## 2 Evaluating Pump Energy Consumption  
In this section, the analytical dependencies used for evaluating the energy efficiency indicators of the motors are described. Figure 2 demonstrates the diagram of the considered pump unit that includes a centrifugal pump and an electric motor powered from the medium-voltage power supply via a step-down transformer. The electric motor is coupled to the pump without intermediate mechanical transmissions. The electrical power \(P_{1}\) consumed by the pump unit from the grid can be determined as the following [40]:  
\[P_{1}=\eta_{motor}\cdot P_{mech}+p_{cable}+p_{T}; \tag{1}\]  
\[P_{mech}=\eta_{pump}\cdot P_{hydr}=\eta_{pump}\cdot\wp\cdot\wp\cdot H\cdot Q =f(Q), \tag{2}\]  
where \(Q\) is the required flowrate; \(H\) is the hydraulic head defined from \(H\)-\(Q\) characteristic of the pump from the catalogue; \(g\) is the acceleration of gravity; \(\rho\) is the density of a liquid; \(P_{hydr}\) is the hydraulic power of the pump; \(P_{mech}\) is the input mechanical power of the pump, \(f(Q)\) is its dependence on \(Q\) obtained from the catalogue; \(\eta_{pump}\) is the pump efficiency; \(\eta_{motor}\) is the motor efficiency; \(p_{cable}\) is the electrical loss in the cable; \(p_{T}\) is the electrical loss in the transformer. Not only the losses in the motor considered but also the losses in the transmission line elements: the cable and transformer. The loss in the cable depends on the phase resistance of the cable and the RMS motor current [52]:  
\[p_{cable}=3\cdot R_{cable}\cdot{1_{motor}}^{2}, \tag{3}\]  
where \(R_{cable}\) is the cable phase resistance; \(I_{motor}\) is the motor current. The RMS motor current can be found as the following:  
\[I_{motor}=P_{mech}/(\surd{3\cdot V_{motor}}\cos\varphi\cdot\eta_{motor}), \tag{4}\]  
Figure 2: Diagram of a single pump unit for fixed-speed operation. where \(V_{motor}\) = 400 V is the line grid voltage; cos\(\varphi\) and \(\eta_{motor}\) are the motor power factor and efficiency, according to data from the manufacturer's catalogue. The transformer losses \(p_{T}\) can be calculated using the manufacturer's data as shown in Section 4. To calculate the mechanical power \(P_{mech}\), the pump characteristics from the manufacturer's datasheets were used [53]. Adjusting the flowrate using a throttling valve is assumed. The characteristics of a centrifugal pump B-NM4 65/25B/B (manufactured by Calpeda S.p.A., Montorso Vicentino, Vicenza, Italy) with the rated power \(P_{rate}\) = 4 kW and with the rated rotational speed \(n\) = 1450 rpm was assumed for the calculation [53]. The pump data are specified in Table 1. \(Q_{BEP}\) denotes the flow at the best efficient point (BEP), and H\({}_{\text{BEP}}\) denotes the pump head at BEP. In this study, five four-pole electric motors with the rated power of 4 kW are compared, namely DOL SynRM (a test prototype [35]), DOL PMSM (manufacturer WEG [54]), and induction motors of three different efficiency classes (manufacturers WEG and Siemens [55; 56; 57]). The efficiency and the power factor of the DOL PMSM and the IMs were taken from the datasheets. There are still no commercially available high-performance DOL SynRMs on the market to the best of our knowledge. ABB Group corporation has announced the launch of IE4 class DOL SynRM [58] production, however, at the moment of writing this manuscript, these motors are still not available on the market. For this reason, to evaluate the characteristics of a DOL SynRM, the data of the experimental sample described in [35] were assumed. Various characteristics of the motors are demonstrated in Table 2, Table 3, and Figure 3. The motor efficiency is specified in Table 3 and Figure 3a. The motor power factor is specified in Table 3 and Figure 3b. The RMS current for the considered motors is compared in Figure 3c. The motor current is calculated using Equation (4).