Table 1 Energy and exergy balance equations for all WPWVCRS components.

Compressor

\({\dot{\text{W}}}_{{{\text{com}}}} = {\dot{\text{m}}}_{1} ({\text{h}}_{2} - {\text{h}}_{1} )\)

\({\text{Ed}}_{{{\text{com}}}} = {\text{T}}_{0} \times \left[ {{\dot{\text{m}}}_{1} ({\text{s}}_{2} - {\text{s}}_{1} )} \right]\)

Condenser

\(\begin{aligned} {\dot{\text{Q}}}_{{{\text{con}}}} { = } & {\dot{\text{m}}}_{{1}} {\text{(h}}_{{3}} - {\text{h}}_{{2}} {)} \\ {\dot{\text{Q}}}_{{{\text{con}}}} { = } & {\dot{\text{m}}}_{{5}} {\text{(h}}_{{6}} - {\text{h}}_{{5}} {)} \\ \end{aligned}\)

\({\text{Ed}}_{{{\text{con}}}} {\text{ }} = {\text{ T}}_{0} \times \left[ {{\dot{\text{m}}}_{1} ({\text{s}}_{3} - {\text{s}}_{2} ) + {\dot{\text{m}}}_{5} ({\text{s}}_{6} - {\text{s}}_{5} )} \right]\)

Expansion valve

\({\text{h}}_{{3}} {\text{ = h}}_{{4}}\)

\({\text{Ed}}_{{{\text{Ex}}{\text{.V}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{1} {\text{(s}}_{4} - {\text{s}}_{3} )} \right]\)

Evaporator

\(\begin{aligned} {\dot{\text{Q}}}_{{{\text{eva}}}} { = } & {\dot{\text{m}}}_{{1}} {\text{(h}}_{{1}} - {\text{h}}_{{4}} {)} \\ {\dot{\text{Q}}}_{{{\text{eva}}}} { = } & {\dot{\text{m}}}_{{8}} {\text{(h}}_{{8}} - {\text{h}}_{{{10}}} {)} \\ \end{aligned}\)

\({\text{Ed}}_{{{\text{eva}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{1} {\text{(s}}_{1} - {\text{s}}_{4} ){\dot{ + \text{m}}}_{8} {\text{C}}_{{{\text{p}}.8}} {\text{ln}}\frac{{{\text{T}}_{8} }}{{{\text{T}}_{{10}} }}} \right]\)

Pump3

\({\dot{\text{W}}}_{{{\text{Pu}}3}} = {\dot{\text{m}}}_{5} ({\text{h}}_{5} - {\text{h}}_{7} )\)

\({\text{Ed}}_{{{\text{Pu3}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{5} {\text{(s}}_{5} - {\text{s}}_{7} )} \right]\)

Cooling tower

\(\begin{aligned} {\dot{\text{Q}}}_{{{\text{WCT}}}} = & {\dot{\text{m}}}_{{{\text{WCT}}}} {\text{C}}_{{{\text{p}}{\text{.WCT}}}} \\&\left( {{\text{T}}_{{{\text{WCT}}{\text{.w}}_{{\text{i}}} }} - {\text{T}}_{{{\text{WCT}}{\text{.w}}_{{\text{o}}} }} } \right) \\ = & {\dot{\text{m}}}_{{6}} {\text{(h}}_{{7}} - {\text{h}}_{{6}} {)} \\ \end{aligned}\)

\({\text{Ed}}_{{{\text{WCT}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{5} {\text{(s}}_{7} - {\text{s}}_{6} ) - \left( {{\dot{\text{Q}}}_{{{\text{WCT}}}} {\text{/T}}_{6} } \right)} \right]\)

Pump 1

\({\dot{\text{W}}}_{{{\text{Pu}}1}} = {\dot{\text{m}}}_{8} ({\text{C}}_{{{\text{p}}.10}} {\text{T}}_{{10}} - {\text{C}}_{{{\text{p}}.9}} {\text{T}}_{9} )\)

