International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
Location based optimization of
Photovoltaic cell due to non-uniform
radiation
E. Mukherjee 1, S.P.Duttagupta 2 and S. Sengupta 3
1
Dept. of Electronics & Telecommunication, VESIT, Mumbai, India
emailelina@gmail.com
2
Dept. of Electrical Engg, IIT Bombay, Mumbai, India
sdgupta@iitb.ac.in
3
Professor, Dept of Computer Engg, VESIT, Mumbai, India
sharmilase@yahoo.com
sdgupta@iitb.ac.in
Professor, Dept of ABSTRACT
Computer Engg, VESIT, Mumbai, India
sharmilase@yahoo.com
The photovoltaic cell industry is still a nascent industry with
huge potential. The wide availability of solar energy, zero emissions, and
comparatively low cost make it a highly attractive proposition for future energy needs. Many PV cell technologies are available to
choose from like amorphous silicon (a-Si), monocrystalline silicon (m-Si), Copper-Indium-Gallium-Selenide (CIGS) etc. Present study
3
Dept of Computer
VESIT,
India
attempts to understand the effect of location variation
(latitude,Engg,
longitude
andMumbai,
elevation)
on the readings of short circuit current (Isc)
sharmilase@yahoo.com
and open circuit voltage (Voc) using only the above-mentioned
technologies. Average monthly insolation (G) and temperature (T) for
56 different locations have been tabulated and Marion’s model has been chosen to compute the Isc and Voc values. Statistical analysis
of the variation of the readings based on location has been attempted to highlight the criteria for selection of different PV technologies
suitable for different locations.
3
Keywords: photovoltaic, open-circuit voltage, short-circuit current, insolation, latitude, longitude, elevation, sensitivity
analysis.
1. INTRODUCTION
The need for a solar cell stemmed from the fact when human being wanted to conquer the space. At the advent of space age
by 1950, the scientists designed photovoltaic cells. During the early 70's the oil industry suffered a set-back and to offset the
high cost of production an initiative was taken for using solar panels on oil rigs. This spurred the growth of terrestrial
applications for photovoltaic cells and today there are different technologies dominating the field. A need is felt to define the
applicability (and non-applicability) of the different PV technologies at different locations to aid in decision making for both
individual customers and large PV cell manufacturers alike. The parameters of interest are open-circuit voltage VOC, shortcircuit current ISC, maximum power PMP and fill factor FF. Among these parameters, the variation of V OC and ISC has been
studied based on different insolation (G) and temperature (T). The G and T of a particular place depend on its latitude,
longitude, and elevation. It is known that VOC is primarily dependent on temperature whereas ISC is primarily dependent on G
[2]. The average insolation of a particular month with its corresponding average temperature is used as input to the equation
cited by Marion [4]. Besides ISC and VOC, the parameters of interest are PMP and fill factor FF, which are also based on
environmental conditions. In this paper, we have compared three different technologies- monocrystalline silicon (m-Si), CIGS
(Copper-Indium-Gallium-Selenide) and amorphous silicon (a-Si) for a particular location based on the available temperature
and insolation data [3].
2. BACKGROUND OF THE PROPOSED WORK
2. 1 Motivations
The standard deviation of ISC for three different technologies was found to be varying due to standard deviation in G over 56
different locations. Similarly, the standard deviation in open-circuit voltage is shown for three different technologies for 56
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
different locations scattered over the globe based on the standard deviation of temperature. The measurement and estimation
of solar flux also depends on collector geometry and its mounting angle. Moreover, solar panels are mounted in the form of
matrix array for maximum power. Numbers of panels that are in series, parallel combinations also play a vital role where
maximum power is concerned. Any place on earth is subjected to cloud variation, whose boundary is difficult to estimate.
Since the effect of cloud is random in nature it will add to complexity in the location based optimization, a reconfigurable
strategy may be adopted on the basis of image of the cloud formed. With a number of solar modules connected in wireless
sensor network, a cloud boundary may be estimated by employing Gauss-Seidel iteration [4].
2.2
Nomenclature
VOC – Open-circuit voltage (V)
ISC - Short-circuit current (A)
VMP- Voltage at maximum power
IMP- Current at maximum power
PMP- Maximum power
PMP(ref)- Maximum power at STC (W)
G -Solar Insolation (W/sq.m.)
