Section 2.2 PWM converter driven DC motor drives

Section 2.2 PWM converter driven DC motor drives 2.2.1 Introduction Controlled power supply for electric drives re obtined mostly by converting the mins AC supply. Power electronic converter circuits employing switching devices such s thyristors, trnsistors, GTOs, diodes, MOSFETSs, IGBTs, diodes nd host of ssocited control nd interfcing circuits re used. The conversion process introduces controllbility to the converters. It llows fst control of voltge, current or power to the motor vi the gte curcuits of the switches in the converters. In this wy the required dynmic response requirements of the drive cn be met. In mny cses the control of the converter circuit lso tkes into ccount other performnce fctors such s power fctor, drive efficiency, motor current ripple, control rnge, sttor nd rotor flux nd so on. Power Supply Power Supply v c Power Converter Armture Field i F v e Power Converter Figure 2.2.1 2.2.1.1 Field circuit requirement The power supply for the field circuit of seprtely excited DC motor is normlly fixed supply, such s diode rectifier terminted with filter. When field wekening is used to operte DC motor to cover speed rnge bove the bse speed, the field DC supply hs to be controllble. Normlly only unidirectionl DC supply for the field is required for such field wekening pplictions. Permnent mgnet excittion for which cse no power source is needed re lso used. Permnent mgnet excittion for low power DC motors, especilly servo-motors, re now lmost universl. 2.2.1.2 Armture circuit requirement The power converter for the rmture my employ one of mny different configurtions of power electronic circuits. There re two brod ctegories. For low power DC motors, especilly servo-motors, switch-mode PWM converters re used. These converters use gte turn- off devices such s MOSFETs, or IGBTs. These re normlly one, two or four qudrnt PWM DC- DC converters, the DC supply for which is derived from single- or three-phse diode bridge rectifier. Lrge power motors re driven from thyristor power converters which employ phsecontrolled single, three- or higher-phse thyristor converter circuits for mking vilble vrible DC supply to the motor. In ll of these converter circuits, the power semiconductor switches operte in the swtiched mode. When the switches re off, they block the voltge of the supply cross them without current flow. When they re on, the voltge drop cross them is low (no more thn 1-3V). So 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 1 July 2011

they do not consume much power in either the on- or the off-stte. The overlp of turn-on nd turn-off trnsients re crefully considered in selecting the switching frequency nd the switching deevices so tht the power loss due to switching is lso low compred to the power delivered to the motor. The power converter circuits thus operte essentilly s switched mode mplifier with high efficiency. For this course, we will ignore the switching trnsients nd overlps of converter switches nd ssume tht power semiconductor switches turn on or off instntneously. The frequency t which the power converter is switched, e.g., 100 Hz for single-phse thyristor bridge converter, 300 Hz for three-phse thyristor bridge converter, 20 khz for PWM MOSFET or IGBT H-bridge converter, nd so on, lso hs profound effect on the dynmics chieveble with motor drive. Power switching devices for low power ppliction tend to hve fster switching cpbility thn for higher power pplictions, which is convenient, since low power motors re normlly operted with high dynmic response nd hence ccurcy. Power converter circuits re ever incresingly required to hve high efficiency, lower hrmonic performnce both t the output nd t the input, hve regenertive or bidirectionl power flow cpbility for certin pplictions, high power fctor, nd low EMC properties. In selecting the power converter for drive, these issues re lso tken into ccount, s fr s prcticble. In the following sections, we will introduce converter circuits for low power dc drives first. These re the pulse-width modulted (PWM) switching converters (often clled regultors) which utilise MOSFETs nd IGBTs. These will be followed by phse controlled thyristors converters which re mostly used in high power dc motor drives. The dvent of IGBTs (insulted gte bipolr trnsistors) in recent yers hs blurred this boundry considerbly. IGBTs now--dys hve voltge nd current rtings pproching 3500V nd 2000A respecively, so tht the lrgest DC motor cn now be driven from PWM converters. Anlysis of the converter nd the seprtely excited DC motors, nd their combined chrcteristics will be included in the following sections. 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 2 July 2011

