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Exergo-economic optimization of concentrated solar photovoltaic and thermoelectric hybrid generator

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Abstract

Exergo-economic analysis of a concentrated photovoltaic–thermoelectric generator (CPV-TEG) hybrid system is investigated. The specific exergy costing is employed to study the cost effectiveness of the CPV-TEG system. A multi-dimensional single-objective optimization is carried out to optimize the CPV-TEG hybrid system. The performance of the CPV-TEG system is found to be better than that of the concentrated photovoltaic (CPV) system alone in terms of overall energy and exergy efficiencies. From an exergo-economic standpoint, the CPV-TEG system is more cost effective as compared to the CPV system alone. The low value of the exergo-economic factor of the system indicated that the associated cost was mostly due to irreversibilities in the system. A compromise is made by optimizing the CPV-TEG system for maximum exergy efficiency using an optimum thermal resistance of the thermoelectric generator (TEG). For the operating conditions and the geometry considered, integration of CPV and TEG is not found to be feasible (in terms of exegetic performance) below certain values of heat transfer coefficients (< 2500 Wm−2 K−1). A minimum value of heat transfer coefficient of 5266 Wm−2 K−1 is determined for a water-cooled heat sink to limit the cell temperature to 100 °C under the studied set of operating conditions and the geometric configuration. Optimization results yielded exergy efficiencies of 42.22% and 43.48% for the stand-alone CPV system and CPV-TEG system, respectively. The minimum costs of electricity under the optimum conditions were obtained as \(0.57\;\$ \; {\text{kW}}\,{\text{h}}^{ - 1}\) and \(0.53\;\$ \; {\text{kW}}\,{\text{h}}^{ - 1}\) for the stand-alone CPV system and CPV-TEG system, respectively.

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Abbreviations

A:

Area, m2

b:

Width of thermoelement, m

B:

Width of TEG module, m

C:

Geometric concentration

\(\dot{C}\) :

Cost rate, \(\$ {\text{s}}^{ - 1}\)

\(\dot{c}\) :

Cost rate per unit exergy, \(\$ {\text{s}}^{ - 1} {\text{W}}^{ - 1}\)

\(\dot{E}\) :

Rate of exergy destroyed, W

f:

Fill factor

F:

Exergo-economic factor

G:

Solar radiation, \({\text{W m}}^{ - 2}\)

h:

Heat transfer coefficient, \({\text{W m}}^{ - 2} {\text{K}}^{ - 1}\)

I:

Electric current (A)

k:

Thermal conductivity, \({\rm W} \,{\rm m}^{ - 1}\,{\rm K}^{ - 1}\)

\(l\) :

Thickness, m

m:

Life span of system, years

\(\dot{Q}\) :

Heat transfer rate, W

q:

Heat transfer per unit area

\(\dot{W}\) :

Electrical power, W

R:

Thermal resistance, \({\text{K W}}^{ - 1}\)

r:

Interest rate, \(\%\)

T:

Temperature K

S:

Seebeck coefficient, \({\text{V K}}^{ - 1}\)

V:

Capital cost, \({\$}\)

\(\dot{X}\) :

Rate of exergy flow, W

\(zT\) :

Thermoelectric figure of merit

\(\dot{Z}\) :

Investment cost rate, \(\$ {\text{s}}^{ - 1}\)

opt:

Optical concentrator

rad:

Radiation

tot:

Total

hs:

Heat sink

ref:

Reference condition

a:

Ambient

sp:

Solder paste

cl:

Copper layer

cr:

Ceramic

ic:

Interconnect

TE:

Thermoelement

p-n:

P and n type

c:

Cold side

h:

Hot side

TEG:

Thermoelectric module

s:

Solar energy

\(\dot{Q}_{\text{hs}}\) :

Rate of heat rejected in heat sink

\(\dot{Q}_{\text{c}}\) :

Rate of heat transfer at cold side

\(\dot{Q}_{\text{h}}\) :

Rate of heat transfer at hot side

k:

Layers of the system

p:

Product

f:

Fuel

\(\eta\) :

Efficiency

\(\varepsilon\) :

Emissivity

\(\beta\) :

Temperature coefficient, \({\text{K}}^{ - 1}\)

\(\dot{\varGamma }\) :

Total irreversibility rate in the system, W

\(\varphi\) :

Exergy efficiency due solar radiation

\(\rho\) :

Electrical resistivity, \(\varOmega {\text{m}}\)

\(\gamma\) :

Electrical resistance, \(\varOmega\)

CRF:

Capital recovery factor

DNI:

Direct normal radiation

CPV:

Concentrated photovoltaic

TEG:

Thermoelectric generator

TIM:

Thermal interface material

SPECO:

Specific exergy costing

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Acknowledgements

The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia for this work under Research Grant RG171001 and by the King Abdullah City for Atomic and Renewable Energy (K.A.CARE) through Research Fellowship Program.

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Authors and Affiliations

  1. Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Kehinde G. Ismaila, Ahmet Z. Sahin & Bekir S. Yilbas

  2. Senior Researcher at K.A.CARE Energy Research and Innovation Center, Dhahran, 31261, Saudi Arabia

    Ahmet Z. Sahin & Bekir S. Yilbas

  3. Center of Research Excellence, Renewable Energy (CoRE-RE), KFUPM, Dhahran, 31261, Saudi Arabia

    Ahmet Z. Sahin & Bekir S. Yilbas

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  1. Kehinde G. Ismaila
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Correspondence to Ahmet Z. Sahin.

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Ismaila, K.G., Sahin, A.Z. & Yilbas, B.S. Exergo-economic optimization of concentrated solar photovoltaic and thermoelectric hybrid generator. J Therm Anal Calorim 145, 1035–1052 (2021). https://doi.org/10.1007/s10973-020-10508-1

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