Three Phase Induction Motors

Transcription

1 Chapter (8) hree Phae Induction Motor Introduction he three-phae induction otor are the ot widely ued electric otor in indutry. hey run at eentially contant peed fro no-load to full-load. However, the peed i frequency dependent and conequently thee otor are not eaily adapted to peed control. We uually prefer d.c. otor when large peed variation are required. Neverthele, the 3-phae induction otor are iple, rugged, low-priced, eay to aintain and can be anufactured with characteritic to uit ot indutrial requireent. In thi chapter, we hall focu our attention on the general principle of 3-phae induction otor. 8.1 hree-phae Induction Motor Like any electric otor, a 3-phae induction otor ha a tator and a rotor. he tator carrie a 3-phae winding (called tator winding) while the rotor carrie a hort-circuited winding (called rotor winding). Only the tator winding i fed fro 3-phae upply. he rotor winding derive it voltage and power fro the externally energized tator winding through electroagnetic induction and hence the nae. he induction otor ay be conidered to be a tranforer with a rotating econdary and it can, therefore, be decribed a a tranforertype a.c. achine in which electrical energy i converted into echanical energy. Advantage (i) It ha iple and rugged contruction. (ii) It i relatively cheap. (iii) It require little aintenance. (iv) It ha high efficiency and reaonably good power factor. (v) It ha elf tarting torque. Diadvantage (i) It i eentially a contant peed otor and it peed cannot be changed eaily. (ii) It tarting torque i inferior to d.c. hunt otor. 181

2 8. Contruction A 3-phae induction otor ha two ain part (i) tator and (ii) rotor. he rotor i eparated fro the tator by a all air-gap which range fro 0.4 to 4, depending on the power of the otor. 1. Stator It conit of a teel frae which encloe a hollow, cylindrical core ade up of thin laination of ilicon teel to reduce hyterei and eddy current loe. A nuber of evenly paced lot are provided on the inner periphery of the laination [See Fig. (8.1)]. he inulated connected to for a Fig.(8.1) balanced 3-phae tar or delta connected circuit. he 3-phae tator winding i wound for a definite nuber of pole a per requireent of peed. Greater the nuber of pole, leer i the peed of the otor and vice-vera. When 3-phae upply i given to the tator winding, a rotating agnetic field (See Sec. 8.3) of contant agnitude i produced. hi rotating field induce current in the rotor by electroagnetic induction.. otor he rotor, ounted on a haft, i a hollow lainated core having lot on it outer periphery. he winding placed in thee lot (called rotor winding) ay be one of the following two type: (i) Squirrel cage type (ii) Wound type (i) Squirrel cage rotor. It conit of a lainated cylindrical core having parallel lot on it outer periphery. One copper or aluinu bar i placed in each lot. All thee bar are joined at each end by etal ring called end ring [See Fig. (8.)]. hi for a peranently hort-circuited winding which i indetructible. he entire contruction (bar and end ring) reeble a quirrel cage and hence the nae. he rotor i not connected electrically to the upply but ha current induced in it by tranforer action fro the tator. hoe induction otor which eploy quirrel cage rotor are called quirrel cage induction otor. Mot of 3-phae induction otor ue quirrel cage rotor a it ha a rearkably iple and robut contruction enabling it to operate in the ot advere circutance. However, it uffer fro the diadvantage of a low tarting torque. It i becaue the rotor bar are peranently hort-circuited and it i not poible to add any external reitance to the rotor circuit to have a large tarting torque. 18

3 Fig.(8.) Fig.(8.3) (ii) Wound rotor. It conit of a lainated cylindrical core and carrie a 3- phae winding, iilar to the one on the tator [See Fig. (8.3)]. he rotor winding i uniforly ditributed in the lot and i uually tar-connected. he open end of the rotor winding are brought out and joined to three inulated lip ring ounted on the rotor haft with one bruh reting on each lip ring. he three bruhe are connected to a 3-phae tar-connected rheotat a hown in Fig. (8.4). At tarting, the external reitance are included in the rotor circuit to give a large tarting torque. hee reitance are gradually reduced to zero a the otor run up to peed. Fig.(8.4) he external reitance are ued during tarting period only. When the otor attain noral peed, the three bruhe are hort-circuited o that the wound rotor run like a quirrel cage rotor. 8.3 otating Magnetic Field Due to 3-Phae Current When a 3-phae winding i energized fro a 3-phae upply, a rotating agnetic field i produced. hi field i uch that it pole do no reain in a fixed poition on the tator but go on hifting their poition around the tator. For thi reaon, it i called a rotating Held. It can be hown that agnitude of thi rotating field i contant and i equal to 1.5 where i the axiu flux due to any phae. 183

4 o ee how rotating field i produced, conider a -pole, 3i-phae winding a hown in Fig. (8.6 (i)). he three phae X, Y and Z are energized fro a 3-phae ource and current in thee phae are indicated a I x, I y and I z [See Fig. (8.6 (ii))]. eferring to Fig. (8.6 (ii)), the fluxe produced by thee current are given by: x y z in ωt in ( ωt 10 ) in ( ωt 40 ) Fig.(8.5) Here i the axiu flux due to any phae. Fig. (8.5) how the phaor diagra of the three fluxe. We hall now prove that thi 3-phae upply produce a rotating field of contant agnitude equal to 1.5. Fig.(8.6) 184

5 (i) At intant 1 [See Fig. (8.6 (ii)) and Fig. (8.6 (iii))], the current in phae X i zero and current in phae Y and Z are equal and oppoite. he current are flowing outward in the top conductor and inward in the botto conductor. hi etablihe a reultant flux toward right. he agnitude of the reultant flux i contant and i equal to 1.5 a proved under: At intant 1, ωt 0. herefore, the three fluxe are given by; x z 0; in y in 3 ( 10 ) ( 40 ) 3 ; Fig.(8.7) he phaor u of y and z i the reultant flux r [See Fig. (8.7)]. It i clear that: eultant flux, (ii) At intant, the current i axiu (negative) in y phae Y and 0.5 axiu (poitive) in phae X and Y. he agnitude of reultant flux i 1.5 a proved under: r co 1. 5 At intant, ωt 30. herefore, the three fluxe are given by; x y z in 30 in ( 90 ) in ( 10 ) Fig.(8.8) he phaor u of x, y and z i the reultant flux r 10 Phaor u of x and z, ' r co Phaor u of ' r and y, r Note that reultant flux i diplaced 30 clockwie fro poition

6 (iii) At intant 3, current in phae Z i zero and the current in phae X and Y are equal and oppoite (current in phae X and Y arc ax. value). he agnitude of reultant flux i 1.5 a proved under: At intant 3, ωt 60. herefore, the three fluxe are given by; x y z in 60 in in ( 60 ) 3 ( 180 ) 0 ; 3 ; Fig.(8.9) he reultant flux r i the phaor u of x and y ( Q z 0 ) co r 1. 5 Note that reultant flux i diplaced 60 clockwie fro poition 1. (iv) At intant 4, the current in phae X i axiu (poitive) and the current in phae V and Z are equal and negative (current in phae V and Z are 0.5 ax. value). hi etablihe a reultant flux downward a hown under: At intant 4, ωt 90. herefore, the three fluxe are given by; x y z in 90 in ( 30 ) in ( 150 ) Fig.(7.10) he phaor u of x, y and z i the reultant flux r 10 Phaor u of z and y, ' r co Phaor u of ' r and x, r Note that the reultant flux i downward i.e., it i diplaced 90 clockwie fro poition

7 It follow fro the above dicuion that a 3-phae upply produce a rotating field of contant value ( 1.5, where i the axiu flux due to any phae). Speed of rotating agnetic field he peed at which the rotating agnetic field revolve i called the ynchronou peed (N ). eferring to Fig. (8.6 (ii)), the tie intant 4 repreent the copletion of one-quarter cycle of alternating current I x fro the tie intant 1. During thi one quarter cycle, the field ha rotated through 90. At a tie intant repreented by 13 or one coplete cycle of current I x fro the origin, the field ha copleted one revolution. herefore, for a -pole tator winding, the field ake one revolution in one cycle of current. In a 4-pole tator winding, it can be hown that the rotating field ake one revolution in two cycle of current. In general, fur P pole, the rotating field ake one revolution in P/ cycle of current. Cycle of current P revolution of field or Cycle of current per econd P revolution of field per econd Since revolution per econd i equal to the revolution per inute (N ) divided by 60 and the nuber of cycle per econd i the frequency f, or f P N f N P NP 10 he peed of the rotating agnetic field i the ae a the peed of the alternator that i upplying power to the otor if the two have the ae nuber of pole. Hence the agnetic flux i aid to rotate at ynchronou peed. Direction of rotating agnetic field he phae equence of the three-phae voltage applied to the tator winding in Fig. (8.6 (ii)) i X-Y-Z. If thi equence i changed to X-Z-Y, it i oberved that direction of rotation of the field i revered i.e., the field rotate counterclockwie rather than clockwie. However, the nuber of pole and the peed at which the agnetic field rotate reain unchanged. hu it i neceary only to change the phae equence in order to change the direction of rotation of the agnetic field. For a three-phae upply, thi can be done by interchanging any two of the three line. A we hall ee, the rotor in a 3-phae induction otor run in the ae direction a the rotating agnetic field. herefore, the 187

8 direction of rotation of a 3-phae induction otor can be revered by interchanging any two of the three otor upply line. 8.4 Alternate Matheatical Analyi for otating Magnetic Field We hall now ue another ueful ethod to find the agnitude and peed of the reultant flux due to three-phae current. he three-phae inuoidal current produce fluxe 1, and 3 which vary inuoidally. he reultant flux at any intant will be the vector u of all the three at that intant. he fluxe are repreented by three variable Fig.(8.11) agnitude vector [See Fig. (8.11)]. In Fig. (8.11), the individual flux direction arc fixed but their agnitude vary inuoidally a doe the current that produce the. o find the agnitude of the reultant flux, reolve each flux into horizontal and vertical coponent and then find their vector u. h v 3 0 co t ωt coωt co( ωt 10 )co60 co( ωt 10 )co60 + he reultant flux i given by; 3 co( ωt 40 )co60 3 co( ωt 40 )co60 Fig.(8.1) in ωt 3 [ co ωt + ( in ωt) ] 1/ 1.5 Contant r h + v hu the reultant flux ha contant agnitude ( 1.5 ) and doe not change with tie. he angular diplaceent of r relative to the OX axi i tan θ θ ωt v h 3 3 in ωt tan ωt coωt hu the reultant agnetic field rotate at contant angular velocity ω( πf) rad/ec. For a P-pole achine, the rotation peed (ω ) i ω P ω rad/ec 188

9 πn or πf... N i in r.p.. 60 P 10 f N P hu the reultant flux due to three-phae current i of contant value ( 1.5 where i the axiu flux in any phae) and thi flux rotate around the tator winding at a ynchronou peed of 10 f/p r.p.. For exaple, for a 6-pole, 50 Hz, 3-phae induction otor, N, 10 50/ r.p.. It ean that flux rotate around the tator at a peed of 1000 r.p Principle of Operation Conider a portion of 3-phae induction otor a hown in Fig. (8.13). he operation of the otor can be explained a under: (i) When 3-phae tator winding i energized fro a 3-phae upply, a rotating agnetic field i et up which rotate round the tator at ynchronou peed N ( 10 f/p). (ii) he rotating field pae through the air gap and cut the rotor conductor, which a yet, are Fig.(1-) tationary. Due to the relative peed between the rotating flux and the tationary rotor, e..f. are induced in the rotor conductor. Since the rotor circuit i hort-circuited, current tart flowing in the rotor conductor. (iii) he current-carrying rotor conductor are placed in the agnetic field produced by the tator. Conequently, echanical force act on the rotor conductor. he u of the echanical force on all the rotor conductor produce a torque which tend to ove the rotor in the ae direction a the rotating field. (iv) he fact that rotor i urged to follow the tator field (i.e., rotor ove in the direction of tator field) can be explained by Lenz law. According to thi law, the direction of rotor current will be uch that they tend to oppoe the caue producing the. Now, the caue producing the rotor current i the relative peed between the rotating field and the tationary rotor conductor. Hence to reduce thi relative peed, the rotor tart running in the ae direction a that of tator field and trie to catch it. 189

10 8.6 Slip We have een above that rotor rapidly accelerate in the direction of rotating field. In practice, the rotor can never reach the peed of tator flux. If it did, there would be no relative peed between the tator field and rotor conductor, no induced rotor current and, therefore, no torque to drive the rotor. he friction and windage would iediately caue the rotor to low down. Hence, the rotor peed (N) i alway le than the uitor field peed (N ). hi difference in peed depend upon load on the otor. he difference between the ynchronou peed N of the rotating tator field and the actual rotor peed N i called lip. It i uually expreed a a percentage of ynchronou peed i.e., N N % age lip, 100 N (i) he quantity N N i oetie called lip peed. (ii) When the rotor i tationary (i.e., N 0), lip, 1 or 100 %. (iii) In an induction otor, the change in lip fro no-load to full-load i hardly 0.1% to 3% o that it i eentially a contant-peed otor. 8.7 otor Current Frequency he frequency of a voltage or current induced due to the relative peed between a vending and a agnetic field i given by the general forula; Frequency N P 10 where N elative peed between agnetic field and the winding P Nuber of pole For a rotor peed N, the relative peed between the rotating flux and the rotor i N N. Conequently, the rotor current frequency f' i given by; (N N)P f ' 10 N P 10 f 190 N N Q N N P Q f 10 i.e., otor current frequency Fractional lip x Supply frequency (i) When the rotor i at tandtill or tationary (i.e., 1), the frequency of rotor current i the ae a that of upply frequency (f' f 1 f f).

