Parametric Optimization of Concentrated Photovoltaic-Thermoelectric Hybrid System

Abstract

The current cutting edge in photovoltaic technology states that the conversion efficiency of photovoltaic (PV) systems has inverse relation and thermoelectric systems has direct relation with temperature. Therefore, cascading of thermoelectric (TE) systems with concentrated photovoltaic (CPV) systems has the potential to improve the total power output of CPV system by effectively utilizing the solar spectrum. The excess thermal energy of the PV system can be utilized as heat input in thermoelectric system to generate power. In this chapter, a thermodynamic model based on the first and second laws of thermodynamics for concentrated photovoltaic-thermoelectric (CPV-TE) hybrid system has been developed and analysed in a MATLAB Simulink environment. Further, the parametric optimization has been carried out to improve the overall performance of the hybrid system. The effect of concentration ratio, resistance ratio, thermal resistance between the TE module and the environment and the thermal resistance between the PV and TE modules has been discussed.

Appendix-A

The temperature-dependent material properties of Bi₂Te₃ and the expressions for P₁ through P₆ and Q₁ through Q₆ are defined as:

s = [sp − (−sn)] = (44448.0 + 1861.2Tm − 1.9810Tm 2) × 10−9	ρn = ρp = (5112.0 + 163.4Tm + 0.6279Tm 2) × 10−10
kn = kp = (62605.0 − 277.7Tm + 0.4131Tm 2) × 10−4	μ = [μp − (−μn)] = (1861.2Tm − 3.962Tm 2) × 10−9
${P}_1=\frac{\alpha_{\mathrm{h}}A\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)-{\alpha}_{\mathrm{h}}\left(2m+1\right)\right]{\psi}_{\mathrm{h}}}{8\left(\rho L+2{R}_{\mathrm{ec}}\right){\left(m+1\right)}^2}$	${Q}_1=\frac{\alpha_{\mathrm{h}}A\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)-{\alpha}_{\mathrm{h}}\right]{\psi}_{\mathrm{c}}}{8\left(\rho L+2{R}_{\mathrm{c}}\right){\left(m+1\right)}^2}$
${P}_2=\frac{\alpha_cA\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)+{\alpha}_{\mathrm{c}}\right]{\psi}_{\mathrm{h}}}{8\left(\rho L+2{R}_{\mathrm{ec}}\right){\left(m+1\right)}^2}$	${Q}_2=\frac{\alpha_cA\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)+{\alpha}_{\mathrm{c}}\left(2m+1\right)\right]{\psi}_{\mathrm{c}}}{8\left(\rho L+2{R}_{\mathrm{c}}\right){\left(m+1\right)}^2}$
${P}_3=\frac{-A\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)\left({\alpha}_{\mathrm{h}}+{\alpha}_{\mathrm{c}}\right)-2m{\alpha}_{\mathrm{h}}{\alpha}_{\mathrm{c}}\right]{\psi}_{\mathrm{h}}}{8\left(\rho L+2{R}_{\mathrm{ec}}\right){\left(m+1\right)}^2}$	${Q}_3=\frac{-A\left(\mathrm{FF}\right)\left[\mu \left(m+1\right)\left({\alpha}_{\mathrm{h}}+{\alpha}_{\mathrm{c}}\right)+2m{\alpha}_{\mathrm{h}}{\alpha}_{\mathrm{c}}\right]{\psi}_{\mathrm{c}}}{8\left(\rho L+2{R}_c\right){\left(m+1\right)}^2}$
${P}_4=\frac{-\left( kA\left(\mathrm{FF}\right){\psi}_{\mathrm{h}}+L\right)}{L}$	${Q}_4=\frac{- kA\left(\mathrm{FF}\right){\psi}_{\mathrm{c}}}{L}$
${P}_5=\frac{kA\left(\mathrm{FF}\right){\psi}_{\mathrm{h}}}{L}$	${Q}_5=\frac{kA\left(\mathrm{FF}\right){\psi}_{\mathrm{h}}+L}{L}$
P6 = TPV	Q6 =  − Ta