## 5 Assessment of Energy Consumption of the Two Considered Pump Systems  
This section is focused on the electrical energy consumption calculation for the two configurations of the mentioned pump systems: single-pump (Figure 3a, Table 1) and multi-pump (Figure 3b, Table 2). In the current simulation, it was assumed that 2-pole induction motors with rated powers of 1500 W and 750 W are used in these pumping systems. These motors have the IE3 energy efficiency level. To determine the efficiency of motors and frequency converters at the operating points calculated in the previous section, the data for seven standard modes are used (according to IEC 60034-30-2) at a certain value of \(T\) and \(n\) (Table 3). Such data are used because the standard IEC 60034-30-2 [26] requires the motor manufacturers to declare the motor efficiency in these seven operating points. Some of the manufacturers provide such data in their catalogs [27]. The data in Table 3 related to the efficiency of the considered induction motors and frequency converters are obtained experimentally. These data were obtained from testing of M3 AA90L2 and M3 AA80B2 motors (IM-1.5 kW and IM-750 W, correspondingly, IE3-class, manufacturer ABB) [28] powered by a frequency converter with a rated power of 1.5 kW (model Optidrive P2, manufacturer Invertek Drives) [29]. This test was performed according to IEC 60034-2-3, Method 2-3-C: Input-output method (Figure 9). Figure 8: The mechanical power of the examined pumping units depending on the flowrate. Figure 9: Test bench. The values of the efficiency of motors and frequency inverters in the considered operating points (Tables 1 and 2) found by the polynomial interpolation of the data in Table 3[4; 30] are shown in Table 4. The following notations are used in Table 4: nmotor is the motor efficiency of the single-pump system; nconv is the frequency converter efficiency of the single-pump system; nmotor1 is the motor efficiency of the multi-pump system for variable speed drive; nconv1 is the frequency converter efficiency of the multi-pump system for variable speed drive; nmotor2 is the efficiency of non-adjustable motor in multi-pump system. With the help of the obtained results from tables (Tables 1, 2 and 4), we can calculate the electric power consumption from the network (\(P_{1}\)), daily electricity consumption (\(E_{day}\)), annual electricity consumption (\(E_{year}\)), total amount of annual electricity costs (\(C_{year}\)), and annual cost savings (\(S_{year}\)) for the multi-pump system with low-power pumps in comparison with the single-pump system:  
\[P_{1}=\frac{P_{mech}}{\eta_{motor}\cdot\eta_{conv}} \tag{12}\]  
\[E_{day}=\frac{t_{\Sigma}}{1000}\cdot\sum_{i=1}^{10}\left(P_{1}(i)\cdot\frac{t_ {i}}{t_{\Sigma}}\right) \tag{13}\]  
\[E_{year}=E_{day}\cdot 365 \tag{14}\]  
\[C_{year}=E_{year}\cdot GT \tag{15}\]  
\[S_{year}=C_{year\,2}-C_{year\,1} \tag{16}\]  
where \(P_{mech}\), and \(\eta_{motor}\) are the mechanical power and efficiency of \(m\)-th electrical motor in the \(i\)-th operation mode; \(\eta_{conv}\) is the efficiency of \(m\)-th frequency converter in the \(i\)-th operation mode; \(t_{\Sigma}\) is the 24 h cycle time; \(t_{i}\) is the duration of the \(i\)-th operation mode; \(GT=0.2036\,\epsilon\)/kWh is the electrical energy costs in Germany in the second quarter of 2019 for 1 kW\(\cdot\)h for industrial applications [31]; \(C_{year\,1}\) and \(C_{year\,2}\) are the total annual energy costs of the multi-pump system (two pumps) and single-pump (one pump) system configurations. The results of the calculation according to Equations (12)-(16) are shown in Tables 5 and 6. Figure 10 shows the dependence of the electric power consumption by the pumping systems from the grid for the mentioned cases. The energy saving possibilities were calculated according to the data in Table 5 (Table 6). Thus, in the case of the multi-pump system (two parallel pumps), the energy