Table 2.

The cost function of different components, cost balance, and auxiliary equations for exergoeconomic analysis of the combined cycle [10,48].

Component	Initial price	Main relation	Auxiliary relation
Air compressor	${\dot{Z}}_{air,com}=71.1{\dot{m}}_{air}\left(\frac{1}{0.9-{\eta }_{com}}\right)\left(\frac{p_2}{p_1}\right)\ln \left(\frac{p_2}{p_1}\right)$	$\dot{C_1}+c_{el,sofc}{\dot{W}}_{air,com}+{\dot{Z}}_{air,com}={\dot{C}}_2$	$c_1=0$
Fuel compressor	${\dot{Z}}_{fuel,com}=71.1{\dot{m}}_{fuel}\left(\frac{1}{0.9-{\eta }_{com}}\right)\left(\frac{p_6}{p_5}\right)\ln \left(\frac{p_6}{p_5}\right)$	$\dot{C_5+c_{el,sofc}{\dot{W}}_{air,com}+{\dot{Z}}_{air,com}={\dot{C}}_6}$	$c_{fuel}=12\left(\raisebox{1ex}{$\$$}\!\left/ \!\raisebox{-1ex}{$Gj$}\right.\right)$
Water pump	${\dot{Z}}_{water,p}=705.48{{\dot{W}}_{water,p}}^{0.71}\left(1+\frac{0.2}{1-{\eta }_{water,p}}\right)$	${\dot{C}}_8+c_{el,sofc}{\dot{W}}_{air,com}+{\dot{Z}}_{air,com}={\dot{C}}_9$	$c_8=0$
Air HX	${\dot{Z}}_{air,hx}=3.130{\left(\frac{A_{air,hx}}{0.093}\right)}^{0.78}$	${\dot{C}}_2+{\dot{C}}_{15}+{\dot{Z}}_{air,hx}={\dot{C}}_3+{\dot{C}}_{16}$	$c_{15}=c_{15}$
Fuel HX	${\dot{Z}}_{fuel,hx}=130{\left(\frac{A_{fuel,hx}}{0.093}\right)}^{0.78}$	${\dot{C}}_6+{\dot{C}}_{14}+{\dot{Z}}_{fuel,hx}={\dot{C}}_7+{\dot{C}}_{15}$	$c_{14}=c_{15}$
Water HX	${\dot{Z}}_{water,hx}=130{\left(\frac{A_{water,hx}}{0.093}\right)}^{0.78}$	${\dot{C}}_9+{\dot{C}}_{13}+{\dot{Z}}_{water,hx}={\dot{C}}_{10}+{\dot{C}}_{14}$	$c_{13}=c_{14}$
Fuel cell	$Z_{SOFC}=A_a{N}_{fc}\left(2.96t_{SOFC,out}-1907\right)$	${\dot{C}}_3+{\dot{C}}_{11}+{\dot{Z}}_{SOFC}={\dot{C}}_{12}+{\dot{C}}_4+c_{26}{\dot{W}}_{SOFC}$	$c_4=c_{26}$ $c_{12}=c_{26}$
Inverter	$Z_{inverter}=100000{\left(\frac{{\dot{W}}_{SOFC}}{500}\right)}^{0.7}$	$c_{26}{\dot{W}}_{SOFC}+{\dot{Z}}_{of,eva}=c_{el,SOFC}{\dot{W}}_{SOFC,ac}$	$-$
Afterburner chamber	$Z_{AB}=46.08{\dot{m}}_4\left(\frac{1+\exp \left(0.018t_{13}-26.4\right)}{0.995-\frac{p_{13}}{p_{12}}}\right)$	${\dot{C}}_4+{\dot{C}}_{12}+{\dot{Z}}_{AB}={\dot{C}}_{13}$	$-$
Hot water HX	$Z_{of,hx}=130{\left(\frac{A_{of,hx}}{0.093}\right)}^{0.78}$	$c_{16}{\dot{Ex}}_{16}+c_{35}{\dot{Ex}}_{35}+{\dot{Z}}_{dhw,hx}=c_{17}{\dot{Ex}}_{17}+c_{36}{\dot{Ex}}_{36}$	$c_{16}=c_{17}$
Generator	$Z_{gen,ACH}=0.322\left(30000+0.75{A_{gen}}^{0.8}\right)$	$c_{17}{\dot{Ex}}_{17}+c_{25}{\dot{Ex}}_{25}+{\dot{Z}}_{gen}=c_{18}{\dot{Ex}}_{18}+c_{19}{\dot{Ex}}_{19}+c_{26}{\dot{Ex}}_{26}$	$\frac{c_{19}{\dot{Ex}}_{19}-c_{25}{\dot{Ex}}_{25}}{{\dot{Ex}}_{19}-{\dot{Ex}}_{25}}=\frac{c_{25}{\dot{Ex}}_{25}-c_{26}{\dot{Ex}}_{26}}{{\dot{Ex}}_{26}-{\dot{Ex}}_{25}}$
Absorber	$Z_{abs,ACH}=0.322\left(30000+0.75{A_{abc}}^{0.8}\right)$	$c_{22}{\dot{Ex}}_{22}+c_{28}{\dot{Ex}}_{28}+c_{31}{\dot{Ex}}_{31}+{\dot{Z}}_{abs}=c_{23}{\dot{Ex}}_{23}+c_{32}{\dot{Ex}}_{32}$	$c_{22}=c_{23}$ $c_{31}=0$
Condenser	$Z_{con,ACH}=0.322\left(30000+0.75{A_{con}}^{0.8}\right)$	$c_{19}{\dot{Ex}}_{19}+c_{29}{\dot{Ex}}_{29}+{\dot{Z}}_{con}=c_{20}{\dot{Ex}}_{20}+c_{30}{\dot{Ex}}_{30}$	$c_{19}=c_{20}$ $c_{29}=0$
Evaporator	$Z_{eva,ACH}=0.322\left(30000+0.75{A_{eva}}^{0.8}\right)$	$c_{21}{\dot{Ex}}_{21}+c_{33}{\dot{Ex}}_{33}+{\dot{Z}}_{eva}=c_{22}{\dot{Ex}}_{22}+c_{34}{\dot{Ex}}_{34}$	$c_{21}=c_{22}$ $c_{33}=0$
Solution HX	$Z_{shx,ACH}=0.322\left(30000+0.75{A_{shx}}^{0.8}\right)$	$c_{24}{\dot{Ex}}_{24}+c_{26}{\dot{Ex}}_{26}+{\dot{Z}}_{shx}=c_{23}{\dot{Ex}}_{23}+c_{32}{\dot{Ex}}_{32}$	$c_{26}=c_{27}$
Solution pump	$Z_{p,ACH}=1120{{\dot{W}}_{p,ACH}}^{0.8}$	$c_{23}{\dot{Ex}}_{23}+c_{el}{\dot{W}}_{sp}+{\dot{Z}}_{sp}=c_{24}{\dot{Ex}}_{24}$	$c_{el}=10\left(\raisebox{1ex}{$\$$}\!\left/ \!\raisebox{-1ex}{$Gj$}\right.\right)$