## 6 Initial Cost and Payback Period of the Motors  
Since the motors have different initial costs, it is necessary to compare not only the energy savings they provide but also their payback period. When calculating the payback period, 2 cases are  
Figure 10: Time dependences for different motors (case 3): (**a**) cost vs. time; (**b**) cost savings compared with IE2 motor vs. time. considered: (1) the case of using a higher class motor instead of an IE2 class motor when a new pump unit is commissioned; (2) the case of replacement of an IE2 class motor with a motor of a higher energy efficiency class in a pump unit in service. The initial investment cost of the 4 kW, the 4-pole IE2 IM is assumed to be 406.1 \(\mathbf{\xi}\)[69]. Studies [70; 71] show that the difference in the market value of the IMs of neighboring energy efficiency classes is usually in the range of 15-30%. A comparison of market price information for specific IM models confirms these findings. For this calculation, we will assume that the IE3 IM price is 22.5% higher than the IE2 IM price. Let us also assume that the IE4 IM price is 22.5% higher than the IE3 IM price. In the literature, there are various estimates of the increase in the cost of the DOL PMSM in comparison to the IE3 IM. Thus, in [70] it is said about the increase in cost by 100%. However, the authors of this paper see no objective reason for such a large increase in cost: Comparison of information on market prices for specific models, as a rule, leads to a difference in the price of IE3 IMs and DOL PMSMs in the range of 30-40%. For this calculation, we will assume that the price of the DOL PMSM is 35% higher than the price of the IE3 IM. Many studies point out that there are no objective reasons for a significant difference in the cost of DOL SynRMs and IE3 IMs [35; 36; 38; 70]. For this calculation, we will assume that the DOL SynRM price is equal to the IE3 IM price. Comparing the initial cost of the motors with the savings in electricity costs calculated in the previous section for case 3 (taking into account the losses in the cable and transformer), we calculate the payback periods of various motors when a new pump unit is put into operation, as:  
\[T_{payback}=(C_{IE2}-C_{motor})/C_{year}, \tag{13}\]  
where \(C_{motor}\) is the initial cost of the considered motor; \(C_{IE2}\) is the initial cost of the efficiency class IE2 motor; \(C_{year}\) is the motor annual energy savings. Table 10 and Figure 11 show the results of calculating the payback period when commissioning a new pump unit. In this case, the payback period for all motors is less than six months. This confirms the high profitability of using energy-efficient motors in new installations. Taking into account the losses in the cable and the transformer, the difference between the payback periods for the IE4 IM and the DOL PMSM (compare the heights of the corresponding columns of the diagrams in Figure 11a,c) is significantly reduced compared to the DOL SynRM. The DOL SynRM has the lowest payback period of 0.12 years. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Value** & **DOL SynRM** & **DOL PMSM** & **IE4 IM** & **IE3 IM** & **IE2 IM** \\ \hline Initial cost \(C_{motor},\mathbf{\xi}\) & 497.5 & 671.6 & 609.4 & 497.5 & 406.1 \\ Payback period, years (case 1) & 0.124 & 0.403 & 0.301 & 0.184 & – \\ Payback period, years (case 2) & 0.121 & 0.327 & 0.270 & 0.184 & – \\ Payback period, years (case 3) & 0.120 & 0.306 & 0.261 & 0.184 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of the payback period (the case of a new pump unit commissioning). Figure 11: _Cont._  
When a new pump unit is put into operation the use of an IE3 class motor can be reasonable in the very short term. Its payback period is 2.2 months (0.184 years), which is less than that of the IE4 IM and the DOL PMSM. However, in the longer term, namely 4 months (0.33 years), the IE4 IM and the DOL PMSM appear to be more cost-effective (see Table 10).