**2. Different outdoor methodologies currently adopted**

#### **2.1 The concept of average photon energy**

In trying to quantify the 'blueness' or 'redness' of outdoor spectrum, Christian *et. al*. adopted the concept of Average Photon Energy (APE) as an alternative (Christian et al., 2002). He defined APE as a measure of the average hue of incident radiation which is calculated using the spectral irradiance data divided by the integrated photon flux density, as in equation 1.

$$APE = \frac{\int\_{a}^{b} E\_i(\lambda)d\lambda}{\int\_{a}^{b} \Phi\_i(\lambda)d\lambda} \tag{1}$$

where : qe = electronic charge Ei(λ) = Spectral irradiance i(λ) = Photon flux density

As an indication of the spectral content, high values of average APE indicate a blue-shifted spectrum, whilst low values correspond to red shifted spectrum. Although this concept at

Spectral Effects on CIS Modules While Deployed Outdoors 443

The spectral factor quantifies the degree of how the solar spectrum matches the cell spectral

With regard to changes in the device parameters, the concept of Useful Fraction used by Gottschalg et al (Gottschalg et al., 2003) clearly demonstrates the effect of varying outdoor spectrum. Useful fraction is defined as the ratio of the irradiance within the spectrally useful

0

<sup>1</sup> ( )( ) *Eg UF G S d G*

Where Eg is the band-gap of the device (normally the cut - off wavelength) and G is the total

0 () () *cut off G Gd* 

Before the CIS module was deployed outdoors, the module underwent a series of testing procedures in order to establish the baseline characteristics. Visual inspection was adopted to check for some physical defects e.g. cracks, and incomplete scribes due to manufacturing errors. Infrared thermography revealed that no hot spots were present before and after outdoor exposure. These procedures were used to isolate the spectral effects with respect to the performance parameters of the module. To establish the seasonal effects on the module's *I-V* curves, three *I-V* curves were selected. One *I-V* curve for a winter season and the 2nd *I-V* curve for summer season were measured. The 3rd *I-V* curve was used to establish whether the module did not degrade when the winter curve was measured. All curves were measured at noon on clear days so that the effect of cloud cover would be negligible. For accurate comparison purposes all *I-V* curves had to be normalized to STC conditions so that the variations in irradiance and temperature would be corrected. Firstly the Isc values were

> mod 100 25 *sc sc ule <sup>I</sup> I T*

(7)

*G*

where *G(λ)* is the spectral irradiance encountered by a PV cell.

STC corrected by using equation 1 (Gottschalg et al., 2005).

where *α* is the module temperature coefficient [A/oC].

  

 

  

(4)

(5)

(6)

2

1 () () *STC STC t I E Rd*

where: *E(λ*) = Irradiance as function of wavelength

response at any given time as compared to the AM1.5 spectrum.

 *ESTC(λ)* = Irradiance at STC *R(λ) =* Reflectivity

**2.4 The useful fraction concept** 

irradiance determined as:

range of the device to the total irradiance.

**3. Methodology used in this study** 

first approximation characterizes the spectral content at a particular time-of-the day, no direct feedback of the device information is obtained since it is independent of the device. The concept of Average Photon Energy (APE) has also been adopted to illustrate the seasonal variation of PV devices (Minemoto et al., 2002; Christian et al., 2002).

#### **2.2 The Air Mass concept**

The mostly commonly adopted procedure (Meyer, 2002; King et al., 1997) is to calculate the Air Mass (AM) value at a specific location and relate the module's electrical parameters. It is standard procedure for PV manufacturers to rate the module's power at a specific spectral condition, AM 1.5 which is intended to be representative of most indoor laboratories and is not a typical spectral condition of most outdoor sites. The question that one has to ask is, why then is AM 1.5 spectrum not ideal? What conditions were optimized in the modeling of AM 1.5 spectra? What are the cost implications on the customer's side when the PV module is finally deployed at spectra different from AM 1.5?