2.2.2 PWM DC-DC Converter (Chopper) for DC drives 2.2.2.1 DC-DC Step-down (Buck) converter T I V s L E D V s D V I L T E Figure 2.2.2() Figure 2.2.2(b) The bove two circuits re equivlent except for the isoltion requirements of their gte drives, motor current nd voltge sensors, nd gte control circuits. The switch T in ech converter circuit is turned on nd off periodiclly, with fixed (usully) switching frequency f s nd vrible duty cycle DT s where T s is the period of switching. The turn-on nd turn-off times, T on nd T off, respectively, re given by Ton Toff Ts ; Ton DTs ; T off = (1 - D)T s ; Ts 1 ; s 2 fs (2.2.1) f Typiclly, f s rnges from 300-1000 Hz for trction drives nd from 10-20 khz for servo nd pplince drives. 2.2.2.2 The Pulsewidth Modultor (PWM) The switching signl with duty cycle D for converter is obtined for pulsewidth modultion circuit (see figure 2.2.5()). The pulsewidth modultor (PWM) circuit compres reference duty cycle signl e c from nother controller with high frequency swtooth or tringulr wveform clled crrier. The crrier frequency f s is the swithing frequency of the converter nd the comprter out hs T on nd T off times the durtions of which is proportionl to the e c (directly for T on nd inversely for T off ). The sum of T on nd T off is the switching period T, thus s T T T on off 1 f s e c PWM D Converter v Figure 2.2.3() 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 3 July 2011

v c v tri t PWM output: High for T ON (when v c > v tri ) Low for T OFF (w hen v c < v tri ); t Figure 2.2.3(b) 2.2.2.3 Armture voltge with continuous conduction We ssume tht E = constnt (i.e., constnt speed nd field excittion). The DC supply voltge V s is ssumed to be smooth nd constnt. The switch opertes with duty cycle D nd the voltge nd current wveforms of the motor nd its bck-emf re s given below I mx I V I min T ON T OFF T s Figure 2.2.4 The verge DC voltge cross the rmture circuit is (from Buck converter nlysis) 1 VDT V V dt DV V (2.2.2) DT s s s s s Ts 0 Ts The ripple content of v my cuse significnt losses leding to motor derting. This lso is prtly responsible for motor torque ripple nd udible noise. The converter type (especilly for the phse controlled converter), switching frequency f s nd rmture circuit inductnce L re selected to llevite these problems to the extent desired. The ripple in v re expressed conveniently with MS vlues of the hrmonic voltge components nd fctor clled the ipple Fctor (F). The ripple voltge components of the rmture voltge v re given by the Fourier series s, 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 4 July 2011

1 V n v cos n t d t sin 2n D 0 n 2 s (2.2.3) 1 V bn v sin n t d t 1 cos 2n D 0 n 2 s (2.2.4) ˆ 2 2 2V cn Vn n b s n sin n D n (2.2.5) 1 bn n tn n D n 2 (2.2.6) Thus, the MS ripple voltge of ny hrmonic number is mximum when D = 0.5. The totl MS vlue of v is given by DT 1 s 2 MS s s V (2.2.7) T s 0 V V dt D V 2 2 2 2 2 1 2 3 4 V V V V V... (2.27) where Vˆ 1 Vˆ 2 Vˆ 3 V 1 ; V 2 ; V 3 ;.. 2 2 2 The MS vlue of the AC voltge cross the rmture is 2 2 2 2 cms 1 2 3 4 V V V V V... (2.2.8) for ll n except n = 0, Also, 2 2 cms MS V V V (2.2.9) The ipple Fctor (F) is expressed s F 2 2 VcMS VMS V 1 D (2.2.10) V V D 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 5 July 2011

2.2.2.4 Armture current with continuous conduction Assuming constnt bck-emf (i.e., constnt speed), the solution for the rmture current i cn be obtined s given below: During intervl 0 t T on di Vs i L E (2.2.11) dt Solving, t s E L L min t i 1 e I e V V E s t/ t/ 1 e Imine (2.2.12) At the end of T on (i.e., DT s ), the i reches its mximum vlue i mx. Thus, mx V E s DT s / DT s / min I 1e I e (2.2.13) During intervl DT s t T s The rmture current free-wheels through the diode nd the motor input voltge is zero (the forwrd diode drop is neglected). Thus, di 0 i L E (2.2.14) dt' where t' t Ton t DTs. Solving (2.2.14) t'/ t'/ i 1e I e (2.2.15) E mx In the stedy-stte, i becomes I min when t' Toff Ts DT s (1 D)Ts. Thus E Imin 1 e I e (1D)T / (1D)T / mx s s (2.2.16) Solving (2.2.13) nd (2.2.16) symultneously, I DT s / Vs 1 e mx T s / 1 e E (2.2.17) 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 6 July 2011