T- Temperature (oC)
Tref – 250C at STC
ISC (Tref) - ISC at STC
VOC (Tref) - VOC at STC
G (ref)- Insolation at STC (1000W/sq.m.)
a- Correction factor for ISC (%/oC)
b - Correction factor for VOC (%/oC)
- Correction factor for PMP (%/oC)
(aT+c)- VOC correction factor for irradiance
2.3
Review of Models for PV Cell
The equivalent circuit of a solar cell is also studied as given in Figure-1. The electrical equivalent of a PV cell contains a
current source I, a diode, a series resistance RS and a parallel resistance RP [1]. Due to temperature sensitivity of a diode, the
voltage across a diode changes and the I-V curve of a PV cell deviates from the ideal diode curve. The effect is manifested as
change in open-circuit voltage and change in short-circuit current.
Figure 1 Equivalent Circuit of a PV Cell
2. 4 Mathematical Aspect
The equations as cited by [2] are hereunder:(T)=Isc(Tref)*G/G(ref)*[1+ a(T-Tref)]
(1)
VOC (T)=VOC(Tref)*[1+b(T-Tref)]*[1+(aT+c)ln(G/G(ref)]
(2)
PMP = G/G(ref)*PMP (ref)[1+γ(T-Tref)]
(3)
PMP =VMP *IMP
(4)
Based on equations (1) through (4) the differential equation of a PV cell for normalized insolation G can be written as
(5)
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
Table 1: List of the sampling locations
Harare
Bombay
Maine
Mombasa
Nagpur
Seattle
Accra
Calcutta
Calgary
Addis Ababa
Havana
Vancouver
Dire Dawa
Abu Dhabi
Winnipeg
Guatemala City
Texas
Ottawa
Dakar
New Delhi
Quebec
Santa Rosa de
Copan
Cairo
Belize City
Managua
Reykjavik
Tashkent
Brussels
Arkhangel
Bangkok
Prague
St. Petersburg
Kathmandu
Madrid
Ostersund
Ulaangom
Helsinki
Darwin
Colombo
Paris
Sydney
Kangnung
London
Wellington
Semipalatinsk
Dublin
Yakutsk
Matsumoto
Yulin
Buenos Aires
Santiago
Lhasa
Brasilia
Cuzco
Nanjing
Manaus
Figure 2 Scatter of the selected sample locations
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
3. Dataset
The dataset for present study comprises of the monthly average insolation for different cities around the world. A total of 56
cities were selected (refer Table-1 and Figure-2) around the globe and their monthly average maximum temperatures in ⁰C
were tabulated. Insolation is normalized, reference insolation G(ref) being 1000W/m2 at STC=25⁰C. Equation (1) and (2) are
used to find the ISC and Voc for different G and T for each technology at a particular location. The reference short-circuit
current ISC(Tref) and reference open-circuit voltage VOC(Tref) for each technology is available from the manufacturer’s
datasheet (refer Table-2). The ISC and VOC values for different G and T are plotted for each technology. The standard
deviation of ISC for m-Si, CIGS and a-Si are plotted at different locations in the order of increasing standard deviation of G.
Similarly, the standard deviation of VOC for m-Si, CIGS and a-Si are plotted at different locations in the order of increasing
standard deviation of T. In addition the latitude, longitude and the elevation are also taken into account to understand the
location based variation of the PV cell parameters. The correction factor for each of these technologies being different
produced different deviation. Subsequently the standard deviation of insolation, temperature, VOC and ISC are calculated for
each location for each technology. A bar graph of standard deviation of I SC is plotted with standard deviation in insolation.
Similarly, a bar graph of standard deviation of Voc has been plotted with standard deviation of temperature.
Table 2: ISC (Tref) and VOC (Tref) for different technologies
Technology
Isc(Tref)
Voc(Tref)
m-Si
8A
45.4V
CIGS
6.2A
20.9V
a-Si
5.1A
23.1V
Figure 3 Plot of standard deviation of Isc for different technologies at different locations
4. RESULTS & DISCUSSION
It is observed that amorphous-silicon (a-Si) has the minimum standard deviation for ISC in almost all of the cases (refer Figure3). Hence, a-Si is selected as the candidate for further understanding of the variation of I SC readings at different locations.
Three location parameters, viz, latitude, longitude and elevation are shortlisted to perform a sensitivity analysis on the I SC
readings.
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
A typical diagrammatic representation of sensitivity analysis to compare relative importance of the parameters for a given
phenomenon can be shown by a tornado diagram. Hence a tornado diagram is plotted using the effect of the three location
parameters viz, latitude, longitude and elevation on ISC values to compare their relative influences on amorphous-silicon. It is
observed that elevation has maximum effect on variation of I SC, followed by latitude. Longitude is found to have the least
effect on ISC variation of a-Si (refer Figure-5).
