## 5 Pump Unit Lifetime Energy Costs
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(i\) & \(t_{d}\)/\(t_{\text{Z}}\), \% & **DOL SynRM x 3** & **DOL PMSM x 3** & **IE4 IM x 3** & **IE3 IM x 3** & **IE2 IM x 3** \\ \cline{2-7} \(P_{\
u}\)W & 1 & 25 & 12,744 & 12,508 & 12,700 & 13,211 & 13,505 \\ \cline{2-7} \(P_{\
u}\)W & 2 & 50 & 12,272 & 12,080 & 12,242 & 12,723 & 13,374 \\ \cline{2-7} \(P_{\
u}\)W & 3 & 25 & 10,830 & 10,764 & 10,828 & 11,258 & 13,007 \\ \hline \multicolumn{7}{c}{\(E_{\text{dary}}\), kW-hour} & 289 & 285 & 288 & 299 & 320 \\ \hline \multicolumn{7}{c}{\(E_{\text{dary}}\), kW-hour} & 105,379 & 103,875 & 105,146 & 109,311 & 116,641 \\ \hline Annual energy savings, kW-hour & 3754 & 4255 & 3832 & 2443 & – \\ \hline Annual cost savings \(C_{\text{dary}}\), \(\boldsymbol{\xi}\) & 764 & 866 & 780 & 497 & – \\ \hline Life cycle energy cost \(C_{\text{d}CC}\), k\(\boldsymbol{\xi}\) & 116.9 & 115.3 & 116.7 & 121.3 & 129.4 \\ \multicolumn{7}{c}{(per 20 years)} \\ \hline Life cycle cost savings \(S_{\text{d}CC}\), k\(\boldsymbol{\xi}\) & 12.5 & 14.2 & 12.8 & 8.13 & – \\ \hline Life cycle cost savings \(S_{\text{d}CC}\), \% & 9.7 & 10.9 & 9.9 & 6.3 & – \\ \multicolumn{7}{c}{(per 20 years)} \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculation of the energy consumption of three pump units considering the cable and transformer losses (case 3, \(m=3\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Motor**} & **Case** & **Annual Cost** & **Life Cycle Energy** & **Life Cycle Cost** & **Life Cycle Cost** \\  & **Number** & **Savings \(C_{\text{d}year}\)**, & **Cost \(C_{\text{d}CC}\), k\(\boldsymbol{\xi}\)** & **Savings, \(S_{\text{d}CC}\), k\(\boldsymbol{\xi}\)** & **Savings, \(S_{\text{d}CC}\), \%** \\  & **m** & \(\boldsymbol{\xi}\) & **(per 20 years)** & **(per 20 years)** & **(per 20 years)** \\ \hline \multirow{3}{*}{DOL SynRM} & 1 & 736 & 103.2 & 12.0 & 10.4 \\  & 2 & 757 & 113.0 & 12.4 & 9.9 \\  & 3 & 764 & 116.9 & 12.5 & 9.7 \\ \hline \multirow{3}{*}{DOL PMSM} & 1 & 658 & 104.5 & 10.8 & 9.3 \\  & 2 & 811 & 112.1 & 13.3 & 10.6 \\  & 3 & 866 & 115.3 & 14.2 & 10.9 \\ \hline \multirow{3}{*}{IE4 IM} & 1 & 675 & 104.2 & 11.0 & 9.6 \\  & 2 & 752 & 113.1 & 12.3 & 9.8 \\  & 3 & 780 & 116.7 & 12.8 & 9.9 \\ \hline \multirow{3}{*}{IE3 IM} & 1 & 497 & 107.1 & 8.1 & 7.1 \\  & 2 & 497 & 117.2 & 8.1 & 6.5 \\  & 3 & 497 & 121.3 & 8.1 & 6.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of the life cycle costs for various considered cases. Figure 9: Life cycle cost savings (20 years) using various motor types: (**a**) case 1 (without cable and transformer losses); (**b**) case 2 (3 pump units, considering the cable loss); (**c**) case 3 (3 pump units, considering the cable and transformer losses). As seen in Figure 9, the IE3 IM provides a life cycle cost savings \(S_{LCC}\) of 8.1 k\(\xi\) with respect to the IE2 IM. However, the amount of savings (8.1 k\(\xi\)) for the IE3 IM is the same for all three considered cases \(m=1\)-3 since the losses in the cable and transformer for the IE3 IM and the IE2 IM differ little (Figure 7). If the losses in the cable and the transformer are not taken into account (first case, \(m=1\)), the savings are greater for the DOL SynRM than for the DOL PMSM and the IE4 IM. Thus, the lifetime savings for the DOL SynRM are12 k\(\xi\), that is 1.2 k\(\xi\) higher than for the DOL PMSM; 1.0 k\(\xi\) higher than for the IE4 IM; and 3.9 k\(\xi\) higher than for the IE3 IM (Figure 9a). However, when taking into account the cable and transformer losses (second and third cases, \(m=2\), 3), the DOL PMSM and the IE4 IM provide greater savings than the DOL SynRM. In the third case, \(m=3\), the DOL PMSM and the IE4 IM provide 2.2 k\(\xi\) and 0.8 k\(\xi\) greater savings, respectively than the DOL SynRM (Figure 9c). The DOL PMSM, in this case, provides the maximum savings among all motors, which is 14.2 thousand \(\xi\) (SLCC = 10.9% higher with respect to the IE2 IM).