The solar spectrum, which is also could be described by air mass factor, has a significant relationship with the performance of photovoltaic modules. The air mass dependence has been investigated by a theoretical method as well as an actual case of three different photovoltaic arrays: polycrystalline silicon, amorphous silicon and cadmium telluride, at the EUIT Agrícola-UPM (Madrid, Spain, 40.4426oN, 3.7295oW). The calculating results show that: AM dependence of poly-Si array is positive because an elevating AM-value indicates a red shift and poly-Si module is more red sensitive; On the contrary, as a-Si module and CdTe module are more blue sensitive, their AM dependences are negative. Furthermore, the outdoor AM dependences of three arrays are corresponding to the calculating results although the thermal annealing effect could be superimposed on spectral effect in the case of a-Si. Keywords: PV system, spectral response, polycrystalline silicon, a-Si, CdT

Alonso Garcia, M. Carmen

Moreda Cantero, Guillermo P.

Muñoz Garcia, Miguel Angel

Wang, Huaxin

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Analysis of air mass dependence of three photovoltaic arrays

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

ANALYSIS OF AIR MASS DEPENDENCE OF THREE PHOTOVOLTAIC ARRAYS 
 
 
 
Huaxin Wang1, M.A. Muñoz1, G.P. Moreda1, M.C. Alonso-García2 
1 Dep. Agrororestry Engineering. LPF-TAGRALIA. ETSIAAB, UPM 
Avda. Complutense, s/n, 28040 Madrid, Spain 
miguelangel.munoz@upm.es Phone: +34 913365458; Fax: +34 913365406 
2 Photovoltaic Laboratory, Renewable Energy, CIEMAT 
Avda. Complutense, 22, 28040 Madrid, Spain 
 
 
 
ABSTRACT: The solar spectrum, which is also could be described by air mass factor, has a significant relationship 
with the performance of photovoltaic modules. The air mass dependence has been investigated by a theoretical 
method as well as an actual case of three different photovoltaic arrays: polycrystalline silicon, amorphous silicon and 
cadmium telluride, at the EUIT Agrícola-UPM (Madrid, Spain, 40.4426oN, 3.7295oW). The calculating results show 
that: AM dependence of poly-Si array is positive because an elevating AM-value indicates a red shift and poly-Si 
module is more red sensitive; On the contrary, as a-Si module and CdTe module are more blue sensitive, their AM 
dependences are negative. Furthermore, the outdoor AM dependences of three arrays are corresponding to the 
calculating results although the thermal annealing effect could be superimposed on spectral effect in the case of a-Si.  
Keywords: PV system, spectral response, polycrystalline silicon, a-Si, CdTe 
 
 
1 INTRODUCTION AND OBJECTIVS  
 
In outdoor conditions, the two main meteorological 
issues affecting the electricity production of a PV module 
are the irradiance and ambient temperature. Besides, 
seasonal variation in solar spectrum contributes to the 
seasonal changed irradiance. Therefore, seasonal 
variation in PV module´s output could be influenced by 
the overlap of thermal effects and spectral changes [1–5]. 
Since different semi-conductor materials have different 
band gaps, they vary in response to radiation of different 
wavelengths, thus vary from each other both in efficiency 
and spectral response.  On the other hand, the spectral 
components of solar radiation also have a seasonal 
change: they are blue-rich in summer and red-rich in 
winter respectively [6]. Commonly, solar spectral 
irradiance distribution can be characterized by three 
approaches: average photon energy [1], useful fraction 
[7], and air mass (AM) [8], which is the path-length 
through the atmosphere and used in this study. 
In this study, the theoretical and the outdoor AM 
dependences of three different arrays: polycrystalline 
silicon (poly-Si), amorphous silicon (a-Si) and cadmium 
telluride (CdTe) are investigated. 
 
 
2 MATERIALS AND METHODS 
 
2.1 Air mass 
The term ´´air mass´´, which is obtained through 
geometrical consideration, describes the relative path 
length that the sun’s rays traverse through the 
atmosphere. It can be a specific substitute in the absence 
of experimental spectral measurements on solar 
irradiance, although it is without the consideration of the 
vapor, turbidity and air pollution. The simplest formula 
(1) for calculating the pressure corrected AM [8] is just 
related to the position of the sun in the sky and the site 
altitude. Complex mathematical expressions of the AM 
provided by [8] and (Gueymard 1995) show no 
difference between equation (2) at zenith angles less than 
80o [10]. 
                       (1)                                                       
                  (2)                                                 
Zs: sun´s zenith angle, calculated based on [11] 
Where:  
P: local air pressure; 
P0: sea level air pressure; 
h: altitude, 650m of Madrid; 
 
 The solar spectral irradiance data shown in Figure 1 
were simulated by the application of SMARTS (Simple 
Model of Atmospheric Radiative Transfer of Sunshine) 
developed by Gueymard. The normalized spectral 
responses of different technologies were provided by the 
accredited independent laboratory (CIEMAT-DER, 
Madrid). 
 
