Techno-economic optimal power rating of induction motors

Depósi o de In es igación de la Uni e sidad de Se illa h ps://idus.us.es/ This is an Accep ed Manusc ip o an a icle published by Else ie in Applied Ene gy, Vol. 240, on Ap il 2019, a ailable a : h ps://doi.o g/10.1016/j.apene gy.2019.02.016 Copy igh 2019 Else ie . En idUS Licencia C ea i e Commons CC BY-NC-ND Techno-economic Op imal Powe Ra ing o Induc ion Mo o s Manuel Bu gos Payán, Juan Manuel Roldán Fe nández, José Ma ía Maza O ega, and Jesús Manuel Riquelme San os Abs ac Elec ic mo o s a e aluable, long-li e indus ial asse s, whose li espan is o en measu ed in decades. A pe iod o unplanned mo o down ime in an indus ial plan equen ly incu s an expendi u e o housands o eu os pe hou . As a consequence, plan enginee s o en ocus hei decisions on eliabili y a he han on ope a ing cos (ene gy bill). Un o una ely, he high p ice o ene gy and i s g owing end mean ha ope a ing cos has an inc easingly nega i e impac on p oduc ion cos and company compe i i eness. The p oblem o selec ing he a ed powe o a line-ope a ed single-speed elec ic mo o o d i e a ime- a iable mechanical load has adi ionally been sol ed, based on he well-es ablished oo mean squa e (RMS) alue o he ime-powe p o ile o he mechanical load. This con en ional me hod o a ing is s ic ly echnical, since he a ed powe o he mo o is de e mined, based only on he powe p o ile o he load. No o he ac o s a e conside ed, such as he ene gy consump ion h oughou he whole in-se ice li e o he mo o , o , e en be e , he whole li e cycle cos (LCC), which is de ined as he ne p esen alue o pu chasing, ins alling, ope a ing (ene gy), main aining and decommissioning he mo o h oughou i s li e. As a consequence, con en ional a ing o en leads o he selec ion o mo o s wi h a powe a ing ha is echnically su icien o d i e he mechanical load, bu insu icien o do so wi h he lowes possible ene gy (losses) consump ion, o e en be e , wi h he lowes possible li e cycle cos . A new analy ical me hod o de e mine he echno-economic op imum powe a ing o a line-ope a ed single-speed elec ic mo o o d i e a ime- a iable mechanical load will be in oduced in his pape . The p oposed me hod akes in o accoun no only he echnical es ic ions due o he ime-powe p o ile o he mechanical load, bu also he whole li e cycle cos . Based on he lis o elec ic mo o s o e ed in he manu ac u e ’s ca alogue, he new me hodology enables he op imum echno-economic a ed powe o he mo o o be calcula ed, which minimizes he ene gy consump ion (ene gy loss) h oughou i s in-se ice li e o i s o al li e cycle cos . The esul s show ha he op imum echno-economic a ing is one o wo a ed-powe le els abo e he con en ional a ing based solely on he RMS load. Keywo ds: Induc ion mo o s; Li e cycle cos ; Ene gy e iciency; CO2 emissions; Powe a ing; Techno-economic op imiza ion. 1. In oduc ion Elec ic mo o s enjoy ex ensi e applica ions as d i e s o a la ge a ie y o equipmen in indus ial and se ice sec o s, as well as in household elec ic appliances. Wi h he ecen i up ion o elec ic mo o s in he powe ain o cu en elec ic ehicles, elec ic 2 mo o s a e now coming in o hei own wi h ega d o oad anspo : one o he ew ields o applica ion ha ha e been la gely oid o elec ic mo o s h oughou he 20 h cen u y, and also a majo con ibu o o ca bon dioxide emissions wo ldwide. Elec ic mo o sys ems a e esponsible o app oxima ely 70% o indus ial elec ici y consump ion and o abou 35% o non- esiden ial elec ici y (se ices) consump ion in he Eu opean Union (EU) [1,2]. In 2015, inal elec ici y consump ion in he EU-28 eached 2743 TWh, mainly on accoun o h ee sec o s: indus y, he sec o wi h he highes consump ion wi h a sha e o 36.34% (997 TWh), ollowed by he se ices sec o , ep esen ing 30.50% (837 TWh), and hen he esiden ial sec o wi h 28.99% (795 TWh) [3]. This means an es ima ed elec ic mo o consump ion o he EU-28 o 698 TWh in indus y and 293 TWh in he se ices sec o in 2015: a o al o 991 TWh (36.11%), which is p ac ically equal o he consump ion o he whole indus y sec o . Gi en ha he EU-28 a e age alue o ca bon dioxide equi alen (CO2eq) ac o emissions was 374 housand (CO2eq)/TWh [4], as a consequence o he ene gy consumed in hese wo sec o s by elec ic mo o s, app oxima ely 371 million onnes o CO2eq we e emi ed in o he a mosphe e in 2015. The ole o elec ic mo o s as majo consume s o elec ici y in indus y and se ice sec o s has been la gely ecognized by policymake s all o e he wo ld [5]. As a esul , almos all he main economies ha e implemen ed some kind o egula ion ega ding mo o e iciency as a me hod o imp o ing p oduc i i y/compe i i eness (sa ings in ope a ing cos ) and mee ing in e na ional commi men s on clima e change (emission educ ions due o ene gy sa ings). Fo example, in he EU, elec ic mo o s (0.75 kW - 375 kW) lie wi hin he scope o he Ecodesign Di ec i e [6,7]. In 2015, acco ding o P odcom (EU s a is ics on he p oduc ion o manu ac u ed goods), 10,511,819 mul i-phase AC mo o s (excluding ac ion mo o s) a ed a 0.75 kW – 375 kW we e sold in he EU-28 [8]. Wi hin his powe ange, he ma ke is clea ly domina ed by h ee-phase AC induc ion mo o s, ep esen ing a ound 85% o he ma ke sha e [9,10]. Issues ela ed o ene gy consump ion by elec ic mo o s and hei ela ed CO2 emissions ha e also been b oadly discussed by esea che s in ol ing a wide a ie y o pe spec i es and publica ions: indus y applica ions [11,12], ene gy sa ing [13,14], he con enience o using high-e iciency mo o s o eplace s anda d mo o s [15], minimum e iciency pe o mance s anda d [16], pa ial load [17] and o e sizing [18,19], ene gy e iciency s anda ds [20,21] and policies [22,23], he in luence o ol age unbalance [24,25] and de a ing [26], ha monics [27] and o he powe quali y issues [28], he con enience o ewinding o eplacing ailed mo o s [29], CO2 emissions [30,31], he a ia ion in losses and e iciency unde a iable speed and load condi ions [32,33], ene gy conse a ion [34,35] and o he s [36,37]. Na u ally, elec omobili y applica ions (elec ic ehicles) a e also ecei ing majo a en ion om he esea ch communi y o m he poin o iew o ene gy managemen [38-40], egene a i e b aking [41,42], he use o ba e ies and ul acapaci o s as ene gy s o age de ices [43], and o he s [44,45]. Focusing on he aspec s mo e di ec ly ela ed o he a ed powe o induc ion mo o s and i s ene gy e iciency class, in 1999, Akbaba [34] analysed he po en ial o ene gy conse a ion in indus y by using ene gy-e icien elec ic mo o s compa ed wi h hose o s anda d e iciency mo o s. Fe ei a, Cisne os-González and de Almeida poin ed ou in [19] ha mos indus ial h ee-phase squi el-cage induc ion mo o s a e o e sized mainly due o he use o sa e y ac o s associa ed wi h unce ain y abou mechanical load equi emen s, conse a i e design ules, and he disc e e a ailabili y o comme cial 3 a ed powe . In ha wo k, he au ho s analysed he po en ial bene i s and d awbacks o mo o o e sizing. Da Cos a Bo oni [18] also ag ees ha he o e sizing p ac ice is mo e a p oblem ela ed o he de iciency o p ope in o ma ion han a lack o “bes p ac ices”. The au ho wa ns ha igu ing ou whe he a mo o is uly o e sized is no a simple ask and p esen s a oad map o p ope ly e alua e whe he a di ec line- ed h ee-phase induc ion mo o is o e sized. The p oblem o selec ing he a ed powe o a line-ope a ed single-speed elec ic mo o o d i e a ime- a iable mechanical load has been sol ed adi ionally, based on he well-es ablished RMS alue o he ime-powe p o ile o he mechanical load. Since 1939, when L.E. Hildeb and published his pape “Du y cycles and mo o a ing” [46], he RMS me hod was ully accep ed by he echnical communi y and has been ound in echnical ex s and eaching handbooks since hen up o he p esen [47]. Ne e heless, his con en ional me hod ully dis ega ds all he aspec s ela ed o ene gy consump ion, e iciency o ope a ing (ene gy) cos , which p ecisely cons i u es he g ea es pa o he o al LCC. Al hough elec ic mo o s emain he subjec o ex ensi e esea ch wo k, he in luence o he selec ion o he op imum mo o o d i e a ce ain mechanical load is a subjec a ely conside ed. Bu his is ce ainly an issue wo h analysing, since he decision ega ding he choice o a pa icula elec ic mo o o d i e a mechanical load de e mines he losses o he mo o load sys em and hus i s ene gy consump ion, ope a ing cos and associa ed CO2 emissions. In o de o make an in o med decision on he in es men o any indus ial equipmen , such as he selec ion o a mo o , i is essen ial o e alua e he ini ial in es men (pu chase, ins alla ion and commissioning cos ), he ne p esen alue o he ope a ing cos (ene gy and main enance) h oughou he whole in-se ice li e o he mo o , and he decommissioning cos (condi ioning o emo al cos and he esidual alue, which is he mo o esale o sc ap alue) a he end o he expec ed li e o he said mo o . Decision- making based on he lowes LCC, al hough o en ecommended [48,10], has ye o become common enginee ing p ac ice. This minimum LCC app oach o e s enginee s a b oade iew o wha can be expec ed om hei decisions. This e alua ion in ol es a aining eliable in o ma ion on he mechanical load and on he elec ic mo o s o compa ison in o de o es ima e he ope a ing condi ions and he ene gy and main enance cos , while also aking in o accoun he ime alue (dep ecia ion) o money and po en ial annual ene gy cos inc eases. I is much mo e common o pe o m a simple payback pe iod analysis which compa es he o al cos o in es men o annual ope a ing sa ings. Un o una ely, he e is no me hod a ailable o he calcula ion o he a ed powe alue o a mo o based on he lowes LCC, since he mo o mus be chosen by e alua ion. To add ess his gap, a new analy ical me hodology o de e mine he op imum powe a ing o a single-speed elec ic mo o o d i e a ime- a iable mechanical load will be in oduced in his pape . The p oposed me hodology akes in o accoun no only he echnical es ic ions, due o he powe p o ile o he mechanical load, bu also ei he he ene gy consump ion h oughou he whole li e o he mo o o he ne p esen alue o pu chasing, ins alling, commissioning, ope a ing (ene gy), main aining and disposing o he mo o o e i s li e cycle. Based on he lis o elec ic mo o s o e ed in he ca alogue o a manu ac u e , he new me hodology enables he calcula ion o he op imum echno- economic a ed powe o he mo o which minimizes ei he he ene gy consump ion (ene gy loss) h oughou i s in-se