How do you optimize a thermoelectric cooler (TEC) for maximum cooling capacity versus maximum COP?

TEC performance depends on operating current: Q_c = αIT_c - 0.5I²R - K(T_h-T_c), where α is Seebeck coefficient, R is electrical resistance, K is thermal conductance. Maximum cooling (Q_c,max) occurs at I_Qmax = αT_c/R but gives COP≈0.3-0.5. Maximum COP occurs at lower current I_COP = αΔT/[R(√(1+ZT_m)-1)] giving COP≈1-2 but 30-50% lower Q_c. Optimization approach: for fixed heat load, select TEC with Q_c,max > 1.5× required load allowing operation at higher COP point; multi-stage TECs for ΔT>50°C (each stage adds ~20°C capability); proper heat sink design critical (hot side Rth < cold side); parallel TECs at reduced current vs single TEC at high current tradeoff; consider Peltier modules with ZT>1 materials (Bi₂Te₃ alloys). System COP must include TEC COP and heat sink fan power for fair comparison with vapor compression.