 
2.2 Theoretical mathematical model: 
 The short circuit density of the three PV technologies 
could be calculated by: 
                                 (3) 
Jsc: short circuit current density of the test module; 
: spectral irradiance of the sunlight at 
different AM values; 
: spectral response of the test module; 
 
 
3 RESULTS AND DISCUSSIONS 
 
3.1 Calculating results 
The calculating results based on equation (3) and 
Figure1, are demonstrated in Figure 2 and 3. 
Figure 2 is simulating the results obtained from a 
pyranometer. In this case, the AM dependence of poly-Si 
is positive, whereas the Isc of a-Si and CdTe would 
decrease with the rising AM values. 
 Figure 3 is simulating the results obtained from a c-Si 
based irradiance sensor. Consequently, there is no AM 
dependence in the Isc of poly-Si. However, the Isc of a-Si 
and CdTe decline faster with the rising AM value.     
 
 
Figure 1: Simulated solar spectrum and spectral response 
of different technologies. 
 
 
Figure 2. Calculating results of three technologies as the 
irradiance sensor is a pyranometer.  
 
 
Figure 3. Calculating results of three technologies as the 
irradiance sensor is a c-Si based sensor. 
 
 
3.2 Outdoor results 
As pre-mentioned, AM is calculated by a 
geographical consideration and fails to contain the 
weather information, which also affects the spectral 
distribution. Thus a pre-clarification about the weather 
condition or a uniform weather condition should be 
decided. All the data shown in Figure 4 was collected 
under clear-sky condition and then corrected and 
normalized: 
 
 Clear-sky condition: the variation of the 
irradiance is less than 10% from the maximum 
value to the minimum value recorded during 
the 15-min recording interval; 
 Irradiance range: the reason of choosing the 
irradiance level at 700W/m2 is inverter clipping 
happens occasionally once the irradiance is 
beyond 800W/m2,  subsequently the Pmp 
would be affected; 
 Correction and normalization: the maximum 
power was linearly corrected to the condition 
(G=1000W/m2, Tc=25oC) using the maximum 
power (Pmp) temperature coefficient provided 
by the manufacturers, and then divided by the 
linear fitted value at AM1.5. 
Figure 4 shows the AM-dependence of the Pmp of 
the three arrays from December 2014 to December 2015. 
The higher AM values indicate the solar spectrum 
tending towards the redder or longer wavelength. 
As depicted in Figure 4, in both the irradiance ranges, 
the AM-dependence of Pmp for poly-Si, CdTe and a-Si 
arrays increased successively. The regression line parallel 
to x-axis in Figure 4a indicates no clear AM-dependence 
of Pmp generated by the poly-Si array, owing to a c-Si 
based reference irradiance sensor and the determinate 
irradiance range. The AM-dependence of Pmp for a-Si 
and CdTe arrays is stronger, suffering a decreasing trend 
for higher AM values (red-shift). The gradient of the 
applied linear least square fit can also provide 
information about the AM-dependence. Comparing the 
two irradiance ranges, the AM-dependence of Pmp 
follow the same pattern for each array. Pmp for a-Si array 
varies at a higher rate 11.22% compared to the 4% 
variation of the CdTe array´s Pmp, due to the narrower 
and more blue-sensitive spectrum response. Note that 
these AM-dependences for a-Si and CdTe are based on a 
c-Si irradiance sensor. Furthermore, as is shown in Figure 
4c, the notable gap between the Pmp gathered from two 
periods, i.e. Apr.2015 –Jun.2015 and Jun.2015 – 
Sep.2015, suggests there are some other factors 
contributing to the seasonal variation of a-Si, besides the 
changeful AM. It will be explained by thermal annealing 
effect and light soaking effect. 
  
 
4 CONCLUSION  
 
• No detective air mass (AM) dependence of 
poly-Si array has been found owing to the 
application of c-Si based irradiance sensor, 
whereas the calculating result shows that poly-
Si has a positive AM dependence; 
• a-Si has the highest AM dependence among the 
three technologies, although there is an overlap 
of thermal annealing effect and spectral effect 
in a-Si array; 
• AM dependence of CdTe array is lower 
compared to the value of a-Si array, due to the 
more red-sensitive spectrum response. 
 
 
ACKNOWLEDGEMENTS 
 
We want to acknowledge the LPF-TAGRACIA research 
group of Technical University of Madrid (UPM) for the 
funding of the project and to CIEMAT for their 
cooperation. Also we want to acknowledge the financial 
support from the program of China Scholarships Council 
(CSC). 
 
Figure 4. Seasonally classified maximum power 
dependence on AM-units for the poly-Si (a), a-Si (b) and 
CdTe (c) array under clear-sky condition. 
 
 
 
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Analysis of air mass dependence of three photovoltaic arrays

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