11 (ii) A the rotor pick up peed, the relative peed between the rotating flux and the rotor decreae. Conequently, the lip and hence rotor current frequency decreae. Note. he relative peed between the rotating field and tator winding i N 0 N. herefore, the frequency of induced current or voltage in the tator winding i f N P/10 the upply frequency. 8.8 Effect of Slip on he otor Circuit When the rotor i tationary, 1. Under thee condition, the per phae rotor e..f. E ha a frequency equal to that of upply frequency f. At any lip, the relative peed between tator field and the rotor i decreaed. Conequently, the rotor e..f. and frequency are reduced proportionally to E and f repectively. At the ae tie, per phae rotor reactance X, being frequency dependent, i reduced to X. Conider a 6-pole, 3-phae, 50 Hz induction otor. It ha ynchronou peed N 10 f/p 10 50/ r.p.. At tandill, the relative peed between tator flux and rotor i 1000 r.p.. and rotor e..f./phae E (ay). If the fullload peed of the otor i 960 r.p.., then, (i) he relative peed between tator flux and the rotor i now only 40 r.p.. Conequently, rotor e..f./phae i reduced to: 40 E E or E (ii) he frequency i alo reduced in the ae ratio to: (iii) he per phae rotor reactance X i likewie reduced to: 40 X 1000 or f 0.04X or X hu at any lip, otor e..f./phae E otor reactance/phae X otor frequency f where E,X and f are the correponding value at tandtill. 191

12 8.9 otor Current Fig. (8.14) how the circuit of a 3-phae induction otor at any lip. he rotor i aued to be of wound type and tar connected. Note that rotor e..f./phae and rotor reactance/phae are E and X repectively. he rotor reitance/phae i and i independent of frequency and, therefore, doe not depend upon lip. Likewie, tator winding value 1 and X 1 do not depend upon lip. Fig.(8.14) Since the otor repreent a balanced 3-phae load, we need conider one phae only; the condition in the other two phae being iilar. At tandtill. Fig. (8.15 (i)) how one phae of the rotor circuit at tandtill. otor current/phae, otor p.f., co I Z E Z + X E + X Fig.(8.15) When running at lip. Fig. (8.15 (ii)) how one phae of the rotor circuit when the otor i running at lip. otor current, E I' Z' E + ( X ) 19

13 otor p.f., co ' Z' + ( X ) 8.10 otor orque he torque developed by the rotor i directly proportional to: (i) rotor current (ii) rotor e..f. (iii) power factor of the rotor circuit E I co or K E I co where I rotor current at tandtill E rotor e..f. at tandtill co rotor p.f. at tandtill Note. he value of rotor e..f., rotor current and rotor power factor are taken for the given condition Starting orque ( ) Let E rotor e..f. per phae at tandtill X rotor reactance per phae at tandtill rotor reitance per phae otor ipedance/phae, otor current/phae, otor p.f., co I Z X Z +...at tandtill E E...at tandtill Z X + X + Starting torque, K EI co K E K E + X E + X + X...at tandtill 193

14 Generally, the tator upply voltage V i contant o that flux per pole et up by the tator i alo fixed. hi in turn ean that e..f. E induced in the rotor will be contant. K K + X 1 where K 1 i another contant. 1 Z It i clear that the agnitude of tarting torque would depend upon the relative value of and X i.e., rotor reitance/phae and tandtill rotor reactance/phae. It can be hown that K 3/ π N. 3 π N E Note that here N i in r.p.. + X 8.1 Condition for Maxiu Starting orque It can be proved that tarting torque will be axiu when rotor reitance/phae i equal to tandtill rotor reactance/phae. Now K (i) + X 1 Differentiating eq. (i) w.r.t. and equating the reult to zero, we get, or d d 1 + X ( K1 ( + X ) + X or X Hence tarting torque will be axiu when: otor reitance/phae Standtill rotor reactance/phae Under the condition of axiu tarting torque, 45 and rotor power factor i lagging [See Fig. (8.16 (ii))]. Fig. (8.16 (i)) how the variation of tarting torque with rotor reitance. A the rotor reitance i increaed fro a relatively low value, the tarting torque increae until it becoe axiu when X. If the rotor reitance i increaed beyond thi optiu value, the tarting torque will decreae. 194 ) 0

15 Fig.(8.16) 8.13 Effect of Change of Supply Voltage K E + X Since E Supply voltage V K V + X where K i another contant. V herefore, the tarting torque i very enitive to change in the value of upply voltage. For exaple, a drop of 10% in upply voltage will decreae the tarting torque by about 0%. hi could ean the otor failing to tart if it cannot produce a torque greater than the load torque plu friction torque Starting orque of 3-Phae Induction Motor he rotor circuit of an induction otor ha low reitance and high inductance. At tarting, the rotor frequency i equal to the tator frequency (i.e., 50 Hz) o that rotor reactance i large copared with rotor reitance. herefore, rotor current lag the rotor e..f. by a large angle, the power factor i low and conequently the tarting torque i all. When reitance i added to the rotor circuit, the rotor power factor i iproved which reult in iproved tarting torque. hi, of coure, increae the rotor ipedance and, therefore, decreae the value of rotor current but the effect of iproved power factor predoinate and the tarting torque i increaed. (i) Squirrel-cage otor. Since the rotor bar are peranently hortcircuited, it i not poible to add any external reitance in the rotor circuit at tarting. Conequently, the talling torque of uch otor i low. Squirrel 195

16 cage otor have tarting torque of 1.5 to tie the full-load value with tarting current of 5 to 9 tie the full-load current. (ii) Wound rotor otor. he reitance of the rotor circuit of uch otor can be increaed through the addition of external reitance. By inerting the proper value of external reitance (o that X ), axiu tarting torque can be obtained. A the otor accelerate, the external reitance i gradually cut out until the rotor circuit i hort-circuited on itelf for running condition Motor Under Load Let u now dicu the behaviour of 3-phae induction otor on load. (i) When we apply echanical load to the haft of the otor, it will begin to low down and the rotating flux will cut the rotor conductor at a higher and higher rate. he induced voltage and reulting current in rotor conductor will increae progreively, producing greater and greater torque. (ii) he otor and echanical load will oon reach a tate of equilibriu when the otor torque i exactly equal to the load torque. When thi tate i reached, the peed will ceae to drop any ore and the otor will run at the new peed at a contant rate. (iii) he drop in peed of the induction otor on increaed load i all. It i becaue the rotor ipedance i low and a all decreae in peed produce a large rotor current. he increaed rotor current produce a higher torque to eet the increaed load on the otor. hi i why induction otor are conidered to be contant-peed achine. However, becaue they never actually turn at ynchronou peed, they are oetie called aynchronou achine. Note that change in load on the induction otor i et through the adjutent of lip. When load on the otor increae, the lip increae lightly (i.e., otor peed decreae lightly). hi reult in greater relative peed between the rotating flux and rotor conductor. Conequently, rotor current i increaed, producing a higher torque to eet the increaed load. evere happen hould the load on the otor decreae. (iv) With increaing load, the increaed load current I' are in uch a direction o a to decreae the tator flux (Lenz law), thereby decreaing the counter e..f. in the tator winding. he decreaed counter e..f. allow otor tator current (I 1 ) to increae, thereby increaing the power input to the otor. It ay be noted that action of the induction otor in adjuting it tator or priary current with 196

17 change of current in the rotor or econdary i very uch iilar to the change occurring in tranforer with change in load. Fig.(8.17) 8.16 orque Under unning Condition Let the rotor at tandtill have per phae induced e..f. E, reactance X and reitance. hen under running condition at lip, otor e..f./phae, E' E otor reactance/phae, X' X otor ipedance/phae, ( ) otor current/phae, otor p.f., Z ' + I' co ' X E' Z' + E + ( X ) ( X ) Fig.(8.18) unning orque, r E' I' co' I' co' ( Q E' ) 197

18 198 ( ) ( ) ( ) ( ) ( ) ) E ( X E K X E K X E X X E Q If the tator upply voltage V i contant, then tator flux and hence E will be contant. ( ) r X K + where K i another contant. It ay be een that running torque i: (i) directly proportional to lip i.e., if lip increae (i.e., otor peed decreae), the torque will increae and vice-vera. (ii) directly proportional to quare of upply voltage ) V E ( Q. It can be hown that value of K 1 3/ π N where N i in r.p.. ( ) ( ) r Z' E N 3 X E N 3 π + π At tarting, 1 o that tarting torque i X E N 3 + π 8.17 Maxiu orque under unning Condition r X K + (i) In order to find the value of rotor reitance that give axiu torque under running condition, differentiate exp. (i) w.r.t. and equate the reult to zero i.e., ( ) [ ] ( ) 0 X ) ( X X K d d r + +

19 + or ( X ) X 0 or X or X hu for axiu torque ( ) under running condition : Now otor reitance/phae Fractional lip Standtill rotor reactance/phae r + X fro exp. (i) above For axiu torque, X. Putting X in the above expreion, the axiu torque i given by; 1 X Slip correponding to axiu torque, /X. It can be hown that: 3 π N E X N - It i evident fro the above equation that: (i) he value of rotor reitance doe not alter the value of the axiu torque but only the value of the lip at which it occur. (ii) he axiu torque varie inverely a the tandtill reactance. herefore, it hould be kept a all a poible. (iii) he axiu torque varie directly with the quare of the applied voltage. (iv) o obtain axiu torque at tarting ( 1), the rotor reitance ut be ade equal to rotor reactance at tandtill orque-slip Characteritic A hown in Sec. 8.16, the otor torque under running condition i given by; K + X If a curve i drawn between the torque and lip for a particular value of rotor reitance, the graph thu obtained i called torque-lip characteritic. Fig. (8.19) how a faily of torque-lip characteritic for a lip-range fro 0 to 1 for variou value of rotor reitance. 199

20 Fig.(8.19) he following point ay be noted carefully: (i) At 0, 0 o that torque-lip curve tart fro the origin. (ii) At noral peed, lip i all o that X i negligible a copared to. /... a i contant Hence torque lip curve i a traight line fro zero lip to a lip that correpond to full-load. (iii) A lip increae beyond full-load lip, the torque increae and becoe axiu at /X. hi axiu torque in an induction otor i called pull-out torque or break-down torque. It value i at leat twice the full-load value when the otor i operated at rated voltage and frequency. (iv) X increae very rapidly o that to X. / X 1/ to axiu torque, the ter ay be neglected a copared... a X i contant hu the torque i now inverely proportional to lip. Hence torque-lip curve i a rectangular hyperbola. (v) he axiu torque reain the ae and i independent of the value of rotor reitance. herefore, the addition of reitance to the rotor circuit doe not change the value of axiu torque but it only change the value of lip at which axiu torque occur Full-Load, Starting and Maxiu orque 00

21 f 1 X + ( X ) + X Note that correpond to full-load lip. (i) f + ( X ) Dividing the nuerator and denoinator on.h.s. by where (ii) X ( / X ) + a ( / X ) a + f a X + X X otor reitance/phae Standtill rotor reactance/phae Dividing the nuerator and denoinator on.h.s. by where ( / X ) + 1 a ( / X ) a + f a X otor reitance/phae Standtill rotor reactance/phae 1 X, we get, X, we get, 8.0 Induction Motor and ranforer Copared An induction otor ay be conidered to be a tranforer with a rotating hortcircuited econdary. he tator winding correpond to tranforer priary and rotor winding to tranforer econdary. However, the following difference between the two are worth noting: (i) Unlike a tranforer, the agnetic circuit of a 3-phae induction otor ha an air gap. herefore, the agnetizing current in a 3-phae induction otor i uch larger than that of the tranforer. For exaple, in an induction otor, it ay be a high a % of rated current wherea it i only 1-5% of rated current in a tranforer. (ii) In an induction otor, there i an air gap and the tator and rotor winding are ditributed along the periphery of the air gap rather than concentrated 01