The modeled AM 1.5 spectrum commonly used for PV module rating was created using a radiative transfer model called BRITE (Riordan et al., 1990). The modeled conditions used for example the sun-facing angle, tilted 37o from the horizontal, was chosen as average latitude for the United States of America. The 1.42 cm of precipitable water vapor and 0.34 cm of ozone in a vertical column from sea level are all gathered from USA data. Ground reflectance was fixed at 0.2, a typical value for dry and bare soil. In principle this spectra is a typical USA spectrum and therefore makes sense to rate PV modules which are to be deployed in USA and the surrounding countries.

AM is simply defined as the ratio of atmospheric mass in the actual observer - sun path to the mass that would exist if the sun was directly overhead at sea level using standard barometric pressure (Meyer, 2002). Although the concept of AM is a good approximation tool for quantifying the degree of 'redness' or 'blueness' of the spectrum, the major draw back is that it is applied under specific weather conditions, i.e., clear sky, which probably is suitable for deserts conditions.

#### **2.3 The spectral factor concept**

Another notion also adopted to evaluate the effect of outdoor spectrum, is the concept of Spectral Factor. As described by Poissant (Poissant et al., 2006), Spectral Factor is defined as a coefficient of the short-circuit current (Isc) at the current spectrum to the short-circuit current at STC (ISTC).

$$m\_{\text{at}} = \frac{I\_{sc}}{I\_{\text{STC}}} \cdot \frac{I\_{\text{STC}}(\lambda)d\lambda}{\int\_{\lambda\_1}^{\lambda\_2} E(\lambda)d\lambda} \tag{2}$$

From equation 2, the Isc and the ISTC is obtained using the equation 3 and 4 respectively.

$$I\_{sc} = \int\_{\mathcal{X}\_1}^{\mathcal{X}\_2} E(\mathcal{X}) R\_{\mathcal{I}}(\mathcal{X}) d\mathcal{X} \tag{3}$$

$$I\_{\rm STC} = \bigwedge\_{\lambda\_1}^{\lambda\_2} E\_{\rm STC}(\mathcal{A}) R\_{\rm t}(\mathcal{A}) d\mathcal{A} \tag{4}$$

first approximation characterizes the spectral content at a particular time-of-the day, no direct feedback of the device information is obtained since it is independent of the device. The concept of Average Photon Energy (APE) has also been adopted to illustrate the

The mostly commonly adopted procedure (Meyer, 2002; King et al., 1997) is to calculate the Air Mass (AM) value at a specific location and relate the module's electrical parameters. It is standard procedure for PV manufacturers to rate the module's power at a specific spectral condition, AM 1.5 which is intended to be representative of most indoor laboratories and is not a typical spectral condition of most outdoor sites. The question that one has to ask is, why then is AM 1.5 spectrum not ideal? What conditions were optimized in the modeling of AM 1.5 spectra? What are the cost implications on the customer's side when the PV

The modeled AM 1.5 spectrum commonly used for PV module rating was created using a radiative transfer model called BRITE (Riordan et al., 1990). The modeled conditions used for example the sun-facing angle, tilted 37o from the horizontal, was chosen as average latitude for the United States of America. The 1.42 cm of precipitable water vapor and 0.34 cm of ozone in a vertical column from sea level are all gathered from USA data. Ground reflectance was fixed at 0.2, a typical value for dry and bare soil. In principle this spectra is a typical USA spectrum and therefore makes sense to rate PV modules which are to be

AM is simply defined as the ratio of atmospheric mass in the actual observer - sun path to the mass that would exist if the sun was directly overhead at sea level using standard barometric pressure (Meyer, 2002). Although the concept of AM is a good approximation tool for quantifying the degree of 'redness' or 'blueness' of the spectrum, the major draw back is that it is applied under specific weather conditions, i.e., clear sky, which probably is

Another notion also adopted to evaluate the effect of outdoor spectrum, is the concept of Spectral Factor. As described by Poissant (Poissant et al., 2006), Spectral Factor is defined as a coefficient of the short-circuit current (Isc) at the current spectrum to the short-circuit

2

( )

 

(2)

(3)

*E d*

( )

 

 

*E d*

*STC*

1 2

.

