (t ij ) follows a


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normal distribution with mean m(t ij ) − m(t i ( j −1) ) and variance σ 2 ∆t ij . The Wiener process presented in this article allows to simulate degradation in path under normal conditions. The simulation of degradation path under accelerated conditions is possible using the accelerated failure time (AFT) model, which is defined as: W (t ij / X ) = W (r ( X )t ij ) (2) where, r ( X ) is the acceleration factor between known conditions X 0 (r ( X 0 ) = 1) and studied constant conditions X. Under accelerated conditions, increments ∆W (t ij ) follow a normal distribution N (m(r ( X )t ij ) − m(r ( X )t i ( j −1) )) , σ 2 r ( X )∆t ij and the probability density function is defined as:

 (X ij − (m(r ( X )t ij ) − m(r ( X )t i ( j −1) )) )2  f ( X ij ) = exp −  2πσ 2 .∆t ij σ 2π .∆t ij   1

(3)

In order for the stochastic degradation process to be monotone, we consider it to be a gamma process. A gamma process is a stochastic process with independent, non-negative increments having a Gamma distribution with an identical scale parameter. The gamma process with shape parameter v and scale parameter u is a continuous time stochastic process {X (t ), t ≥ 0} with the following properties:

X (0) = 0 with probability one; X (t ) has independent increments; X (t ) − X ( s ) ≈ G (v(t − s ), u ) For all t > s ≥ 0, where, G ( x v, u ) is the probability density function of a random variable X having a gamma distribution with shape parameter v and scale parameter u given by 1 G ( x v, u ) = x v −1 exp(− x u ) I ( 0,∞ ) ( x) v Γ(v)u 1 x ∈ (0, ∞) where, I ( 0,∞ ) ( x) =  0 x ∉ (0, ∞) -

∞

and

Γ(v) = ∫ x v −1e − x dx is the complete gamma function.

4.2

Output Power Degradation Model

0

By Using the Jet Propulsion Laboratory’s recommendation The power degradation D(t) corresponds to the power losses of a photovoltaic module versus the initial power [14], the degradation model of photovoltaic module output power is given by: D(t ) = 1 − exp(−b.t.a ) (4) where, a and b are degradation parameters. The main degradation mode for module is corrosion which is due to the influence of temperature and humidity. 4.3

Long Term Degradation Model

Field exposure of nearly 14 years shows a linear reduction in maximum power in crystalline silicon-based modules, occurring mainly through a reduction in fill factor.

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Exposure in hot and dry, and temperate climates indicates climate has little effect on the rate of degradation. Seasonal variations in the performance of different amorphous silicon modules have been determined using a solar simulator. The empirical model describing both seasonal and long term behavior is given by the following formula. P = C 0 − C1 . cos(2.π .(t / 365.25) + C 2 ) − C 3 log(t + C 4 ) (5) The a-Si modules show a logarithmic decrease in Pmax with an approximately sinusoidal seasonal variation [15]. 4.4

PVUSA Regression Model

The Photovoltaic for Utility Scale Applications (PVUSA) methodology was used to determine long-term degradation rates. In this methodology, as a first step, the maximum power in monthly intervals is normalized to PVUSA Test Conditions (PTC) by using the following equation: [16] P = E.(a1 + a 2 .E + a 3 .Tambient + a 4 .ws ) (6) where, P is the maximum DC power, E is the irradiance, T ambient is the ambient temperature, ws is the wind speed, and a 1 to a 4 are regression coefficients. 4.5

Mixed Weibull Degradation Model

A mixed distribution comprises two or more distributions. Mixture arises when the population of interest contains two or more non homogeneous subpopulations. Such cases occur frequently in practice. A common example is that a good subpopulation is mixed with a substandard subpopulation due to manufacturing process variation and material flaws. The substandard subpopulation fails in early time, but the good one survives considerably longer. In addition to the mixture of good and bad products, a manufacturing process fed with components from different suppliers usually produces non homogeneous subpopulations. The use condition, such as environmental stresses or usage rate, is also a factor contributing to the mixture of life distributions. A mixture of two distributions is usually of most interest. It is perhaps the most common mixed distribution in practice because of its inherent flexibility [17]. The pdf of the mixed Weibull distributions of two degradations processes f 1 (t ) and f 2 (t ) is: f (t ) = ρf 1 (t ) + (1 − ρ ) f 2 (t )

f (t ) = ρ

β1 η1 β1

(7)

  t  β2    t  β1  β 2 β 2 −1 β1 −1   + (1 − ρ ) β t exp −    exp −   t 2  η 2    η1   η 2    

λ (t ) =

β η

 x −γ   η

  

(8)

β −1

(9)

. The associated cdf is: F (t ) = ρF1 (t ) + (1 − ρ ) F2 (t )   t  β2    t  β1  F (t ) = 1 − exp −    + (1 − ρ ) exp −     η 2    η1      

(10) t >0

(11)


5.

