# Energy Efficiency Analysis of Fixed-Speed Pump Drives with Various Types of Motors
## 3 Assessment of the Energy Consumption of the Pump Unit  
The operation of the pump unit was considered in modes wherein water flow over the duty cycle changed in accordance with the typical characteristic of HVAC applications. A typical pump duty cycle (Figure 3) defined by EC regulations [25] is characterized by four modes. A notable feature of this cycle is that, most of the time, the pump operates at a flow rate much less than the rated value. For example, with the flow of 25% of the rated value, the pump operates for the fraction of time \(t_{i}/t_{\Sigma}=44\%\) where \(t_{\Sigma}\) is the total operation time taken to be equal to 24 h and \(t_{i}\) is the pump operation time in the said mode. Herein, the fraction of the operation time in the rated mode did not exceed 6%. Such a flow-time profile is typical for systems with widely varying demand of flow rate, i.e., for variable flow systems [5]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Type** & \(P_{RATE}\) **(W)** & \(n\) **(rpm)** & \(Q_{BEP}\) **(m3/h)** & \(H_{BEP}\) **(m)** & **Efficiency (\%)** \\ \hline Value & NM4 40/25B & 2200 & 1450 & 19 & 17.8 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nameplate data of the pump. Figure 3: Time dependence of water consumption per cycle. The electric motor was connected directly to the mains, i.e., motor speed was not adjusted using a frequency converter over the course of the cycle, and the flow \(Q\) of the pump was adjusted using a throttle. In this case, the water pressure changed in accordance with the \(Q\)-\(H\) curve of the pump, and the operating point was the intersection point of the pump characteristic and the hydraulic system characteristic. Figure 4 shows the interpolation results of the \(Q\)-\(H\) characteristic of the selected pump and the starting points, according to manufacturer data [17]. The mechanical (input) power curve of the pump as a function of flow is reported by the pump manufacturer (Figure 4b). From the curve, the pump power was determined in four operation modes (25%, 50%, 75%, and 100% of the flow). The flow corresponding to 100% was determined based on the pump efficiency curve [17], corresponding to maximum efficiency. Based on the known nameplate data, the efficiencies of the electric motors (Table 2) at the four operation modes of the pump unit were determined using polynomial interpolation of the loss curve \(\Sigma P_{loss.M}\) of each electric motor. As seen in [PERSON] and [PERSON] [26], the correlation between the electric motor loss and load is described well using a second-order polynomial, the coefficients of which can be easily obtained from the efficiencies at three points provided by the electric motors manufacturers. The obtained efficiency values are provided in Table 3, which also shows the following values for each operating mode: flow, pump head, and mechanical output power of the electric motors as percentages of the rated output. It can be observed that the pump ran in underload modes (\(Q\) < 100%) for most of the time. It was assumed that the head varied according to the \(Q\)-\(H\) curve of the pump (Figure 4a). The real electric power consumed from the mains in each mode was calculated according to Equation (4):  
\[P_{1.i.m}=P_{moch.i.m}/\eta_{M.i.m}, \tag{4}\]  
where \(\eta_{M.i.m}\) is the efficiency of the \(m\)th motor in the \(i\)th mode of operation. Calculation results are given in the Table 4.  
The daily energy consumption for each electric motor over a full duty cycle of the pump unit in accordance with the corresponding load profile was determined using the Equation (5). \[E_{d.m}=t_{\Sigma}\cdot\sum_{i=1}^{4}\left(P_{1.i.m}\cdot\frac{t_{i}}{t_{ \Sigma}}\right). \tag{5}\]  
Figure 4: (**a**) \(Q\)-\(H\) curve of the pump. (**b**) Dependence of the pump power on water flow [17].