Numerical and Experimental Investigation on a Thermo-Photovoltaic Module for Higher Efficiency Energy Generation

  • Hossein Karami-Lakeh
  • Reza Hosseini-AbardehEmail author
  • Hassan Kaatuzian


One major problem of solar cells is the decrease in efficiency due to an increase in temperature when operating under constant irradiation of solar energy. The combination of solar cell and a thermoelectric generator is one of the methods proposed to solve this problem. In this paper, the performance of thermo-photovoltaic system is studied experimentally as well as through numerical simulation. In the experimental part, design, manufacture and test of a novel thermo-photovoltaic system assembly are presented. Results of the assembled system showed that with reduction of one degree (Centigrade) in the temperature of solar cell under investigation, and about 0.2 % increase in the efficiency will be obtained in comparison with given efficiency at that specified temperature. The solar cell in a hybrid-assembled system under two cooling conditions (air cooling and water cooling) obtained an efficiency of 8 % and 9.5 %, respectively, while the efficiency of a single cell under the same radiation condition was 6 %. In numerical simulation part, photo-thermoelectric performance of system was analyzed. Two methods for evaluation of thermoelectric performance were used: average properties and finite element method. Results of simulation also demonstrate an increase in solar cell efficiency in the combined system in comparison with that of the single cell configuration.


Solar cell Thermoelectric Thermo-photovoltaic Efficiency 

List of symbols


Solar cell area (m\(^{2}\))


Absorption coefficient

\(A_n \)

Cross-sectional area of n-type arm (m\(^{2})\)

\(A_p \)

Cross-sectional area of p-type arm (m\(^{2})\)


Solar irradiation (W\(\cdot \)m\(^{-2}\))

\(E_g \)

Band-gap energy (eV)


Convective heat transfer coefficient (W\(\cdot \)m\(^{-2}\) \(\cdot \hbox {K}^{-1}\))


Electric current (A)

\(I_0 \)

Reverse saturation current (A)

\(I_{\mathrm{max}} \)

Electric current of solar cell at maximum power manner (A)

\(I_{sc} \)

Short-circuit current (A)


Current density (A\(\cdot \)m\(^{-2}\))


Effective conductance of thermoelectric couple (W\(\cdot \)K\(^{-1}\))

\(K_{FF} \)

Fill factor


Boltzmann constant: \(1.38 064 852\times 10^{-23}\)J\(\cdot \)K\(^{-1}\)

\(k_n \)

n-Type arm’s thermal conductivity (W\(\cdot \)m\(^{-1}\cdot \)K\(^{-1}\))

\(k_p \)

p-Type arm’s thermal conductivity (W\(\cdot \)m\(^{-1}\cdot \)K\(^{-1}\))


Thickness of the junction (m)

\(N_n \)

n-Type dopant concentration (atom\(\cdot \)cm\(^{-3}\))

\(N_p \)

p-Type dopant concentration (atom\(\cdot \)cm\(^{-3}\))

\(n_{ph} \)

Number of photons with enough energy

\(m_0 \)

Electron rest mass: \(9.10 938 356\times 10^{-31}\hbox { kg}\)


Effective mass of electron (kg)


Effective mass of hole (kg)

\(P_{\mathrm{Cell}} \)

Output power of solar cell (W)

\(P_{\mathrm{max}} \)

Maximum power output from cell (W)

\(P_{\mathrm{TEG}} \)

Output power of thermoelectric generator (W)


Electron charge, \(1.6 021 765\times 10^{-19}\,{^{\circ }}\hbox {C}\)

\(Q_c \)

Heat transferred from TEG to the heat sink (W)

\(Q_h \)

Heat transferred to hot side of TEG (W)


Effective electric resistance of thermoelectric couple (\(\Omega \))

\(R_L \)

External load resistance (\(\Omega \))

\(T_{\mathrm{air}} \)

Ambient temperature (\({^{\circ }}\hbox {C}\))

\(T_{\mathrm{ave}} \)

Average operating temperature of thermoelectric (\({^{\circ }}\hbox {C}\))

\(T_c \)

Cold-side temperature (\({^{\circ }}\hbox {C}\))

\(T_{\mathrm{Cell}} \)

Solar cell temperature (\({^{\circ }}\hbox {C}\))

\(T_h \)

Hot-side temperature (\({^{\circ }}\hbox {C}\))

\(T_n \)

n-Type arm temperature (\({^{\circ }}\hbox {C}\))

\(T_p \)

p-Type arm temperature (\({^{\circ }}\hbox {C}\))

\(T_{\mathrm{Sky}} \)

Sky effective temperature (\({^{\circ }}\hbox {C}\))

\(V_{\mathrm{max}} \)

Voltage of solar cell at maximum power manner (V)

\(V_{\mathrm{oc}} \)

Open-circuit voltage (V)


Figure of merit (1\(\cdot \)K\(^{-1}\))


\(\alpha _c \)


\(\alpha _{pn} \)

p–n Junction Seebeck coefficient (V\(\cdot \)K\(^{-1}\))

\(\epsilon \)


\(\eta _{\mathrm{cell}} \)

Efficiency of solar cell (%)

\(\eta _{\mathrm{total}} \)

Total efficiency of module (%)

\(\gamma \)

Thompson coefficient (V\(\cdot \)K\(^{-1}\))

\(\pi \)

Peltier coefficient of p–n couple (V)

\(\rho _n \)

Electric resistivity of n-type arm (\(\Omega \)m)

\(\rho _p \)

Electric resistivity of p-type arm (\(\Omega \)m)

\(\rho \)


\(\sigma \)

Stefan–Boltzmann constant: \(5.69\times 10^{-8 }\) W\(\cdot \)m\(^{-2}\) \(\cdot \) K\(^{-4}\)

\(\tau _n \)

Life time of electron (s)

\(\tau _p \)

Life time of hole (s)


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Hossein Karami-Lakeh
    • 1
  • Reza Hosseini-Abardeh
    • 2
    Email author
  • Hassan Kaatuzian
    • 3
  1. 1.Mechanical Engineering DepartmentAmirkabir University of TechnologyTehranIran
  2. 2.Mechanical Engineering Department, Center of Excellence Energy and ControlAmirkabir University of TechnologyTehranIran
  3. 3.Head of Photonics Research Laboratory, Electrical Engineering DepartmentAmirkabir University of TechnologyTehranIran

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