SEPR Calculator

Formulas

\[% \begin{align*}% n &:= 54 && \text{( number of data bins )}\\% J &:= \{1,\ldots,n\} && \text{( bin-index set )}\\% K &:= \{A,B,C,D\}\subseteq J && \text{( interpolation subset )}\\% j &:= \text{[variable index in $J$]} && \text{( referred to $j$-bin )}\\% k &:= \text{[variable index in $K$]} && \text{( referred to $k$-bin )}\\% T_j &:= \text{[listed in Table VI]} && \text{( $j$-bin outdoor temper.$ $ )}\\% h_j &:= \text{[listed in Table VI]} && \text{( $j$-bin duration )}\\% T_A &:= 32\ \unicode{176}\text{C} && \text{( reference outdoor temper.$ $ )}\\% T_B &:= 25\ \unicode{176}\text{C} && \text{( $B$-bin outdoor temper.$ $ )}\\% T_C &:= 15\ \unicode{176}\text{C} && \text{( $C$-bin outdoor temper.$ $ )}\\% T_D &:= 5\ \unicode{176}\text{C} && \text{( $D$-bin outdoor temper.$ $ )}\\% P_k &:= \text{[input]} && \text{( cooling capacity at $T_k$ )}\\% P_j &:= \text{[interpolated from values in $K$]} && \text{( cooling capacity at $T_j$ )}\\% D_k &:= \text{[input]} && \text{( power input at $T_k$ )}\\% COP_k &:= P_k/D_k && \text{( coeff.$ $ of perform.$ $ at $T_k$ )}\\% COP_j &:= \text{[interpolated from values in $K$]} && \text{( coeff.$ $ of perform.$ $ at $T_j$ )}\\% \eta &:= \begin{cases}% 0.2 &\text{for low temp.} \\% 0.4 &\text{for medium temp.} % \end{cases} && \text{( variable load )}\\% \eta_j &:= \begin{cases}% 1 &\text{for }T_A{\leqslant}T_j \\% \frac{T_j-T_D}{T_A-T_D} &\text{for }T_D{<}T_j{<}T_A \\% 0 &\text{for }T_j{\leqslant}T_D % \end{cases} && \text{( variable load ratio at $T_j$ )}\\% PR_j &:= \eta\cdot\eta_j+1-\eta && \text{( part load ratio at $T_j$ )}\\% od_j &:= P_A\cdot PR_j && \text{( $j$-bin cooling demand )}\\% aod &:= \sum_{j\in J}od_j\cdot h_j && \text{( annual cooling demand )}\\% Cdc &:= 0.25 && \text{( degradation coefficient )}\\% s_j &:= \begin{cases}% 0 &\text{for }T_A{\leqslant}T_j \\% 1-od_j/P_j &\text{for }T_j{<}T_A % \end{cases} && \text{( capacity surplus at $T_j$ )}\\% \delta_j&:= s_j\cdot Cdc && \text{( degradation coeff.$ $ at $T_j$ )}\\% PD_j &:= (1-\delta_j)\cdot COP_j && \text{( degradated COP at $T_j$ )}\\% aec &:= \sum_{j\in J}od_j\cdot h_j/PD_j && \text{( annual el.$ $ consumption )}\\% SEPR &:= aod/aec && \text{( seasonal energy perf.$ $ ratio )} % \end{align*}% \]

References

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