# Energy Efficiency Analysis of Fixed-Speed Pump Drives with Various Types of Motors
## 4 Assessment of the Energy Efficiency Index of the Pump Unit  
The energy efficiency of circulators operating primarily with a variable flow is evaluated in accordance with the EU regulation [25]. The profile indicated in Figure 3 and adopted as a typical pump load profile according to this document [25] is used to perform the calculations in Section 3. [PERSON] [8] suggests that the energy efficiency index (EEI) that is already well-established for the assessment of energy efficiency of circulators can be used for other types of pumps and fluid machinery.  
Thus, EEI is the most suitable indicator for assessing the energy efficiency of variable flow systems for various purposes, in contrast to the minimum efficiency index (MEI), which is based on efficiencies in a relatively limited range of operating points (75-110% of the flow) [8] and is defined in the regulation [40].  
According to the Europump association approach [41] (p. 12) and to [PERSON] et al. [42], EEI is defined by the formula:  
\[EEI=P_{1.avg}/P_{1.avg}, \tag{10}\]  
where \(P_{1.avg}\) is the average electric power consumed by the pump, which is determined using the following formula [41]:  
\[P_{1.avg}=\sum_{i=1}^{4}\left[\left(\frac{t_{i}}{t_{\Sigma}}\right)\cdot P_{1.i}\right]. \tag{11}\]  
The denominator in Equation (10), \(P_{1.avg}\), is the electric power of the reference system, which according to References [41; 42], is determined using Equation (11):  
\[P_{1.ref}=P_{hybrid.ref}/(\eta_{motor.ref}-\eta_{pump.min.req}), \tag{12}\]  
In both formulae, \(P_{hybrid.ref}\) is the hydraulic power of the reference system, which is defined as the product of flow \(Q_{BEP}\) (m\({}^{3}\)/s) and pump head \(H_{BEP}\) (Pa).  
In Equation (12), \(\eta_{motor.ref}\) is the efficiency of the reference electric motor [6], which was taken to be equal to 86.7% as the corresponding efficiency of a four-pole 2.2 kW electric motor of IE3 energy efficiency class. \(\eta_{pump.min.req}\) is the minimum required efficiency of the reference pump at the best efficiency point [40], which depends on the coefficient \(C\) determined by the type of pump, the rated rotational speed \(n\) of the pump and energy efficiency thereof, the flow \(Q_{BEP}\), and the specific speed \(n_{s}\), which in turn depends on \(H_{BEP}\) and \(n\). A detailed calculation of \(\eta_{pump.min.req}\) is not provided in the present document.  
Calculation results for Equations (10)-(12) are shown in Table 6.  
By observing the data in Table 6, it is evident that the EEI values for a pump unit with various electric motors corresponds to the patterns made apparent in Figure 5a,b. Therefore, EEI characterizes the energy consumption of a pump unit more objectively than the energy efficiency class (IE) of the electric motor, which depends only on the efficiency in the rated mode.  
It should be noted that for circulators subject to the EC regulation [25], since 2005, there has been a voluntary labeling of products by members of the Europump Association using the A-G letter grade for the energy efficiency class. The introduction of such labeling for industrial pump units may also be a consideration.