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A Case Study

The loss on energy life of a degraded PV module varies between 1-3% in the first and the second year. After this period, the loss of the energy is estimated to 0.7/annum. The degradation of PV module is caused by two mechanisms. The first is the initial photon degradation associated to the first process where the function of the degradation performance is exponentially distributed (Weibull function with β = 1 ). However the second process is the continuous degradation and the function of the degradation performance follows the Weibull distribution ( β ≠ 1) . In this case we consider two degradation intervals; the first interval is between the time of installation to the second year (the importance of degradation rate), and the second is after this year. The degradation performance (energy loss) caused by the initial photon mechanism is modeled as exponential with degradation rate λ = 0.8 in the first interval of our study, and after this period the value of the degradation rate becomes λ = 0.13 . The degradation performance caused by continuous degradation mechanism follows Weibull distribution with, β 1 = 0.69,η1 = 189 in the first interval of two years, and β 2 = 0.61,η 2 = 190 in the rest of its life. Plot D(t) is the degradation function representing the increasing energy loss of a module and it represents the probability of degradation at the end of the warranty life. The Weibull parameters and degradation rate λ are obtained after analyses of data related to the energy loss in the period of life of the PV module (20 years). The degradation fraction or the mixture factor ρ represents the probability of the performance loss caused by the irradiance (photon degradation), its value is obtained after data analysis. The degradation model of photovoltaic module developed in our case is given as follows: β1     D(t ) = 1 − 0.418 exp(−λ1t ) − 0.582 exp −  t   t ≤ 2 years   η1       (12)   t  β2     λ ( ) 1 0 . 418 exp( ) 0 . 582 exp 2 D t t t years = − − − − >    2  η 2         t  0.69   D (t ) = 1 − 0.418 exp(−0.8t ) − 0.582 exp −   t ≤ 2 years    189    0.61   t   D (t ) = 1 − 0.418 exp(−0.13t ) − 0.582 exp −     t > 2 years    190   

(13)

To see the effects of the initial photon degradation and the long term continuous degradation on the energy life, we have assumed the following criteria: • Pmax initial 100W, • Module life-time 20 years, • Solar irradiance input 1095kWh per annum, • Price of energy produced by PV system which costs 6.00Euro/Wp for a module with the lifetime of 20 years is estimated to 0.58Euro/kWh.

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Figure 2: Lifetime Energy Loss versus Time (in years)

The energy life of the module is thus the sum of annual production per year minus the degradation losses. A perfectly none degrading 100W’s module would then have a 20year energy life of 2.19MWh.In figure 2; the annual loss of energy life with percentage is shown, where the loss of the energy decrease considerably in the two first years to achieve the value of 0.57% in the twentieth year of its life.

Figure 3: Cumulative Loss of Energy Life (%) versus Time (in years)

Figure 4: Cumulative Loss of Energy (kWh) versus Time (in years)

Figure 5: Annual Cost of Energy Loss versus Time (in years)

Figure 6: Total Cost of Energy Loss versus Time (in years)

The value of the annual cumulative loss of energy with the percentage and kilowatt hour (kWh), are presented in the figures 3 and 4 respectively. After analyzing the obtained results, the loss of the energy attains the value of 242 kWh for one module, and it will represent a very important loss for the huge installation of solar energy. The effect of


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initial photon degradation and the long term continuous degradation on the cost of loss energy is given in figures 5 and 6, representing respectively; the annual cost of energy loss and the total cost of energy loss. This latter is evaluated to 141 Euros per one PV module and it is considered very representative compared with the price of the module itself. Finally, the reliability of the PV module is given by the following formula: R(t ) = 1 − D(t ) (14) Its function is represented in the figure 7.

Figure 7: Reliability Function versus Time (in years) The reliability of the photovoltaic module studied in our case achieves the value of 0.79 after 50 years of functioning, where it decreases considerably in the first ten years. 6.

Conclusion

The combination of failure mechanism studies and the reliability evaluation are pertinent to define the residual life of the components, and it is of great interest in the case of photovoltaic system. This latter is the heart of electricity production of the future. It is important to achieve the goal of electricity sustainability and it is adequate to the case of Algeria, where it is considered as a most sunny country. The novelty introduced in this paper was the consideration of mixed Weibull distribution in reliability data analysis where the results are more realistic compared to the case using conventional distribution, such as: Weibull, exponential and normal ones. Particularly, in this present work we have developed a degradation model that predicts PV module reliability based on field degradation data. The results of this study indicate that PV module design would guarantee 89% power after 20 years of life and moreover there is visible evidence that this degradation or the energy loss are increasing with time. Considering the calculations made in end life energy generation, these losses can amount to 11% or on term of energy it is estimated to 242 kWh in its warranty life estimated around 20 years. Also, cost of energy loss is evaluated to be 141 Euro. The obtained results allow to the decision maker to reach better information that reduces the performances of the system and practicing suitable maintenance actions (intervals of maintenance actions). References [1]

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For biographies of the authors, please refer to page 505 of IJPE, Vol.9, No. 5, September 2013.