ice li e o i s o al LCC. The e o e, he p oposal cons i u es a clea ad ance wi h espec o he s a e o he a because he ial-and-e o 4 p ocedu es a e su passed. The p oposed me hodology is able o di ec ly compu e, in an analy ical way, he mo o a ed powe by minimizing he selec ed objec i e unc ion o gi en loading condi ions. As can be obse ed, he echno-economic app oach o he p oposed a ing me hod is much mo e comp ehensi e han he con en ional and well-es ablished me hod o he RMS alue o he load (which comple ely igno es ene gy cos ) and could be seen as an ex ension o an e olu ion o he con en ional me hod, which is al eady able o in eg a e (by aking in o accoun ) bo h he echnical es ic ions imposed by he mechanical load and he ope a ing (ene gy) cos h oughou he whole in-se ice li e o he mo o . A e his in oduc ion, he emainde o he pape is o ganized as ollows. The con en ional me hod o de e mining he a ed powe o a mo o is e iewed in Sec ion 2, wi h i s main weaknesses explained. Sec ion 3 p esen s he heo y o he p oposed me hod, including analy ical exp essions o op imum a ed powe , o minimum ene gy (losses) and o he minimum LCC. The main esul s o a case s udy a e p esen ed and b ie ly discussed in Sec ion 4, whe e he ad an ages o he p oposed op imiza ion me hod in e ms o ene gy and cos sa ings a e also be shown. A sensi i i y analysis o demons a e he obus ness o he solu ions is included in his sec ion. Finally, Sec ion 5 summa izes he main indings o he wo k. A lis p ice o IE2 and IE3 me ic mo o s om a wo ldwide elec ic mo o manu ac u e has been included in he Appendix. 2. Selec ing he Ra ing Powe o a Mo o The p oblem o selec ing he a ed powe o a line-ope a ed single-speed elec ic mo o o d i e a ime- a iable mechanical load, P( ), has adi ionally been sol ed, based on he well-es ablished RMS alue o he ime-powe p o ile o he mechanical load [47,48]. Acco dingly, a mo o , wi h a ed powe (con inuous unning du y S1), PR, equal o o abo e he RMS alue o he mechanical load powe p o ile, PRMS, is selec ed om among hose a ailable, PRi, in he ca alogue o he manu ac u e (PR = min(PRi) ≥ PRMS), while obse ing peak load es ic ions. This well-es ablished app oach is mainly ocused on wo ideas: • Main enance o he empe a u e o he windings below hei maximum allowable limi , he eby p e en ing a p ema u e he mal ailu e which could sho en he expec ed in-se ice li e o he mo o . • Minimiza ion o he pu chase (and ins alla ion) cos o he mo o . I should be bo ne in mind, howe e , ha any mo o wi h powe a ed o e he RMS alue o he powe p o ile ope a es wi h a empe a u e below he maximum pe mi ed by he insula ion, and will ha e a longe in-se ice li e han expec ed, since i has become less p one o ailu e. The selec ion o he mo o wi h he lowes a ed powe compa ible wi h he mechanical load p o ile in ac only gua an ees he minimum pu chase cos . Ne e heless, he pu chase cos used o be a e y small p opo ion (less han 5-10%) o he LCC o he mo o , since he cos o ene gy o ms he g ea es pa o he o al cos [49-51]. As a consequence, con en ional a ing is nowadays ques ioned, mainly due o he ac ha i comple ely dis ega ds he cos o ene gy, which cons i u es he g ea es pa o he o al p esen cos . 5 3. Ma e ials and Me hods The p oblem o de e mining he echno-economic op imum a ed powe o a line- ope a ed single-speed cage induc ion mo o o d i ing a speci ied ime- a iable mechanical load (a an ea ly p ojec s age) is add essed in his wo k. Al hough he use o powe con e e s is becoming popula , line-ope a ed mo o s a e s ill he mos common solu ion o d i ing indus ial loads. Based on he lis p ice and he echnical da a o elec ic mo o s o e ed in he ca alogue o a manu ac u e , he new me hod enables he analy ical de e mina ion o no only he a ed powe o he mo o , which minimizes ene gy consump ion (ene gy loss) h oughou i s in-se ice li e, bu also i s o al LCC. The basic inpu da a can be classi ied in o h ee main ca ego ies: • Mechanical load. I is necessa y o asce ain he (expec ed) ime-powe p o ile o he mechanical load, P( ), h oughou he yea ly ope a ing ime, T. • Mo o . The lis p ice and he echnical da a om a manu ac u e ’s ca alogue a e equi ed. All o he mo o s should possess he same gene al cha ac e is ics: speed (numbe o poles), ol age, equency, e iciency class, insula ion class. • Economic da a. The p ice o he elec ic ene gy and i s expec ed yea ly a e o g ow h a e equi ed, as a e he discoun a e and he es ima ed in-se ice li e o he mo o . The equi ed in o ma ion is p esen ed in g ea e de ail in he ollowing sec ions. 3.1 Powe losses Table 1 summa izes he e iciency da a o low- ol age, ou -pole, gene al-pe o mance, cas -i on mo o s om a mul ina ional manu ac u e , o he IE3 and IE2 e iciency classes [52]. As can be obse ed, al hough e iciency a he 100% ( ull) load le el is he only alue o a ed e iciency ha mus be de e mined acco ding o he IEC 60034-2-1 [53], mos manu ac u e s also include mo o e iciency a he 75% and 50% load le el in hei ca alogues (see Appendix). The e iciency da a gi en in he manu ac u e ’s ca alogue enable a model o powe losses, PL(PR,Ppu = P/PR), o be ex ac ed o e e y mo o in ha ca alogue. Fo each a ed powe , PR, and no malized o ela i e powe load, Ppu, he e iciency da a, η(PR,Ppu), allow he powe losses o be calcula ed co esponding o each ela i e powe 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 his wo k, a simpli ied quad a ic binomial model o powe losses, PL(PR,Ppu), has been conside ed. This quad a ic binomial powe -loss model has wo e ms: • Cons an losses, kLF. This e m desc ibes he cons an o ixed no-load powe losses, independen o he mo o load. This e m basically co esponds o he sum o he i on losses and ic ion and windage losses. • Va iable losses, kLV·P2pu. This second e m desc ibes he a ia ion in he load- dependen losses wi h he squa e o he no malized o ela i e powe load, Ppu. 6 This e m la gely co esponds o he Joule e ec in he (s a o and o o ) conduc o s. 