From equation 2, the Isc and the ISTC is obtained using the equation 3 and 4 respectively.

2

1 () () *sc <sup>t</sup> I ER d* 

*sc <sup>t</sup> STC*

*I*

*m*

*I*

1

seasonal variation of PV devices (Minemoto et al., 2002; Christian et al., 2002).

module is finally deployed at spectra different from AM 1.5?

deployed in USA and the surrounding countries.

suitable for deserts conditions.

current at STC (ISTC).

**2.3 The spectral factor concept** 

**2.2 The Air Mass concept** 

where: *E(λ*) = Irradiance as function of wavelength *ESTC(λ)* = Irradiance at STC *R(λ) =* Reflectivity

The spectral factor quantifies the degree of how the solar spectrum matches the cell spectral response at any given time as compared to the AM1.5 spectrum.

#### **2.4 The useful fraction concept**

With regard to changes in the device parameters, the concept of Useful Fraction used by Gottschalg et al (Gottschalg et al., 2003) clearly demonstrates the effect of varying outdoor spectrum. Useful fraction is defined as the ratio of the irradiance within the spectrally useful range of the device to the total irradiance.

$$
\hbar LF = \frac{1}{G} \int\_0^{E\_\sharp} G(\lambda) S(\lambda) d\lambda \tag{5}
$$

Where Eg is the band-gap of the device (normally the cut - off wavelength) and G is the total irradiance determined as:

$$\mathbf{G}(\lambda) = \int\_0^{\lambda\_{\text{int}}} \mathbf{G}(\lambda) d\lambda \tag{6}$$

where *G(λ)* is the spectral irradiance encountered by a PV cell.

#### **3. Methodology used in this study**

Before the CIS module was deployed outdoors, the module underwent a series of testing procedures in order to establish the baseline characteristics. Visual inspection was adopted to check for some physical defects e.g. cracks, and incomplete scribes due to manufacturing errors. Infrared thermography revealed that no hot spots were present before and after outdoor exposure. These procedures were used to isolate the spectral effects with respect to the performance parameters of the module. To establish the seasonal effects on the module's *I-V* curves, three *I-V* curves were selected. One *I-V* curve for a winter season and the 2nd *I-V* curve for summer season were measured. The 3rd *I-V* curve was used to establish whether the module did not degrade when the winter curve was measured. All curves were measured at noon on clear days so that the effect of cloud cover would be negligible. For accurate comparison purposes all *I-V* curves had to be normalized to STC conditions so that the variations in irradiance and temperature would be corrected. Firstly the Isc values were STC corrected by using equation 1 (Gottschalg et al., 2005).

$$I\_{sc} = \left(\frac{I\_{sc}}{G} \times 100\right) + \left(25 - T\_{\text{mod }ule}\right) \times a \tag{7}$$

where *α* is the module temperature coefficient [A/oC].

Spectral Effects on CIS Modules While Deployed Outdoors 445

3rd parameter Gaussian distribution function was used to describe the distribution pattern and to accurately determine the variance of points from the peak value (central value). The peaks of the Gaussian distribution was obtained by firstly creating frequency bins for the WUF and determine the frequency of the points in each bin expressed as a percentage. The bins were imported into SigmaPlot 10 and the peak 3rd Gaussian distribution function was used to accurately generate the peak WUF. Figure 1 illustrates the frequency distribution

bins for a-Si:H module.

0

during the study period.

Weighted Useful Fraction.

0.653

where: a = highest frequency x = WUF value

 xo = WUF centre value b = deviation (2)

0.658

Fig. 1. Frequency distribution of WUF for a-Si:H module

obtained using the peak Gaussian distribution of the form:

0.663

0.668

0.673

0.678

Evident from figure 1 is an increase in WUF frequency at specific WUF value. This percentage frequency represents the number of data points measured at a specific WUF

The centre of the points, which corresponds to the spectrum the device "prefers" most, was

Figure 2 illustrates a typical Gaussian distribution used to accurately determine the mean

Also illustrated is the width of the distribution as measured by the standard deviation or variance (standard deviation squared = 2). In order to interpret the results generated from each Gaussian distribution, two main terminologies had to be fully understood so that the results have a physical meaning and not just a statistical meaning. The standard deviation () quantifies the degree of data scatter from one another, usually it is from the mean value.

