Table 1 Energy and Exergy balance equations for all components of model 2.

AC

\(\:{\dot{W}}_{AC}={\dot{m}}_{\text{air\:}}\left({h}_{23}-{h}_{22}\right)\)

\(\:{\dot{E}}_{D,AC}=\:{\dot{W}}_{AC}+{\dot{E}}_{22}-{\dot{E}}_{23}\)

CC

\(\:{\dot{m}}_{\text{a}\text{i}\text{r}}{h}_{23}+{\dot{m}}_{\text{f}\text{u}\text{e}\text{l}}\text{L}\text{H}\text{V}={\dot{(m}}_{\text{f}\text{u}\text{e}\text{l}}+{\dot{m}}_{\text{a}\text{i}\text{r}}){h}_{25}\)

\(\:{\dot{E}}_{D,CC}=\:({\dot{E}}_{23}+{\dot{E}}_{24})-{\dot{E}}_{25}\)

GT

\(\:{\dot{W}}_{GT}={\dot{m}}_{25}\left({h}_{25}-{h}_{26}\right)\)

\(\:{\dot{E}}_{D,GT}=({\dot{E}}_{25}-{\dot{E}}_{26})-{\dot{W}}_{GT}\:\)

HRSG

\(\:{{Q}_{HRSG}=\dot{m}}_{25}\left({h}_{26}-{h}_{27}\right)+{\dot{m}}_{19}({h}_{19}-{h}_{20})={\dot{m}}_{14}\left({h}_{1}-{h}_{14}\right)\)

\(\:{\dot{E}}_{D,HRSG}=\left({\dot{E}}_{26}-{\dot{E}}_{27}\right)+\left({\dot{E}}_{19}-{\dot{E}}_{20}\right)+\left({\dot{E}}_{14}-{\dot{E}}_{1}\right)\)

HPST

\(\:{\dot{W}}_{\text{H}\text{P}\text{S}\text{T}}=\:{\dot{m}}_{1}\left({h}_{1}-{h}_{2}\right)\)

\(\:{\dot{E}}_{D,HPST}=\:\:{\dot{E}}_{1}-{\dot{E}}_{2}-{\dot{W}}_{HPST}\)

IPST

\(\:{\dot{W}}_{\text{I}\text{P}\text{S}\text{T}}=\:{\dot{m}}_{3}\left({h}_{3}-{\text{h}}_{5}\right)\)

\(\:{\dot{E}}_{D,IPST}=\:{\dot{E}}_{3}-{\dot{E}}_{5}-{\dot{W}}_{IPST}\)

LPST

\(\:{\dot{W}}_{\text{L}\text{P}\text{S}\text{T}}=\:{\dot{m}}_{6}\left({h}_{6}-{\text{h}}_{8}\right)\)

\(\:{\dot{E}}_{D,LPST}=\:{\dot{E}}_{6}-{\dot{E}}_{8}-{\dot{W}}_{LPST}\)

Cond₁

\(\:{\dot{Q}}_{{\text{C}\text{o}\text{n}\text{d}}_{1}}={\dot{m}}_{8}\left({h}_{8}-{\text{h}}_{9}\right)\:\)

\(\:{\dot{E}}_{D,{\text{C}\text{o}\text{n}\text{d}}_{1}}=\:\left({\dot{E}}_{8}-{\dot{E}}_{9}\right)+\left({\dot{E}}_{15}-{\dot{E}}_{16}\right)\)

P₄

\(\:{\dot{W}}_{{P}_{4}\text{}}={\dot{m}}_{20}\left({h}_{21}-{h}_{20}\right)\)

\(\:{\dot{E}}_{D,{P}_{4}}=\:{\dot{W}}_{P1}+{\dot{E}}_{20}-{\dot{E}}_{21}\)

P₁

\(\:{\dot{W}}_{{P}_{1}\text{}}={\dot{m}}_{9}\left({h}_{10}-{h}_{9}\right)\)

