Techno-economic optimal power rating of induction motors

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Applied Energy, Vol. 240, on April 2019, available at: https://doi.org/10.1016/j.apenergy.2019.02.016 Copyright 2019 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND Techno-economic Optimal Power Rating of Induction Motors Manuel Burgos Payán, Juan Manuel Roldán Fernández, José María Maza Ortega, and Jesús Manuel Riquelme Santos Abstract Electric motors are valuable, long-life industrial assets, whose lifespan is often measured in decades. A period of unplanned motor downtime in an industrial plant frequently incurs an expenditure of thousands of euros per hour. As a consequence, plant engineers often focus their decisions on reliability rather than on operating cost (energy bill). Unfortunately, the high price of energy and its growing trend mean that operating cost has an increasingly negative impact on production cost and company competitiveness. The problem of selecting the rated power of a line-operated single-speed electric motor to drive a time-variable mechanical load has traditionally been solved, based on the well-established root mean square (RMS) value of the time-power profile of the mechanical load. This conventional method of rating is strictly technical, since the rated power of the motor is determined, based only on the power profile of the load. No other factors are considered, such as the energy consumption throughout the whole in-service life of the motor, or, even better, the whole life cycle cost (LCC), which is defined as the net present value of purchasing, installing, operating (energy), maintaining and decommissioning the motor throughout its life. As a consequence, conventional rating often leads to the selection of motors with a power rating that is technically sufficient to drive the mechanical load, but insufficient to do so with the lowest possible energy (losses) consumption, or even better, with the lowest possible life cycle cost. A new analytical method to determine the techno-economic optimum power rating of a line-operated single-speed electric motor to drive a time-variable mechanical load will be introduced in this paper. The proposed method takes into account not only the technical restrictions due to the time-power profile of the mechanical load, but also the whole life cycle cost. Based on the list of electric motors offered in the manufacturer’s catalogue, the new methodology enables the optimum techno-economic rated power of the motor to be calculated, which minimizes the energy consumption (energy loss) throughout its in-service life or its total life cycle cost. The results show that the optimum techno-economic rating is one or two rated-power levels above the conventional rating based solely on the RMS load. Keywords: Induction motors; Life cycle cost; Energy efficiency; CO2 emissions; Power rating; Techno-economic optimization. 1. Introduction Electric motors enjoy extensive applications as drivers of a large variety of equipment in industrial and service sectors, as well as in household electric appliances. With the recent irruption of electric motors in the power train of current electric vehicles, electric 2 motors are now coming into their own with regard to road transport: one of the few fields of application that have been largely void of electric motors throughout the 20th century, and also a major contributor to carbon dioxide emissions worldwide. Electric motor systems are responsible for approximately 70% of industrial electricity consumption and for about 35% of non-residential electricity (services) consumption in the European Union (EU) [1,2]. In 2015, final electricity consumption in the EU-28 reached 2743 TWh, mainly on account of three sectors: industry, the sector with the highest consumption with a share of 36.34% (997 TWh), followed by the services sector, representing 30.50% (837 TWh), and then the residential sector with 28.99% (795 TWh) [3]. This means an estimated electric motor consumption for the EU-28 of 698 TWh in industry and 293 TWh in the services sector in 2015: a total of 991 TWh (36.11%), which is practically equal to the consumption of the whole industry sector. Given that the EU-28 average value of carbon dioxide equivalent (CO2eq) factor emissions was 374 thousand t(CO2eq)/TWh [4], as a consequence of the energy consumed in these two sectors by electric motors, approximately 371 million tonnes of CO2eq were emitted into the atmosphere in 2015. The role of electric motors as major consumers of electricity in industry and service sectors has been largely recognized by policymakers all over the world [5]. As a result, almost all the main economies have implemented some kind of regulation regarding motor efficiency as a method for improving productivity/competitiveness (savings in operating cost) and meeting international commitments on climate change (emission reductions due to energy savings). For example, in the EU, electric motors (0.75 kW - 375 kW) lie within the scope of the Ecodesign Directive [6,7]. In 2015, according to Prodcom (EU statistics on the production of manufactured goods), 10,511,819 multi-phase AC motors (excluding traction motors) rated at 0.75 kW – 375 kW were sold in the EU-28 [8]. Within this power range, the market is clearly dominated by three-phase AC induction motors, representing around 85% of the market share [9,10]. Issues related to energy consumption by electric motors and their related CO2 emissions have also been broadly discussed by researchers involving a wide variety of perspectives and publications: industry applications [11,12], energy saving [13,14], the convenience of using high-efficiency motors to replace standard motors [15], minimum efficiency performance standard [16], partial load [17] and oversizing [18,19], energy efficiency standards [20,21] and policies [22,23], the influence of voltage unbalance [24,25] and derating [26], harmonics [27] and other power quality issues [28], the convenience of rewinding or replacing failed motors [29], CO2 emissions [30,31], the variation in losses and efficiency under variable speed and load conditions [32,33], energy conservation [34,35] and others [36,37]. Naturally, electromobility applications (electric vehicles) are also receiving major attention from the research community form the point of view of energy management [38-40], regenerative braking [41,42], the