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 induc ion mo o s (CENELEC-design): e iciency da a o gene al-pe o mance cas -i on mo o s designed o low ol age (440 V, 50 Hz), ou poles, IP 55, IC 411, and insula ion class F ( empe a u e ise class B) [52]. IE3 (p emium e iciency) IE2 (high e iciency) Ou pu 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 * E iciency acco ding o IEC 60034-30-1; 2014 [54] This quad a ic binomial powe -loss model is simila o ha p oposed in IEC/TS 60034- 31 [50], which is based on he in e media e esul s o cons an s ν0 and νL, calcula ed om he e iciency a he ull load and 3/4 load le els. A simila ma ix model o powe losses, based on h ee known alues o e iciency co esponding o h ee e e ence ela i e loads (100%, 75% and 50%), was also used in [19]. Fo each mo o , he alues o he wo cons an s o he model o losses, kLF and kLV, can be iden i ied om he lineal eg ession o he da a on powe losses e sus he squa ed no malized powe in Table 1. Table 2 shows he alue o he cons an s o he model o 7 losses iden i ied by linea eg ession o he powe -loss da a, which a e de e mined by (1) om he manu ac u e ’s e iciency da a. Table 2. Coe icien s o he binomial powe -loss model, PL(PR,Ppu) = kLF + kLV·P2pu, o IE3 and IE2 cage induc ion mo o s in Table 1. IE3 (p emium e iciency) IE2 (high e iciency) Ra ed powe Coe icien s Goodness o i Coe icien s Goodness o i PR (kW) kLF (kW) kLV (kW) De e mina ion coe icien R2 Co ela ion coe icien kLF (kW) kLV (kW) De e mina ion coe icien R2 Co ela ion coe icien 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, Figu e 1 shows he poin clouds o he ixed-loss cons an s (PR, kLF(PR)) and a iable-loss cons an s (PR, kLV(PR)) in Table 2 as unc ions o he a ed powe o each o he mo o s. This igu e also shows he espec i e linea eg ession lines o each o hese cons an s wi h he a ed powe o he mo o s. Fo IE3 mo o s, he linea eg ession i ing esul s 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), he powe -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 Ra ed powe , PR(kW) Powe -loss coe icien s, 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 Ra ed powe , PR(kW) Powe -loss coe icien s, kLF,kLV (kW) IE2 Figu e 1. Poin clouds and lines o linea eg ession co esponding o he ixed-loss cons an s (PR, kLF(PR)) and a iable-loss cons an s (PR, kLV(PR)) as unc ions o he a ed powe o he IE3 and IE2 cage induc ion mo o s in Table 1. Fo IE3 mo o s, he linea eg ession i ing esul s 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), he powe -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) Fo IE2 mo o s, he coe icien s o he powe -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 i s app oach o he op imum powe a ing o minimum powe losses By using he coe icien s o he binomial powe -loss model, Figu e 2 shows he a ia ion in powe losses wi h he powe load o i e IE3 mo o s a ed 22 kW, 30 kW, 37 kW, 45 kW and 55 kW. As can be obse ed, as he powe load g ows, he cu es o losses cu o , wo by wo, a poin s 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 ou in e sec ion poin s allow o he de ini ion o i e powe -load in e als, ela i e o he losses: • Fo a powe load lowe han ha co esponding o he i s c ossing poin , P22-30 (P ≤ 15.98 kW), he minimum powe losses co espond o he mo o a ed 22 kW. • Fo a powe load be ween he poin s P22-30 and P30-37 (15.98 kW < P ≤ 18.01 kW), he minimum powe losses co espond o he mo o a ed 30 kW. • Fo a powe load be ween he poin s P22-37 and P37-45 (18.01 kW < P ≤ 24.08 kW), he minimum powe losses co espond o he mo o a ed 37 kW. 15 Finally, he cos o he ene gy loss du ing he i s yea o ope a ion can be calcula ed using he powe -loss model (3), w i en as: 2 2 ( , ( )) ( , ( ))· · · ( · )· · RMS EL R L R E LFF LFV R LVF LVV R E R P C P P E P P p T k k P k k P p P  =  + + +   As a esul , he o al cos o he i s yea o ope a ion o he mo o can be exp essed as he sum o he annual cos o he mechanical ene gy and he annual cos o he losses du ing he i s yea : 2 2 ( , ( )) ( ( )) ( , ( )) · · ( · )· · O R M EL R RMS m LFF LFV R LVF LVV R E R C P P C P C P P P T P k k P k k P p P =+   + + + +   In o de o calcula e he cumula ed p esen o ac ual alue o he cos o he ene gy loss h oughou he whole in-se ice li e o he mo o , CPEL, i is necessa y o conside he dep ecia ion e ec o he money in each o he N u u e yea s o expec ed li e o he mo o , by means o he discoun a e, d, and he e ec o he annual