Integration of photovoltaic and thermoelectric
system to harvest wide spectrum of solar radiation

Gaurav Kumara

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a Department of Mechanical
Engineering, 2181
Glenn L. Martin Hall, Building 088

University of Maryland, College Park, MD 20742, USA

 

Abstract

The most advanced modern day Photovoltaic (PV)
cells can use only about 50% of the solar radiation 17 since only low
wavelength solar spectrum is used by PV cells to generate electricity, high
wavelength infrared radiation and higher are not used by PV cells. To make
things worse, infrared radiation heats up the PV cells increasing its operating
temperature and thereby reducing its efficiency. This study reviews the integration
of photovoltaic (PV) and thermoelectric (TE) technologies for harvesting wide range
of solar spectrum to generate electricity. One of the common techniques
employed to do so is ‘spectrum beam splitting’ in which short wavelength
spectrum is directly used by PV devices to generate electricity and high
wavelength solar radiation is used to generate electricity using TE devices 1.
With integrated PV and TE system, full solar spectrum can be exploited.

Keywords: Photovoltaic cell; Thermoelectric device; Spectrum
beam splitting; Integrated device.

1.     Introduction

European Union and China have planned to
harvest 20% and 15% respectively, of their total power generation from
renewable energy sources by 2020 and globally there has been an equally strong
drive towards renewable energy sources 1. The amount of solar radiation incident
on earth’s surface is approximately 1.2 × 105 Tera Watts whereas the
present energy consumption of the planet is roughly three orders of magnitude
lower 2 3. Artificially solar power can be harvested either in forms of electricity
(solar photovoltaic PV) or heat energy (solar thermal). Theoretically, the
upper limit of conversion efficiency of solar PV panels is estimated to be approximately
30% 4 5 6 7. However, practically the efficiency of these devices are
affected by multiple parameters and typically it is 40–50% below the upper
limit mentioned above 8. Due to such limitations on efficiency of these
devices it is practically impossible to harvest wide spectrum of solar
radiation using a single semi-conductor material 9. Although a combination of
various specialized materials with intermediate band gaps can be used to
overcome this problem, but it would expensive and hence would not be feasible
10 11. On the other hand, within the last decade there has been intense research
on thermoelectric materials which can convert waste heat directly into
electricity, to increase the efficiency of energy consumption. This opens up a
door to an alternative option which is to integrate PV cells with thermo-electric
generator which can convert solar thermal energy into electricity. However, low
efficiency of TE devices and elevated operating temperature of PV cells which
reduces its efficiency are some of the major obstacles in this technique. In
order to alleviate these problem, spectrum beam splitting technique has drawn
attention in which PV cells and TE devices would run in parallel, and the beam
splitter would allow only low wavelength solar radiation to reach the PV cells,
thereby reducing its operating temperature as well as the heat load 1213. Fig.
1 depicts the fraction of solar spectrum which can be used for PV cells and TE
devices respectively in an integrated system 17. In order to achieve good
performance for these systems it is important to create a sharp spectral split
between the photovoltaic (low wavelength) and thermal (high wavelength) components
of the system and then convert the solar irradiation into electron–hole pairs
or heat, respectively. Spectral beam splitting technique has multiple
advantages like eliminating the current-matching condition for stacked multi-junctions,
eliminating the requirement for lattice matching between neighboring cells, the
system is reasonably insensitive to spectral conditions like fluctuations in
humidity etc., and most importantly it minimizes photon entropy which has been
shown to increase the theoretical maximum efficiency by approximately 5% 26.

Fig.1 Fractions of solar spectrum used for PV and TE devices 17

2.    
Related work

The basic idea for a hybrid of PV and TE
devices had been published in 2008 by Tritt 19. Since then many papers have
been published on combining PV and TE devices, Baranowski et al.
(2012) 20 claimed efficiency of 15.9 % for concentrated solar thermoelectric
generators (STEG). A substantial amount of work has been dedicated towards
concentrating solar power on to thermoelectric generators, Chávez Urbiola and
Vorobiev (2013) 21 designed a hybrid system in which hot water produced from
co-generation was used as a coolant for hot side of TE generator and achieved
approximately 5% electrical efficiency. Leon et al. (2012) 22 and
Lertsatitthanakorn et al. (2013) 23 24 used different strategies for
designing TEG and cooling technique to evaluate the effectiveness of
concentrated solar power on hybrid systems. McEnany et al. (2011) 25 claimed
that under high operating temperature and optical irradiance, more than 10%
efficiency can be achieved by cascading TEGs.

3.     Description of integrated system

 Physically
there is Shockley–Queisser limit of 31% on solar energy conversion efficiency by
photovoltaic cells 18 which in turn puts a limit on the power density for
space constrained applications. There are three major factors responsible for this
loss in solar conversion efficiency of a semi-conductor device with single
absorption threshold: (1) loss S1, energy barrier where photons below threshold
energy Eg are not absorbed; (2) loss S2, thermalization where
photons with energy higher than Eg can generate electron-hole pairs and
lose energy in the form of heat; and (3) loss S3, small fraction of excited
states recombine with the ground state 14.