use of batteries and ultracapacitors as energy storage devices [43], and others [44,45]. Focusing on the aspects more directly related to the rated power of induction motors and its energy efficiency class, in 1999, Akbaba [34] analysed the potential of energy conservation in industry by using energy-efficient electric motors compared with those of standard efficiency motors. Ferreira, Cisneros-González and de Almeida pointed out in [19] that most industrial three-phase squirrel-cage induction motors are oversized mainly due to the use of safety factors associated with uncertainty about mechanical load requirements, conservative design rules, and the discrete availability of commercial 3 rated power. In that work, the authors analysed the potential benefits and drawbacks of motor oversizing. Da Costa Bortoni [18] also agrees that the oversizing practice is more a problem related to the deficiency of proper information than a lack of “best practices”. The author warns that figuring out whether a motor is truly oversized is not a simple task and presents a road map to properly evaluate whether a direct line-fed three-phase induction motor is oversized. The problem of selecting the rated power of a line-operated single-speed electric motor to drive a time-variable mechanical load has been solved traditionally, based on the well-established RMS value of the time-power profile of the mechanical load. Since 1939, when L.E. Hildebrand published his paper “Duty cycles and motor rating” [46], the RMS method was fully accepted by the technical community and has been found in technical texts and teaching handbooks since then up to the present [47]. Nevertheless, this conventional method fully disregards all the aspects related to energy consumption, efficiency or operating (energy) cost, which precisely constitutes the greatest part of the total LCC. Although electric motors remain the subject of extensive research work, the influence of the selection of the optimum motor to drive a certain mechanical load is a subject rarely considered. But this is certainly an issue worth analysing, since the decision regarding the choice of a particular electric motor to drive a mechanical load determines the losses of the motor load system and thus its energy consumption, operating cost and associated CO2 emissions. In order to make an informed decision on the investment of any industrial equipment, such as the selection of a motor, it is essential to evaluate the initial investment (purchase, installation and commissioning cost), the net present value of the operating cost (energy and maintenance) throughout the whole in-service life of the motor, and the decommissioning cost (conditioning or removal cost and the residual value, which is the motor resale or scrap value) at the end of the expected life of the said motor. Decisionmaking based on the lowest LCC, although often recommended [48,10], has yet to become common engineering practice. This minimum LCC approach offers engineers a broader view of what can be expected from their decisions. This evaluation involves attaining reliable information on the mechanical load and on the electric motors for comparison in order to estimate the operating conditions and the energy and maintenance cost, while also taking into account the time value (depreciation) of money and potential annual energy cost increases. It is much more common to perform a simple payback period analysis which compares the total cost of investment to annual operating savings. Unfortunately, there is no method available for the calculation of the rated power value of a motor based on the lowest LCC, since the motor must be chosen by evaluation. To address this gap, a new analytical methodology to determine the optimum power rating of a single-speed electric motor to drive a time-variable mechanical load will be introduced in this paper. The proposed methodology takes into account not only the technical restrictions, due to the power profile of the mechanical load, but also either the energy consumption throughout the whole life of the motor or the net present value of purchasing, installing, commissioning, operating (energy), maintaining and disposing of the motor over its life cycle. Based on the list of electric motors offered in the catalogue of a manufacturer, the new methodology enables the calculation of the optimum technoeconomic rated power of the motor which minimizes either the energy consumption (energy loss) throughout its in-service life or its total LCC. Therefore, the proposal constitutes a clear advance with respect to the state of the art because the trial-and-error 4 procedures are surpassed. The proposed methodology is able to directly compute, in an analytical way, the motor rated power by minimizing the selected objective function for given loading conditions. As can be observed, the techno-economic approach of the proposed rating method is much more comprehensive than the conventional and well-established method of the RMS value of the load (which completely ignores energy cost) and could be seen as an extension or an evolution of the conventional method, which is already able to integrate (by taking into account) both the technical restrictions imposed by the mechanical load and the operating (energy) cost throughout the whole in-service life of the motor. After this introduction, the remainder of the paper is organized as follows. The conventional method of determining the rated power of a motor is reviewed in Section 2, with its main weaknesses explained. Section 3 presents the theory of the proposed method, including analytical expressions for optimum rated power, for minimum energy (losses) and for the minimum LCC. The main results of a case study are presented and briefly discussed in Section 4, where the advantages of the proposed optimization method in terms of energy and cost savings are also be shown. A sensitivity analysis to demonstrate the robustness of the solutions is included in this section. Finally, Section 5 summarizes the main findings of the work. A list price of IE2 and IE3 metric motors from a worldwide electric motor manufacturer has been included in the Appendix. 