\(\:{\dot{E}}_{D,{P}_{1}}=\:{\dot{W}}_{P1}+{\dot{E}}_{9}-{\dot{E}}_{10}\)

P₂

\(\:{\dot{W}}_{{P}_{2}\text{}}={\dot{m}}_{11}\left({h}_{12}-{h}_{11}\right)\)

\(\:{\dot{E}}_{D,{P}_{2}}=\:{\dot{W}}_{P2}+{\dot{E}}_{11}-{\dot{E}}_{12}\)

P₂

\(\:{\dot{W}}_{{P}_{3}\text{}}={\dot{m}}_{13}\left({h}_{14}-{h}_{13}\right)\)

\(\:{\dot{E}}_{D,{P}_{3}}=\:{\dot{W}}_{P1}+{\dot{E}}_{13}-{\dot{E}}_{14}\)

OFWH₁

\(\:{\dot{Q}}_{{\text{O}\text{F}\text{W}\text{H}}_{1}}=\:\left({{\dot{m}}_{10}h}_{10}+{\dot{m}}_{7}{\text{h}}_{7}\right)=\left({\dot{m}}_{11}{h}_{11}\right)\)

\(\:{\dot{E}}_{D,{\text{O}\text{F}\text{W}\text{H}}_{1}}=\:{\dot{E}}_{7}+{\dot{E}}_{10}-{\dot{E}}_{11}\)

OFWH₂

\(\:{\dot{Q}}_{{\text{O}\text{F}\text{W}\text{H}}_{2}}=\:\left({\dot{m}}_{12}{h}_{12}+{{\dot{m}}_{4}\text{h}}_{4}\right)=\left({\dot{m}}_{13}{h}_{13}\right)\)

\(\:{\dot{E}}_{D,{\text{O}\text{F}\text{W}\text{H}}_{2}}=\:{\dot{E}}_{4}+{\dot{E}}_{12}-{\dot{E}}_{13}\)

ORT

\(\:{\dot{W}}_{\text{S}\text{T}}={\dot{m}}_{29}\left({h}_{29}-{h}_{30}\right)\)

\(\:{\dot{E}}_{\text{D},\:\text{S}\text{T}}={\dot{E}}_{29}-{\dot{E}}_{30}-{\dot{W}}_{\text{O}\text{R}\text{T}}\)

HE

\(\:{\dot{Q}}_{HE}={\dot{m}}_{30}\left({h}_{30}-{h}_{31}\right)\)

\(\:{\dot{E}}_{\text{D},\text{H}\text{E}}={\dot{E}}_{30}+{\dot{E}}_{33}-{\dot{E}}_{31}-{\dot{E}}_{34}\)

Cond₂

\(\:{\dot{Q}}_{{\text{C}\text{o}\text{n}\text{d}}_{2}}={\dot{m}}_{31}\left({h}_{31}-{\text{h}}_{32}\right)\:\)

\(\:{\dot{E}}_{D,{\text{C}\text{o}\text{n}\text{d}}_{2}}=\:\left({\dot{E}}_{31}-{\dot{E}}_{32}\right)+\left({\dot{E}}_{35}-{\dot{E}}_{36}\right)\)

ORP

\(\:{\dot{W}}_{\text{ORP}\text{4}}={\dot{m}}_{32}\left({h}_{33}-{h}_{32}\right)\)

\(\:{\dot{E\:}}_{\text{D\:}\text{Pump4\:}}={\dot{W}}_{\text{ORP}}+{\dot{E}}_{32}-{\dot{E}}_{33}\)

Evap₁

\(\:{\dot{Q}}_{{Evap}_{1}}={\dot{m}}_{27}\left({h}_{27}-{h}_{28}\right)\)

\(\:{\dot{E}}_{\text{D},{Evap}_{1}}={\dot{E}}_{27}+{\dot{E}}_{34}-{\dot{E}}_{28}-{\dot{E}}_{29}\)

PTC collectors

\(\:{\dot{Q}}_{solar}=\:{\eta\:}_{PTC}{*A}_{ap}*DNI\)

