Lesson 12a: Three Phase Induction Motors

Transcription

1 1 Leo 1a: Thee hae Iductio Moto ET 33b Ac Moto, Geeato ad owe Sytem Leaig Objective Afte thi peetatio you will be able to: Explai how a thee-phae iductio moto opeate Compute the ychoou peed of a iductio moto ad the lip betwee moto oto ad tato magetic field Compute the powe that coe that ai gap of a iductio moto Explai how the paamete of a iductio moto cicuit model elate to it pefomace Idetify model equatio 1

2 3 Thee-hae Iductio Moto Moto Cotuctio Roto Stato Stato - magetic tuctue (io coe) ad widig that ceate magetic field. Coected to thee-phae voltage Roto - io coe ad coducto that otate ad dive the haft of the moto. Coducto ca be eithe coppe ba (quiel cage) o woud coil (woud-oto) 4 Thee-hae Iductio Moto The thee-phae voltage V a, V b ad V c ceate fluxe that add i pace ad time to ceate a otatig magetic field without phyical motio. Flux wave otate at a peed give by: 10f Whee = ychoou peed f = ac voltage fequecy = umbe of pole (ot pole pai)

3 5 Sychoou Speed Example 1a-1: Fou pole moto opeatig o a 60 Hz ytem. What i the peed at which the magetic field otate 10f 4 pole f 60 Hz pm 4 Whe upplied fom 60 Hz ytem, i multiple of 60 6 Iductio Moto Opeatio Fo a Iductio Moto to Rotate 3-phae voltage poduce otatig magetic field i tato Cuet i iduced i oto by movig magetic field Iduced cuet i oto poduce a magetic field i oto Field i oto iteact with the field i the tato to poduce toque (oto "chae" tato field) 3

4 7 Slip ad Slip Speed To iduce cuet i oto thee mut be a peed diffeece betwee the oto ad the otatig magetic field. Thi peed diffeece i called lip peed l Whee l = lip peed = ychoou peed = oto peed Defie lip a pe uit value Slip iceae a load iceae 8 Slip ad Developed Toque At tat up = 0. Aumig = 1800 RM detemie the lip Slip i 1 at locked oto (tatup) At full load toque moto pi at ated peed Rated peed =1750 pm: typical fo 4 pole iductio moto Rated lip vay of. Slip at No-load Roto pi at ealy, o =1798 typical fo uloaded 4 pole moto Slip i ea zeo whe thee i o-load o the moto 4

5 9 Thee-hae Iductio Moto Advatage Diadvatage Smooth owe Tafe owe almot cotat i 3-phae ytem owe pulate i igle phae moto Simple Cotuctio No buhe o othe high maiteace pat Ca ot eaily cotol peed 10 Iductio Moto Toque-Speed Chaacteitic Typical Toque-Speed Chaacteitic of Iductio Moto Statig Beakove Toque Toque T m ( ) 100 Moto deig detemie peed chaacteitic hape Opeatig age Statig toque i developed whe =0 pm. I thi cae appoximately 100 N-m Shape of toque peed chaacteitic deped o deig of moto 5

6 11 Slip Speed & Roto Voltage/Fequecy Diffeece betwee peed of otatig magetic field ad oto called lip peed l Whee l = lip peed Slip peed iceae a load iceae ad oto fequecy i a fuctio of lip f 10 Whee: = ychoou peed = p.u lip f = fequecy of oto iduced voltage 1 Slip Speed & Roto Voltage/Fequecy With the oto blocked =0, =1 f f 10 tato f Whee: f tato = tato voltage fequecy f = blocked oto fequecy At tatup tato voltage fequecy ad oto voltage fequecy ae equal I opeatio lip ot equal 1, o geeally.. Iduced V max at =1 f E f E Whee: E = voltage iduced i oto at lip E = voltage iduced with =0 (Blocked oto) 6

7 13 Moto Roto Cicuit Model Moto ha eitace ad iductive eactace. X L deped o f o x f L x f L x X Roto eactace i tem of blocked oto iductace Roto Impedace z R jx R jx Roto cuet E I R j x E R jx Moto Roto Cicuit Model 14 Some algeba give I R E jx Roto cuet deped o lip which i elated to moto peed hae agle of Z deped o lip ( R chage), o impedace agle ad F p chage with moto lip. Thi mea oto cuet magitude ad phae agle chage with lip Roto cuet magitude I R E X Roto cuet phae agle Roto powe facto ta X R 1 Whee = oto cuet agle F p co( ) 7

8 15 Moto Roto Cicuit Model Roto hae Shift Roto Cuet Opeatig age Opeatig age 16 Iductio Moto Ai Gap owe Defie powe tafeed aco the ai gap i the iductio moto S gap E Whee E I * E 0 I I - I ectagula fom Sgap E I co( ) j E I i( ) With the followig compoet gap E I co( ) Q gap E I i( ) gap = active powe povidig haft powe, fictio, widage, ad oto eitace loe. Q gap = eactive powe that ocillate aco ai gap Roto F p ad the magitude of the I detemie gap active powe, gap E i aumed to be cotat becaue it i popotioal to the flux deity which i aumed to be cotat 8

9 17 Active owe Aco Ai-Gap Compoet gap mech Whee mech = active powe coveted to haft powe cl = oto coducto loe cl Total 3-phae oto loe cl 3I R 18 Active owe Aco Ai-Gap Total gap powe gap 3I R 9