inc ease in he p ice o ene gy, ΔpE, esul ing 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 C P P C P P dd d C P P C P P k dd == + = = = ++ +− == +  whe e he equi alen discoun a e is: 1E eq E dp dp − =+ and he cumula i e p esen alue coe icien is: (1 ) 1 (1 ) N eq PN eq eq d kdd +− =+ The p esen o ac ual cos o he mo o o e i s N expec ed yea s o in-se ice li e, conside ing an equi alen discoun a e, deq, can be exp essed 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 I P C P C P P C P V P d I P E P E P P p k C P V P P k c c P T P k k P k k P p k P = + = − − + − + + = − − + − +   − + − + + + +    The e o e, he op imum a ed powe o he mo o , which minimizes he LCC, can be ob ained by cancelling ou he pa ial de i a i e o he LCC, wi h espec o he a ed powe , esul ing in: 2 42 2· ( , ( )) · · · · · 0 LVF R LVV REQ PV LFV RMS E P R R R k P k LCC P P k c k P T p k P P P   = − − − + =      16 This minimum condi ion can also be w i en 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+ − + = G ouping he coe icien s o he cubic equa ion: ( ) 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+ − − = Acco dingly, he minimum condi ion can be w i en 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 sol ed using Ca dano’s me hod. The e o e, he op imum a ed powe , which minimizes he LCC o he mo o , esul s 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 = +  + −  ++ whe e he disc iminan , 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      = −         ++     I is wo h no ing ha , when he equi alen discoun a e app oaches ze o, he p esen ope a ing cos , ha is, he p esen cos o he ene gy h oughou he li e-cycle, app oaches N imes he annual cos o he ene gy: ( ) ( ) ( ) ( ) 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 C P C P P d C P C P P N E P E P P p N E P P p N →→ =  =+   +  = + = + =  This means ha , i he decommissioning cos is app oxima ely cancelled ou by he esidual alue, and he ini ial in es men can be dis ega ded when compa ed wi h he p esen ope a ing cos s, which is o en he case, hen bo h op imum condi ions, minimum LCC and minimum ene gy (o ene gy loss), come in o 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 I P C P P C P V P C P P C P C P P d C P C P P N E P E P P p N E P P p →→ →→ = = − − − +   = +   +  = + = + =  N Consequen ly, he op imum a ed powe o minimum LCC app oaches he op imum a ed powe o minimum ene gy o losses: ( ) min min min min 0 lim ( ) ( ) eq R LCC R R L R EL d P P LCC P E P →   = In o he wo ds, he op imum a ed powe minimizing he ene gy o ene gy loss is a p ac ical uppe limi o he op imum a ed powe minimizing he LCC, 17 PR LCCmin  PR PLmin. This esul can be use ul in hose common cases whe e he lis p ice o he mo o s is no longe a ailable, as will be shown la e . 4. Case S udy In he EU, on 1 Janua y, 2017, he hi d and las ie o he Ene gy Using P oduc s (EUP) Di ec i e o elec ic mo o s (EU Ecodesign Di ec i e) [6,7] came in o o ce. Since hen, he Minimum Ene gy Pe o mance S anda ds (MEPS) o elec ic mo o s equi e new mo o s sold in he EU ma ke (wi h a a ed ou pu om 0.75 kW-355 kW) mus sa is y he IE3 e iciency class (o IE2, i i ed o a Va iable Speed D i e-VSD). Fo ha eason, he p oposed me hod will be es ed wi h IE3 (p emium e iciency) mo o s, despi e he low le el o losses o his e iciency class. Fo he pu pose o compa ison, esul s o IE2 (high e iciency) mo o s will also be shown. The e e ence scena io o he case s udy add esses he p ojec -s age selec ion o he echno-economic op imum a ed powe (du y ype S1), PR, o an IE3, line-ope a ed single-speed cage induc ion mo o om Table 1 o d i e a ime- a iable mechanical powe load, P( ), o T = 8760 ope a ing hou s a yea . Figu e 4 shows he conside ed annual ime- a iable mechanical powe load, P( ), in which P100% = 30 kW has been selec ed as he 100% powe load. 0 5 10 15 20 25 30 0 1250 2500 3750 5000 (Hou s/yea ) Powe load 0 16.7 33.3 50.0 66.7 83.3 100 (kW) (%) 4780 2260 1720 Figu e 4. Annual ime- a iable mechanical powe load, P( ). Acco dingly, he annual mean and he RMS alues o he mechanical powe load esul in: 1( )· 24.3kW m k k k P P T ==  2 1( )· 27.7 kW RMS k k k P P T ==  As a esul , ollowing he con en ional me hod, a mo o a ed PR(RMS) = 30 kW should be chosen, which is he i s a ed powe o e he alue PRMS = 27.7 kW, as ound in he manu ac u e ’s ca alogue (Table 1). I is easy o check ha he alue o he peak o 18 maximum load powe , PMAX = P100% = 30 kW, does no exceed he a ed powe o he mo o a any ime, since PR(RMS) = 30 kW  PMAX = 30 kW. Table 3 summa izes he coe icien s o he powe -loss model and he pu chase-cos model o he IE3 and IE2 mo o s, whose a ed powe s a e 30 kW, 37 kW and 45 kW, as de e mined by linea eg ession i ing (see Appendix B o a simpli ied calcula ion o hese coe icien s). As will be shown, his wo-s ep ange o powe a ing conside s he expec ed op imum a ed powe o he mo o . A discoun ac o , kd = 0.4, and a esidual alue equi alen o he sum o he decommissioning and he auxilia y cos s (kR = kD + kA) ha e been conside ed o he sake o simplici y. Table 3. Coe icien s o he powe -loss model and he pu chase-cos (lis p ice) model o mo o s a ed a 30 kW, 37 kW and 45 kW. Ra ed Powe Powe losses