**WUF Bins**

0.683

0.688

0.693

<sup>2</sup> exp 0.5 / *<sup>o</sup> f a xx b* (11)

0.698

0.703

0.708

20

40

60

**Frequency (%)**

80

100

Each point on the *I-V* curve had to be adjusted according to equation 8.

$$I\_2 = I\_1 + I\_{sc} \times \left[ \left( \frac{1000}{G} \right) - 1 \right] + \alpha \left( 25 - T\_{\text{mod } ulle} \right) \tag{8}$$

where: *I1* = measured current at any point *I2* = new corrected current *G* = measured irradiance

The corresponding voltage points were also corrected according to equation 9.

$$V\_2 = V\_1 - R\_s \times \left(I\_2 - I\_1\right) + \beta \times \left(25 - T\_{\text{mod }ule}\right) \tag{9}$$

$$\begin{array}{lclcl}\text{where:} & V\_{\text{I}} & = & \text{measured voltage at a corresponding point for } l\_{\text{I}}\\ R\_{\text{s}} & = & \text{internal series resistance of the module [2]}\\ \beta & = & \text{voltage temperature coefficient of the module [V/c\$C]}\\ V\_{\text{2}} & = & \text{new corrected voltage}\end{array}$$

The outdoor spectrum was also measured for winter and summer periods in order to compare them for possible changes in the quality of the two spectra (figure 5). With regard to changes in the device parameters, the concept of Weighted Useful Fraction (WUF) (Simon and Meyer, 2008; Simon and Meyer, 2010) was used to clearly demonstrate the effect of varying outdoor spectrum. This concept was developed due to some limitations noted with other outdoor spectral characterization techniques (Christian et al., 2002).

The methodology used by Gottschalg et al (Gottschalg et al, 2002) makes use the assumption that the energy density (W/m2/nm) within the spectral range of the device at a specific wavelength is totally absorbed (100%). But in reality the energy density at a specific wavelength has a specific absorption percentage, which should be considered when determining the spectral response within the device range. It was therefore necessary to introduce what is referred to as the Weighted Useful Fraction (WUF) (Simon and Meyer, 2008; Simon and Meyer, 2010).

$$\text{WLIF} = \frac{1}{\text{Gtot}} \int\_0^{E\_\chi} G(\lambda) d(\lambda) \text{SR}(\lambda) \tag{10}$$

where: *G(λ)* is the integrated energy density within device spectral range with its corresponding absorption percentage evaluated at each wavelength.

As a quick example, at 350 nm for a-Si device, its corresponding energy density (W/m2/nm) is 20% of the irradiance (W/m2) received which contribute to the electron-hole (e-h) creation and for mc-Si at the same wavelength, 60% is used to create e-h pairs. But the concept of Useful Fraction considers that at each wavelength, all the energy received contributes to the e-h, which is one of the short comings observed from this methodology. The idea of using Weighted Useful Faction was to address these short falls which tend to over estimate the overall device spectral response.

The data obtained using the concept of Weighted Useful Fraction represents a statistical phenomenon of occurrences. Therefore the Gaussian distribution as a statistical tool was used to interpret the data simply because of a mathematical relationship (Central Limit Theorem). In this case the theorem holds because the sample is large (major condition of the theorem) and therefore the Gaussian distribution is suitable to be applied. In this study, the 3rd parameter Gaussian distribution function was used to describe the distribution pattern and to accurately determine the variance of points from the peak value (central value). The peaks of the Gaussian distribution was obtained by firstly creating frequency bins for the WUF and determine the frequency of the points in each bin expressed as a percentage. The bins were imported into SigmaPlot 10 and the peak 3rd Gaussian distribution function was used to accurately generate the peak WUF. Figure 1 illustrates the frequency distribution bins for a-Si:H module.