I DT / Vs min T / s e 1 s e 1 E (2.2.18) Îripple ImxImin V S DTS/ DTS/ 1 e VS e 1 TS/ TS/ 1e e 1 (2.2.19) 2.2.3 T- chrcteistics with continuous conduction By obtining I min nd I mx, we cn determine the rmture current wveform completely. It is then possible to find its verge vlue, I, nd therefore the developed torque ( k ' T fi). ecognising tht the nlysis is strted with the ssumption of costnt speed (or ), we therefore find the developed torque for the ssumed speed (or bck-emf). By repeting this clcultion, we find the complete torque speed chrcteristic of the motor for the D selected. While this method is trivil for continuous conduction, which the lterntive steps below will indicte, the method is generl, nd useful for generl nlysis or modeling of DC drive. 2.2.3.1 Anlysis for continuous conduction In the stedy-stte, the voltge drop cross L is zero, so tht ssuming continuous conduction, V DVs I E (2.2.20) ' E f m s E K DV I (2.2.21) I DVs E (2.2.22) DV I DV I (2.2.23) s s m ' ' KE f KEK f I f The torque-speed chrcteristic of the motor cn be found from eqution 2.2.23, by replcing I with the expression of torque interms of I. For exmple, for seprtely excited motor with rted field excittion, I T / K T, so tht T DVs KT m (2.2.24) KE 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 7 July 2011

Speed, rpm 1600 1400 1200 1000 800 600 400 200 Q1 D = 1 D = 0.8 D = 0.6 D = 0.4 D = 0.2 0 0 50 100 150 Torque, Nm Figure 2.2.5 T- chrcteristics of SE DC motor drive under 1Q PWM converter drive (with CCM) 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 8 July 2011

2.2.4 Opertion with discontinuous current The rmture current cn become discontinuous t ny speed if the lod is light. Note tht t V zero lod, i is zero nd the motor runs t. During the time when the rmture ' KE f current is zero in ech switching period, trnsistor T nd the freewheeling diode D (refer to figure 2.2.2) re both off nd the rmture voltge v is no longer zero becuse the bck emf of the rmture then ppers cross the rmture terminls, s indicted in figure 2.2.6. T I V s L D E Figure 2.2.6(). Power Circuit I mx V DC T on T of E T on Figure 2.2.6(b). Wveforms 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 9 July 2011

A. Armture voltge with disc conduction The rmture current flls to zero t time t (corresponding to the conduction ngle ). The rmture voltge is now v V for 0 t DT s s = 0 for DT s t t = E for t t T s The verge vlue of the rmture voltge is V 1 T s 0 T s v dt t DVs 1 E Ts (2.2.25) The MS rmture voltge is DTs T 1 s 2 2 VMS Vs dt E dt T s 0 t DV t 1 E 2 2 s Ts (2.2.26) It cn be shown tht the Fourier compnents of the rmture voltge with discontinuoud conduction re: Vs E t n sin2nd sin2n n n Ts Vs E 2 nt bn 1 cos2 nd 1 cos n n Ts (2.2.27) (2.2.28) c Vˆ b (2.2.29) 2 2 n n n n B. Armture current with discontinuous conduction During 0 t DT s With discontinuous current, rmture current strts in ech switching from zero becuse I min is zero. Thus, from (2.2.12), Vs E i 1 e t/ (2.2.30) 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 10 July 2011

The mximum rmture current will occur t t = DT s, so tht Vs E Imx 1 e DT / s (2.2.31) During freewheeling (i.e., diode conducting) From (2.2.15) i 1 e I e E t'/ mx t'/ E V E ( tdt s ) / s DT s / ( tdt s ) / 1e 1 e e (2.2.32) The rmture current i becomes zero t t = t, so tht, DT s/ E V E 0 1e 1 e e (t DT s )/ s (t DT s )/ V E t lne 1 1e E DT / s DT / s s (2.2.33) The boundry between continuous nd discontinuous conduction for given E is defined when I min in eqution (2.2.18) just flls to zero t T s, i.e., t t = T s, stisfying the condition, D'T / s E e 1 T s / V e 1 s (2.2.34) where D' is the duty cycle t the boundry between continuous nd discontinuous conduction for given E. D' cn be found from (2.2.33) by setting t = T s. For given E. If D > D', then conduction is continuous or if D < D', then conduction is discontinuous Eqution 2.2.34 gives the dotted boundry between continuous nd discontinuous conduction in figure 2.2.4, for given motor for vrious duty cycle D nd bck-emf E. The rmture inductnce L, or rther the time constnt, L, hs importnt role in determining the conduction of current in the rmture. The higher the inductnce the lower is the likelyhood of discontinuous current. Once t is found from (2.2.33), the DC vlue of rmture voltge V, is then esily clculted from (2.2.25). It should be noted tht with discontinuous conduction, motor speed drops more rpidly with increse of lod torque 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 11 July 2011