PL(PR,Ppu) = kLF(PR) + kLV(PR)·P2pu Lis p ice PR (kW) kLF (kW) kLV (kW) CP (€) IE3 (p emium e iciency) 30 0.7355 1.3197 3338 37 0.8398 1.5707 4068 45 0.9955 1.7779 4882 Linea eg ession 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 e iciency) 30 0.9247 1.5909 3025 37 1.1401 1.7896 3651 45 1.4145 1.9359 4444 Linea eg ession 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 Figu e 5 shows he e olu ion o he EU-28 a e age semi-annual elec ici y p ices o indus ial consume s (Band-IC: annual consump ion be ween 0.5 and 2 GWh), all axes and le ies included [60]. Acco dingly, an elec ici y p ice o pE = 148.55 €/MWh, he EU-28 a e age elec ici y p ice in 2015, has been conside ed in he e e ence scena io. The linea eg ession o p ice da a i ing shows ha he elec ici y p ice g ows a an a e age annual a e o 2·2.1625 = 4.325 €/MWh, o ΔpE = (4.325/148.55)·100 = 2.91%/yea . 19 Figu e 5. 2008-2015: EU-28 a e age semi-annual elec ici y p ices o indus ial consume s (Band-IC: annual consump ion be ween 0.5 and 2 GWh), all axes and le ies included (Eu os a code [n g_pc_205]). Da a i ing by linea eg ession. Table 4 shows he a e age li e ime o an AC mo o in e ms o a ed powe [50]. Acco dingly, a li espan o N = 15 yea s has been used o calcula e he LCC o he mo o . Table 4. A e age li e ime o an AC mo o in e ms o a ed powe [50]. 0.75 kW − 1.1 kW 1.1 kW − 11 kW 11 kW − 110 kW 110 kW − 370 kW 10 yea s 12 yea s 15 yea s 20 yea s Finally, a (un a ou able) discoun a e, d = 5%, has been used in he e e ence scena io. This alue is sligh ly highe han he a e age eal yield on longe - e m go e nmen deb in he EU o e he pe iod 2001-2016, 4.61%, as shown in Table 5 [61]; and highe han he “social discoun a e” o 4% ecommended in Tool #54 o he Toolbox Complemen [62] o he Be e Regula ion Guideline o he EU. Table 5. 2001-2016: EU-28 a e age annual eal yield on longe - e m go e nmen deb [Eu os a code: eim 050]. Yea 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 Yea 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 Resul s and discussion Table 6 and Figu e 6 summa ize he main esul s o he e e ence scena io o he case s udy conside ed. Since he alue o he RMS powe o he load p o ile was PRMS = 27.7 kW, a mo o a ed PR(RMS) = 30 kW should be selec ed, acco ding o he con en ional ule. I an IE3 mo o we e selec ed, his mo o would d i e he mechanical load wi h an annual ene gy loss o 16.35 MWh/y, and a whole LCC o 438.99 k€. Acco ding o he p oposed me hod, he op imum a ing o he mo o wi h minimum annual ene gy loss is PR ELmin = 46.31 kW > PRMS = 27.7 kW. As a esul , a mo o wi h 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 Elec ici y P ice (€/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 Elec ici y P ice (€/MWh) 20 an op imum a ed powe , PR(ELmin) = 45 kW, should be selec ed om he manu ac u e ’s ca alogue (since he ene gy loss co esponding o he mo o a ed 37 kW is highe ). I is wo h no ing ha his esul could also be well an icipa ed wi h he eg ession line o minimum losses in Figu e 2: • Since he alue o he RMS powe o he load, PRMS = 27.7 kW, is placed be ween he c ossing poin s P37-45 and P45-55, (24.08 kW < PRMS = 27.7 kW ≤ 32.87 kW), he minimum ene gy loss co esponds o he mo o a ed 45 kW. • The app oxima e alue o he minimum annual ene gy loss can now be es ima ed wi h (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 e y close o he exac esul (14.62 MWh/y). Table 6. Summa y o esul s o he e e ence scena io o he case s udy. IE3 (p emium e iciency) Ra ed powe PR (kW) Ene gy loss EL (MWh/y) Ene gy E (MWh/y) Ene gy e iciency  E (%) Li e cycle cos │LCC│ (k€) P esen cos o ene gy 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 e iciency) Ra ed powe PR (kW) Ene gy loss EL (MWh/y) Ene gy E (MWh/y) Ene gy e iciency  E (%) Li e cycle cos │LCC│ (k€) P esen cos o ene gy 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 Powe (kW) Ene gy Losses, EL(MWh/yea ) Li e-Cycle Cos , 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 Ene gy Losses, EL(MWh/yea ) Li e-Cycle Cos , LCC (k€) 400 410 420 430 440 450 460 IE3 20 30 40 50 60 Powe (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) Figu e 6. Va ia ion o he annual ene gy loss, EL(PR), and he LCC, │LCC(PR)│, wi h he a ed powe o he mo o o IE3 mo o s (le -hand side) and o IE2 mo o s ( igh -hand side). I he minimum LCC is conside ed, hen he p oposed me hod leads o a mo o wi h an op imum a ed powe o PR LCCmin = 42.65 kW (PRMS = 27.7 kW < PR LCCmin = 42.65 kW < PR ELmin = 46.31 kW). Acco dingly, a mo o wi h a a ed powe o PR(LCCmin) = 45 kW should be selec ed om he manu ac u e ’s ca alogue ( he LCC co esponding o he mo o a ed 37 kW is sligh ly highe ). As can be obse ed, o he conside ed case, he a ed powe s o he mo o s wi h minimum annual ene gy loss and minimum LCC coincide, i.e., PR(ELmin) = 45 kW = PR(LCCmin) = 45 kW, and bo h esul in being wo s eps highe in he manu ac u e ’s ca alogue han he a ed powe o he mo o based on he RMS powe , PR(RMS) = 30 kW. The echno-economic op imum IE3 a ed powe would: • Reduce he annual ene gy loss up o EL(PR(ELmin) = PR(LCCmin) = 45 kW) = 14.62 MWh/y, which cons i u es 10.59% (1.73 MWh/y) less han ha co esponding o