2. Selecting the Rating Power of a Motor The problem of selecting the rated power of a line-operated single-speed electric motor to drive a time-variable mechanical load, P(t), has traditionally been solved, based on the well-established RMS value of the time-power profile of the mechanical load [47,48]. Accordingly, a motor, with rated power (continuous running duty S1), PR, equal to or above the RMS value of the mechanical load power profile, PRMS, is selected from among those available, PRi, in the catalogue of the manufacturer (PR = min(PRi) ≥ PRMS), while observing peak load restrictions. This well-established approach is mainly focused on two ideas: • Maintenance of the temperature of the windings below their maximum allowable limit, thereby preventing a premature thermal failure which could shorten the expected in-service life of the motor. • Minimization of the purchase (and installation) cost of the motor. It should be borne in mind, however, that any motor with power rated over the RMS value of the power profile operates with a temperature below the maximum permitted by the insulation, and will have a longer in-service life than expected, since it has become less prone to failure. The selection of the motor with the lowest rated power compatible with the mechanical load profile in fact only guarantees the minimum purchase cost. Nevertheless, the purchase cost used to be a very small proportion (less than 5-10%) of the LCC of the motor, since the cost of energy forms the greatest part of the total cost [49-51]. As a consequence, conventional rating is nowadays questioned, mainly due to the fact that it completely disregards the cost of energy, which constitutes the greatest part of the total present cost. 5 3. Materials and Methods The problem of determining the techno-economic optimum rated power of a lineoperated single-speed cage induction motor for driving a specified time-variable mechanical load (at an early project stage) is addressed in this work. Although the use of power converters is becoming popular, line-operated motors are still the most common solution for driving industrial loads. Based on the list price and the technical data of electric motors offered in the catalogue of a manufacturer, the new method enables the analytical determination of not only the rated power of the motor, which minimizes energy consumption (energy loss) throughout its in-service life, but also its total LCC. The basic input data can be classified into three main categories: • Mechanical load. It is necessary to ascertain the (expected) time-power profile of the mechanical load, P(t), throughout the yearly operating time, T. • Motor. The list price and the technical data from a manufacturer’s catalogue are required. All of the motors should possess the same general characteristics: speed (number of poles), voltage, frequency, efficiency class, insulation class. • Economic data. The price of the electric energy and its expected yearly rate of growth are required, as are the discount rate and the estimated in-service life of the motor. The required information is presented in greater detail in the following sections. 3.1 Power losses Table 1 summarizes the efficiency data of low-voltage, four-pole, general-performance, cast-iron motors from a multinational manufacturer, for the IE3 and IE2 efficiency classes [52]. As can be observed, although efficiency at the 100% (full) load level is the only value of rated efficiency that must be determined according to the IEC 60034-2-1 [53], most manufacturers also include motor efficiency at the 75% and 50% load level in their catalogues (see Appendix). The efficiency data given in the manufacturer’s catalogue enable a model of power losses, PL(PR,Ppu = P/PR), to be extracted for every motor in that catalogue. For each rated power, PR, and normalized or relative power load, Ppu, the efficiency data, η(PR,Ppu), allow the power losses to be calculated corresponding to each relative power load: ·1 ( , / ) · · 1 ( , ) ( , ) pu R L R pu R pu R pu R R pu R pu PP P P P P P P P P P P P P P   = = − = −    (1) In this work, a simplified quadratic binomial model of power losses, PL(PR,Ppu), has been considered. This quadratic binomial power-loss model has two terms: • Constant losses, kLF. This term describes the constant or fixed no-load power losses, independent of the motor load. This term basically corresponds to the sum of the iron losses and friction and windage losses. • Variable losses, kLV·P2pu. This second term describes the variation in the loaddependent losses with the square of the normalized or relative power load, Ppu. 6 This term largely corresponds to the Joule effect in the (stator and rotor) conductors. 22 2 ( , / ) L R pu R LF LV LF LV pu R P P P P P P k k k k P P = = + = + (2) Table 1. Cage induction motors (CENELEC-design): efficiency data of general-performance cast-iron motors designed for low voltage (440 V, 50 Hz), four poles, IP 55, IC 411, and insulation class F (temperature rise class B) [52]. IE3 (premium efficiency) IE2 (high efficiency) Output kW Full load 100% * 3/4 load 75% 1/2 load 50% Full load 100% * 3/4 load 75% 1/2 load 50% 0.25 73.5 70.1 63.8 67.0 63.1 56.6 0.37 77.3 74.9 69.8 69.5 69.0 64.4 0.55 80.8 80.7 78.0 73.5 73.2 69.2 0.75 82.5 81.2 77.6 79.6 78.5 74.4 1.1 84.1 83.4 80.9 81.4 80.7 77.2 1.5 85.3 84.4 82.1 82.8 82.6 79.8 2.2 86.7 86.1 84.1 84.3 84.2 81.9 3 87.7 87.7 86.5 85.5 85.4 83.3 4 88.6 88.9 88.1 86.6 86.2 84.6 5.5 89.6 90.4 90.2 87.7 87.5 86.2 7.5 90.4 90.7 90.3 88.7 88.6 87.5 11 91.4 91.8 91.1 89.8 89.9 89.2 15 92.1 92.4 91.6 90.6 91.1 90.5 18.5 92.6 93.2 92.9 91.2 91.5 90.6 22 93.0 93.5 93.3 91.6 91.3 90.2 30 93.6 93.8 93.4 92.3 92.4 92.0 37 93.9 94.1 93.8 92.7 92.7 92.2 45 94.2 94.4 94.0 93.1 93.0 92.3 55 94.6 94.7 94.0 93.5 93.4 92.7 75 95.0 95.2 94.8 94.2 94.2 93.5 90 95.2 95.3 94.8 94.4 94.6 94.1 110 95.4 95.4 94.8 94.7 94.6 93.8 132 95.6 95.8 95.3 95.0 95.0 94.3 160 95.8 96.0 95.8 95.2 95.3 94.6 200 96.0 96.4 96.4 95.3 95.4 94.9 250 96.0 96.0 95.6 95.2 95.2 94.4 315 96.0 96.0 95.6 95.5 95.5 94.8 355 96.0 96.2 95.8 95.5 95.7 95.2 * Efficiency according to IEC 60034-30-1; 2014 [54] This quadratic binomial power-loss model is similar to that proposed in IEC/TS 60034- 31 [50], which is based on the intermediate results or constants ν0 and νL, calculated from the efficiency at the full load and 3/4 load levels. A similar matrix model of power losses, based on three known values of efficiency corresponding to three reference relative loads (100%, 75% and 50%), was also used in [19]. For each motor, the values of the two constants of the model of losses, kLF and kLV, can be identified from the lineal