\({\text{Ed}}_{{{\text{Pu1}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{8} {\text{C}}_{{{\text{p}}.9}} {\text{ln}}\frac{{{\text{T}}_{{10}} }}{{{\text{T}}_{9} }}} \right]\)

Pump 2

\({\dot{\text{W}}}_{{{\text{Pu2}}}} = {\dot{\text{m}}}_{11} ({\text{h}}_{13} - {\text{h}}_{12} )\)

\({\text{Ed}}_{{{\text{Pu2}}}} {\text{ = T}}_{0} \times \left[ {{\dot{\text{m}}}_{{11}} {\text{(s}}_{{13}} - {\text{s}}_{{12}} )} \right]\)

Ice storage tank

\(\dot{\text{Q}}_{{\text{ISB}}} = \dot{\text{Q}}_{{8 - 9}} + \dot{\text{Q}}_{{11 - 13}} + \dot{\text{Q}}_{l}\)

\({\dot{\text{E}d}}_{{{\text{ISB}}}} {\text{ = T}}_{0} \times {\dot{\text{S}}}_{{{\text{gen}}{\text{.ISB}}}}\)

\(\begin{aligned} {\dot{\text{S}}}_{{{\text{gen}}{\text{.ISB}}}} = & - \frac{1}{{{\text{T}}_{0} }}{\dot{\text{Q}}}_{{\text{l}}} - \frac{1}{{{\text{T}}_{{13}} }}{\dot{\text{Q}}}_{{11 - 13}} - \frac{1}{{{\text{T}}_{9} }}{\dot{\text{Q}}}_{{8 - 9}} \\ \quad & {\text{ + }}\Delta {\dot{\text{S}}}_{{{\text{ISB}}{\text{.freez}}}} {\text{ + }}\Delta {\dot{\text{S}}}_{{{\text{ISB}}{\text{.melt}}}} \\ \end{aligned}\)

Air handling unit

\(\begin{aligned} {\dot{\text{Q}}}_{{{\text{AHU}}}} { = } & {\dot{\text{m}}}_{{{11}}} {\text{(h}}_{{{12}}} - {\text{h}}_{{{11}}} {)} \\ {\dot{\text{Q}}}_{{{\text{AHU}}}} { = } & {\dot{\text{m}}}_{{{14}}} {\text{(h}}_{{{15}}} - {\text{h}}_{{{14}}} {)} \\ \end{aligned}\)

\({\text{Ed}}_{{{\text{AHU}}}} = {\text{T}}_{0} \times \left[ \begin{aligned} & {\dot{\text{m}}}_{{11}} ({\text{s}}_{{12}} - {\text{s}}_{{11}} ) \\ & + {\dot{\text{m}}}_{{15}} ({\text{s}}_{{15}} - {\text{s}}_{{14}} ) \\ \end{aligned} \right]\)

Wind turbine

\(\begin{aligned} {\text{Po}}_{{{\text{real}}{\text{.pro}}}} { = } & {\text{ C}}_{{{\text{p}}{\text{.a,max}}}} {\upeta }_{{{\text{tr}}}} {\upeta }_{{{\text{gen}}}} \\ \quad & \times \frac{{1}}{{2}}{\uprho }_{{{\text{air}}}} {\text{A}}_{{{\text{s}}{\text{.a}}}} {\text{v}}_{{{\text{Wi}}}}^{{3}} \\ \end{aligned}\)

\(\begin{aligned} {\text{Ed}}_{{{\text{WT}}}} = & \left[ \begin{aligned} & \Delta {\text{Ex}}_{{{\text{physical}}{\text{.WT}}}} + \Delta {\text{Ex}}_{{{\text{chemical}}{\text{.WT}}}} \\ & + \Delta {\text{Ex}}_{{{\text{kinitic}}{\text{.WT}}}} - {\text{Po}}_{{{\text{ave}}}} - \dot{\text{Q}}_{{{\text{waste}}}} \\ \end{aligned} \right] \\ \quad & \times \left( {1 - \frac{{{\text{T}}_{0} }}{{{\text{T}}_{{{\text{gen}}{\text{.WT}}}} }}} \right) \\ \end{aligned}\)