he con en ionally a ed mo o PR RMS = 30 kW. • Reduce he whole LCC up o │LCC(PR(ELmin) = PR(LCCmin) = 45 kW)│= 436.63 k€, which is 0.54% (2.36 k€) less han ha co esponding o he con en ionally a ed mo o PR RMS = 30 kW. • Inc ease he o e all ene gy e iciency up o  E(PR(ELmin) = PR(LCCmin) = 45 kW) = 93.14%, which is 0.81% g ea e han ha co esponding o he con en ionally a ed mo o PR RMS = 30 kW. Al hough he amoun o he inc ease in ene gy e iciency would seem o be small, i is in ac ma kedly g ea e han he inc ease in he a ed e iciency be ween he con en ionally a ed mo o , PR RMS = 30 kW, and he op imum a ed mo o ,  R(PR = 45 kW) -  R(PR = 30 kW) = 94.2 – 93.6 = 0.6%. • Reduce he cumula i e p esen cos o he losses in he LCC up o CPEL(PR(ELmin) = PR(LCCmin) = 45 kW) = 27.83 k€ (6.37% o LCC), which is 10.59% (3.30 k€) less han ha co esponding o he con en ionally mo o a ed 22 a PR RMS = 30 kW (31.13 k€, 7.09% o he LCC). Acco dingly, he inc emen o he ini ial cos , I(PR = 45 kW) - I(PR = 30 kW) = 926 € is o se by he cos sa ings o e 5.9 yea s, ha is, only sligh ly mo e han a hi d o he expec ed li e o he mo o . A ough ex apola ion o he pa icula esul s o his IE3 case o he 2015 da a o elec ic mo o consump ion in he EU-28 sec o s o indus y and se ices would lead o: • an annual po en ial ene gy sa ing o 7.48 TWh/y (0.75% o al sa ing), • an annual po en ial sa ing in ope a ing cos s o 14.24 G€/y, and • an annual po en ial sa ing in emissions o CO2eq o 2.80 million (CO2eq)/y. Figu e 6 (le -hand side) shows he e olu ion o he annual ene gy loss, EL(PR), and he whole LCC, LCC(PR), wi h he a ed powe o he mo o . This igu e (and Table 6) clea ly con i m ha he op imum a ed powe , based on he minimum LLC, PR LCCmin = 42.65 kW, is a li le lowe han he op imum based only on ene gy o ene gy loss, PR ELmin = 46.31 kW, due o he e ec o conside ing o he ini ial cos o he mo o . This igu e also shows ha he RMS powe o he load, PRMS = 27.7 kW, he a ed powe based on he minimum LLC, PR LCCmin = 42.65 kW, and he op imum a ed powe based only on ene gy o ene gy loss, PR ELmin = 46.31 kW, a e bo h in an inc easing sequence. Figu e 6 (le ) shows ha bo h he ene gy loss and he LCC a e L-shaped. Fo IE3 mo o s, as he powe g ows, bo h cu es all o he minimum poin s, a e which hey inc ease e y slowly. As a esul , bo h cu es exhibi a he la minimum poin s. Table 6 shows ha he pe o mance indica o s o he mo o a ed 55 kW a e only a li le wo se han hose co esponding o he op imum a ed 45 kW mo o (1.6% o ene gy and 0.2% o he LCC), al hough i is s ill be e han he con en ional mo o a ed PR RMS = 30 kW (1.50 MWh/y less ene gy and 1.28 k€ less LCC). This a he la minimum egion could be ad an ageous in he design o a mo o -pu chasing policy wi h a educed numbe o a ed powe s, since he e is a b oad ange o mechanical loads su ounding he la egion o he minimum poin . Fo he echno-economic op imum a ed mo o , he RMS load ep esen s a no malized o ela i e load o Ppu = PRMS /PR LCCmin = 27.7/45 = 0.6156, which means ha he empe a u e o he windings will emain well below he allowable maximum. Conside ing class F insula ion (155ºC) wi h a empe a u e ise B (ΔθM = 130 – 50 = 80 K, a s anda d ai -cooling empe a u e o 40°C and 10 K o he ho spo empe a u e ma gin), which is he mos common equi emen ac oss indus y oday, and also conside ing ha he empe a u e ise is p opo ional o he powe losses, he empe a u e ise esul s 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     = = = = ==   = = = = + == + The e o e, he educ ion in he empe a u e ise unde i s allowable maximum is: (1 0.6018)· (1 0.6018)·80 31.85K MM     − = −  = − = An app oxima ion o he Mon singe ’s ule s a es ha a empe a u e ise o 10 K hal es he expec ed li e ime o he isola ions. Con e sely, a educ ion in he empe a u e o 10 23 K doubles he expec ed he mal li e o he insula ions. Acco dingly, i is expec ed ha he he mal li e o he op imum a ed mo o will ex end well beyond he 15 yea s ini ially expec ed. The bo om pa o Table 6 (Figu e 6) shows ha simila esul s a e eached wi h IE2 mo o s, bu wi h an op imum a ed powe o 37 kW. E en hough he ene gy loss (+4.11 MWh/y) and he LCC (+7.10 k€) o his IE2 mo o a e highe han hose co esponding o he 45 kW IE3 mo o , hey s ill emain lowe han hose co esponding o he IE2 mo o a ed PR RMS = 30 kW (–2.27 MWh/y and –3.78 k€, espec i ely). The inc emen o he ini ial cos o he op imum IE2 a ed mo o , I(PR = 37 kW) - I(PR = 30 kW) = 376 €, is o se by he sa ings in cos s o e 2.7 yea s, ha is, less han a i h o he expec ed li e o he mo o . Table 6 also shows ha he pe o mance indica o s o he IE2 mo o a ed a 45 kW a e only a li le wo se han hose co esponding o he op imum a ed mo o a 37 kW, bu a e s ill be e han he con en ional mo o a ed a PR RMS = 30 kW. I is wo h no ing ha he di e ence (sa ing) in he LCC o he IE3 and IE2 op imum a ed powe mo o s (7.10 k€), is almos 10 imes he di e ence in ini ial cos (739 €). A ough ex apola ion o he pa icula esul s o he IE2 case o he 2015 da a o elec ic mo o consump ion in he EU-28 sec o s o indus y and se ices would lead o: • an annual po en ial ene gy sa ing o 5.59 TWh/y (0.56% o al sa ing), • an annual po en ial sa ing in ope a ing cos s o 9.90 