regression of the data on power losses versus the squared normalized power in Table 1. Table 2 shows the value of the constants of the model of 7 losses identified by linear regression of the power-loss data, which are determined by (1) from the manufacturer’s efficiency data. Table 2. Coefficients of the binomial power-loss model, PL(PR,Ppu) = kLF + kLV·P2pu, for IE3 and IE2 cage induction motors in Table 1. IE3 (premium efficiency) IE2 (high efficiency) Rated power Coefficients Goodness of fit Coefficients Goodness of fit PR (kW) kLF (kW) kLV (kW) Determination coefficient R2 Correlation coefficient kLF (kW) kLV (kW) Determination coefficient R2 Correlation coefficient 0.25 0.0650 0.0255 0.9961 0.9980 0.0878 0.0360 0.9895 0.9947 0.37 0.0709 0.0380 0.9983 0.9991 0.0811 0.0805 0.9975 0.9988 0.55 0.0594 0.0710 0.9995 0.9997 0.0958 0.1016 0.9980 0.9990 0.75 0.0916 0.0677 0.9997 0.9998 0.1074 0.0844 0.9995 0.9997 1.1 0.1046 0.1039 0.9993 0.9996 0.1319 0.1189 0.9992 0.9996 1.5 0.1339 0.1259 0.9966 0.9983 0.1478 0.1629 0.9989 0.9994 2.2 0.1667 0.1720 0.9985 0.9992 0.1863 0.2226 0.9996 0.9998 3.0 0.1734 0.2483 0.9995 0.9997 0.2302 0.2778 0.9998 0.9999 4.0 0.1897 0.3257 0.9999 0.9999 0.2833 0.3384 0.9980 0.9990 5.5 0.1846 0.4531 0.9999 1.0000 0.3345 0.4399 0.9985 0.9993 7.5 0.2758 0.5234 0.9992 0.9996 0.4013 0.5577 0.9987 0.9994 11.0 0.3681 0.6647 0.9997 0.9998 0.4789 0.7754 0.9988 0.9994 15.0 0.4831 0.8003 0.9995 0.9997 0.5273 1.0266 0.9998 0.9999 18.5 0.4430 1.0310 0.9994 0.9997 0.6784 1.1027 0.9996 0.9998 22.0 0.4997 1.1552 1.0000 1.0000 0.9356 1.0914 0.9977 0.9988 30.0 0.7355 1.3197 0.9997 0.9999 0.9247 1.5909 0.9980 0.9990 37.0 0.8398 1.5707 0.9994 0.9997 1.1401 1.7896 0.9975 0.9988 45.0 0.9955 1.7779 0.9999 1.0000 1.4145 1.9359 0.9981 0.9990 55.0 1.2840 1.8491 0.9996 0.9998 1.6376 2.2020 0.9984 0.9992 75.0 1.4232 2.5218 1.0000 1.0000 1.9445 2.6785 0.9999 0.9999 90.0 1.7778 2.7595 1.0000 1.0000 1.9750 3.3592 0.9999 1.0000 110 2.2579 3.0483 1.0000 1.0000 2.8050 3.3577 0.9999 0.9999 132 2.2770 3.7736 0.9987 0.9993 2.9986 3.9456 1.0000 1.0000 160 2.3514 4.6718 0.9999 0.9999 3.3545 4.6832 0.9988 0.9994 200 2.1808 6.1390 0.9999 0.9999 3.8725 5.9878 1.0000 1.0000 250 4.2477 6.2010 0.9992 0.9996 5.6330 6.9379 0.9993 0.9996 315 5.3521 7.8132 0.9992 0.9996 6.5326 8.2851 0.9997 0.9999 355 5.3670 9.3737 0.9991 0.9995 6.2609 10.4043 0.9989 0.9994 Finally, Figure 1 shows the point clouds of the fixed-loss constants (PR, kLF(PR)) and variable-loss constants (PR, kLV(PR)) in Table 2 as functions of the rated power of each of the motors. This figure also shows the respective linear regression lines of each of these constants with the rated power of the motors. For IE3 motors, the linear regression fitting results in: 2 ( ) · 0.1735 0.0152· ( 0.9712) LF R LFF LFV R R k P k k P P R + = + = 2 ( ) · 0.3253 0.0254· ( 0.9878) LV R LVF LVV R R k P k k P P R + = + = Using (2), the power-loss model yields: 22 ( , / ) · · ( · )· L R pu R LF LV pu LFF LFV R LVF LVV R pu P P P P P k k P k k P k k P P= = + = + + + (3) 8 IE3 kLF(PR) = 0.0152·PR+ 0.1735 R2= 0.9712 kLV(PR) = 0.0254·PR+ 0.3253 R2= 0.9878 0 2.5 5.5 7.5 10.0 0100 200 300 400 Rated power, PR(kW) Power-loss coefficients, kLF,kLV (kW) 0100 200 300 400 0 2.5 5.5 7.5 10.0 kLF(PR) = 0.0191·PR+ 0.2838 R2= 0.9815 kLV(PR) = 0.0273·PR+ 0.3741 R2= 0.9885 Rated power, PR(kW) Power-loss coefficients, kLF,kLV (kW) IE2 Figure 1. Point clouds and lines of linear regression corresponding to the fixed-loss constants (PR, kLF(PR)) and variable-loss constants (PR, kLV(PR)) as functions of the rated power for the IE3 and IE2 cage induction motors in Table 1. For IE3 motors, the linear regression fitting results in: 2 ( ) · 0.1735 0.0152· ( 0.9712) LF R LFF LFV R R k P k k P P R + = + = 2 ( ) · 0.3253 0.0254· ( 0.9878) LV R LVF LVV R R k P k k P P R + = + = Using (2), the power-loss model yields: 22 ( , / ) · · ( · )· L R pu R LF LV pu LFF LFV R LVF LVV R pu P P P P P k k P k k P k k P P= = + = + + + (3) For IE2 motors, the coefficients of the power-loss model yield: 2 ( ) · 0.2838 0.0191· ( 0.9815) LF R LFF LFV R R k P k k P P R + = + = 2 ( ) · 0.3741 0.0237· ( 0.9885) LV R LVF LVV R R k P k k P P R + = + = 3.1.1 A first approach to the optimum power rating for minimum power losses By using the coefficients of the binomial power-loss model, Figure 2 shows the variation in power losses with the power load for five IE3 motors rated 22 kW, 30 kW, 37 kW, 45 kW and 55 kW. As can be observed, as the power load grows, the curves of losses cut off, two by two, at points P22-30 (15.98, 1.11), P30-37 (18.01, 1.27), P37-45 (24.08, 1.51) and P45-55 (32.87, 1.94). These four intersection points allow for the definition of five power-load intervals, relative to the losses: • For a power load lower than that corresponding to the first crossing point, P22-30 (P ≤ 15.98 kW), the minimum power losses correspond to the motor rated 22 kW. • For a power load between the points P22-30 and P30-37 (15.98 kW < P ≤ 18.01 kW), the minimum power losses correspond to the motor rated 30 kW. • For a power load between the points P22-37 and P37-45 (18.01 kW < P ≤ 24.08 kW), the minimum power losses correspond to the motor rated 37 kW. 15 Finally, the cost of the energy loss during the first year of operation can be calculated using the power-loss model (3), written as: 2 2 ( , ( )) ( , ( ))· · · ( · )· · RMS EL R L R E LFF LFV R LVF LVV R E R P C P P t E P P t p T k k P k k P p P  =  + + +   As a result, the total cost of the first year of operation of the motor can be expressed as the sum of the annual cost of the mechanical energy and the annual cost of the losses during the first year: 2 2 ( , ( )) ( ( )) ( , ( )) · · ( · )· · O R M EL R RMS m LFF LFV R LVF LVV R E R C P P t C P t C P P t P T P k k P k k P p P =+   + + + +   In order to calculate the cumulated present or actual value of the cost of the energy loss throughout the whole in-service life of the motor, CPEL, it is necessary to consider the depreciation effect of the money in each of the N future years of expected life of the motor, by means of the discount rate, d, and the effect of the annual increase in the price of energy, ΔpE, resulting in: 11 (1 ) 1 ( ( , ( ))) ( , ( )) ( , ( )) (1 ) (1 ) (1 ) 1 ( , ( )) ( , ( ))· (1 ) n NN E PEL EL R EL R EL R nn nn eq N eq EL R EL R P N eq eq p C NPV C P P t C P P t C P P t dd d C P P t C P P t k dd == + = = = ++ +− == +  where the equivalent discount rate is: 