22 on a core a in a tranforer. herefore, the leakage reactance of tator and rotor winding are quite large copared to that of a tranforer. (iii) In an induction otor, the input to the tator and rotor are electrical but the output fro the rotor i echanical. However, in a tranforer, input a well a output i electrical. (iv) he ain difference between the induction otor and tranforer lie in the fact that the rotor voltage and it frequency are both proportional to lip. If f i the tator frequency, E i the per phae rotor e..f. at tandtill and X i the tandtill rotor reactance/phae, then at any lip, thee value are: otor e..f./phae, E' E otor reactance/phae, X' X otor frequency, f' f 8.1 Speed egulation of Induction Motor Like any other electrical otor, the peed regulation of an induction otor i given by: where N0 NF.L. % age peed regulation 100 N F.L. N 0 no-load peed of the otor N F.L. full-load peed of the otor If the no-load peed of the otor i 800 r.p.. and it fall-load peed in 780 r.p.., then change in peed i r.p.. and percentage peed regulation 0 100/780.56%. At no load, only a all torque i required to overcoe the all echanical loe and hence otor lip i all i.e., about 1%. When the otor i fully loaded, the lip increae lightly i.e., otor peed decreae lightly. It i becaue rotor ipedance i low and a all decreae in peed produce a large rotor current. he increaed rotor current produce a high torque to eet the full load on the otor. For thi reaon, the change in peed of the otor fro noload to full-load i all i.e., the peed regulation of an induction otor i low. he peed regulation of an induction otor i 3% to 5%. Although the otor peed doe decreae lightly with increaed load, the peed regulation i low enough that the induction otor i claed a a contant-peed otor. 8. Speed Control of 3-Phae Induction Motor 0

23 N (1 )N (1 10 f ) P An inpection of eq. (i) reveal that the peed N of an induction otor can be varied by changing (i) upply frequency f (ii) nuber of pole P on the tator and (iii) lip. he change of frequency i generally not poible becaue the coercial upplie have contant frequency. herefore, the practical ethod of peed control are either to change the nuber of tator pole or the otor lip. 1. Squirrel cage otor he peed of a quirrel cage otor i changed by changing the nuber of tator pole. Only two or four peed are poible by thi ethod. wo-peed otor ha one tator winding that ay be witched through uitable control equipent to provide two peed, one of which i half of the other. For intance, the winding ay be connected for either 4 or 8 pole, giving ynchronou peed of 1500 and 750 r.p.. Four-peed otor are equipped with two eparate tator winding each of which provide two peed. he diadvantage of thi ethod are: (i) It i not poible to obtain gradual continuou peed control. (ii) Becaue of the coplication in the deign and witching of the interconnection of the tator winding, thi ethod can provide a axiu of four different ynchronou peed for any one otor.. Wound rotor otor he peed of wound rotor otor i changed by changing the otor lip. hi can be achieved by; (i) varying the tator line voltage (ii) varying the reitance of the rotor circuit (iii) inerting and varying a foreign voltage in the rotor circuit 8.3 Power Factor of Induction Motor Like any other a.c. achine, the power factor of an induction otor i given by; Power factor, co Active coponent of current (I co ) otal current (I) he preence of air-gap between the tator and rotor of an induction otor greatly increae the reluctance of the agnetic circuit. Conequently, an induction otor draw a large agnetizing current (I ) to produce the required flux in the air-gap. (i) At no load, an induction otor draw a large agnetizing current and a all active coponent to eet the no-load loe. herefore, the induction otor take a high no-load current lagging the applied voltage (i) 03

24 by a large angle. Hence the power factor of an induction otor on no load i low i.e., about 0.1 lagging. (ii) When an induction otor i loaded, the active coponent of current increae while the agnetizing coponent reain about the ae. Conequently, the power factor of the otor i increaed. However, becaue of the large value of agnetizing current, which i preent regardle of load, the power factor of an induction otor even at fullload eldo exceed 0.9 lagging. 8.4 Power Stage in an Induction Motor he input electric power fed to the tator of the otor i converted into echanical power at the haft of the otor. he variou loe during the energy converion are: 1. Fixed loe (i) Stator iron lo (ii) Friction and windage lo he rotor iron lo i negligible becaue the frequency of rotor current under noral running condition i all.. Variable loe (i) Stator copper lo (ii) otor copper lo Fig. (8.0) how how electric power fed to the tator of an induction otor uffer loe and finally converted into echanical power. he following point ay be noted fro the above diagra: (i) Stator input, P i Stator output + Stator loe Stator output + Stator Iron lo + Stator Cu lo (ii) otor input, P r Stator output It i becaue tator output i entirely tranferred to the rotor through airgap by electroagnetic induction. (iii) Mechanical power available, P P r otor Cu lo hi echanical power available i the gro rotor output and will produce a gro torque g. (iv) Mechanical power at haft, P out P Friction and windage lo Mechanical power available at the haft produce a haft torque h. Clearly, P P out Friction and windage lo 04

25 8.5 Induction Motor orque Fig.(8.0) he echanical power P available fro any electric otor can be expreed a: where π N P 60 watt N peed of the otor in r.p.. torque developed in N- 60 P 9.55 π N P N N - If the gro output of the rotor of an induction otor i P and it peed i N r.p.., then gro torque developed i given by: Siilarly, g h P 9.55 N P 9.55 N out N - N - Note. Since windage and friction lo i all, g h,. hi auption hardly lead to any ignificant error. 8.6 otor Output If g newton-etre i the gro torque developed and N r.p.. i the peed of the rotor, then, πng Gro rotor output 60 watt If there were no copper loe in the rotor, the output would equal rotor input and the rotor would run at ynchronou peed N. 05

26 (i) otor input πn g 60 watt otor Cu lo otor input otor output π 60 g (N N) otor Cu lo N N otor input N otor Cu lo otor input (ii) Gro rotor output, P otor input otor Cu lo otor input otor input P otor input (1 ) (iii) (iv) Gro rotor output otor input otor Cu lo Gro rotor output 1 1 N N It i clear that if the input power to rotor i P r then P r i lot a rotor Cu lo and the reaining (1 )P r i converted into echanical power. Conequently, induction otor operating at high lip ha poor efficiency. Note. Gro rotor output otor input 1 If the tator loe a well a friction and windage loe arc neglected, then, Gro rotor output Ueful output otor input Stator input Ueful output Stator output 1 Efficiency Hence the approxiate efficiency of an induction otor i 1. hu if the lip of an induction otor i 0.15, then it approxiate efficiency i or 87.5%. 8.7 Induction Motor orque Equation he gro torque g developed by an induction otor i given by; 06

27 Now g otor input otor input π N 60 otor input π N (See Sec. 8.6) ( I' )... N... N otor Cu lo 3 (i) A hown in Sec. 8.16, under running condition, I' E + ( X where K ranforation ratio otor input Alo otor input g ) 3 3 otor input π N K E + ( X E K E 1 + ( X otor turn/phae Stator turn/phae + ( X 3 π N K E1 + ( X) ) 1 ) 1 1 E ) 3 E + ( X ) i r.p.. i r.p.. (Putting e value of I' in eq.(i)) 1 3 K E + ( X ) (Putting e value of I' in eq.(i)) + ( X )...in ter of E 3...in ter of E 1 π N Note that in the above expreion of g, the value E 1, E, and X repreent the phae value. 8.8 Perforance Curve of Squirrel-Cage Motor he perforance curve of a 3-phae induction otor indicate the variation of peed, power factor, efficiency, tator current and torque for different value of load. However, before giving the perforance curve in one graph, it i deirable to dicu the variation of torque, and tator current with lip. (i) Variation of torque and tator current with lip Fig. (8.1) how the variation of torque and tator current with lip for a tandard quirrel-cage otor. Generally, the rotor reitance i low o that full- 07

28 load current occur at low lip. hen even at full-load f' ( f) and. therefore, X' ( π f' L ) are low. Between zero and full-load, rotor power factor ( co ' ) and rotor ipedance ( Z' ) reain practically contant. herefore, rotor current I' (E' /Z' ) and, therefore, torque ( r ) increae directly with the lip. Now tator current I 1 increae in proportion to I'. hi i hown in Fig. (8.1) where r and I 1 are indicated a traight line fro no-load to full-load. A load and lip are increaed beyond full-load, the increae in rotor reactance becoe appreciable. he increaing value of rotor ipedance not only decreae the rotor power factor co ' ( /Z' ) but alo lower the rate of increae of rotor current. A a reult, the torque r and tator current I 1 do not increae directly with lip a indicated in Fig. (8.1). With the decreaing power factor and the lowered rate of increae in rotor current, the tator current I 1 and torque r increae at a lower rate. Finally, torque r reache the axiu value at about 5% lip in the tandard quirrel cage otor. hi axiu value of torque i called the pullout torque or breakdown torque. If the load i increaed beyond the breakdown point, the decreae in rotor power factor i greater than the increae in rotor current, reulting in a decreaing torque. he reult i that otor low down quickly and coe to a top. Fig.(8.1) In Fig. (8.1), the value of torque at tarting (i.e., 100%) i 1.5 tie the fullload torque. he tarting current i about five tie the full-load current. he otor i eentially a contant-peed achine having peed characteritic about the ae a a d.c. hunt otor. (ii) Perforance curve Fig. (8.) how the perforance curve of 3-phae quirrel cage induction otor. 08

29 Fig.(8.) he following point ay be noted: (a) At no-load, the rotor lag behind the tator flux by only a all aount, ince the only torque required i that needed to overcoe the no-load loe. A echanical load i added, the rotor peed decreae. A decreae in rotor peed allow the contant-peed rotating field to weep acro the rotor conductor at a fater rate, thereby inducing large rotor current. hi reult in a larger torque output at a lightly reduced peed. hi explain for peed-load curve in Fig. (8.). (b) At no-load, the current drawn by an induction otor i largely a agnetizing current; the no-load current lagging the applied voltage by a large angle. hu the power factor of a lightly loaded induction otor i very low. Becaue of the air gap, the reluctance of the agnetic circuit i high, reulting in a large value of no-load current a copared with a tranforer. A load i added, the active or power coponent of current increae, reulting in a higher power factor. However, becaue of the large value of agnetizing current, which i preent regardle of load, the power factor of an induction otor even at full-load eldo exceed 90%. Fig. (8.) how the variation of power factor with load of a typical quirrelcage induction otor. Output (c) Efficiency Output + Loe he loe occurring in a 3-phae induction otor are Cu loe in tator and rotor winding, iron loe in tator and rotor core and friction and windage loe. he iron loe and friction and windage loe are alot independent of load. Had I been contant, the efficiency of the otor would have increaed with load. But I lo depend upon load. 09

30 herefore, the efficiency of the otor increae with load but the curve i dropping at high load. (d) At no-load, the only torque required i that needed to overcoe no-load loe. herefore, tator draw a all current fro the upply. A echanical load i added, the rotor peed decreae. A decreae in rotor peed allow the contant-peed rotating field to weep acro the rotor conductor at a fater rate, thereby inducing larger rotor current. With increaing load, the increaed rotor current are in uch a direction o a to decreae the taler flux, thereby teporarily decreaing the counter e..f. in the tator winding. he decreaed counter e..f. allow ore tator current to flow. (e) Output orque Speed Since the peed of the otor doe not change appreciably with load, the torque increae with increae in load. 8.9 Equivalent Circuit of 3-Phae Induction Motor at Any Slip In a 3-phae induction otor, the tator winding i connected to 3-phae upply and the rotor winding i hort-circuited. he energy i tranferred agnetically fro the tator winding to the hort-circuited, rotor winding. herefore, an induction otor ay be conidered to be a tranforer with a rotating econdary (hort-circuited). he tator winding correpond to tranforer priary and the rotor finding correpond to tranforer econdary. In view of the iilarity of the flux and voltage condition to thoe in a tranforer, one can expect that the equivalent circuit of an induction otor will be iilar to that of a tranforer. Fig. (8.3) how the equivalent circuit (though not the only one) per phae for an induction otor. Let u dicu the tator and rotor circuit eparately. Fig.(8.3) Stator circuit. In the tator, the event are very iilar to thoe in the tranforer prial y. he applied voltage per phae to the tator i V 1 and 1 and X 1 are the tator reitance and leakage reactance per phae repectively. he applied voltage V 1 produce a agnetic flux which link the tator winding (i.e., priary) a well a the rotor winding (i.e., econdary). A a reult, elf- 10

