Section Induction motor drives

Transcription

1 Section nduction motor drive Electric Drive Sytem ntroduction he AC induction motor i by far the mot widely ued motor in the indutry. raditionally, it ha been ued in contant and lowly variable-peed (or adjutable-peed) drive application which do not cater for fat dynamic procee. Procee with fat dynamic repone of medium power range (a few hundred kw) have traditionally been driven by bruhed DC motor drive. At the low power end, bruhle PM DC and AC motor drive have become attractive alternative to bruhed DC motor drive. Due to recent elopment of everal new control technologie, uch a vector (indirect rotor flux oriented) and direct torque control, induction machine are now-a-day alo applied in highly dynamic application. he underlying reaon for thi i the fact that the cage induction motor i much cheaper and more rugged than DC or the PM AC motor. For thee reaon, the adjutable-peed induction motor drive till i the main workhore in indutry. hi ection tart with induction motor drive which fall into the adjutable-peed drive category. he control of thee drive i baed on the teady-tate equivalent circuit of the induction motor. t may be noted here that the dynamic performance (uch a acceleration and deceleration) of thi motor can not be addreed by thee teady-tate repreentation ecap uing the teady-tate equivalent circuit he underlying principle behind the operation of an induction motor i the concept of rotating magnetic field produced by the three-phae AC current in the pace ditributed tator winding. n the teady-tate, with inuoidal upply at a fixed frequency f 1, the peed of thi rotating field i given by N f p 1 yn1 rev/ec (5.1.1) f p p 1 1 yn1 mechanical rad/ec (5.1.) where f 1 i the upply frequency and p i the number of pole pair. For balanced three-phae upply and ditributed tator winding the air-gap field i ditributed inuoidally along the periphery of the rotor and will caue inuoidal voltage to be induced in the rotor winding when the rotor rotate at a contant peed N rot1. he conequent current that flow in the rotor circuit elop the torque that drive the rotor uch that it trie to follow the revolving field. n doing o it tend to minimie the voltage that are induced in it a well known effect potulated by Lenz. f the magnetic flux linkage with a tationary winding i repreented by mco f1t, it Nd induce a voltage e f1nmin1t where N i the number of turn of the dt winding, and f 1 i the frequency of the flux linkage with the tationary winding. n term of MS value, E 4.44N f1. m 1 July 011

2 Electric Drive Sytem n the cae of the induction motor, the rotor follow the air-gap flux with a peed which i lightly lower than the peed of the revolving field. he difference between the two peed i the lip peed. he effective rate of flux linkage of the rotor circuit i reduced due to the lip. hi lip i defined by Nyn1 Nrot1 yn1 rot1 (5.1.3) N yn1 yn1 where N rot1 and rot1 are rotor peed in mechanical rev/ec and rad/ec, repectively. Jut a the air-gap field peed rev/ec i expreed by Nyn1 f 1 / p, imilarly, the rotor peed may alo be given by Nrot1 f / p rev/ec, where f i rotor peed in Hz. t can be eaily hown that f1 f1 f fr (5.1.4) t hould be obviou that f 1, not f, i the frequency f r of the induced voltage and current in the rotor circuit. he magnitude of the voltage induced in the rotor i alo dependent on lip it being of zero amplitude and frequency when the rotor rotate exactly at ynchronou peed and of maximum amplitude and frequency (f 1 ) when the rotor i at tandtill. hu E E (5.1.5) tan dtill he teady-tate equivalent circuit he rotor circuit per-phae in the teady-tate (at contant frequency) can be repreented a X X E X E E 1 (a) (b) (c) Figure otor equivalent circuit he rotor repreentation when combined with the tator give the total per-phae equivalent circuit of figure Note that all rotor parameter have now been referred to the tator, taking into account the turn ratio between the tator and rotor. hu, a, X a X, 1 tan dtill E ae E and a tan dtill where a i the tator-rotor turn ratio. he ubcript tandtill ha been dropped in the equivalent circuit of figure 5.1., and henceforth, for the ake of brevity. July 011