implying poor speed regultion. ise of speed during discontinuous conduction lso implies loss of gin of the converter supplying the rmture. Hence discontinuous conduction should be voided by proper selection of rmture inductnce L nd switching frequency, f s. The motor inductnce nd switching frequency re normlly so chosen tht the rmture current remins continuous for the lightest lod. Note tht these two items cn not often be chosen freely, becuse there re prcticl nd cost constrints tht pply. m DC CCM D = 1 D = 0.75 D = 0.5 D = 0.25 T, Nm Figure 2.2.7. Torque-speed chrcteristic of S. E. DC motor with continuous conduction 2.2.5 Anlysis of rmture current wveform from Fourier series The rmture current wveform contins ripples which cuses dditionl motor heting nd torque pulstion. The dditionl (i 2 ) heting effect is more conveniently shown in terms of the MS rmture current given by, 2 2 2 2 IMS I I1 I2 I 3... (2.2.35) where I 1, I 2, I 3, nd so on re the MS vlues of ripple components of current in the rmture. These cn be found by dividing ech component of the ripple voltge by the rmture impednce to the corresponding ripple frequency. CCM f s = 5kHz, D = 0.5 FFT of v under CCM nd DCM conditions. DCM 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 12 July 2011

Thus I n ˆV / 2 n 2 nl 2 (2.2.36) where ˆV n is the pek vlue of the sinusoidl ripple component of frequency n. It is given by c n in equtions 2.2.5 (for continuous conduction) or 2.2.27-29 (for discontinuous conduction). The input power to the rmture, ignoring other losses, cn be written s T s 2 (2.2.37) 0 1 P v i dt I E I in MS Ts Note the DC power input to the motor, neglecting core losses, is given by 2 P I E I (2.2.38) The second terms on the HS of equtions 2.2.37 nd 2.2.38 represent the developed power which includes mechnicl power to lod nd friction nd windge. The iron losses (hysteresis nd eddy-current) re not represented by these descriptions. 2.2.6 egenertive PWM converter driven S. E. DC motor - Opertion in Qudrnt 2 A regenertive converter (Type 2) is used to drive the DC motor in qudrnt 2 for efficiently brking the motor in the forwrd direction. ecll tht opertion in qudrnt 1 is for forwrd motoring while opertion in qudrnt 2 if forwrd brking. In this qudrnt, the motor hs positive bck emf nd its rmture is mde to flow in the reverse (negtive) direction using the bck emf to force it. This is indicted in figure 2.2.8. D L E V s I + T Figure 2.2.8. egenertive converter drive. With regenertive drive in qudrnt 2, the motor speed is positive (i.e., in forwrd direction). When the switch T is ON, the voltge pplied to rmture is zero nd the rmture current reverses nd becomes more negtive (i.e., flls). When the switch is OFF, the rmture inductnce L forces the rmture current to flow through diode D bck to dc source ginst V s, becomes less negtive (i.e., rises) with time, nd returns some of the rottionl energy of the motor bck to the dc source. These trnsients re indicted in figure 2.2.9. 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 13 July 2011

(1D)T s DT s Figure 2.2.9 2.2.6.1 Anlysis of rmture current in Qudrnt 2 with CCM nd constnt bck emf. With the ON nd OFF times defined s mentioned bove nd shown in figure 2.2.9, for 0 t T on V E L di i dt s (2.2.39) nd for t - T on t T s, di 0 i L E (2.2.40) dt Equtions 2.2.39 nd 2.2.40 re the sme s equtions 2.2.11 nd 2.2.14 for the sme conditions of opertion, so their soultions should be identicl. Thus, from equtions 2.2.17-2.2.19, I DT s / Vs 1 e mx T s / 1 e E (2.2.41) I DT / Vs min T / s e 1 s e 1 E (2.2.42) Îripple I mx I min (2.2.43) 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 14 July 2011

