# Energy Efficiency Analysis of Fixed-Speed Pump Drives with Various Types of Motors
## 3 Assessment of the Energy Consumption of the Pump Unit
For the year-round operation of the pump unit, the annual energy consumption was calculated as follows:  
\[E_{y,m}=E_{d,m}\cdot 365. \tag{6}\]  
The cost of electricity consumed (in Euro), considering the accepted grid tariffs \(GT=0.1987\,\)C/kW-h for non-household consumers [27] for Germany in the second half of 2018, was calculated as follows:  
\[C_{y,m}=E_{y,m}\cdot GT. \tag{7}\]  
We also assessed the energy consumption during the whole life cycle of the pump system, which is usually 15-20 years [28; 29]. We defined the energy cost for the lifespan of \(n=20\) years without taking into account the maintenance costs and the initial cost of the motors since the market cost of the motors depends on many factors and this was beyond of the topic of the present paper. Besides, the pump lifetime cost often consists mostly of the energy cost (\(>\)50-60%) [28; 29]. The net present value (NPV) of the lifecycle cost was calculated as follows:  
\[C_{LCCen,m}=C_{y,m}/(1+(y-p))^{n} \tag{8}\]  
where \(y\) is the interest rate (assumed to be 0.04) and \(p\) is the expected annual inflation (assumed to be 0.02) [28; 29]. In order to correlate the cost of electricity consumed with using various electric motors in pump units, the differences between the costs of electricity required by the electric motor with the highest \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Motor** & **1** & **2** & **3** & **4** \\ \hline
1. LSPMSM SEW DRU J & 996.2 & 1266.1 & 1520.3 & 1742.3 \\
2. LSPMSM Synchro-VERT & 971.3 & 1258.6 & 1527.4 & 1760.8 \\
3. LSPMSM WEG WQUattro & 1022.6 & 1295.2 & 1550.9 & 1773.1 \\
4. IM Siemens 1 LE1004 & 982.2 & 1262.0 & 1526.3 & 1757.5 \\
5. IM WEG W22 & 992.9 & 1264.8 & 1524.4 & 1753.8 \\
6. IM Siemens 1 LE1003 & 1003.1 & 1289.9 & 1562.5 & 1802.5 \\
7. IM WEG W21 & 1004.4 & 1293.1 & 1566.0 & 1805.0 \\
8. IM ABB M3 BP & 1029.4 & 1309.4 & 1576.4 & 1812.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Power consumption \(P_{1,\mu}\) (W). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mode Number \(i\)** & **1** & **2** & **3** & **4** \\ \hline Operation time (\%) & 44 & 35 & 15 & 6 \\ Operation time (h/day) & 10.56 & 8.4 & 3.6 & 1.44 \\ \(Q_{i}\) (\%) & 25 & 50 & 75 & 100 \\ \(Q_{i}\) (m\({}^{3}\)/h) & 4.75 & 9.50 & 14.25 & 19.00 \\ \(H_{pump,i}\) (\%) & 120 & 118 & 113 & 100 \\ \(H_{pump,i}\) (m) & 21.4 & 21.0 & 20.2 & 17.8 \\ \(P_{mech,i}\) (W) & 851 & 1116 & 1361 & 1573 \\ \(P_{mech,i}\) (\%) & 38.7 & 50.7 & 61.9 & 71.5 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c} \hline \hline
1. LSPMSM SEW DRU J & 85.5 & 88.1 & 89.5 & 90.3 \\
2. LSPMSM SynchroVERT & 87.7 & 88.6 & 89.1 & 89.3 \\
3. LSPMSM WEG WQUattro & 83.3 & 86.1 & 87.8 & 88.7 \\
4. IM Siemens 1 LE1004 & 86.7 & 88.4 & 89.2 & 89.5 \\
5. IM WEG W22 & 85.8 & 88.2 & 89.3 & 89.7 \\
6. IM Siemens 1 LE1003 & 84.9 & 86.5 & 87.1 & 87.3 \\
7. IM WEG W21 & 84.8 & 86.3 & 86.9 & 87.2 \\
8. IM ABB M3 BP & 82.7 & 85.2 & 86.3 & 86.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Interpolated values of efficiency of electric motors. energy consumption (IE3 class motor No. 8 manufactured by ABB, Zurich, Switzerland) and the other seven motors were calculated according to Equation (9). The calculation results according to Equations (4)-(9) are summarized in Tables 4 and 5, and are also shown in Figures 5 and 6. \[S_{y,m}=C_{y,8}-C_{y,(I\ldots\ 7)} \tag{9}\]  
Figure 5 shows that the electric motor 3 (LSPMSM of the IE4 the class) consumed more electricity than IMs 6 and 7 of the IE3 class in the considered duty cycle, but less electricity than IM 8 of the IE3 class. Thus, the said IE4 class electric motor provided lower cost savings compared to the IE3 class electric motors 6 and 7. LSPMSMs 1 and 2 had energy consumptions approximately matching those of IMs 4 and 5 of the IE4 class. The lowest energy consumption was exhibited by electric motor 2 (SynchroVERT LSPMSM) and the greatest energy consumption was exhibited by electric motor 8 (IM by ABB). Figure 5: (**a**) Annual energy consumption.