Similarly, from the plot of the standard deviation of VOC values with different standard deviation of temperature for the three
different technologies at various locations, it is observed that the standard deviation of V OC parameter of CIGS is the
minimum (refer Figure-4). Hence, the standard deviation of VOC readings from CIGS is selected for a sensitivity analysis for
the effect of the three location parameters – latitude, longitude and elevation. A tornado diagram is plotted to compare the
relative effect of these parameters. It is observed that latitude has a pronounced effect on voltage variation of VOC, followed
by longitude and elevation has the least effect on the Voc variation of CIGS (refer Figure-6).
Figure 4 Plot of standard deviation of Voc for different technologies at different locations
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
Figure 5 Sensitivity analysis of a-Si (I) for latitude, longitude and elevation for selected dataset
Figure 6 Sensitivity analysis of CIGS (V) for latitude, longitude and elevation for selected dataset
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
5. CONCLUSION
From the above study it may be concluded that there is a trade-off between the variation of ISC and VOC derived from PV cells
based on the latitude, longitude and elevation. To get a stabilised supply of current the a-Si technology seems best suited
(refer Figure-3) while CIGS technology offers a stable voltage supply for PV cells (refer Figure-4). The tornado diagram
(refer Figure-5) based on standard deviation of ISC suggests that deviation in current in an a-Si module is most sensitive to
elevation than the other two location-based parameters, viz, latitude and longitude. The tornado diagram (refer Figure-6)
based on standard deviation of VOC of CIGS suggests that deviation in voltage in a CIGS module is most sensitive to latitude
than the other two location-based parameters, viz, longitude and elevation.
The above facts would aid in decision making on a technical standpoint for choosing PV cells at different locations.
Commercial aspects will also come into play in such decision-making and the present study is a purely technical summary for
the location-based variation of different PV technologies. Further work on data collection from additional cities along with
different PV technologies of first generation (Si-wafer based) and second generation (thin film based) may help in reducing
any statistical bias from location based sampling. Adding cost factors may add to the completeness for any recommendations
to be made for viability of different PV technologies at different locations. A further study on lifecycle costing (LCC) may be
carried out based on location. LCC is based on capital cost, operation and maintenance cost and replacement cost. The effect
of insolation and temperature of different location may affect the same technology very differently. Hence, LCC may vary
location-wise for the same technology. An optimization decision then should take into account the LCC of different
technologies for a particular location.
For a particular location the design and structure requirement will be different and hence the requirement of cooling. The
reconfigurablity of a structure may vary from location to location as well. Hence a further study can be made taking into
account all these parameters mentioned above.
References
[1] Chetan Singh Solanki, Solar Photovoltaics, Fundamentals, Technologies and Applications, PHI Learning Pvt. Ltd, 2012,
[2] Pooja Sharma, Siddhartha P Duttagupta, Vivek Agarwal, “Characterization & modelling of flexible photovoltaic
modules for portable power appications”, In Proceedings of IEEE Xplore, Sustainable Power generation & Supply,
SUPERGEN, pp. 1-7, 2009.
[3] Data source: www.nrel.gov/rredc/PVwatts/ [Accessed Nov. 3-5, 2013]
[4] B. Patnaik, P. Sharma, E. Trimurthulu, S.P.Duttagupta, “Reconfiguration strategy for optimization of solar photovoltaic
array under non-uniform illumination conditions”, In the Proceedings of IEEE Xplore, Photovoltaic Specialists Conference
(PVSC), pp.001859-001864, 2011.
AUTHORS
Corresponding Author
Elina Mukherjee received her degree in Electronics & Telecommunication Engineering in 2008 from
IETE. Thereafter she joined VESIT for post-graduation in 2012 as a GATE scholar. She is interested in
non-conventional energy like photovoltaic cell. She worked as a faculty member in the Dept. of
Instrumentation Technology for 12 years.
Siddhartha P. Duttagupta obtained his B.Tech. from the Indian Institute of Technology, Kharagpur in
1991 and the Ph.D. from the University of Rochester, New York in 1998. He taught at Boise State
University from 1997-2002, before moving to the Indian Institute of Technology, Bombay in 2002, where
he is currently an Associate Professor. Dr. Duttagupta's research interests are in the area of microsytems
and microfabrication. He has worked in the areas of micropower generation, power management, and
onchip cooling. He has published and presented over 50 papers in these areas, and acted as a referee for
Organized By: Vivekanand Education Society's Institute Of Technology
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
ISSN 2319 - 4847
Special Issue for International Technological Conference-2014
leading international journals. Dr. Duttagupta has been involved with many sponsored projects from
agencies based in the USA and in India. He is a member of the IEEE.
Prof. S.Sengupta, a faculty of V.E.S.I.T., Mumbai is teaching UG and PG students for 17 years and has
research publications in wireless and mobile communication, networking and image processing. She is
currently pursuing PhD. in Electronics Engineering from Mumbai University.
Organized By: Vivekanand Education Society's Institute Of Technology