\(\:{\dot{E}}_{Q,solar}=\:\left(1-\frac{{T}_{0}}{{T}_{sun}}\right){\dot{Q}}_{solar}\)

TES

\(\:{\dot{Q}}_{TST}={\dot{m}}_{17}\left({h}_{17}+{h}_{18}\right)\)

\(\:{\dot{E}}_{\text{D},\text{T}\text{S}\text{T}}={\dot{E}}_{17}+{\dot{E}}_{21}-{\dot{E}}_{19}-{\dot{E}}_{18}\)

Gen

\(\:{\dot{Q}}_{Gen}={\dot{m}}_{28}\left({h}_{28}-{h}_{37}\right)\)

\(\:{\dot{E}}_{\text{D,Gen}\text{}}={\dot{E}}_{28}+{\dot{E}}_{3\text{*}}-{\dot{E}}_{37}-{\dot{E}}_{7\text{*}}-{\dot{E}}_{4\text{*}}\)

Abs

\(\:{\dot{Q}}_{ABC}={{\dot{m}}_{1\text{*}}h}_{1\text{*}}-{{\dot{m}}_{6\text{*}}h}_{6\text{*}}-{{\dot{m}}_{10\text{*}}h}_{10\text{*}}\)

\(\:{\dot{E}}_{\text{D,Abs}}={\dot{E}}_{10\text{*}}+{\dot{E}}_{6\text{*}}-{\dot{E}}_{12\text{*}}+{\dot{E}}_{13\text{*}}-{\dot{E}}_{1\text{*}}\)

SHE

\(\:{\dot{Q}}_{SHE}={\dot{m}}_{2\text{*}}\left({h}_{3\text{*}}-{h}_{2\text{*}}\right)\)

\(\:{\dot{E}}_{\text{D,SHE\:}\text{}}={\dot{E}}_{4\text{*}}+{\dot{E}}_{2\text{*}}-{\dot{E}}_{5\text{*}}-{\dot{E}}_{3\text{*}}\)

P₅

\(\:{\dot{W}}_{{P}_{5}}{=\dot{m}}_{1\text{*}}\left({h}_{2\text{*}}-{h}_{1\text{*}}\right)\)

\(\:{\dot{E}}_{\text{D,}{P}_{5}\text{}}={\dot{W}}_{{P}_{5}}+{\dot{E}}_{2*}-{\dot{E}}_{1*}\)

Evap₂

\(\:{\dot{Q}}_{{Evap}_{2}}={\dot{m}}_{10\text{*}}\left({h}_{10\text{*}}-{h}_{9\text{*}}\right)\)

\(\:{\dot{E}}_{\text{D,}{Evap}_{2}\text{}}={\dot{E}}_{10\text{*}}+{\dot{E}}_{22}-{\dot{E}}_{9\text{*}}-{\dot{E}}_{11\text{*}}\)

Ev₁

\(\:{\dot{m}}_{5\text{*}}{h}_{5\text{*}}={{\dot{m}}_{6\text{*}}h}_{6\text{*}}\)

\(\:{\dot{E}}_{\text{D,Ev1}\text{}}={\dot{E}}_{5\text{*}}-{\dot{E}}_{6\text{*}}\)

Ev₂

\(\:{\dot{m}}_{8\text{*}}{h}_{8\text{*}}={{\dot{m}}_{9\text{*}}h}_{9\text{*}}\)

\(\:{\dot{E}}_{\text{D,Ev2}\text{}}={\dot{E}}_{2\text{*}}-{\dot{E}}_{9\text{*}}\)

Cond₃

\(\:{\dot{Q}}_{{Cond}_{3}}={\dot{m}}_{7\text{*}}\left({h}_{8\text{*}}-{h}_{7\text{*}}\right)\)

\(\:{\dot{E}}_{\text{D,}{Cond}_{3}\text{}}={\dot{E}}_{7\text{*}}-{\dot{E}}_{14\text{*}}+{\dot{E}}_{15\text{*}}-{\dot{E}}_{8\text{*}}\)