1E eq E dp dp − =+ and the cumulative present value coefficient is: (1 ) 1 (1 ) N eq PN eq eq d kdd +− =+ The present or actual cost of the motor over its N expected years of in-service life, considering an equivalent discount rate, deq, can be expressed as: ( ) ( ) 1 2 2 (1 ) ( , ( )) ( ) ( ( )) ( , ( )) ( ) ( ) (1 ) ( ) ( ( )) ( , ( )) · · ( ) ( ) ·( · ) · · ( · )· · · n NE R R M EL R D R R R n n R M L R E P D R R R RMS EQ PF PV R m LFF LFV R LVF LVV R E P R p LCC P P t I P C P t C P P t C P V P d I P E P t E P P t p k C P V P P k c c P T P k k P k k P p k P = + = − − + − + + = − − + − +   − + − + + + +    Therefore, the optimum rated power of the motor, which minimizes the LCC, can be obtained by cancelling out the partial derivative of the LCC, with respect to the rated power, resulting in: 2 42 2· ( , ( )) · · · · · 0 LVF R LVV REQ PV LFV RMS E P R R R k P k LCC P P t k c k P T p k P P P   = − − − + =      16 This minimum condition can also be written as: ( ) ( ) 3 3 2 · · · 2 · · · · · 0 EQ PV R LFV R LVF LVV R RMS E P k c P k P k k P P T p k+ − + = Grouping the coefficients of the cubic equation: ( ) 3 2 2 · · · · · · · · · · 2 · · · · 0 EQ PV LFV E P R LVV RMS E P R LVF RMS E P k c k T p k P k P T p k P k P T p k+ − − = Accordingly, the minimum condition can be written as: 22 3· · · · 2 · · · · 0 · · · · · · · · LVV RMS E P LVF RMS E P RR EQ PV LFV E P EQ PV LFV E P k P T p k k P T p k PP k c k T p k k c k T p k − − = ++ , which can be solved using Cardano’s method. Therefore, the optimum rated power, which minimizes the LCC of the motor, results in: 22 33 · · · · · · · · · · · · · · · · LVF RMS E P LVF RMS E P R LCCmin EQ PV LFV E P EQ PV LFV E P k P T p k k P T p k Pk c k T p k k c k T p k = +  + −  ++ where the discriminant, Δ, is: 23 22 · · · · · · · · · · · · 3( · · · · ) LVF RMS E P LVV RMS E P EQ PV LFV E P EQ PV LFV E P k P T p k k P T p k k c k T p k k c k T p k      = −         ++     It is worth noting that, when the equivalent discount rate approaches zero, the present operating cost, that is, the present cost of the energy throughout the life-cycle, approaches N times the annual cost of the energy: ( ) ( ) ( ) ( ) 00 1 1 lim ( , ( )) lim ( ( )) ( , ( )) (1 ) ( ( )) ( , ( )) · ( ( )) ( , ( )) · · ( , ( ))· · eq eq N PO R M EL R n dd neq M EL R M L R E RE C P P t C P t C P P t d C P t C P P t N E P t E P P t p N E P P t p N →→ =  =+   +  = + = + =  This means that, if the decommissioning cost is approximately cancelled out by the residual value, and the initial investment can be disregarded when compared with the present operating costs, which is often the case, then both optimum conditions, minimum LCC and minimum energy (or energy loss), come into play: ( ) ( ) ( ) ( ) ( ) ( ) 00 00 1 lim ( , ( )) lim ( ) ( , ( )) ( ) ( ) 1 lim ( , ( )) lim ( ( )) ( , ( )) (1 ) ( ( )) ( , ( )) · ( ( )) ( , ( )) · · ( , ( ))· · eq eq eq eq R R PO R D R R R dd N PO R M EL R n dd neq M EL R M L R E RE LCC P P t I P C P P t C P V P C P P t C P t C P P t d C P t C P P t N E P t E P P t p N E P P t p →→ →→ = = − − − +   = +   +  = + = + =  N Consequently, the optimum rated power for minimum LCC approaches the optimum rated power for minimum energy or losses: ( ) min min min min 0 lim ( ) ( ) eq R LCC R R L R EL d P P LCC P E P →   = In other words, the optimum rated power minimizing the energy or energy loss is a practical upper limit for the optimum rated power minimizing the LCC, 17 PR LCCmin  PR PLmin. This result can be useful in those common cases where the list price of the motors is no longer available, as will be shown later. 4. Case Study In the EU, on 1 January, 2017, the third and last tier of the Energy Using Products (EUP) Directive for electric motors (EU Ecodesign Directive) [6,7] came into force. Since then, the Minimum Energy Performance Standards (MEPS) for electric motors require new motors sold in the EU market (with a rated output from 0.75 kW-355 kW) must satisfy the IE3 efficiency class (or IE2, if fitted to a Variable Speed Drive-VSD). For that reason, the proposed method will be tested with IE3 (premium efficiency) motors, despite the low level of losses for this efficiency class. For the purpose of comparison, results for IE2 (high efficiency) motors will also be shown. The reference scenario of the case study addresses the project-stage selection of the techno-economic optimum rated power (duty type S1), PR, of an IE3, line-operated single-speed cage induction motor from Table 1 to drive a time-variable mechanical power load, P(t), for T = 8760 operating hours a year. Figure 4 shows the considered annual time-variable mechanical power load, P(t), in which P100% = 30 kW has been selected as the 100% power load. 0 5 10 15 20 25 30 0 1250 2500 3750 5000 (Hours/year) Power load 0 16.7 33.3 50.0 66.7 83.3 100 (kW) (%) 4780 2260 1720 Figure 4. Annual time-variable mechanical power load, P(t). Accordingly, the annual mean and the RMS values of the mechanical power load result in: 1( )· 24.3kW m k k k P P t t T ==  2 1( )· 27.7 kW RMS k k k P P t t T ==  As a result, following the conventional method, a motor rated PR(RMS) = 30 kW should be chosen, which is the first rated power over the value PRMS = 27.7 kW, as found in the manufacturer’s catalogue (Table 1). It is easy to check that the value of the peak or 18 maximum load power, PMAX = P100% = 30 kW, does not exceed the rated power of the motor at any time, since PR(RMS) = 30 kW  PMAX = 30 kW. Table 3 summarizes the coefficients of the power-loss model and the purchase-cost model of the IE3 and IE2 motors, whose rated powers are 30 kW, 37 kW and 45 kW, as determined by linear regression fitting (see Appendix B for a simplified calculation of these coefficients). As will be shown, this two-step range of power rating considers the expected optimum rated power of the motor. A discount factor, kd = 0.4, and a residual value equivalent to the sum of the decommissioning and the auxiliary costs (kR = kD + kA) have been considered for the sake of simplicity. Table 3. Coefficients of the power-loss model and the purchase-cost (list price) model for motors rated at 30 kW, 37 kW and 45 kW. Rated Power Power losses PL(PR,Ppu) = kLF(PR) + kLV(PR)·P2pu List price PR (kW) kLF (kW) kLV (kW) CP (€) IE3 (premium efficiency) 30 0.7355 1.3197 3338 37 0.8398 1.5707 4068 45 0.9955 1.7779 4882 Linear regression kLF(PR) ≈ kLFF + kLFV·PR kLFF = 0.2080 kLFV = 0.0174 kLV(PR) ≈ kLVF + kLVV·PR kLVF = 0.4197 kLVV = 0.0304 CP(PR) ≈ cPF + cPV·PR cPF = 254.20 cPV = 102.91 IE2 (high efficiency) 30 0.9247 1.5909 3025 37 1.1401 1.7896 3651 45 1.4145 1.9359 4444 Linear regression kLF(PR) ≈ kLFF + kLFV·PR kLFF = -0.0607 kLFV = 0.0327 kLV(PR) ≈ kLVF + kLVV·PR kLVF = 0.9176 kLVV = 0.0229 CP(PR) ≈ cPF + cPV·PR cPF = 170.93 cPV = 94.71 Figure 5 shows the evolution of the EU-28 average semi-annual electricity prices for industrial consumers (Band-IC: annual consumption between 0.5 and 2 GWh), all taxes and levies included [60]. Accordingly, an electricity price of pE = 148.55 €/MWh, the EU-28 average electricity price in 2015, has been considered in the reference scenario. The linear regression of price data fitting shows that the electricity price grows at an average annual rate of 2·2.1625 = 4.325 €/MWh, or ΔpE = (4.325/148.55)·100 = 2.91%/year. 19 Figure 5. 