3 Electric Drive Sytem 1 1 X 1 a A X 1 c c m X m E ae E 1 1 A Figure he exact per-phae equivalent circuit he c /X m branch of an induction motor repreentation can not be moved to the input terminal of the circuit, a can be done for a tranformer, without ignificant lo of accuracy. hi i due the air gap of the M which caue much larger magnetiing current than in a tranformer. he tator impedance voltage drop in an induction motor, a a reult, i much larger than in a tranformer. he approximate equivalent circuit of figure i however widely ued. Note that c appear to have been neglected, but thi i not entirely true. he iron lo repreented by c i now included in the no-load lo which i the power eloped in motor rotate with no-load lip nl. 1 when the 1 1 X 1 a A X m 1 X m E ae E 1 1 A Figure he approximate per-phae, teady-tate equivalent circuit of an induction motor Developed torque and - characteritic From the repreentation of figure , the following relationhip in term of motor parameter referred to the tator and the rotor lip can be found. Power in the rotor circuit, 3 E1 + 1L P = 3 = (5.1.6) Developed output power, 3 July 011

4 Electric Drive Sytem o Slip power, P P P l o (5.1.7) P P P P 3 (5.1.8) Developed output torque, P o rot1 3 1 / N rot1 Nm (5.1.9) 3 1 / N 1 rot1 3 / 3 / P N (5.1.10) yn1 yn1 yn1 From (5.1.) and (5.1.4) 1 3p 3p f f f 1 1 (5.1.11) For given motor parameter and input voltage 1, can be calculated uing hevenin repreentation, a hown in figure 5.1.4, of the equivalent circuit of figure h X h A X h A 1 Figure he hevenin equivalent circuit hu h h h X X (5.1.1) 4 July 011

5 3p h 1 h Xh X Electric Drive Sytem (5.1.13) where f h 1 1 ; f 1 being the tator upply frequency. X m 1 X X 1 1 m (5.1.14) jx jx Z jx m 1 1 h h h 1 j X1 Xm (5.1.15) Note that for X m >> ( 1 and X 1 ), h 1, X h X 1, and h 1. - characteritic of figure for variou input voltage can be obtained from equation (5.1.13). hee characteritic of an M for 1 in the range from 0.5pu to 1pu are a hown in figure Note the operating mode of the motor in motoring, generating and plugging mode of operation. n motoring mode, i.e, in quadrant 1 (Q1), the machine operate a a motor with poitive torque and peed, normally operating with a mall poitive lip (0.05 < < 0.1). n the regenerative mode in quadrant (Q), the machine peed i higher than the ynchronou peed 1, and the eloped torque i negative, hence the machine run a a generator becaue i now negative. n quadrant 4 (Q4), the machine operate in the braking mode. t terminal are interchanged, o that the ynchronou peed become negative. he operating lip exceed 1 and P o become negative even though P remain poitive (ee equation 5.1.3, & ). he negative P o implie that thi power mut be upplied by the mechanical load to the rotor, thu leading to ome braking. t may be noted that the regenerative mode of operation give more efficient and effective braking than plugging. Generating yn1 1 = 0.5 pu 1 = 0.7 pu 1 = 1 pu < 0 = 0 1 = 1 pu 1 = 0.7 pu 1 = 0.5 pu Motoring = 1 0 orque, Nm > 1 Plugging yn1 = Figure characteritic with variable voltage and contant input frequency 5 July 011

6 Electric Drive Sytem Operation with mall lip. From efficiency and motor heating conideration, it i not practical to operate induction machine with a high lip. For mall lip, H Xh X and From (5.1.13),. (5.1.16) h 3p h 1 h Xh X (5.1.17) hu, with mall lip, the eloped torque approximately given by p Nm (5.1.18) 3 h 1 Normally, the operating lip i mall and in the range: Normally alo, h Operation with high lip. Operation with high lip implie high rotor current (ee Eq ). hi alo implie high rotor power lo, compared to the output power P o or the total rotor power P (ee Eqn and 5.1.8). n other word, with high lip operation, efficiency of the motor fall and rotor temperature rie due to high rotor power lo. hu, high-lip operation hould be avoided. Fan and impeller type load require low torque at low peed and thu may be uitable for high-lip operation. Note that when operation i with high lip, ay at tarting, equation cannot be ued for calculating the eloped torque. Equation ha to be ued intead Condition for maximum eloped torque. he condition for the maximum mechanical (eloped) torque can be found by differentiating (5.1.17) and by equating d / d 0. Alternatively, the condition for maximum eloped torque hould be ame a the condition for maximum power tranfer into the rotor. hi condition i found to be m X X h h (5.1.19) m X X h h (5.1.0) From (5.1.13) or (5.1.17) 6 July 011

7 Electric Drive Sytem max 3p h 1 X X h h h Nm (5.1.1) Note that the maximum eloped torque, max, i independent of the rotor reitance. 7 July 011