Fig. 1. Frequency distribution of WUF for a-Si:H module

Evident from figure 1 is an increase in WUF frequency at specific WUF value. This percentage frequency represents the number of data points measured at a specific WUF during the study period.

The centre of the points, which corresponds to the spectrum the device "prefers" most, was obtained using the peak Gaussian distribution of the form:

$$f = a \exp\left[-0.5\left(\left(x - x\_o\right)/b\right)^2\right] \tag{11}$$

444 Solar Cells – Thin-Film Technologies

 2 1 mod <sup>1000</sup> 1 25 *sc ule III <sup>T</sup> G*

The corresponding voltage points were also corrected according to equation 9.

other outdoor spectral characterization techniques (Christian et al., 2002).

corresponding absorption percentage evaluated at each wavelength.

*VVR I I T* 2 1 *<sup>s</sup>* 2 1

where: *V1* = measured voltage at a corresponding point for *I1 Rs* = internal series resistance of the module [Ω]

*β* = voltage temperature coefficient of the module [V/oC]

The outdoor spectrum was also measured for winter and summer periods in order to compare them for possible changes in the quality of the two spectra (figure 5). With regard to changes in the device parameters, the concept of Weighted Useful Fraction (WUF) (Simon and Meyer, 2008; Simon and Meyer, 2010) was used to clearly demonstrate the effect of varying outdoor spectrum. This concept was developed due to some limitations noted with

The methodology used by Gottschalg et al (Gottschalg et al, 2002) makes use the assumption that the energy density (W/m2/nm) within the spectral range of the device at a specific wavelength is totally absorbed (100%). But in reality the energy density at a specific wavelength has a specific absorption percentage, which should be considered when determining the spectral response within the device range. It was therefore necessary to introduce what is referred to as the Weighted Useful Fraction (WUF) (Simon and Meyer,

 

(10)

<sup>1</sup> ( )

0

where: *G(λ)* is the integrated energy density within device spectral range with its

As a quick example, at 350 nm for a-Si device, its corresponding energy density (W/m2/nm) is 20% of the irradiance (W/m2) received which contribute to the electron-hole (e-h) creation and for mc-Si at the same wavelength, 60% is used to create e-h pairs. But the concept of Useful Fraction considers that at each wavelength, all the energy received contributes to the e-h, which is one of the short comings observed from this methodology. The idea of using Weighted Useful Faction was to address these short falls which tend to over estimate the

The data obtained using the concept of Weighted Useful Fraction represents a statistical phenomenon of occurrences. Therefore the Gaussian distribution as a statistical tool was used to interpret the data simply because of a mathematical relationship (Central Limit Theorem). In this case the theorem holds because the sample is large (major condition of the theorem) and therefore the Gaussian distribution is suitable to be applied. In this study, the

*Eg WUF G d SR Gtot*

(8)

25 mod*ule* (9)

Each point on the *I-V* curve had to be adjusted according to equation 8.

where: *I1* = measured current at any point

 *I2* = new corrected current *G* = measured irradiance

*V2 =* new corrected voltage

2008; Simon and Meyer, 2010).

overall device spectral response.

where: a = highest frequency x = WUF value xo = WUF centre value b = deviation (2)

Figure 2 illustrates a typical Gaussian distribution used to accurately determine the mean Weighted Useful Fraction.

Also illustrated is the width of the distribution as measured by the standard deviation or variance (standard deviation squared = 2). In order to interpret the results generated from each Gaussian distribution, two main terminologies had to be fully understood so that the results have a physical meaning and not just a statistical meaning. The standard deviation () quantifies the degree of data scatter from one another, usually it is from the mean value.

Spectral Effects on CIS Modules While Deployed Outdoors 447

Fraction (WUF), from which the predominant effect of the spectrum can be observed and analyzed. Due to a large number of data obtained, all results analyses were made using only data corresponding to global irradiance (Gglobal) > 100 W/m2. This was done to reduce

Although the outdoor parameters might 'mimic' the STC conditions, the performance of the PV device will not perform to that expectation. By analyzing the effect of outdoor environment, the spectrum received is largely influenced by solar altitude and atmospheric

Figure 3 illustrates the seasonal effects on the CIS module current-voltage *(I-V)*  characteristics when deployed outdoor, first on 31 January 2008 and later on 12 June 2008.