2008-2015: EU-28 average semi-annual electricity prices for industrial consumers (Band-IC: annual consumption between 0.5 and 2 GWh), all taxes and levies included (Eurostat code [nrg_pc_205]). Data fitting by linear regression. Table 4 shows the average lifetime of an AC motor in terms of rated power [50]. Accordingly, a lifespan of N = 15 years has been used to calculate the LCC of the motor. Table 4. Average lifetime of an AC motor in terms of rated power [50]. 0.75 kW − 1.1 kW 1.1 kW − 11 kW 11 kW − 110 kW 110 kW − 370 kW 10 years 12 years 15 years 20 years Finally, a (unfavourable) discount rate, d = 5%, has been used in the reference scenario. This value is slightly higher than the average real yield on longer-term government debt in the EU over the period 2001-2016, 4.61%, as shown in Table 5 [61]; and higher than the “social discount rate” of 4% recommended in Tool #54 of the Toolbox Complement [62] to the Better Regulation Guideline of the EU. Table 5. 2001-2016: EU-28 average annual real yield on longer-term government debt [Eurostat code: teimf050]. Year 2001 2002 2003 2004 2005 2006 2007 2008 EU-28 bond yields (%) 5.30 5.06 5.00 4.91 4.81 4.72 4.60 4.49 Year 2009 2010 2011 2012 2013 2014 2015 2016 EU-28 bond yields (%) 4.41 4.37 4.35 4.34 4.34 4.35 4.36 4.38 4.1 Results and discussion Table 6 and Figure 6 summarize the main results of the reference scenario of the case study considered. Since the value of the RMS power of the load profile was PRMS = 27.7 kW, a motor rated PR(RMS) = 30 kW should be selected, according to the conventional rule. If an IE3 motor were selected, this motor would drive the mechanical load with an annual energy loss of 16.35 MWh/y, and a whole LCC of 438.99 k€. According to the proposed method, the optimum rating of the motor with minimum annual energy loss is PR ELmin = 46.31 kW > PRMS = 27.7 kW. As a result, a motor with 100 110 120 130 140 150 160 2008s1 2008s2 2009s1 2009s2 2010s1 2010s2 2011s1 2011s2 2012s1 2012s2 2013s1 2013s2 2014s1 2014s2 2015s1 2015s2 y= 2.1625·x+ 119.7 R² = 0.8996 Electricity Price (€/MWh) 100 110 120 130 140 150 160 100 110 120 130 140 150 160 2008s1 2008s2 2009s1 2009s2 2010s1 2010s2 2011s1 2011s2 2012s1 2012s2 2013s1 2013s2 2014s1 2014s2 2015s1 2015s22008s1 2008s2 2009s1 2009s2 2010s1 2010s2 2011s1 2011s2 2012s1 2012s2 2013s1 2013s2 2014s1 2014s2 2015s1 2015s2 y= 2.1625·x+ 119.7 R² = 0.8996 Electricity Price (€/MWh) 20 an optimum rated power, PR(ELmin) = 45 kW, should be selected from the manufacturer’s catalogue (since the energy loss corresponding to the motor rated 37 kW is higher). It is worth noting that this result could also be well anticipated with the regression line of minimum losses in Figure 2: • Since the value of the RMS power of the load, PRMS = 27.7 kW, is placed between the crossing points P37-45 and P45-55, (24.08 kW < PRMS = 27.7 kW ≤ 32.87 kW), the minimum energy loss corresponds to the motor rated 45 kW. • The approximate value of the minimum annual energy loss can now be estimated with (4): ( , ) 8760· ( , ) 8760·(0.32 0.049·27.7) 14.69 MWh/y L R PLmin RMS L R PLmin RMS E P P P P P P== = + = which is very close to the exact result (14.62 MWh/y). Table 6. Summary of results for the reference scenario of the case study. IE3 (premium efficiency) Rated power PR (kW) Energy loss EL (MWh/y) Energy E (MWh/y) Energy efficiency  E (%) Life cycle cost │LCC│ (k€) Present cost of energy losses CPEl/│LCC│ (%) PRMS = 27.70 17.10 230.20 91.97 440.28 7.40 30 16.35 229.45 92.33 438.99 7.09 37 15.05 228.15 92.94 436.95 6.56 PR LCCmin = 42.65 - - - 436.58 - 45 14.62 227.72 93.14 436.63 6.37 PR ELmin = 46.31 14.61 - - - - 55 14.85 227.95 93.03 437.71 6.46 75 16.47 229.57 92.27 442.05 7.10 IE2 (high efficiency) Rated power PR (kW) Energy loss EL (MWh/y) Energy E (MWh/y) Energy efficiency  E (%) Life cycle cost │LCC│ (k€) Present cost of energy losses CPEl/│LCC│ (%) PRMS = 27.70 21.00 234.10 90.15 447.51 8.93 30 20.05 233.14 90.59 445.83 8.56 37 18.73 231.83 91.21 443.73 8.04 PR LCCmin = 38.65 - - - 443.67 - PR ELmin = 40.14 18.63 - - - - 45 18.82 231.92 91.17 444.37 8.07 55 20.06 233.16 90.59 447.29 8.54 75 24.10 237.20 88.69 456.14 10.06 21 5 10 15 20 25 30 35 20 30 40 50 60 Power (kW) Energy Losses, EL(MWh/year) Life-Cycle Cost, LCC (k€) 400 410 420 430 440 450 460 IE2 LCC(PRMS) EL(PR= 37 kW) = 18.7 MWh/y PR= 45 kW PR= 30 kW PR= 55 kW PR= 37 kW EL(P) LCC(P) LCC(PR= 37 kW) = 444 k€ PR(ELmin) EL(PRMS) PR(LCCmin) 5 10 15 20 25 30 35 Energy Losses, EL(MWh/year) Life-Cycle Cost, LCC (k€) 400 410 420 430 440 450 460 IE3 20 30 40 50 60 Power (kW) LCC(PRMS) PR(LCCmin) PR(ELmin) PR= 45 kW PR= 37 kW PR= 30 kW PR= 55 kW EL(PR= 45 kW) = 14.6 MWh/y LCC(PR= 45 kW) = 437 k€ EL(PRMS) EL(P) LCC(P) Figure 6. Variation of the annual energy loss, EL(PR), and the LCC, │LCC(PR)│, with the rated power of the motor for IE3 motors (left-hand side) and for IE2 motors (right-hand side). If the minimum LCC is considered, then the proposed method leads to a motor with an optimum rated power of PR LCCmin = 42.65 kW (PRMS = 27.7 kW < PR LCCmin = 42.65 kW < PR ELmin = 46.31 kW). Accordingly, a motor with a rated power of PR(LCCmin) = 45 kW should be selected from the manufacturer’s catalogue (the LCC corresponding to the motor rated 37 kW is slightly higher). As can be observed, for the considered case, the rated powers of the motors with minimum annual energy loss and minimum LCC coincide, i.e., PR(ELmin) = 45 kW = PR(LCCmin) = 45 kW, and both result in being two steps higher in the manufacturer’s catalogue than the rated power of the motor based on the