10 19 Active owe Aco Ai-Gap Slip elated to the amout of mechaical load o moto. Moe mechaical load moe active powe aco gap Combie powe balace equatio with defiitio of gap ad cl mech 3I R (1 ) 0 Active owe Aco Ai-Gap Roto eitace effect the amout of mechaical powe developed Divide R Ito two pat: oto lo eitace ad the eitace that epeet mechaical load R R (1 ) R 10

11 1 Active owe Aco Ai-Gap e phae model of the oto Developed Toque ad Mechaical owe Mechaical powe i tem of ad 1- o 1- Subtitute ito the peviou equatio fo mechaical powe mech 3I R 11

12 3 Developed Toque ad Mechaical owe Mechaical powe elated to oto eitace ad cuet To fid toque divide mechaical powe by peed T d 180R R E X N - m 4 Developed Toque ad Mechaical owe Thi equatio aume a ideal tato o loe. Ued to geeate toque-peed cuve oto eitace effect the developed powe ad, theefoe toque 1

13 5 Moto Loe Efficiecy & owe Facto i = Electic powe i to moto cl = Stato coducto loe; coe = Coe loe; cl = Roto coducto loe; fw = Fictio ad widage; tay = Stay loe; haft = Mechaical powe output (ated H); mech = Electic powe coveted to mechaical powe i oto. 6 Developed Toque ad Mechaical owe owe coveted gap cl Total active powe aco ai gap cl = oto coducto loe mech gap (1 ) otio of active gap powe coveted to mechaical powe mech = haft + fw + tay 13

14 7 owe Balace Equatio owe i mut equal powe out plu loe mech Rated haft powe (H): haft = mech fw - tay Fom tato ide: gap = i cl - coe 8 owe Balace Equatio Total appaet electic powe i Fid i fom F p ad S i value Alo, give a moto efficiecy at a output level o i S i haft i 3 I Fp S i i L V LL Ca fid i 14

15 9 Example 1a- A 3-phae 60 Hz, 75 Hp, 4 pole moto opeate at a ated temial voltage of 30 V Ude ated coditio it daw a lie cuet of 186 A ad ha a efficiecy of 90%. The followig loe ae meaued: Coe loe = 173 W Stato coducto loe = 10 W Roto coducto loe = 116 W Fid: a) the iput powe b) the total loe c) the ai gap powe d) the haft peed e) the moto powe facto f) combied mechaical loe 30 Example 1a- Solutio (1) a) Fid iput powe A b) Fid the total loe Loe ae the diffeece betwee the iput ad output powe A 15

16 31 Example 1a- Solutio () c) Fid the gap powe A 3 Example 1a- Solutio (3) d) Fid haft peed Fom above Fid ychoou peed 16

17 33 Example 1a- Solutio (4) A e) Moto powe facto atio of appaet powe to active powe A 34 Example 1a- Solutio (5) f) Combied mechaical loe A 17

18 35 Example 1a-3 A 3-phae 30V, 5 H, 60Hz, 4 pole moto oto abob 0,00 W whe upplyig a ukow haft load. The oto coppe loe ae meaued at 975 W whe upplyig thi load. The fictio ad widage loe ae kow to be 50 W. Detemie a) the haft peed; b) mechaical powe developed; c) toque developed i the oto; d) haft toque; e) pecet of ated hoepowe that the moto i deliveig. 36 Example 1a-3 Solutio (1) a) Moto peed b) Mechaical powe developed i gap le oto coducto loe A 18

19 37 Example 1a-3 Solutio () c) Compute developed toque i lb-ft A d) Compute haft toque with haft powe A 38 Example 1a-3 Solutio (3) e) ecet Load 19

20 Full Iductio Moto Model e phae cicuit imila to tafome 39 V = tato voltage (lie voltage) R fe = equivalet coe eitace R = tato widig eitace R = actual oto eitace X = tato leakage eactace X = actual blocked-oto eactace X M = tato coe magetizig eactace a = N1/N atio of tato to oto tu 40 Full Iductio Moto Model e phae moto model-oto quatitie efeed to tato. Whee: I1 = tato cuet I = I /a : oto cuet efeed to tato R = R a oto eitace efeed to tato X = X a blocked oto eactace efeed to the tato E = E a blocked oto voltage efeed to the tato 0

21 41 Full Iductio Moto Model Remembe, R ca be witte a: R R (1 ) R a a a R The powe, toque peed ad efficiecy ca ow be foud aalytically fom the model if iput, output ad model paamete ae kow. 4 Full Iductio Moto Model Ue cicuit aalyi techique to detemie moto pefomace 1

22 43 Full Iductio Moto Model Z Z R jx Z Z Z 0 Z 0 Roto impedace Z 0 R R fe fe jx jx Zi Z Z1 whee Z1 R1 jx1 Total moto model impedace (pe phae) M M aallel combiatio of coe value V I1 Stato cuet E I1 Z i Z Iduced oto voltage efeed to tato 44 Full Iductio Moto Model I E Z Total powe elatiohip cl 3 I 1 Roto cuet efeed to tato R 1 Total tato coducto loe cl 3 I R Total oto coducto loe gap cl mech cl (1 ) Note: all powe equatio ae fo total thee-phae powe

23 45 Full Iductio Moto Model haft mech fw tay Shaft powe i mechaical powe developed le mechaical loe T D 7.04 mech (lb - ft) Roto developed toque. Whee = oto peed T haft 7.04 haft (lb - ft) Shaft toque Fially coe 3 E R fe The tato coe loe ae depedet o the voltage 46 Ed Leo 1a: Thee hae Iductio Moto ET 33b Ac Moto, Geeato ad owe Sytem 3