G€/y, and • an annual po en ial sa ing in emissions o CO2eq o 2.09 million (CO2eq)/y. As expec ed, Figu e 6 shows ha he cu es o he ene gy loss and he LCC o IE2 mo o s a e highe han he co esponding cu es o IE3 mo o s. This igu e also shows ha , while cu es o IE3 mo o s a e L-shaped, he highe losses o IE2 mo o s, as well as he g ea e di e ence in losses be ween mo o s consecu i ely a ed, esul ed in he cu es o IE2 mo o s being mo e V-shaped. Fo IE2 mo o s, as he powe g ows, he cu e alls o he minimum poin as e han does he cu e o he IE3 mo o s. As he minimum IE2 cu es also g ow as e han hose o IE3 mo o s, IE2 cu es exhibi a mo e ma ked minimum poin and he op imum a ed mo o is close o he RMS powe . Con e sely, he highe he e iciency class, he g ea e he dis ance be ween he op imum a ing and he RMS powe . The highe alue o he a ed powe o he op imized mo o s may imply a ce ain deg ee o con lic be ween he size o he mo o ame and he oom a ailable, which could lead o ex a cos s in commissioning and ins alla ion. In he p ojec s age, he di icul ies caused by size a e easily manageable, bu can p o e o be a limi a ion when eplacing an old mo o . Ne e heless, a su ey o he IE3 mo o ca alogue shows ha , o he 18 mo o s eco ded, he e a e only h ee mo o s ( a ed powe s) ha do no sha e he sha heigh wi h any o he mo o . The emaining 15 mo o s ( a ed powe ) sha e a sha heigh wi h a leas one mo o . Fo he case o he 25 mo o s in he IE2 ca alogue, he e a e only ou mo o s ( a ed powe s) ha do no sha e a sha heigh , while he emaining 21 mo o s ( a ed powe ) sha e a sha heigh wi h a leas one mo o . Ano he con lic ing si ua ion may occu when conside ing he eplacemen o a mo o d i ing an applica ion wi h a g owing o que-speed load cu e. In such a case, i should be bo ne in mind ha , he highe he mo o e iciency class and a ed powe , he highe he sha o que, he speed (lowe slip), and he mechanical powe deli e ed. Acco dingly, i may happen ha he educ ion in powe losses o he new mo o (g ea e 24 a ed powe o be e e iciency class) was less han he inc ease in he mechanical powe in he sha , which would lead o an inc ease in ac i e powe consump ion [63,64]. Fo he sake o simplici y, he small change in he ope a ing poin ( o que and speed o slip) has no been aken in o accoun in his wo k. Ne e heless, in he design o p ojec s age o a new applica ion, he enginee can easily adjus he applica ion o he chosen mo o (g ea e a ed powe o be e e iciency class); hus, he sligh speed inc ease in he selec ed mo o ough no o pose an issue [19]. As p e iously men ioned, he g ea e alue o he op imized a ed powe leads he mo o o ope a e wi h a educed ela i e load, which means an ex ension o he expec ed mo o li e ime, since a longe winding insula ion and bea ing li e ime a e bo h expec ed. As a esul o he lowe ope a ing empe a u e, an inc ease in he mo o endu ance o o e loads o ol age unbalance can also be expec ed, as well as a be e ole ance owa ds he e ec s o he ha monic dis o ion [19]. These all ep esen signi ican ad an ages o op imized a ed powe mo o s, since, as men ioned, eliabili y is he main ocus o plan enginee s. 4.2 Sensi i i y es In o de o es he obus ness o he solu ion sugges ed by he p oposed me hod, an analysis o he in luence o he main pa ame e s on he solu ion o he e e ence case scena io is pe o med. S a ing wi h he e e ence scena io, his es analyses he e ec on he op imum a ing o a ying, ac oss a b oad ange, ce e is pa ibus, he ope a ional hou s pe yea , T, he p ice o he ene gy, pE, he discoun ac o in he pu chase cos , kd, he discoun a e, d, and he li espan, N. Figu e 7 summa izes he esul s o IE3 mo o s. Figu e 7. IE3 mo o s. Op imum a ed powe o minimum ene gy loss, PR(ELmin), and minimum LCC, PR(LCCmin): In luence o he ope a ing hou s pe yea , T, he cos o ene gy, pE, he discoun ac o in he pu chase cos , kd, he discoun a e, d, and he li e span, N. I can be obse ed ha he p oposed solu ion is highly obus since he op imum a ed powe o he minimum LCC only shi s om i s alue in he e e ence scena io, PR(LCCmin) = 45 kW, o PR(LCCmin) = 37 kW, when: • he ope a ing hou s pe yea a e educed o 5000 hou s/yea o ewe ( i s ow below he g aph), • he p ice o ene gy alls o 75 €/MWh o 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) Op imum Ra ed Powe (kW) IE3 010 20 40 kd(%)30 31 Table C.2. Cage induc ion mo o s om manu ac u e B: e iciency da a o gene al-pe o mance, cas -i on mo o s designed o low ol age (440 V, 50 Hz), ou poles, IP 55, IC 411 and insula ion class F ( empe a u e ise class B). IE3 (p emium e iciency) IE2 (high e iciency) Ou pu 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 Re e ences [1] Be oldi, P., López-Lo en e, J., Labanca, N., 2016; Ene gy Consump ion and Ene gy E iciency T ends in he EU-28 2000-2014; EUR 27972 EN; doi 10.2788/581574 h p://publica ions.j c.ec.eu opa.eu/ eposi o y/handle/JRC101177 [2] Anibal T. de Almeida, Joao Fong, Hugh Falkne , Paolo Be oldi, Policy op ions o p omo e ene gy e icien elec ic mo o s and d i es in he EU, Renewable and Sus ainable Ene gy Re iews, Volume 74, July 2017, Pages 1275-1286, ISSN 1364-0321, h ps://doi.o g/10.1016/j. se .2017.01.112. 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