Fig. 3. Comparison of the CIS I-V characteristics for a typical summer clear sky and winter

0 5 10 15 20 25 **Voltage (V)**

**C) Day Time Isc (A) Pmax (W) WUF Average**

The January *I-V* curve was taken a few days after deployment of the modules while operating at outdoor conditions. Two aspects needed to be verified with this comparative analysis of the I-V curves for that time frame: Firstly the state of the module, i.e. whether it did not degrade within this time frame needed to be ascertained so that any effect on device Isc, FF and efficiency would be purely attributed to spectral effects. Secondly, this was done to see the effect of seasonal changes on the *I-V* characteristics. Since the outdoor conditions are almost the same when the measurements were taken, the I-V curves were normalized to STC conditions using the procedure mentioned in section 2. Since the 3 *I-V* curves had been corrected for both temperature and irradiance, therefore any

clear sky. The accompanying table lists the conditions before corrections to STC.

January 1049.73 41 12h30 3.08 43.8 0.977 June 1029.44 42 12h30 2.56 38.2 0.962 **% difference 1.9 2.4 - 17 13 1.5** 

*SpectralRange o device C C T f WUF* versus the Weighted Useful

January June December

aspect is to plot <sup>1</sup> ( )

scatter without compromising the validity of the results

composition, which in turn affect device performance.

**Gglobal (W/m2**

**) Tmodule (<sup>o</sup>**

**4. Results and discussion** 

Isc = 17%

0.0

0.5

1.0

1.5

2.0

**Current (A)**

2.5

3.0

3.5

In simple statistics, the data represented by the Gaussian distribution implies that 68% of the values (on either side) lie within the 1st standard deviation (1) and 95% of the values lie within the 2nd standard deviation. The confidence interval level was also analyzed when determining the mean value. The confidence interval quantifies the precision of the mean, which was vital in this analysis since the mean represents the WUF spectrum from which the devices responds best during the entire period of outdoor exposure. The increase in standard deviation means that the device spends less time on the corresponding WUF spectrum. Ideally it represents the error margin from the mean value. The percentage frequency value corresponding to the mean WUF value represents the percentage of the total time of outdoor exposure to which the device was responding best to that spectrum.

Fig. 2. Illustration of Gaussian distribution used to determine the mean WUF.

Depending on how the data is distributed, the Gaussian curve 'tails' differently from each side of the mean value. The increase in in this case reveals two crucial points regarding the statistical data in question. Firstly, it quantifies the total time spent at a specific spectrum as the increases during the entire period of monitoring. Secondly it reveals the entire spectral range to which PV devices respond. From figure 2, the standard deviation increases from 1 to 8 on one side of the mean WUF and from the other side varies from 1 to 3. The total range of the WUF is from 0.64 to 0.7 although it spends less time from spectral range where standard deviation is greater than a unit. A high confidence level of each Gaussian distribution indicates the accuracy of the determined mean. All results presented in this work showed a high confidence level.

Normalization of Isc was achieved by dividing the module's Isc with the total irradiance within the device spectral range (GSpectral Range). The commonly adopted correlation existing between the module's Isc and back-of-module temperature is of the form *sc* 0 1 *device S pectralRange I C CT G* (Gottschalg et al., 2004). Firstly, the relationship between *sc SpectralRange I <sup>G</sup>* (which is referred to as *SpectralRange* from this point onwards) is plotted against back-of-module temperature. The empirical coefficient C0 and C1 are obtained. The second aspect is to plot <sup>1</sup> ( ) *SpectralRange o device C C T f WUF* versus the Weighted Useful Fraction (WUF), from which the predominant effect of the spectrum can be observed and analyzed. Due to a large number of data obtained, all results analyses were made using only data corresponding to global irradiance (Gglobal) > 100 W/m2. This was done to reduce scatter without compromising the validity of the results