31 induced e..f. E 1 i induced in the tator winding and utually induced e..f. E' ( E K E 1 where K i tranforation ratio) i induced in the rotor winding. he flow of tator current I 1 caue voltage drop in 1 and X 1. V1 E1 + I1(1 + j X1)...phaor u When the otor i at no-load, the tator winding draw a current I 0. It ha two coponent viz., (i) which upplie the no-load otor loe and (ii) agnetizing coponent I which et up agnetic flux in the core and the airgap. he parallel cobination of c and X, therefore, repreent the no-load otor loe and the production of agnetic flux repectively. I + 0 Iw I otor circuit. Here and X repreent the rotor reitance and tandtill rotor reactance per phae repectively. At any lip, the rotor reactance will be X he induced voltage/phae in the rotor i E' E K E 1. Since the rotor winding i hort-circuited, the whole of e..f. E' i ued up in circulating the rotor current I'. E' I' ( + j X) he rotor current I' i reflected a I" ( K I' ) in the tator. he phaor u of I" and I 0 give the tator current I 1. It i iportant to note that input to the priary and output fro the econdary of a tranforer are electrical. However, in an induction otor, the input to the tator and rotor are electrical but the output fro the rotor i echanical. o facilitate calculation, it i deirable and neceary to replace the echanical load by an equivalent electrical load. We then have the tranforer equivalent circuit of the induction otor. It ay be noted that even though the frequencie of tator and rotor current are different, yet the agnetic field due to the rotate at ynchronou peed N. he tator current produce a agnetic flux which rotate at a peed N. At lip, the peed of rotation of the rotor field relative to the rotor urface in the direction of rotation of the rotor i 10 f ' 10 f P P N But the rotor i revolving at a peed of N relative to the tator core. herefore, the peed of rotor Fig.(8.4) 11

32 field relative to tator core N + N (N N) + N N hu no atter what the value of lip, the tator and rotor agnetic field are ynchronou with each other when een by an oberver tationed in pace. Conequently, the 3-phae induction otor can be regarded a being equivalent to a tranforer having an air-gap eparating the iron portion of the agnetic circuit carrying the priary and econdary winding. Fig. (8.4) how the phaor diagra of induction otor Equivalent Circuit of the otor We hall now ee how echanical load of the otor i replaced by the equivalent electrical load. Fig. (8.5 (i)) how the equivalent circuit per phae of the rotor at lip. he rotor phae current i given by; I' E + ( X Matheatically, thi value i unaltered by writing it a: I' ( /) E ) + (X ) A hown in Fig. (8.5 (ii)), we now have a rotor circuit that ha a fixed reactance X connected in erie with a variable reitance / and upplied with contant voltage E. Note that Fig. (8.5 (ii)) tranfer the variable to the reitance without altering power or power factor condition. Fig.(8.5) he quantity / i greater than ince i a fraction. herefore, / can be divided into a fixed part and a variable part ( / ) i.e.,

33 (i) he firt part i the rotor reitance/phae, and repreent the rotor Cu lo. (ii) he econd part 1 1 i a variable-reitance load. he power delivered to thi load repreent the total echanical power developed in the rotor. hu echanical load on the induction otor can be replaced by a variable-reitance load of value 1 1. hi i 1 L 1 Fig. (8.5 (iii)) how the equivalent rotor circuit along with load reitance L ranforer Equivalent Circuit of Induction Motor Fig. (8.6) how the equivalent circuit per phae of a 3-phae induction otor. Note that echanical load on the otor ha been replaced by an equivalent electrical reitance L given by; 1 1 L (i) Fig.(8.6) Note that circuit hown in Fig. (8.6) i iilar to the equivalent circuit of a tranforer with econdary load equal to given by eq. (i). he rotor e..f. in the equivalent circuit now depend only on the tranforation ratio K ( E /E 1 ). herefore; induction otor can be repreented a an equivalent tranforer connected to a variable-reitance load L given by eq. (i). he power delivered to L repreent the total echanical power developed in the rotor. Since the equivalent circuit of Fig. (8.6) i that of a tranforer, the econdary (i.e., rotor) value can be tranferred to priary (i.e., tator) through the appropriate ue of tranforation ratio K. ecall that when hifting reitance/reactance fro econdary to priary, it hould be divided by K wherea current hould be ultiplied by K. he equivalent circuit of an induction otor referred to priary i hown in Fig. (8.7). 13

34 Fig.(8.7) Note that the eleent (i.e., ' L ) encloed in the dotted box i the equivalent electrical reitance related to the echanical load on the otor. he following point ay be noted fro the equivalent circuit of the induction otor: (i) At no-load, the lip i practically zero and the load ' L i infinite. hi condition reeble that in a tranforer whoe econdary winding i open-circuited. (ii) At tandtill, the lip i unity and the load ' L i zero. hi condition reeble that in a tranforer whoe econdary winding i hort-circuited. (iii) When the otor i running under load, the value of ' L will depend upon the value of the lip. hi condition reeble that in a tranforer whoe econdary i upplying variable and purely reitive load. (iv) he equivalent electrical reitance ' L related to echanical load i lip or peed dependent. If the lip increae, the load ' L decreae and the rotor current increae and otor will develop ore echanical power. hi i expected becaue the lip of the otor increae with the increae of load on the otor haft. 8.3 Power elation he tranforer equivalent circuit of an induction otor i quite helpful in analyzing the variou power relation in the otor. Fig. (8.8) how the equivalent circuit per phae of an induction otor where all value have been referred to priary (i.e., tator). Fig.(8.8) 14

35 (i) 1 ' otal electrical load ' 1 + ' Power input to tator 3V1 I1 co1 here will be tator core lo and tator Cu lo. he reaining power will be the power tranferred acro the air-gap i.e., input to the rotor. 3 I" ' (ii) otor input ( ) otor Cu lo ( ) 3 I" ' otal echanical power developed by the rotor i P otor input otor Cu lo 3 I" 1 3 I" ' 1 ( ) ( ) ( ) ' 3 I" ' hi i quite apparent fro the equivalent circuit hown in Fig. (8.8). (iii) If g i the gro torque developed by the rotor, then, P or 3( I" ) π N 60 or 3( I" ) ' ' g 1 N 1 π 60 1 π N 60 1 g g π N (1 ) g or ( I" ) ' [ Q N N (1 ) ] or 3 g g ( I" ) 3 ' π N ( I" ) ' N N - 60 N - Note that haft torque h will be le than g by the torque required to eet windage and frictional loe. 15

36 8.33 Approxiate Equivalent Circuit of Induction Motor A in cae of a tranforer, the approxiate equivalent circuit of an induction otor i obtained by hifting the hunt branch ( c X ) to the input terinal a hown in Fig. (8.9). hi tep ha been taken on the auption that voltage drop in 1 and X 1 i all and the terinal voltage V 1 doe not appreciably differ fro the induced voltage E 1. Fig. (8.9) how the approxiate equivalent circuit per phae of an induction otor where all value have been referred to priary (i.e., tator). Fig.(8.9) he above approxiate circuit of induction otor i not o readily jutified a with the tranforer. hi i due to the following reaon: (i) Unlike that of a power tranforer, the agnetic circuit of the induction otor ha an air-gap. herefore, the exciting current of induction otor (30 to 40% of full-load current) i uch higher than that of the power tranforer. Conequently, the exact equivalent circuit ut be ued for accurate reult. (ii) he relative value of X 1 and X in an induction otor are larger than the correponding one to be found in the tranforer. hi fact doe not jutify the ue of approxiate equivalent circuit (iii) In a tranforer, the winding are concentrated wherea in an induction otor, the winding are ditributed. hi affect the tranforation ratio. In pite of the above drawback of approxiate equivalent circuit, it yield reult that are atifactory for large otor. However, approxiate equivalent circuit i not jutified for all otor Starting of 3-Phae Induction Motor he induction otor i fundaentally a tranforer in which the tator i the priary and the rotor i hort-circuited econdary. At tarting, the voltage induced in the induction otor rotor i axiu (Q 1). Since the rotor ipedance i low, the rotor current i exceively large. hi large rotor current i reflected in the tator becaue of tranforer action. hi reult in high tarting current (4 to 10 tie the full-load current) in the tator at low power 16

37 factor and conequently the value of tarting torque i low. Becaue of the hort duration, thi value of large current doe not har the otor if the otor accelerate norally. However, thi large tarting current will produce large line-voltage drop. hi will adverely affect the operation of other electrical equipent connected to the ae line. herefore, it i deirable and neceary to reduce the agnitude of tator current at tarting and everal ethod are available for thi purpoe Method of Starting 3-Phae Induction Motor he ethod to be eployed in tarting a given induction otor depend upon the ize of the otor and the type of the otor. he coon ethod ued to tart induction otor are: (i) Direct-on-line tarting (ii) Stator reitance tarting (iii) Autotranforer tarting (iv) Star-delta tarting (v) otor reitance tarting Method (i) to (iv) are applicable to both quirrel-cage and lip ring otor. However, ethod (v) i applicable only to lip ring otor. In practice, any one of the firt four ethod i ued for tarting quirrel cage otor, depending upon,the ize of the otor. But lip ring otor are invariably tarted by rotor reitance tarting Method of Starting Squirrel-Cage Motor Except direct-on-line tarting, all other ethod of tarting quirrel-cage otor eploy reduced voltage acro otor terinal at tarting. (i) Direct-on-line tarting hi ethod of tarting in jut what the nae iplie the otor i tarted by connecting it directly to 3-phae upply. he ipedance of the otor at tandtill i relatively low and when it i directly connected to the upply yte, the tarting current will be high (4 to 10 tie the full-load current) and at a low power factor. Conequently, thi ethod of tarting i uitable for relatively all (up to 7.5 kw) achine. elation between tarling and F.L. torque. We know that: But otor input π N k otor Cu lo otor input ( I' ) k 3 or ( I' ) 17

38 1 1 or I ( Q I' I ) If I t i the tarting current, then tarting torque ( t ) i It ( Q at tarting 1) If I f i the full-load current and f i the full-load lip, then, I f t f f I If t f f When the otor i tarted direct-on-line, the tarting current i the hort-circuit (blocked-rotor) current I c. t f I I c f f Let u illutrate the above relation with a nuerical exaple. Suppoe I c 5 I f and full-load lip f hen, t f t I I f c f f 5 I If f 0.04 (5) Note that tarting current i a large a five tie the full-load current but tarting torque i jut equal to the full-load torque. herefore, tarting current i very high and the tarting torque i coparatively low. If thi large tarting current flow for a long tie, it ay overheat the otor and daage the inulation. (ii) Stator reitance tarting In thi ethod, external reitance are connected in erie with each phae of tator winding during tarting. hi caue voltage drop acro the reitance o that voltage available acro otor terinal i reduced and hence the tarting current. he tarting reitance are gradually cut out in tep (two or ore tep) fro the tator circuit a the otor pick up peed. When the otor attain rated peed, the reitance are copletely cut out and full line voltage i applied to the rotor. hi ethod uffer fro two drawback. Firt, the reduced voltage applied to the otor during the tarting period lower the tarting torque and hence increae the accelerating tie. Secondly, a lot of power i wated in the tarting reitance. 18

39 Fig.(8.30) elation between tarting and F.L. torque. Let V be the rated voltage/phae. If the voltage i reduced by a fraction x by the inertion of reitor in the line, then voltage applied to the otor per phae will be xv. Now or I t x I c t f t f I I t f I x If c f f hu while the tarting current reduce by a fraction x of the rated-voltage tarting current (I c ), the tarting torque i reduced by a fraction x of that obtained by direct witching. he reduced voltage applied to the otor during the tarting period lower the tarting current but at the ae tie increae the accelerating tie becaue of the reduced value of the tarting torque. herefore, thi ethod i ued for tarting all otor only. (iii) Autotranforer tarting hi ethod alo ai at connecting the induction otor to a reduced upply at tarting and then connecting it to the full voltage a the otor pick up ufficient peed. Fig. (8.31) how the circuit arrangeent for autotranforer tarting. he tapping on the autotranforer i o et that when it i in the circuit, 65% to 80% of line voltage i applied to the otor. At the intant of tarting, the change-over witch i thrown to tart poition. hi put the autotranforer in the circuit and thu reduced voltage i applied to the circuit. Conequently, tarting current i liited to afe value. When the otor attain about 80% of noral peed, the changeover witch i thrown to 19