RMS power, PR(RMS) = 30 kW. The techno-economic optimum IE3 rated power would: • Reduce the annual energy loss up to EL(PR(ELmin) = PR(LCCmin) = 45 kW) = 14.62 MWh/y, which constitutes 10.59% (1.73 MWh/y) less than that corresponding to the conventionally rated motor PR RMS = 30 kW. • Reduce the whole LCC up to │LCC(PR(ELmin) = PR(LCCmin) = 45 kW)│= 436.63 k€, which is 0.54% (2.36 k€) less than that corresponding to the conventionally rated motor PR RMS = 30 kW. • Increase the overall energy efficiency up to  E(PR(ELmin) = PR(LCCmin) = 45 kW) = 93.14%, which is 0.81% greater than that corresponding to the conventionally rated motor PR RMS = 30 kW. Although the amount of the increase in energy efficiency would seem to be small, it is in fact markedly greater than the increase in the rated efficiency between the conventionally rated motor, PR RMS = 30 kW, and the optimum rated motor,  R(PR = 45 kW) -  R(PR = 30 kW) = 94.2 – 93.6 = 0.6%. • Reduce the cumulative present cost of the losses in the LCC up to CPEL(PR(ELmin) = PR(LCCmin) = 45 kW) = 27.83 k€ (6.37% of LCC), which is 10.59% (3.30 k€) less than that corresponding to the conventionally motor rated 22 at PR RMS = 30 kW (31.13 k€, 7.09% of the LCC). Accordingly, the increment of the initial cost, I(PR = 45 kW) - I(PR = 30 kW) = 926 € is offset by the cost savings over 5.9 years, that is, only slightly more than a third of the expected life of the motor. A rough extrapolation of the particular results of this IE3 case to the 2015 data of electric motor consumption in the EU-28 sectors of industry and services would lead to: • an annual potential energy saving of 7.48 TWh/y (0.75% total saving), • an annual potential saving in operating costs of 14.24 G€/y, and • an annual potential saving in emissions of CO2eq of 2.80 million t(CO2eq)/y. Figure 6 (left-hand side) shows the evolution of the annual energy loss, EL(PR), and the whole LCC, LCC(PR), with the rated power of the motor. This figure (and Table 6) clearly confirm that the optimum rated power, based on the minimum LLC, PR LCCmin = 42.65 kW, is a little lower than the optimum based only on energy or energy loss, PR ELmin = 46.31 kW, due to the effect of considering of the initial cost of the motor. This figure also shows that the RMS power of the load, PRMS = 27.7 kW, the rated power based on the minimum LLC, PR LCCmin = 42.65 kW, and the optimum rated power based only on energy or energy loss, PR ELmin = 46.31 kW, are both in an increasing sequence. Figure 6 (left) shows that both the energy loss and the LCC are L-shaped. For IE3 motors, as the power grows, both curves fall to the minimum points, after which they increase very slowly. As a result, both curves exhibit rather flat minimum points. Table 6 shows that the performance indicators of the motor rated 55 kW are only a little worse than those corresponding to the optimum rated 45 kW motor (1.6% for energy and 0.2% for the LCC), although it is still better than the conventional motor rated PR RMS = 30 kW (1.50 MWh/y less energy and 1.28 k€ less LCC). This rather flat minimum region could be advantageous in the design of a motor-purchasing policy with a reduced number of rated powers, since there is a broad range of mechanical loads surrounding the flat region of the minimum point. For the techno-economic optimum rated motor, the RMS load represents a normalized or relative load of Ppu = PRMS /PR LCCmin = 27.7/45 = 0.6156, which means that the temperature of the windings will remain well below the allowable maximum. Considering class F insulation (155ºC) with a temperature rise B (ΔθM = 130 – 50 = 80 K, a standard air-cooling temperature of 40°C and 10 K for the hotspot temperature margin), which is the most common requirement across industry today, and also considering that the temperature rise is proportional to the power losses, the temperature rise results in: 2 2 ( 45 kW, 27.7 kW) ( 45 kW, 27.7 kW) ( 45 kW, 45 kW) ( 45 kW, 45 kW) 0.9955 1.7779·0.6156 0.60 0.9955 1.7779·1 R RMS L R RMS M R L R R P P P P P P P P P P     = = = = ==   = = = = + == + Therefore, the reduction in the temperature rise under its allowable maximum is: (1 0.6018)· (1 0.6018)·80 31.85K MM     − = −  = − = An approximation of the Montsinger’s rule states that a temperature rise of 10 K halves the expected lifetime of the isolations. Conversely, a reduction in the temperature of 10 23 K doubles the expected thermal life of the insulations. Accordingly, it is expected that the thermal life of the optimum rated motor will extend well beyond the 15 years initially expected. The bottom part of Table 6 (Figure 6) shows that similar results are reached with IE2 motors, but with an optimum rated power of 37 kW. Even though the energy loss (+4.11 MWh/y) and the LCC (+7.10 k€) of this IE2 motor are higher than those corresponding to the 45 kW IE3 motor, they still remain lower than those corresponding to the IE2 motor rated PR RMS = 30 kW (–2.27 MWh/y and –3.78 k€, respectively). The increment of the initial cost for the optimum IE2 rated motor, I(PR = 37 kW) - I(PR = 30 kW) = 376 €, is offset by the savings in costs over 2.7 years, that is, less than a fifth of the expected life of the motor. Table 6 also shows that the performance indicators of the IE2 motor rated at 45 kW are only a little worse than those corresponding to the optimum rated motor at 37 kW, but are still better than the conventional motor rated at PR RMS = 30 kW. It is worth noting that the difference (saving) in the LCC of the IE3 and IE2 optimum rated power motors (7.10 k€), is almost 10 times the difference in initial cost (739 €). A rough extrapolation of the particular results of the IE2 case to the 2015 data of electric motor consumption in the EU-28 sectors of industry and services would lead to: • an annual potential energy saving of 5.59 TWh/y (0.56% total saving), • an annual potential saving in operating costs of 9.90 G€/y, and • an annual potential saving in emissions of CO2eq of 2.09 million t(CO2eq)/y. As expected, Figure 6 shows that the curves of the energy loss and the LCC of IE2 motors are higher than the corresponding curves for IE3 motors. This figure also shows that, while curves of IE3 motors are L-shaped, the higher losses of IE2 motors, as well as the greater difference in losses between motors consecutively rated, resulted in the curves of IE2 motors being more V-shaped. For IE2 motors, as the power grows, the curve falls