Table 3 Cost balance equations.

From: Performance analysis of integrated solar and natural gas combined cycle power plants in high solar potential regions

Component

Exergetic cost rate balance equation

Auxiliary equation

AC

\(\:{\dot{C}}_{22}+{\dot{C}}_{W,AC}+{\dot{Z}}_{AC}={\dot{C}}_{23}\)

\(\:{c}_{w,AC}=\:{c}_{w,GT}\)

CC

\(\:{\dot{C}}_{24}+{\dot{C}}_{23}+{\dot{Z}}_{CC}={\dot{C}}_{25}\)

\(\:\frac{{\dot{C}}_{23}}{{\dot{E}}_{23}}=\:\frac{{\dot{C}}_{25}}{{\dot{E}}_{25}}\)

GT

\(\:{\dot{C}}_{25}+{\dot{Z}}_{W,GT}={\dot{C}}_{26}+{\dot{C}}_{GT}\)

\(\:\frac{{\dot{C}}_{25}}{{\dot{E}}_{25}}=\:\frac{{\dot{C}}_{26}}{{\dot{E}}_{26}}\)

HRSG

\(\:{\dot{C}}_{26}+{\dot{C}}_{19}+{\dot{C}}_{14}+{\dot{Z}}_{HRSG}={\dot{C}}_{27}+{\dot{C}}_{20}+{\dot{C}}_{1}\)

\(\:\frac{{\dot{C}}_{26}}{{\dot{E}}_{26}}=\:\frac{{\dot{C}}_{27}}{{\dot{E}}_{27}}\)

HPST

\(\:{\dot{C}}_{1}+{\dot{Z}}_{W,HPST}={\dot{C}}_{2}+{\dot{C}}_{W,HPST}\)

\(\:\frac{{\dot{C}}_{1}}{{\dot{E}}_{1}}=\:\frac{{\dot{C}}_{2}}{{\dot{E}}_{2}}\)

IPST

\(\:{\dot{C}}_{3}+{\dot{Z}}_{W,IPST}={\dot{C}}_{5}+{\dot{C}}_{W,IPST}\)

\(\:\frac{{\dot{C}}_{3}}{{\dot{E}}_{3}}=\:\frac{{\dot{C}}_{5}}{{\dot{E}}_{5}\:}\)

LPST

\(\:{\dot{C}}_{6}+{\dot{Z}}_{W,LPST}={\dot{C}}_{8}+{\dot{C}}_{W,LPST}\)

\(\:\frac{{\dot{C}}_{6}}{{\dot{E}}_{6}}=\:\frac{{\dot{C}}_{8}}{{\dot{E}}_{8}}\)

Cond1

\(\:{\dot{C}}_{8}+{\dot{C}}_{15}+{\dot{Z}}_{{cond}_{1}}={\dot{C}}_{9}+{\dot{C}}_{14}\)

\(\:\frac{{\dot{C}}_{8}}{{\dot{E}}_{8}}=\:\frac{{\dot{C}}_{9}}{{\dot{E}}_{9}}\)

Cond2

\(\:{\dot{C}}_{31}+{\dot{C}}_{35}+{\dot{Z}}_{{cond}_{2}}={\dot{C}}_{32}+{\dot{C}}_{36}\)

\(\:\frac{{\dot{C}}_{31}}{{\dot{E}}_{31}}=\:\frac{{\dot{C}}_{32}}{{\dot{E}}_{32}}\)

P4

\(\:{\dot{C}}_{20}+{\dot{C}}_{W,{P}_{4}}+{\dot{Z}}_{{P}_{4}}={\dot{C}}_{21}\)

\(\:{c}_{w,{P}_{4}}=\:{c}_{w,HPST}\)

P1

\(\:{\dot{C}}_{9}+{\dot{C}}_{W,{P}_{1}}+{\dot{Z}}_{{P}_{1}}={\dot{C}}_{10}\)

\(\:{c}_{w,{P}_{1}}=\:{c}_{w,HPST}\)

P2

\(\:{\dot{C}}_{11}+{\dot{C}}_{W,{P}_{2}}+{\dot{Z}}_{{P}_{2}}={\dot{C}}_{12}\)

\(\:{c}_{w,{P}_{2}}=\:{c}_{w,HPST}\)

P3

\(\:{\dot{C}}_{13}+{\dot{C}}_{W,{P}_{3}}+{\dot{Z}}_{{P}_{3}}={\dot{C}}_{14}\)

\(\:{c}_{w,{P}_{3}}=\:{c}_{w,LHST}\)

OFWH1

\(\:{\dot{C}}_{10}+{\dot{C}}_{7}+{\dot{Z}}_{{OFWH}_{1}}={\dot{C}}_{11}\)

 

OFWH2

\(\:{\dot{C}}_{12}+{\dot{C}}_{4}+{\dot{Z}}_{{OFWH}_{2}}={\dot{C}}_{13}\)

 