40 run poition. hi take out the autotranforer fro the circuit and put the otor to full line voltage. Autotranforer tarting ha everal advantage viz low power lo, low tarting current and le radiated heat. For large achine (over 5 H.P.), thi ethod of tarting i often ued. hi ethod can be ued for both tar and delta connected otor. Fig.(8.31) elation between tarting And F.L. torque. Conider a tar-connected quirrel-cage induction otor. If V i the line voltage, then voltage acro otor phae on direct witching i V 3 and tarting current i I t I c. In cae of autotranforer, if a tapping of tranforation ratio K (a fraction) i ued, then phae voltage acro otor i KV 3 and I t K I c, Now t f t f I I t f I K If c f K I If f c f I K If c f Fig.(8.3) 0

41 he current taken fro the upply or by autotranforer i I 1 KI K I c. Note that otor current i K tie, the upply line current i K tie and the tarting torque i K tie the value it would have been on direct-on-line tarting. (iv) Star-delta tarting he tator winding of the otor i deigned for delta operation and i connected in tar during the tarting period. When the achine i up to peed, the connection are changed to delta. he circuit arrangeent for tar-delta tarting i hown in Fig. (8.33). he ix lead of the tator winding are connected to the changeover witch a hown. At the intant of tarting, the changeover witch i thrown to Start poition which connect the tator winding in tar. herefore, each tator phae get V 3 volt where V i the line voltage. hi reduce the tarting current. When the otor pick up peed, the changeover witch i thrown to un poition which connect the tator winding in delta. Now each tator phae get full line voltage V. he diadvantage of thi ethod are: (a) With tar-connection during tarting, tator phae voltage i 1 3 tie the line voltage. Conequently, tarting torque i ( 1 3) or 1/3 tie the value it would have with -connection. hi i rather a large reduction in tarting torque. (b) he reduction in voltage i fixed. hi ethod of tarting i ued for ediu-ize achine (upto about 5 H.P.). elation between tarting and F.L. torque. In direct delta tarting, Starting current/phae, I c V/Z c where V line voltage Starting line current In tar tarting, we have, Now or where Starting current/phae, t f t f I I t f 1 3 I I c f f 3 Ic V 3 I t Z f I c c 3 I I c tarting phae current (delta) I f F.L. phae current (delta) f 1 3 I f c 1

42 Fig.(8.33) Note that in tar-delta tarting, the tarting line current i reduced to one-third a copared to tarting with the winding delta connected. Further, tarting torque i reduced to one-third of that obtainable by direct delta tarting. hi ethod i cheap but liited to application where high tarting torque i not neceary e.g., achine tool, pup etc Starting of Slip-ing Motor Slip-ring otor are invariably tarted by rotor reitance tarting. In thi ethod, a variable tar-connected rheotat i connected in the rotor circuit through lip ring and full voltage i applied to the tator winding a hown in Fig. (8.34). Fig.(8.34) (i) At tarting, the handle of rheotat i et in the OFF poition o that axiu reitance i placed in each phae of the rotor circuit. hi reduce the tarting current and at the ae tie tarting torque i increaed. (ii) A the otor pick up peed, the handle of rheotat i gradually oved in clockwie direction and cut out the external reitance in each phae of the rotor circuit. When the otor attain noral peed, the change-over witch i in the ON poition and the whole external reitance i cut out fro the rotor circuit.

43 8.38 Slip-ing Motor Veru Squirrel Cage Motor he lip-ring induction otor have the following advantage over the quirrel cage otor: (i) High tarting torque with low tarting current. (ii) Sooth acceleration under heavy load. (iii) No abnoral heating during tarting. (iv) Good running characteritic after external rotor reitance are cut out. (v) Adjutable peed. he diadvantage of lip-ring otor are: (i) he initial and aintenance cot are greater than thoe of quirrel cage otor. (ii) he peed regulation i poor when run with reitance in the rotor circuit 8.39 Induction Motor ating he naeplate of a 3-phae induction otor provide the following inforation: (i) Horepower (ii) Line voltage (iii) Line current (iv) Speed (v) Frequency (vi) eperature rie he horepower rating i the echanical output of the otor when it i operated at rated line voltage, rated frequency and rated peed. Under thee condition, the line current i that pecified on the naeplate and the teperature rie doe not exceed that pecified. he peed given on the naeplate i the actual peed of the otor at rated fullload; it i not the ynchronou peed. hu, the naeplate peed of the induction otor ight be 1710 r.p.. It i the rated full-load peed Double Squirrel-Cage Motor One of the advantage of the lip-ring otor i that reitance ay be inerted in the rotor circuit to obtain high tarting torque (at low tarting current) and then cut out to obtain optiu running condition. However, uch a procedure cannot be adopted for a quirrel cage otor becaue it cage i peranently hort-circuited. In order to provide high tarting torque at low tarting current, double-cage contruction i ued. Contruction A the nae ugget, the rotor of thi otor ha two quirrel-cage winding located one above the other a hown in Fig. (8.35 (i)). (i) he outer winding conit of bar of aller cro-ection hort-circuited by end ring. herefore, the reitance of thi winding i high. Since the 3

44 outer winding ha relatively open lot and a poorer flux path around it bar [See Fig. (8.35 (ii))], it ha a low inductance. hu the reitance of the outer quirrel-cage winding i high and it inductance i low. (ii) he inner winding conit of bar of greater cro-ection hort-circuited by end ring. herefore, the reitance of thi winding i low. Since the bar of the inner winding are thoroughly buried in iron, it ha a high inductance [See Fig. (8.35 (ii))]. hu the reitance of the inner quirrelcage winding i low and it inductance i high. Fig.(8.35) Working When a rotating agnetic field weep acro the two winding, equal e..f. are induced in each. (i) At tarting, the rotor frequency i the ae a that of the line (i.e., 50 Hz), aking the reactance of the lower winding uch higher than that of the upper winding. Becaue of the high reactance of the lower winding, nearly all the rotor current flow in the high-reitance outer cage winding. hi provide the good tarting characteritic of a high-reitance cage winding. hu the outer winding give high tarting torque at low tarting current. (ii) A the otor accelerate, the rotor frequency decreae, thereby lowering the reactance of the inner winding, allowing it to carry a larger proportion of the total rotor current At the noral operating peed of the otor, the rotor frequency i o low ( to 3 Hz) that nearly all the rotor current flow in the low-reitance inner cage winding. hi reult in good operating efficiency and peed regulation. Fig. (8.36) how the operating characteritic of double quirrel-cage otor. he tarting torque of thi otor range fro 00 to 50 percent of full-load torque with a tarting current of 4 to 6 tie the full-load value. It i claed a a high-torque, low tarting current otor. 4

45 Fig.(8.36) 8.41 Equivalent Circuit of Double Squirrel-Cage Motor Fig. (8.37) how a ection of the double quirrel cage otor. Here o and i are the per phae reitance of the outer cage winding and inner cage winding wherea X o and X i are the correponding per phae tandtill reactance. For the outer cage, the reitance i ade intentionally high, giving a high tarting torque. For the inner cage winding, the reitance i low Fig.(8.37) and the leakage reactance i high, giving a low tarting torque but high efficiency on load. Note that in a double quirrel cage otor, the outer winding produce the high tarting and accelerating torque while the inner winding provide the running torque at good efficiency. Fig. (8.38 (i)) how the equivalent circuit for one phae of double cage otor referred to tator. he two cage ipedance are effectively in parallel. he reitance and reactance of the outer and inner rotor are referred to the tator. he exciting circuit i accounted for a in a ingle cage otor. If the agnetizing current (I 0 ) i neglected, then the circuit i iplified to that hown in Fig. (8.38 (ii)). Fig.(8.38) 5

46 6 Fro the equivalent circuit, the perforance of the otor can be predicted. otal ipedance a referred to tator i o i o i 1 1 o i o ' Z Z' Z' Z' X j Z' 1 Z' 1 1 X j Z

47 Chapter (9) Single-Phae Motor Introduction A the nae ugget, thee otor are ued on ingle-phae upply. Singlephae otor are the ot failiar of all electric otor becaue they are extenively ued in hoe appliance, hop, office etc. It i true that inglephae otor are le efficient ubtitute for 3-phae otor but 3-phae power i norally not available except in large coercial and indutrial etablihent. Since electric power wa originally generated and ditributed for lighting only, illion of hoe were given ingle-phae upply. hi led to the developent of ingle-phae otor. Even where 3-phae ain are preent, the ingle-phae upply ay be obtained by uing one of the three line and the neutral. In thi chapter, we hall focu our attention on the contruction, working and characteritic of coonly ued ingle-phae otor. 9.1 ype of Single-Phae Motor Single-phae otor are generally built in the fractional-horepower range and ay be claified into the following four baic type: 1. Single-phae induction otor (i) plit-phae type (iii) haded-pole type (ii) capacitor type. A.C. erie otor or univeral otor 3. epulion otor (i) epulion-tart induction-run otor (ii) epulion-induction otor 4. Synchronou otor (i) eluctance otor (ii) Hyterei otor 9. Single-Phae Induction Motor A ingle phae induction otor i very iilar to a 3-phae quirrel cage induction otor. It ha (i) a quirrel-cage rotor identical to a 3-phae otor and (ii) a ingle-phae winding on the tator. 7

48 Unlike a 3-phae induction otor, a ingle-phae induction otor i not elftarting but require oe tarting ean. he ingle-phae tator winding produce a agnetic field that pulate in trength in a inuoidal anner. he field polarity revere after each half cycle but the field doe not rotate. Conequently, the alternating flux cannot produce rotation in a tationary quirrel-cage rotor. However, if the rotor of a ingle-phae otor i rotated in one direction by oe echanical ean, it will continue to run in the direction of rotation. A a atter of fact, the rotor quickly accelerate until it reache a peed lightly below the ynchronou peed. Once the otor i running at thi peed, it will continue to rotate even though ingle-phae current i flowing through the tator winding. hi ethod of tarting i generally not convenient for large otor. Nor can it be eployed fur a otor located at oe inacceible pot. Fig. (9.1) how ingle-phae induction otor having a quirrel cage rotor and a inglephae ditributed tator winding. Such a otor inherently doc not develop any tarting torque and, therefore, will not tart to rotate if the tator winding i connected to ingle-phae a.c. upply. However, if the Fig.(9.1) rotor i tarted by auxiliary ean, the otor will quickly attain e final peed. hi trange behaviour of ingle-phae induction otor can be explained on the bai of double-field revolving theory. 9.3 Double-Field evolving heory he double-field revolving theory i propoed to explain thi dilea of no torque at tart and yet torque once rotated. hi theory i baed on the fact that an alternating inuoidal flux ( co ωt) can be repreented by two revolving fluxe, each equal to one-half of the axiu value of alternating flux (i.e., /) and each rotating at ynchronou peed (N 10 f/p, ω πf) in oppoite direction. he above tateent will now be proved. he intantaneou value of flux due to the tator current of a ingle-phae induction otor i given by; coωt Conider two rotating agnetic fluxe 1 and each of agnitude / and rotating in oppoite direction with angular velocity ω [See Fig. (9.)]. Let the two fluxe tart rotating fro OX axi at Fig.(9.) 8

49 t 0. After tie t econd, the angle through which the flux vector have rotated i at. eolving the flux vector along-x-axi and Y-axi, we have, otal X-coponent co ωt + co ωt otal Y-coponent in ωt in ωt 0 eultant flux, ( co t) 0 co t ω + ω coωt hu the reultant flux vector i co ωt along X-axi. herefore, an alternating field can be replaced by two relating field of half it aplitude rotating in oppoite direction at ynchronou peed. Note that the reultant vector of two revolving flux vector i a tationary vector that ocillate in length with tie along X-axi. When the Fig.(9.3) rotating flux vector are in phae [See Fig. (9.3 (i))], the reultant vector i ; when out of phae by 180 [See Fig. (9.3 (ii))], the reultant vector 0. Let u explain the operation of ingle-phae induction otor by double-field revolving theory. (i) otor at tandtill Conider the cae that the rotor i tationary and the tator winding i connected to a ingle-phae upply. he alternating flux produced by the tator winding can be preented a the u of two rotating fluxe 1 and, each equal to one half of the axiu value of alternating flux and each rotating at ynchronou peed (N 10 f/p) in oppoite direction a hown in Fig. (9.4 (i)). Let the flux 1 rotate in anti clockwie direction and flux in clockwie direction. he flux 1 will reult in the production of torque 1 in the anti clockwie direction and flux will reult in the production of torque In the clockwie direction. At tandtill, thee two torque are equal and oppoite and the net torque developed i zero. herefore, ingle-phae induction otor i not elf-tarting. hi fact i illutrated in Fig. (9.4 (ii)). Note that each rotating field tend to drive the rotor in the direction in which the field rotate. hu the point of zero lip for one field correpond to 00% lip for the other a explained later. he value of 100% lip (tandtill condition) i the ae for both the field. 9