Areas S1, S2, and S3 as shown in Fig. 2 are
representatives of these three losses respectively and only S4 can be delivered
to the load. As can be seen, when distance between the outer curve and inner
curve reduces, type-3 loss also reduces. The actual work W by each absorbed
photon can be calculated using the equation below 10:

where K, e, h, c, T, C,

 are Boltzmann constant, charge of an electron,
Planck’s constant, speed of light, operating temperature, concentration ratio
and solar flux in photons respectively. From above equation it can be derived
that voltage at maximum power is given by:

Fig.2
Graphical analysis of the efficiency of a single band gap PV cell 10

The effect of operating temperature on PV cells
can be derived from the above equations, and as can be seen in Fig. 3,
efficiency of PV cell reduces as operating temperature increases, which
indicates that cooling/ super-cooling of PV cell is instrumental in affecting
performance of PV cells. Similarly, effect of concentration ratio on PV cell
performance has been studied and as can been from Fig. 4, concentration ratio
has much smaller effect on cell performance as compared to operating
temperature, however concentrating devices has cost benefits i.e. by reducing
the amount of area required to convert a fixed amount of solar energy 13.
However increasing concentration ratio has indirect negative effects too as it
can increasing the PV cell temperature or cooling load per unit cell.

                

Fig. 3
Effect of operating temperature on efficiency of PV cell                      Fig.4
Effect of concentration ratio on performance of PV cell

For semi-conductors with wide band gaps, a
large amount of solar energy is not absorbed since energy of photons is less
than Eg. Hence if this portion of solar spectrum can be removed using
a spectrum beam splitter, it would not only reduce the cooling load, but this
energy can also be used by TE generators for energy recovery 15.

Just like PV cells, the performance of
thermoelectric generators also depends on several factors which are the hot
side temperature Th, cold side temperature Tc and
thermoelectric constant ZT of the material used for TE device:

where                                                             

k,

 and S are material properties represent the thermal
conductivity, electrical conductivity and Seebeck coefficient respectively.
Typically thermoelectric constant ZT= 1 for modern thermoelectrics, ZT= 2 for
nano-scale microstructures produced in lab and ZT= 4 for quantum tunneling
thermionic converters 9. Effect of hot side and cold side temperatures on
efficiency of TE device are shown in Fig. 5 and Fig. 6 respectively. Mathematically
it is evident that increasing the hot side temperature and reducing the cold
side temperature would result in better efficiency of TE devices, however reducing
cold side temperature is more prominent when it comes to TE devices with small
thermoelectric constant. Using a TE device to harvest long wavelength solar
spectrum in combination with a PV cell can boost the overall performance of the
system by approx. 10% of the PV 17. Also, it can be seen that as value of ZT
for the material increases the theoretical efficiency approaches Carnot
efficiency. Thus using a TE device to harvest long wavelength solar spectrum in
combination with a PV cell can boost the overall performance of the system by
approx. 10% of the PV 17

     

Fig. 5
Effect of hot side temperature on efficiency of TE device      Fig. 6 Effect of cold side temperature on
efficiency of TE device

As can be seen in Fig. 7 1, in order to
ensure low operating temperature for PV cell and low cold side temperature for
TE device, the PV cell and TE generator are constructed on different sides of
the cooling chamber. The beam splitter directs the short wavelength solar
radiation towards the PV cell and long wavelength radiation is used to generate
high temperature thermal energy which is used for hot side of the TE generator.
During off-peak times cooling chamber is cooled using ambient air, and excess electricity
is stored in a deep freezer in form of high grade cold which can be used by
cooling chamber during peak times to enhance the power output of both PV cell
and TE device.

Fig. 7
Schematic of integrated PV-TE device 1

4.     System performance

The overall efficiency of the integrated system
is defined as:

where

 and

 represent the operational efficiencies of PV
and TE system respectively which are ratios of actual power output to the ideal
power output for PV and TE systems respectively. Operational efficiency takes
into consideration the heat losses too that occur in heat storage process for
TE device. Typically operational efficiencies for advanced PV and TE devices
are ~0.8, hence

 would be a reasonable approximation 9. Total
conversion efficiency can be written as a function of

,
C, ZT,

 and

:

An optimal band gap

 can be determined by maximizing the above
mentioned

 depending on PV operating temperature,
concentration ratio, and hot and cold side temperatures. Fig. 8 1 shows that
optimal band gap does not vary much with change in operating temperature, and
optimal band gap reduces with increase in concentration ratio. With optimal
band gap, contour of constant total efficiencies has been plotted with
operating temperature and concentration ratio as shown in Fig. 9 1 which
reveals that for same operating temperature, higher concentration ratio gives
higher total efficiency. An increase of concentration ratio by 10 times
increases the total efficiency by approx. 0.8%, which is equivalent to reducing
the operating temperature by 14K. Also regardless of the concentration ratio,
the total efficiency can be improved by approx. 30%, by reducing the operating
temperature to 160K 1. However increasing the concentration ratio increases
the cooling power load due to which the concentration ratio must be kept below
100 for all applications 16.

 

Fig. 8 Change in optimal band gap with Tc
and C 1                  Fig. 9 Contour
of total efficiency with Tc and C 1

Total efficiency of the integrated system also
increases with increase in hot side temperature as can be seen in Fig. 10 1,
however the rate of increase of total efficiency reduces with increase in

.
As compared to

,
doubling the thermoelectric constant ZT results in approx. 2% increase in total
efficiency.

Fig. 10 Total efficiency with Th and
ZT 1

Conclusion

This paper reviews the concept of a hybrid
PV-TE device for efficiently harvesting wide solar spectrum. An optimal band
gap material would perform well at both peak and off-peak times over wide range
of operating temperatures and increasing the hot side temperature,
concentration ratio and thermoelectric constant will improve the overall
efficiency of the integrated system. The simple structure also ensures that
this system can potentially be used as domestic power generator.

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