ORT

\(\:{\dot{C}}_{29}+{\dot{Z}}_{W,ORT}={\dot{C}}_{30}+{\dot{C}}_{ORT}\)

\(\:\frac{{\dot{C}}_{29}}{{\dot{E}}_{29}}=\:\frac{{\dot{C}}_{30}}{{\dot{E}}_{30}}\)

HE

\(\:{\dot{C}}_{30}+{\dot{C}}_{34}+{\dot{Z}}_{HE}={\dot{C}}_{31}+{\dot{C}}_{33}\)

\(\:\frac{{\dot{C}}_{30}}{{\dot{E}}_{30}}=\:\frac{{\dot{C}}_{31}}{{\dot{E}}_{31}}\)

P4

\(\:{\dot{C}}_{32}+{\dot{C}}_{W,{P}_{4}}+{\dot{Z}}_{P4}={\dot{C}}_{33}\)

\(\:{c}_{w,{P}_{4}}=\:{c}_{w,ORT}\)

Evap1

\(\:{\dot{C}}_{27}+{\dot{C}}_{34}+{\dot{Z}}_{HRorg}={\dot{C}}_{28}+{\dot{C}}_{29}\)

\(\:\frac{{\dot{C}}_{34}}{{\dot{E}}_{34}}=\:\frac{{\dot{C}}_{29}}{{\dot{E}}_{29}}\)

PTC

\(\:{\dot{C}}_{18}+{\dot{C}}_{q,solar}+{\dot{Z}}_{PTC}={\dot{C}}_{17}\)

\(\:{\dot{C}}_{q,solar}=0\)

TES

\(\:{\dot{C}}_{17}+{\dot{C}}_{21}+{\dot{Z}}_{TES}={\dot{C}}_{19}+{\dot{C}}_{18}\)

\(\:\frac{{\dot{C}}_{17}}{{\dot{E}}_{17}}=\:\frac{{\dot{C}}_{19}}{{\dot{E}}_{19}}\)

Gen

\(\:{\dot{C}}_{28}+{\dot{C}}_{3*}++{\dot{Z}}_{GEN}={\dot{C}}_{37}+{\dot{C}}_{7*}+{\dot{C}}_{4*}\)

\(\:\frac{{\dot{C}}_{4*}-{\dot{C}}_{3*}}{{\dot{E}}_{4*}-{\dot{E}}_{3*}}=\:\frac{{\dot{C}}_{7*}-{\dot{C}}_{3*}}{{\dot{E}}_{7*}-{\dot{E}}_{3*}}\)

P5

\(\:{\dot{C}}_{1*}+{\dot{C}}_{W,{P}_{5}}+{\dot{Z}}_{{P}_{5}}={\dot{C}}_{2*}\)

\(\:{c}_{w,{P}_{5}}=\:{c}_{w,ORT}\)

SHE

\(\:{\dot{C}}_{2*}+{\dot{C}}_{4*}+{\dot{Z}}_{SHE}={\dot{C}}_{3*}+{\dot{C}}_{5*}\)

\(\:\frac{{\dot{C}}_{4*}}{{\dot{E}}_{4*}}=\:\frac{{\dot{C}}_{5*}}{{\dot{E}}_{5*}}\)

Ev1

\(\:{\dot{C}}_{5*}+{\dot{Z}}_{EXV1}={\dot{C}}_{6*}\)

 

Abs

\(\:{\dot{C}}_{6*}+{\dot{C}}_{13}+{\dot{C}}_{10}+{\dot{Z}}_{Abs}={\dot{C}}_{1*}+{\dot{C}}_{12*}\)

\(\:\frac{{\dot{C}}_{6*}+{\dot{C}}_{10*}}{{\dot{E}}_{6*}+{\dot{E}}_{10*}}=\:\frac{{\dot{C}}_{1*}}{{\dot{E}}_{1*}}\:,\:\:{c}_{13*}=0\)

Evap2

\(\:{\dot{C}}_{9*}+{\dot{C}}_{11*}+{\dot{Z}}_{{Evap}_{2}}={\dot{C}}_{22*}+{\dot{C}}_{10*\:}\)

\(\:\frac{{\dot{C}}_{9*}}{{\dot{E}}_{9*}}=\:\frac{{\dot{C}}_{10*}}{{\dot{E}}_{10*}}\)\(\:{c}_{11*}=0\)

Ev2

\(\:{\dot{C}}_{8*}+{\dot{Z}}_{{Ev}_{2}}={\dot{C}}_{9*}\)

 

Cond3

\(\:{\dot{C}}_{7*}+{\dot{C}}_{15*}+{\dot{Z}}_{{cond}_{2}}={\dot{C}}_{8*}+{\dot{C}}_{14*}\)

\(\:\frac{{\dot{C}}_{7*}}{{\dot{E}}_{7*}}=\:\frac{{\dot{C}}_{8*}}{{\dot{E}}_{8*}}\)

\(\:{c}_{15*}=0\)

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