50 Fig.(9.4) (ii) otor running Now aue that the rotor i tarted by pinning the rotor or by uing auxiliary circuit, in ay clockwie direction. he flux rotating in the clockwie direction i the forward rotating flux ( f ) and that in the other direction i the backward rotating flux ( b ). he lip w.r.t. the forward flux will be where N N N f N ynchronou peed N peed of rotor in the direction of forward flux he rotor rotate oppoite to the rotation of the backward flux. herefore, the lip w.r.t. the backward flux will be b b N N N ( N) N + N N N N (N N) N N N + N hu fur forward rotating flux, lip i (le than unity) and for backward rotating flux, the lip i (greater than unity). Since for uual rotor reitance/reactance ratio, the torque at lip of le than unity arc greater than thoe at lip of ore than unity, the reultant torque will be in the direction of the rotation of the forward flux. hu if the otor i once tarted, it will develop net torque in the direction in which it ha been tarted and will function a a otor. 30

51 Fig. (9.5) how the rotor circuit for the forward and backward rotating fluxe. Note that r /, where i the tandtill rotor reitance i.e., r i equal to half the tandtill rotor reitance. Siilarly, x X / where X i the tandtill rotor reactance. At tandtill, 1 o that ipedance of the two circuit are equal. herefore, rotor current are equal i.e., I f I b. However, when the rotor rotate, the ipedance of the two rotor circuit are unequal and the rotor current I b i higher (and alo at a lower power factor) than the rotor current I f. heir..f., which oppoe the tator..f., will reult in a reduction of the backward rotating flux. Conequently, a peed increae, the forward flux increae, increaing the driving torque while the backward flux decreae, reducing the oppoing torque. he otor-quickly accelerate to the final peed. Fig.(9.5) 9.4 Making Single-Phae Induction Motor Self-Starting he ingle-phae induction otor i not elftarting and it i undeirable to reort to echanical pinning of the haft or pulling a belt to tart it. o ake a ingle-phae induction otor elf-tarting, we hould oehow produce a revolving tator agnetic field. hi ay be achieved by converting a ingle-phae upply into two-phae upply through the ue of an additional winding. When the otor attain ufficient peed, the tarting ean (i.e., additional winding) ay be reoved depending upon the type of the otor. A a atter of fact, ingle-phae Fig.(9.6) induction otor are claified and naed according to the ethod eployed to ake the elf-tarting. (i) Split-phae otor-tarted by two phae otor action through the ue of an auxiliary or tarting winding. 31

52 (ii) Capacitor otor-tarted by two-phae otor action through the ue of an auxiliary winding and a capacitor. (iii) Shaded-pole otor-tarted by the otion of the agnetic field produced by ean of a hading coil around a portion of the pole tructure. 9.5 otating Magnetic Field Fro -Phae Supply A with a 3-phae upply, a -phae balanced upply alo produce a rotating agnetic field of contant agnitude. With the exception of the haded-pole otor, all ingle-phae induction otor are tarted a -phae achine. Once o tarted, the otor will continue to run on ingle-phae upply. Let u ee how -phae upply produce a rotating agnetic field of contant agnitude. Fig. (9.10 (i)) how -pole, -phae winding. he phae X and Y are energized fro a two-phae ource and current in thee phae arc indicated a I x and I y [See Fig. (9.10 (ii))]. eferring to Fig. (9.10 (ii)), the fluxe produced by thee current arc given by; Y in ωt and X in( ωt + 90 ) coωt Here i the axiu flux due to either phae. We hall now prove that thi -phae upply produce a rotating agnetic field of contant agnitude equal to. (i) At intant 1 [See (Fig (ii)) and Fig. (9.10 (iii))], the current i zero in phae Y and axiu in phae X. With the current in the direction hown, a reultant flux i etablihed toward the right. he agnitude of the reultant flux i contant and i equal to a proved under: At intant 1, ωt 0 0 and Fig.(9.7) eultant flux, Y r X + Y ) + (0) X ( (ii) At intant [See Fig. (9.10 (ii)) and Fig. (9.10 (iii))], the current i till in the ae direction in phae X and an equal current flowing in phae Y. hi etablihe a reultant flux of the ae value (i.e., r ) a proved under: At intant, ωt 45 eultant flux, Y and r ( X ) + ( Y ) X Fig.(9.8) + 3

53 Note that reultant flux ha the ae value (i.e. ) but turned 45 clockwie fro poition 1. (iii) At intant 3 [See Fig. (9.10 (ii)) and Fig. (9.10 (iii))], the current in phae. X ha decreaed to zero and current in phae Y ha increaed to axiu. hi etablihe a reultant flux downward a proved under: Fig.(9.9) Fig.(9.10) 33

54 At intant 3, ωt 90 and 0 Y X r X + Y ) (0) + ( ) ( Note that reultant flux ha now turned 90 clockwie fro poition 1. he reader ay note that in the three intant conidered above, the reultant flux i contant and i equal to. However, thi contant reultant flux i hining it poition (clockwie in thi cae). In other word, the rotating flux i produced. We hall continue to conider other intant to prove thi fact. (iv) At intant 4 [See Fig. (9.10 (ii)) and Fig. (9.10 (iii))], the current in phae X ha revered and ha the ae value a that of phae Y. hi etablihe a reultant flux equal to turned 45 clockwie fro poition 3. At intant 4, r ωt 135 X + Y Y Fig.(9.11) r X + Y ( ) + (0) Fig.(9.1) (vi) Diagra 6, 7, and 8 [See Fig. (9.10 (iii))] indicate the direction of the reultant flux during the reaining ucceive intant. and + X (v) At intant 5 [See Fig. (9.10 (ii)) and Fig. (9.10 (iii))], the current in phae X i axiu and in phae Y i zero. hi etablihe a reultant flux equal to toward left (or 90 clockwie fro poition 3). At intant 5, ωt 180 Y 0 and X It follow fro the above dicuion that a -phae upply produce a rotating agnetic field of contant value ( the axiu value of one of the field). Note: If the two winding arc diplaced 90 electrical but produce field that are not equal and that are not 90 apart in tie, the reultant field i till rotating but i not contant in agnitude. One effect of thi nonunifor rotating field i the production of a torque that i non-unifor and that, therefore, caue noiy operation of the otor. Since -phae operation ceae once the otor i tarted, the operation of the otor then becoe ooth. 34

55 9.6 Split-Phae Induction Motor he tator of a plit-phae induction otor i provided with an auxiliary or tarting winding S in addition to the ain or running winding M. he tarting winding i located 90 electrical fro the ain winding [See Fig. (9.13 (i))] and operate only during the brief period when the otor tart up. he two winding are o reigned that the tarting winding S ha a high reitance and relatively all reactance while the ain winding M ha relatively low reitance and large reactance a hown in the cheatic connection in Fig. (9.13 (ii)). Conequently, the current flowing in the two winding have reaonable phae difference c (5 to 30 ) a hown in the phaor diagra in Fig. (9.13 (iii)). Fig.(9.13) Operation (i) When the two tator winding are energized fro a ingle-phae upply, the ain winding carrie current I while the tarting winding carrie current I. (ii) Since ain winding i ade highly inductive while the tarting winding highly reitive, the current I and I have a reaonable phae angle a (5 to 30 ) between the a hown in Fig. (9.13 (iii)). Conequently, a weak revolving field approxiating to that of a -phae achine i produced which tart the otor. he tarting torque i given by; ki I in α where k i a contant whoe agnitude depend upon the deign of the otor. (iii) When the otor reache about 75% of ynchronou peed, the centrifugal witch open the circuit of the tarting winding. he otor then operate a a ingle-phae induction otor and continue to accelerate till it reache the 35

56 noral peed. he noral peed of the otor i below the ynchronou peed and depend upon the load on the otor. Characteritic (i) he inning torque i 15 to tie the full-loud torque id (lie tarting current i 6 to 8 tie the full-load current. (ii) Due to their low cot, plit-phae induction otor are ot popular inglephae otor in the arket. (iii) Since the tarting winding i ade of fine wire, the current denity i high and the winding heat up quickly. If the tarting period exceed 5 econd, the winding ay burn out unle the otor i protected by built-in-theral relay. hi otor i, therefore, uitable where tarting period are not frequent. (iv) An iportant characteritic of thee otor i that they are eentially contant-peed otor. he peed variation i -5% fro no-load to fullload. (v) hee otor are uitable where a oderate tarting torque i required and where tarting period are infrequent e.g., to drive: (a) fan (b) wahing achine (c) oil burner (d) all achine tool etc. he power rating of uch otor generally lie between 60 W and 50 W. 9.7 Capacitor-Start Motor he capacitor-tart otor i identical to a plit-phae otor except that the tarting winding ha a any turn a the ain winding. Moreover, a capacitor C i connected in erie with the tarting winding a hown in Fig. (9.14 (i)). he value of capacitor i o choen that I lead I by about 80 (i.e., α ~ 80 ) which i coniderably greater than 5 found in plit-phae otor [See Fig. (9.14 (ii))]. Conequently, tarting torque ( k I I in α) i uch ore than that of a plit-phae otor Again, the tarting winding i opened by the centrifugal witch when the otor attain about 75% of ynchronou peed. he otor then operate a a ingle-phae induction otor and continue to accelerate till it reache the noral peed. Characteritic (i) Although tarting characteritic of a capacitor-tart otor are better than thoe of a plit-phae otor, both achine poe the ae running characteritic becaue the ain winding are identical. (ii) he phae angle between the two current i about 80 copared to about 5 in a plit-phae otor. Conequently, for the ae tarting torque, the current in the tarting winding i only about half that in a plit-phae otor. herefore, the tarting winding of a capacitor tart otor heat up le 36

57 quickly and i well uited to application involving either frequent or prolonged tarting period. Fig.(9.14) (iii) Capacitor-tart otor are ued where high tarting torque i required and where the tarting period ay be long e.g., to drive: (a) copreor (b) large fan (c) pup (d) high inertia load he power rating of uch otor lie between 10 W and 7-5 kw. 9.8 Capacitor-Start Capacitor-un Motor hi otor i identical to a capacitor-tart otor except that tarting winding i not opened after tarting o that both the winding reain connected to the upply when running a well a at tarting. wo deign are generally ued. (i) In one deign, a ingle capacitor C i ued for both tarting and running a hown in Fig.(9.15 (i)). hi deign eliinate the need of a centrifugal witch and at the ae tie iprove the power factor and efficiency of the otor. Fig.(9.15) (ii) In the other deign, two capacitor C 1 and C are ued in the tarting winding a hown in Fig. (9.15 (ii)). he aller capacitor C 1 required for optiu running condition i peranently connected in erie with the 37

58 tarting winding. he uch larger capacitor C i connected in parallel with C 1 for optiu tarting and reain in the circuit during tarting. he tarting capacitor C 1 i diconnected when the otor approache about 75% of ynchronou peed. he otor then run a a ingle-phae induction otor. Characteritic (i) he tarting winding and the capacitor can be deigned for perfect -phae operation at any load. he otor then produce a contant torque and not a pulating torque a in other ingle-phae otor. (ii) Becaue of contant torque, the otor i vibration free and can be ued in: (a) hopital (6) tudio and (c) other place where ilence i iportant. 9.9 Shaded-Pole Motor he haded-pole otor i very popular for rating below 0.05 H.P. (~ 40 W) becaue of it extreely iple contruction. It ha alient pole on the tator excited by ingle-phae upply and a quirrelcage rotor a hown in Fig. (9.16). A portion of each pole i urrounded by a hort-circuited turn of copper trip called hading coil. Fig.(9.16) Operation he operation of the otor can be undertood by referring to Fig. (9.17) which how one pole of the otor with a hading coil. (i) During the portion OA of the alternating-current cycle [See Fig. (9.17)], the flux begin to increae and an e..f. i induced in the hading coil. he reulting current in the hading coil will be in uch a direction (Lenz law) o a to oppoe the change in flux. hu the flux in the haded portion of the pole i weakened while that in the unhaded portion i trengthened a hown in Fig. (9.17 (ii)). (ii) During the portion AB of the alternating-current cycle, the flux ha reached alot axiu value and i not changing. Conequently, the flux ditribution acro the pole i unifor [See Fig. (9.17 (iii))] ince no current i flowing in the hading coil. A the flux decreae (portion BC of the alternating current cycle), current i induced in the hading coil o a to oppoe the decreae in current. hu the flux in the haded portion of the 38