With continuous conduction nd stedy-speed opertions in qudrnt 2, equtions 2.2.20-2.2.24 will lso pply, so tht stright-line T- chrcteristics of figure 2.2.4 extends into qudrnt 2 with slopes of the chrcteristics unchnged. D = 1.0 D = 0.75 D = 0.5 m, rpm D = 0.25 T, Nm 0 Figure 2.2.10 T- chrcteristics in qudrnt 2 with CCM 2.2.7 Two nd four qudrnt opertion of PWM DC drive 2.2.7.1 Two-qudrnt PWM DC-DC converter drive The forwrd driving (Type 1) nd regenertive (Type 2) converters of figure 2.2.2(b) nd 2.2.8 respectively, cn be combined into 2-qudrnt drive, s shown in figure 2.2.11. T1 nd D2 comprise the forwrd motoring converter; T2 nd D1 comprise the forwrd regenertive converter. With complementry switching of T1 nd T2, the current (in blue) in figure 2.2.13 my flow in both directions in ech cycle of switching. This 2-qudrnt converter drives DC motor with fst ccelertion nd decelertion in the forwrd direction, llowing opertion in qudrnts 1 nd 2. Qudrnts covered by this converter re shown in Figure 2.12. T 1 D 1 I L E V s T 2 D 2 Figure 2.2.11 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 15 July 2011

DT s (1D)T s Figure 2.2.12 1600 1400 D = 1 1200 D = 0.8 Speed, rpm 1000 800 600 400 Q2 Q1 D = 0.6 D = 0.4 200 D = 0.2 0-150 -100-50 0 50 100 150 Torque, Nm Figure 2.2.13 T- chrcteristics of SE DC motor drive under 2Q PWM converter drive (CW with CCM) 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 16 July 2011

2.2.8 Four-Qudrnt Converter Four qudrnt choppers re normlly used for driving servo motors bi-directionlly with fst response. Driving nd regenertive brking re obtined in both directions through the sme converter. Two switching schemes re normlly used. The switching frequency is generlly in the bnd from 10 to 20 khz to reduce udible noise. V, T1 D1 T3 D3 I L V s T4 D4 T 2 D2 I, T Figure 2.2.14 Four qudrnt drive Figure 2.2.15 Qudrnts 1500 D = 1 1000 Q2 Q1 D = 0.6 Speed, rpm 500 0-500 -1000 Q3 Q4 D = 0.2 D = 0.2 D = 0.6-1500 D = 1-150 -100-50 0 50 100 150 Torque, Nm Fig. 2.2.16 T- chrcteristics of SE DC motor drive under 4Q PWM converter drive (with CCM). 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 17 July 2011

2.2.9 Two-qudrnt converter for motor field circuit The regulted field circuit of DC mchines requires unidirectionl current. However, it my require high dynmic response, especilly when field wekening is used bove bse speed. The regenertive circuit of figure 2.2.16 is suitble for such pplictions. T1, T2 with D1 regulte the field current t the required the DC level. Normlly T1 is ON continuously. Increse in I f is rrnged through duty-cycle control of T2. When reduction in I f is required, T1 is turned off nd T2 is modulted so s to pply V f cross the field coil when T2 is off. The inductive energy of L f is thus regenerted into field DC source V f to force quick reduction in I f. T 1 I f f L f D2 V f V f D1 T 2 I f Figure 2.2.17 2.2.10 Switching Scheme A. Bipolr switching scheme In this scheme, digonl trnsistor pirs re switched together in ech switching cycle. The two trnsistors in ech rm re switched in complementry mnner. When pir of trnsistors is turned off, the rmture current previously flowing through the trnsistors is forced to flow bck to the dc mins vi the feedbck diodes. B. Unipolr Scheme In this scheme, only one trnsistor in digonl pth my be turned off t ny one time to regulte the current through the motor to given reference vlue. The other trnsistor is kept on to free-wheel the rmture current. Becuse the rmture current now hs freewheeling pth without hving to flow throgh the DC source, this switching scheme reduces the mplitude of current ripple in the motor. Both switches in digonl pth re turned on only during regenertive opertion. 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 18 July 2011

2.2.11 PWM switching frequency The following should be considered before selecting the switching frequency. for the switching frequency the following should be stisfied 2fsL >> High switching frequency reduces the current ripple I I losses. It lso voids discontinuous conduction. mx nd motor f s should be much higher thn thecurrent nd speed control bndwidths. Thus f s > 10 current nd control bndwidths. min f s should be higher thn ny significnt resonnt frequencies. f s should be sufficiently high to void udible noise. Too high switching frequency will result in excessive switching losses in the switching devices (trnsistors). Too high switching frequency limits the rnge of output nd introduces offset into the power converter input-output chrcteristics. At high switching frequencies the finite dely times of gte switching circuits nd ded-times for device protection my become comprble to the switching period. 2.2 PWM converter driven F. hmn (EET, UNSW) DC motor drives 19 July 2011