to the minimum point faster than does the curve for the IE3 motors. As the minimum IE2 curves also grow faster than those for IE3 motors, IE2 curves exhibit a more marked minimum point and the optimum rated motor is closer to the RMS power. Conversely, the higher the efficiency class, the greater the distance between the optimum rating and the RMS power. The higher value of the rated power of the optimized motors may imply a certain degree of conflict between the size of the motor frame and the room available, which could lead to extra costs in commissioning and installation. In the project stage, the difficulties caused by size are easily manageable, but can prove to be a limitation when replacing an old motor. Nevertheless, a survey of the IE3 motor catalogue shows that, of the 18 motors recorded, there are only three motors (rated powers) that do not share the shaft height with any other motor. The remaining 15 motors (rated power) share a shaft height with at least one motor. For the case of the 25 motors in the IE2 catalogue, there are only four motors (rated powers) that do not share a shaft height, while the remaining 21 motors (rated power) share a shaft height with at least one motor. Another conflicting situation may occur when considering the replacement of a motor driving an application with a growing torque-speed load curve. In such a case, it should be borne in mind that, the higher the motor efficiency class and rated power, the higher the shaft torque, the speed (lower slip), and the mechanical power delivered. Accordingly, it may happen that the reduction in power losses of the new motor (greater 24 rated power or better efficiency class) was less than the increase in the mechanical power in the shaft, which would lead to an increase in active power consumption [63,64]. For the sake of simplicity, the small change in the operating point (torque and speed or slip) has not been taken into account in this work. Nevertheless, in the design or project stage of a new application, the engineer can easily adjust the application to the chosen motor (greater rated power or better efficiency class); thus, the slight speed increase in the selected motor ought not to pose an issue [19]. As previously mentioned, the greater value of the optimized rated power leads the motor to operate with a reduced relative load, which means an extension to the expected motor lifetime, since a longer winding insulation and bearing lifetime are both expected. As a result of the lower operating temperature, an increase in the motor endurance to overloads or voltage unbalance can also be expected, as well as a better tolerance towards the effects of the harmonic distortion [19]. These all represent significant advantages of optimized rated power motors, since, as mentioned, reliability is the main focus of plant engineers. 4.2 Sensitivity test In order to test the robustness of the solution suggested by the proposed method, an analysis of the influence of the main parameters on the solution for the reference case scenario is performed. Starting with the reference scenario, this test analyses the effect on the optimum rating of varying, across a broad range, ceteris paribus, the operational hours per year, T, the price of the energy, pE, the discount factor in the purchase cost, kd, the discount rate, d, and the lifespan, N. Figure 7 summarizes the results for IE3 motors. Figure 7. IE3 motors. Optimum rated power for minimum energy loss, PR(ELmin), and minimum LCC, PR(LCCmin): Influence of the operating hours per year, T, the cost of energy, pE, the discount factor in the purchase cost, kd, the discount rate, d, and the life span, N. It can be observed that the proposed solution is highly robust since the optimum rated power for the minimum LCC only shifts from its value in the reference scenario, PR(LCCmin) = 45 kW, to PR(LCCmin) = 37 kW, when: • the operating hours per year are reduced to 5000 hours/year or fewer (first row below the graph), • the price of energy falls to 75 €/MWh or less, 30 35 40 45 50 PR(ELmin) = 45 kW PR(LCCmin) = 45 kW PR(LCCmin) = 37 kW 1000 2000 3000 4000 5000 6000 7000 8000 8760 T(h/y) 50 75 100 125 150 175 pE(€/MWh) 17 16 15 14 13 12 11 10 9d(%) 10 15 20 25 N(y) Optimum Rated Power (kW) IE3 010 20 40 kd(%)30 31 Table C.2. Cage induction motors from manufacturer B: efficiency data of general-performance, cast-iron motors designed for low voltage (440 V, 50 Hz), four poles, IP 55, IC 411 and insulation class F (temperature rise class B). IE3 (premium efficiency) IE2 (high efficiency) Output kW Full load 100% 3/4 load 75% 1/2 load 50% Full load 100% 3/4 load 75% 1/2 load 50% 0.75 82.5 82.0 80.0 89.0 89.0 88.7 1.1 84.5 84.5 83.0 89.5 89.5 89.2 1.5 85.5 86.0 84.0 90.2 90.2 89.0 2.2 87.0 87.0 86.5 91.0 91.0 90.6 3 88.0 88.0 87.0 91.6 91.8 91.5 4 88.8 89.1 88.7 92.3 92.5 92.2 5.5 89.7 89.6 89.0 92.8 93.0 92.6 7.5 90.6 90.8 90.5 93.2 93.2 93.0 9.2 91.0 91.0 90.3 93.6 93.7 93.2 11 91.6 91.8 91.1 94.0 93.9 93.6 15 92.3 92.5 92.2 94.4 94.4 93.8 18.5 92.8 92.8 92.2 94.7 94.7 94.1 22 93.2 93.0 92.3 95.0 95.0 94.3 30 93.7 93.6 92.9 95.2 95.2 94.6 37 94.1 94.0 93.4 95.4 95.4 95.0 45 94.4 94.1 93.7 95.4 95.4 94.8 55 94.7 94.7 94.3 95.6 95.6 94.9 75 95.2 95.1 94.5 95.6 95.6 95.0 90 95.4 95.4 94.9 95.7 95.7 95.2 110 95.6 95.5 94.7 95.7 95.7 95.3 132 95.8 95.7 95.1 95.8 95.8 95.4 150 95.9 95.8 95.4 95.8 95.8 95.4 160 96.0 95.9 95.2 95.8 95.8 95.5 185 96.0 96.1 95.5 95.8 95.8 95.5 200 96.0 96.3 96.0 95.8 95.8 95.5 220 96.2 96.1 95.8 95.8 95.9 95.5 250 96.2 96.2 96.0 95.8 95.9 95.5 260 96.2 96.2 96.0 95.8 95.9 95.5 280 96.2 96.0 95.9 95.5 95.0 94.5 300 96.2 96.0 95.8 95.5 95.0 94.5 315 96.3 96.3 96.1 89.0 89.0 88.7 330 96.2 96.0 95.8 89.5 89.5 89.2 355 96.5 96.5 95.9 90.2 90.2 89.0 400 96.2 96.1 95.7 91.0 91.0 90.6 450 96.2 96.1 95.8 91.6 91.8 91.5 500 96.3 96.3 95.9 92.3 92.5 92.2 32 References [1] Bertoldi, P., López-Lorente, J., Labanca, N., 2016; Energy Consumption and Energy Efficiency Trends in the EU-28 2000-2014; EUR 27972 EN; doi 10.2788/581574 http://publications.jrc.ec.europa.eu/repository/handle/JRC101177 [2] Anibal T. de Almeida, Joao Fong, Hugh Falkner, Paolo Bertoldi, Policy options to promote energy efficient electric motors and drives in the EU, Renewable and Sustainable Energy Reviews, Volume 74, July 2017, Pages 1275-1286, ISSN 1364-0321, https://doi.org/10.1016/j.rser.2017.01.112. 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