59 pole i trengthened while that in the unhaded portion i weakened a hown in Fig. (9.17 (iv)). Fig.(9.17) (iii) he effect of the hading coil i to caue the field flux to hift acro the pole face fro the unhaded to the haded portion. hi hifting flux i like a rotating weak field oving in the direction fro unhaded portion to the haded portion of the pole. (iv) he rotor i of the quirrel-cage type and i under the influence of thi oving field. Conequently, a all tarting torque i developed. A oon a thi torque tart to revolve the rotor, additional torque i produced by ingle-phae induction-otor action. he otor accelerate to a peed lightly below the ynchronou peed and run a a ingle-phae induction otor. Characteritic (i) he alient feature of thi otor are extreely iple contruction and abence of centrifugal witch. (ii) Since tarting torque, efficiency and power factor are very low, thee otor are only uitable for low power application e.g., to drive: (a) all fan (6) toy (c) hair drier (d) dek fan etc. he power rating of uch otor i upto about 30 W. 39

60 9.10 Equivalent Circuit of Single-Phae Induction Motor It wa tated earlier that when the tator of a ingle-phae induction otor i con heeled to ingle-phae upply, the tator current produce a pulating flux that i equivalent to two-contant-aplitude fluxe revolving in oppoite direction at the ynchronou peed (double-field revolving theory). Each of thee fluxe induce current in the rotor circuit and produce induction otor action iilar to that in a 3-phae induction otor herefore, a ingle-phae induction otor can to iagined to be coniting of two otor, having a coon tator winding but with their repective rotor revolving in oppoite direction. Each rotor ha reitance and reactance half the actual rotor value. Let 1 reitance of tator winding X 1 leakage reactance of tator winding X total agnetizing reactance ' reitance of the rotor referred to the tator X' leakage reactance of the rotor referred to the tator (i) revolving theory. At tandtill. At tandtill, the otor i iply a tranforer with it econdary hort-circuited. herefore, the equivalent circuit of ingle-phae otor at tandtill will be a hown in Fig. (9.18). he double-field revolving theory ugget that characteritic aociated with each revolving field will be jut one-half of the characteritic aociated with the actual total flux. herefore, each rotor ha reitance and reactance equal to ' / and X' / repectively. Each rotor i aociated with half the Fig.(9.18) 40

61 total agnetizing reactance. Note that in the equivalent circuit, the core lo ha been neglected. However, core lo can be repreented by an equivalent reitance in parallel with the agnetizing reactance. At tandtill, f b. herefore, E f E b. Now E f 4.44 f N f ; E b 4.44 f N b where V 1 ~ E f + E b I 1 Z f + I 1 Z b Z f ipedance of forward parallel branch Z b ipedance of backward parallel branch (ii) otor running. Now conider that the otor i pinning at oe peed in the direction of the forward revolving field, the lip being. he rotor current produced by the forward field will have a frequency f where f i the tator frequency. Alo, the rotor current produced by the backward field will have a frequency of ( )f. Fig. (9.19) how the equivalent circuit of a ingle-phae induction otor when the rotor i rotating at lip. It i clear, fro the equivalent circuit that under running condition, E f becoe uch greater than E b becaue the ter ' / increae very uch a tend toward zero. Converely, E^ fall becaue the ter ' /( ) decreae ince ( ) tend toward. Conequently, the forward field increae, increaing the driving torque while the backward field decreae reducing the oppoing torque. Fig.(9.19) otal ipedance of the circuit.i given by; 41

62 Z r Z 1 + Z f + Z b where Z j X 1 Z Z f b I V X ' X' j + j ' X X' + j + X ' X' j + j ( ) ' X X' + j + ( ) 1 1 / Zr 9.11 A.C. Serie Motor or Univeral Motor A d.c. erie otor will rotate in the ae direction regardle of the polarity of the upply. One can expect that a d.c. erie otor would alo operate on a ingle-phae upply. It i then called an a.c. erie otor. However, oe change ut be ade in a d.c. otor that i to operate atifactorily on a.c. upply. he change effected are: (i) he entire agnetic circuit i lainated in order to reduce the eddy current lo. Hence an a.c. erie otor require a ore expenive contruction than a d.c. erie otor. (ii) he erie field winding ue a few turn a poible to reduce the reactance of the field winding to a iniu. hi reduce the voltage drop acro the field winding. (iii) A high field flux i obtained by uing a low-reluctance agnetic circuit. (iv) here i coniderable parking between the bruhe and the coutator when the otor i ued on a.c. upply. It i becaue the alternating flux etablihe high current in the coil hort-circuited by the bruhe. When the hort-circuited coil break contact fro the coutator, exceive parking i produced. hi can be eliinated by uing high-reitance lead to connect the coil to the coutator egent. Contruction 4

63 he contruction of en a.c. erie otor i very iilar to a d.c. erie otor except that above odification are incorporated [See Fig. (9.0)]. Such a otor can be operated either on a.c. or d.c. upply and the reulting torque-peed curve i about the ae in each cae. For thi reaon, it i oetie called a univeral otor. Operation When the otor i connected to an a.c. upply, the ae alternating current flow through the field and arature winding. he field winding produce an alternating Fig.(9.0) flux that react with the current flowing in the arature to produce a torque. Since both arature current and flux revere iultaneouly, the torque alway act in the ae direction. It ay be noted that no rotating flux i produced in thi type of achine; the principle of operation i the ae a that of a d.c. erie otor. Characteritic he operating characteritic of an a.c. erie otor are iilar to thoe of a d.c. erie otor. (i) he peed increae to a high value with a decreae in load. In very all erie otor, the loe are uually large enough at no load that liit the peed to a definite value ( ,000 r.p..). (ii) he otor torque i high for large arature current, thu giving a high tarting torque. (iii) At full-load, the power factor i about 90%. However, at tarting or when carrying an overload, the power factor i lower. Application he fractional horepower a.c. erie otor have high-peed (and correponding all ize) and large tarting torque. hey can, therefore, be ued to drive: (a) high-peed vacuu cleaner (b) ewing achine (c) electric haver (d) drill (e) achine tool etc. 9.1 Single-Phae epulion Motor A repulion otor i iilar to an a.c. erie otor except that: 43

64 (i) bruhe are not connected to upply but are hort-circuited [See Fig. (9.1)]. Conequently, current are induced in the arature conductor by tranforer action. (ii) the field tructure ha non-alient pole contruction. By adjuting the poition of hort-circuited bruhe on the coutator, the tarting torque can be developed in the otor. Contruction he field of tator winding i wound like the ain winding of a plit-phae otor and i connected directly to a ingle-phae ource. he arature or rotor i iilar to a d.c. otor arature with dru type winding connected to a coutator (not hown in the figure). However, the bruhe are not connected to upply but are connected to each other or hort-circuited. Short-circuiting the bruhe effectively ake the rotor into a type of quirrel cage. he ajor difficulty with an ordinary ingle-phae induction otor i the low tarting torque. By uing a coutator otor with bruhe hort-circuited, it i poible to vary the tarting torque by changing the bruh axi. It ha alo better power factor than the conventional ingle-phae otor. Principle of operation Fig.(9.1) he principle of operation i illutrated in Fig. (9.1) which how a two-pole repulion otor with it two hort-circuited bruhe. he two drawing of Fig. (9.1) repreent a tie at which the field current i increaing in the direction hown o that the left-hand pole i N-pole and the right-hand pole i S-pole at the intant hown. (i) In Fig. (9.1 (i)), the bruh axi i parallel to the tator field. When the tator winding i energized fro ingle-phae upply, e..f. i induced in the arature conductor (rotor) by induction. By Lenz law, the direction of the e..f. i uch that the agnetic effect of the reulting arature current will oppoe the increae in flux. he direction of current in arature conductor will be a hown in Fig. (9.1 (i)). With the bruh axi in the poition hown in Fig. (9.1 (i)), current will flow fro bruh B to 44

65 bruh A where it enter the arature and flow back to bruh B through the two path ACB and ADB. With bruhe et in thi poition, half of the arature conductor under the N-pole carry current inward and half carry current outward. he ae i true under S-pole. herefore, a uch torque i developed in one direction a in the other and the arature reain tationary. he arature will alo reain tationary if the bruh axi i perpendicular to the tator field axi. It i becaue even then net torque i zero. (ii) If the bruh axi i at oe angle other than 0 or 90 to the axi of the tator field, a net torque i developed on the rotor and the rotor accelerate to it final peed. Fig. (9.1 (ii)) repreent the otor at the ae intant a that in Fig. (9.1 (i)) but the bruhe have been hifted clockwie through oe angle fro the tator field axi. Now e..f. i till induced in the direction indicated in Fig. (9.1 (i)) and current flow through the two path of the arature winding fro bruh A to bruh B. However, becaue of the new bruh poition, the greater part of the conductor under the N- pole carry current in one direction while the greater part of conductor under S-pole carry current in the oppoite direction. With bruhe in the poition hown in Fig. (9.1 (ii), torque i developed in the clockwie direction and the rotor quickly attain the final peed. (iii) he direction of rotation of the rotor depend upon the direction in which the bruhe are hifted. If the bruhe are hifted in clockwie direction fro the tator field axi, the net torque act in the clockwie direction and the rotor accelerate in the clockwie direction. If the bruhe Fig.(9.) are hifted in anti-clockwie direction a in Fig. (9.). the arature current under the pole face i revered and the net torque i developed in the anti-clockwie direction. hu a repulion otor ay be ade to rotate in either direction depending upon the direction in which the bruhe are hifted. (iv) he total arature torque in a repulion otor can be hown to be a in α where α angle between bruh axi and tator field axi For axiu torque, α 90 or α 45 45

66 hu adjuting α to 45 at tarting, axiu torque can be obtained during the tarting period. However, α ha to be adjuted to give a uitable running peed. Characteritic (i) he repulion otor ha characteritic very iilar to thoe of an a.c. erie otor i.e., it ha a high tarting torque and a high peed at no load. (ii) he peed which the repulion otor develop for any given load will depend upon the poition of the bruhe. (iii) In coparion with other ingle-phae otor, the repulion otor ha a high tarring torque and relatively low tarting current epulion-start Induction-un Motor Soetie the action of a repulion otor i cobined with that of a inglephae induction otor to produce repulion-tart induction-run otor (alo called repulion-tart otor). he achine i tarted a a repulion otor with a correponding high tarting torque. At oe predeterined peed, a centrifugal device hort-circuit the coutator o that the achine then operate a a ingle-phae induction otor. he repulion-tart induction-run otor ha the ae general contruction of a repulion otor. he only difference i that in addition to the baic repulionotor contruction, it i equipped with a centrifugal device fitted on the arature haft. When the otor reache 75% of it full pinning peed, the centrifugal device force a hort-circuiting ring to coe in contact with the inner urface of the coutator. hi nort-circuit all the coutator bar. he rotor then reeble quirrel-cage type and the otor run a a ingle-phae induction otor. At the ae tie, the centrifugal device raie the bruhe fro the coutator which reduce the wear of the bruhe and coutator a well a ake the operation quiet. Characteritic (i) he tarting torque i.5 to 4.5 tie the full-load torque and the tarting current i 3.75 tie the full-load value. (ii) Due to their high tarting torque, repulion-otor were ued to operate device uch a refrigerator, pup, copreor etc. However, they poed a eriou proble of aintenance of bruhe, coutator arid the centrifugal device. Conequently, anufacturer have topped aking the in view of the developent of capacitor otor which are all in ize, reliable and low-priced. 46

67 9.14 epulion-induction Motor he repulion-induction otor produce a high tarting torque entirely due to repulion otor action. When running, it function through a cobination of induction-otor and repulion otor action. 47

68 Contruction Fig. (9.3) how the connection of a 4-pole repulion-induction otor for 30 V operation. It conit of a tator and a rotor (or arature). (i) he tator carrie a ingle ditributed winding fed fro ingle-phae upply. (ii) he rotor i provided with two independent winding placed one inide the other. he inner winding i a quirrel-cage winding with rotor bar peranently hort-circuited. Placed over the quirrel cage winding i a repulion coutator arature winding. he repulion winding i connected to a coutator on which ride hort-circuited bruhe. here i no centrifugal device and the repulion winding function at all tie. Operation Fig.(9.3) (i) When ingle-phae upply i given to the tator winding, the repulion winding (i.e., outer winding) i active. Conequently, the otor tart a a repulion otor with a correponding high tarting torque. (ii) A the otor peed increae, the current hift fro the outer to inner winding due to the decreaing ipedance of the inner winding with increaing peed. Conequently, at running peed, the quirrel cage winding carrie the greater part of rotor current. hi hifting of repulionotor action to induction-otor action i thu achieved without any witching arrangeent. (iii) It ay be een that the otor tart a a repulion otor. When running, it function through a cobination of principle of induction and repulion; the forer being predoinant. Characteritic (i) he no-load peed of a repulion-induction otor i oewhat above the ynchronou peed becaue of the effect of repulion winding. However, 48

69 the peed at full-load i lightly le than the ynchronou peed a in an induction otor. (ii) he peed regulation of the otor i about 6%. (iii) he tarting torque i.5 to 3 tie the full-load torque; the lower value being for large otor. he tarting current i 3 to 4 tie the full-load current. hi type of otor i ued for application requiring a high tarting torque with eentially a contant running peed. he coon ize are 0.5 to 5 H.P Single-Phae Synchronou Motor Very all ingle-phae otor have been developed which run at true ynchronou peed. hey do not require d.c. excitation for the rotor. Becaue of thee characteritic, they are called unexcited ingle-phae ynchronou otor. he ot coonly ued type are: (i) eluctance otor (ii) Hyterei otor he efficiency and torque-developing ability of thee otor i low; he output of ot of the coercial otor i only a few watt eluctance Motor It i a ingle-phae ynchronou otor which doe not require d.c. excitation to the rotor. It operation i baed upon the following principle: Whenever a piece of ferroagnetic aterial i located in a agnetic field; a force i exerted on the aterial, tending to align the aterial o that reluctance of the agnetic path that pae through the aterial i iniu. Contruction Fig.(9.4) A reluctance otor (alo called ynchronou reluctance otor) conit of: 49

70 (i) (ii) a tator carrying a ingle-phae winding along with an auxiliary winding to produce a ynchronou-revolving agnetic field. a quirrel-cage rotor having unyetrical agnetic contruction. hi i achieved by yetrically reoving oe of the teeth fro the quirrelcage rotor to produce alient pole on the rotor. A hown in Fig. (9.4 (i)), 4 ailent pole have been produced on e rotor. he alient pole created on the rotor ut be equal to the pole on the tator. Note that rotor alient pole offer low reductance to the tator flux and, therefore, becoe trongly agnetized. Operation (i) When ingle-phae tator having an auxiliary winding i energized, a ynchronouly-revolving field i produced. he otor tart a a tandard quirrel-cage induction otor and will accelerate to near it ynchronou peed. (ii) A the rotor approache ynchronou peed, the rotating tator flux will exert reluctance torque on the rotor pole tending to align the alient-pole axi with the axi of the rotating field. he rotor aue a poition where it alient pole lock with the pole of the revolving field [See Fig. (9.4 (ii))]. Conequently, the otor will continue to run at the peed of revolving flux i.e., at the ynchronou peed. (iii) When we apply a echanical load, the rotor pole fall lightly behind the tator pole, while continuing to turn at ynchronou peed. A the load on the otor i increaed, the echanical angle between the pole increae progreively. Neverthele, agnetic attraction keep the rotor locked to the rotating flux. If the load i increaed beyond the aount under which the reluctance torque can aintain ynchronou peed, the rotor drop out of tep with the revolving field. he peed, then, drop to oe value at which the lip i ufficient to develop the neceary torque to drive the load by induction-otor action. Characteritic (i) hee otor have poor torque, power factor and efficiency. (ii) hee otor cannot accelerate high-inertia load to ynchronou peed. (iii) he pull-in and pull-out torque of uch otor are weak. Depite the above drawback, the reluctance otor i cheaper than any other type of ynchronou otor. hey are widely ued for contant-peed application uch a tiing device, ignalling device etc. 50

71 9.17 Hyterei Motor It i a ingle-phae otor whoe operation depend upon the hyterei effect i.e., agnetization produced in a ferroagnetic aterial lag behind the agnetizing force. Contruction It conit of: (i) (ii) a tator deigned to produce a ynchronouly-revolving field fro a ingle-phae upply. hi i accoplihed by uing peranent-plit capacitor type contruction. Conequently, both the winding (i.e., tarting a well a ain winding) reain connected in the circuit during running operation a well a at tarting. he value of capacitance i o adjuted a to reult in a flux revolving at ynchronou peed. a rotor coniting of a ooth cylinder of agnetically hard teel, without winding or teeth. Operation (i) When the tator i energized fro a ingle-phae upply, a ynchronoulyrevolving field (aued in anti-clockwie direction) i produced due to plit-phae operation. (ii) he revolving tator flux agnetize the rotor. Due to hyterei effect, the axi of agnetization of rotor will lag behind the axi of tator field by hyterei lag angle a a hown in Fig. (9.5). hu the rotor and tator pole are locked. If the rotor i tationary, the tarting torque produced i given by: r in α where tator flux. r rotor flux. Fro now onward, the rotor accelerate to ynchronou peed with a unifor torque. (iii) After reaching ynchroni, the otor continue to run at ynchronou peed and adjut it torque angle o a to develop the torque required by the load. Characteritic (i) A hyterei otor can ynchronize any load which it can accelerate, no atter how great the inertia. It i becaue the torque i unifor fro tandtill to ynchronou peed. (ii) Since the rotor ha no teeth or alient pole or winding, a hyterei otor i inherently quiet and produce ooth rotation of the load. 51

72 Fig.(9.5) (iii) he rotor take on the ae nuber of pole a the tator field. hu by changing the nuber of tator pole through pole-changing connection, we can get a et of ynchronou peed for the otor. Application Due to their quiet operation and ability to drive high-inertia toad, hyterei otor are particularly well uited for driving (i) electric clock (ii) tiing device (iii) tape-deck (iv)fro-table and other preciion audio-equipent. 5

73 Chapter (11) Synchronou Motor Introduction It ay be recalled that a d.c. generator can be run a a d.c. otor. In like anner, an alternator ay operate a a otor by connecting it arature winding to a 3-phae upply. It i then called a ynchronou otor. A the nae iplie, a ynchronou otor run at ynchronou peed (N 10f/P) i.e., in ynchroni with the revolving field produced by the 3-phae upply. he peed of rotation i, therefore, tied to the frequency of the ource. Since the frequency i fixed, the otor peed tay contant irrepective of the load or voltage of 3- phae upply. However, ynchronou otor are not ued o uch becaue they run at contant peed (i.e., ynchronou peed) but becaue they poe other unique electrical propertie. In thi chapter, we hall dicu the working and characteritic of ynchronou otor Contruction A ynchronou otor i a achine that operate at ynchronou peed and convert electrical energy into echanical energy. It i fundaentally an alternator operated a a otor. Like an alternator, a ynchronou otor ha the following two part: (i) a tator which houe 3-phae arature winding in the lot of the tator core and receive power fro a 3-phae upply [See (Fig. (11.1)]. (ii) a rotor that ha a et of alient pole excited by direct current to for alternate N and S pole. he exciting coil are connected in erie to two lip ring and direct current i fed into the winding fro an external exciter ounted on the rotor haft. he tator i wound for the ae nuber of pole a the rotor pole. A in the cae of an induction otor, the nuber of pole deterine the ynchronou peed of the otor: Fig.(11.1) 93

74 where Synchronou peed, 10f N P f frequency of upply in Hz P nuber of pole An iportant drawback of a ynchronou otor i that it i not elf-tarting and auxiliary ean have to be ued for tarting it. 11. Soe Fact about Synchronou Motor Soe alient feature of a ynchronou otor are: (i) A ynchronou otor run at ynchronou peed or not at all. It peed i contant (ynchronou peed) at all load. he only way to change it peed i to alter the upply frequency (N 10 f/p). (ii) he outtanding characteritic of a ynchronou otor i that it can be ade to operate over a wide range of power factor (lagging, unity or leading) by adjutent of it field excitation. herefore, a ynchronou otor can be ade to carry the echanical load at contant peed and at the ae tie iprove the power factor of the yte. (iii) Synchronou otor are generally of the alient pole type. (iv) A ynchronou otor i not elf-tarting and an auxiliary ean ha to be ued for tarting it. We ue either induction otor principle or a eparate tarting otor for thi purpoe. If the latter ethod i ued, the achine ut be run up to ynchronou peed and ynchronized a an alternator Operating Principle he fact that a ynchronou otor ha no tarting torque can be eaily explained. (i) Conider a 3-phae ynchronou otor having two rotor pole N and S. hen the tator will alo be wound for two pole N S and S S. he otor ha direct voltage applied to the rotor winding and a 3-phae voltage applied to the tator winding. he tator winding produce a rotating field which revolve round the tator at ynchronou peed N ( 10 f/p). he direct (or zero frequency) current et up a two-pole field which i tationary o long a the rotor i not turning. hu, we have a ituation in which there exit a pair of revolving arature pole (i.e., N S S S ) and a pair of tationary rotor pole (i.e., N S ). (ii) Suppoe at any intant, the tator pole are at poition A and B a hown in Fig. (11. (i)). It i clear that pole N S and N repel each other and o do the pole S S and S. herefore, the rotor tend to ove in the anticlockwie direction. After a period of half-cycle (or ½ f 1/100 econd), the polaritie of the tator pole are revered but the polaritie of the rotor pole reain the ae a hown in Fig. (11. (ii)). Now S S and N attract 94

75 each other and o do N S and S. herefore, the rotor tend to ove in the clockwie direction. Since the tator pole change their polaritie rapidly, they tend to pull the rotor firt in one direction and then after a period of half-cycle in the other. Due to high inertia of the rotor, the otor fail to tart. Fig.(10.) Hence, a ynchronou otor ha no elf-tarting torque i.e., a ynchronou otor cannot tart by itelf. How to get continuou unidirectional torque? If the rotor pole are rotated by oe external ean at uch a peed that they interchange their poition along with the tator pole, then the rotor will experience a continuou unidirectional torque. hi can be undertood fro the following dicuion: (i) Suppoe the tator field i rotating in the clockwie direction and the rotor i alo rotated clockwie by oe external ean at uch a peed that the rotor pole interchange their poition along with the tator pole. (ii) Suppoe at any intant the tator and rotor pole are in the poition hown in Fig. (11.3 (i)). It i clear that torque on the rotor will be clockwie. After a period of half-cycle, the tator pole revere their polaritie and at the ae tie rotor pole alo interchange their poition a hown in Fig. (11.3 (ii)). he reult i that again the torque on the rotor i clockwie. Hence a continuou unidirectional torque act on the rotor and ove it in the clockwie direction. Under thi condition, pole on the rotor alway face pole of oppoite polarity on the tator and a trong agnetic attraction i et up between the. hi utual attraction lock the rotor and tator together and the rotor i virtually pulled into tep with the peed of revolving flux (i.e., ynchronou peed). (iii) If now the external prie over driving the rotor i reoved, the rotor will continue to rotate at ynchronou peed in the clockwie direction becaue the rotor pole are agnetically locked up with the tator pole. It i due to 95

76 thi agnetic interlocking between tator and rotor pole that a ynchronou otor run at the peed of revolving flux i.e., ynchronou peed. Fig.(11.3) 11.4 Making Synchronou Motor Self-Starting A ynchronou otor cannot tart by itelf. In order to ake the otor elf-tarting, a quirrel cage winding (alo called daper winding) i provided on the rotor. he daper winding conit of copper bar ebedded in the pole face of the alient pole of the rotor a hown in Fig. (11.4). he bar are hort-circuited at the end to for in effect a partial quirrel cage winding. he daper winding erve Fig.(11.4) to tart the otor. (i) o tart with, 3-phae upply i given to the tator winding while the rotor field winding i left unenergized. he rotating tator field induce current in the daper or quirrel cage winding and the otor tart a an induction otor. (ii) A the otor approache the ynchronou peed, the rotor i excited with direct current. Now the reulting pole on the rotor face pole of oppoite polarity on the tator and a trong agnetic attraction i et up between the. he rotor pole lock in with the pole of rotating flux. Conequently, the rotor revolve at the ae peed a the tator field i.e., at ynchronou peed. (iii) Becaue the bar of quirrel cage portion of the rotor now rotate at the ae peed a the rotating tator field, thee bar do not cut any flux and, therefore, have no induced current in the. Hence quirrel cage portion of the rotor i, in effect, reoved fro the operation of the otor. 96