PULSEWIDTH-modulated (PWM) voltage-source inverters

Transcription

1 674 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 Carrer-Based PWM-VSI Overmodulaton Strateges: Analyss, Comparson, and Desgn Ahmet M. Hava, Student Member, IEEE, Russel J. Kerkman, Fellow, IEEE, and Thomas A. Lpo, Fellow, IEEE Abstract In ths paper, the overmodulaton regon voltagegan characterstcs and waveform qualty of carrer-based pulsewdth-modulated (PWM) methods are nvestgated. Through detaled analytcal study, voltage-gan characterstcs are extracted ndependent of carrer frequency. The nfluence of blankng tme and mnmum pulsewdth (MPW) control on the nverter gan characterstcs are studed and shown to be sgnfcant. A comparatve evaluaton of the modulator characterstcs reveals the advantageous hgh-modulatonrange characterstcs of dscontnuous PWM methods and, n partcular, the superor overmodulaton performance of a dscontnuous PWM method. The modulaton methods under consderaton are tested on a PWM voltage-source nverter (VSI)- fed nducton motor drve n the laboratory, and the theoretcal results are verfed by experments. Also, a gan lnearzaton technque s presented and expermentally verfed. The results of ths study are useful n desgn, performance predcton, and development of hgh-performance overmodulaton strateges for PWM-VSI drves. Index Terms Current harmoncs, nverter, overmodulaton, voltage gan. I. INTRODUCTION PULSEWIDTH-modulated (PWM) voltage-source nverters (VSI s) are wdely utlzed n ac motor drve applcatons and at a smaller quantty n controlled rectfer applcatons as a means of dc ac power converson devces. Many PWM-VSI drves employ carrer-based PWM methods due to ther fxed swtchng frequency, low rpple current, and well-defned harmonc spectrum characterstcs. Utlzng the conventonal VSI structure shown n Fg. 1, whch has eght dscrete voltage-output states, carrer-based PWM methods program a per carrer cycle average output voltage equal to the reference voltage. Employng the trangle-ntersecton technque [1] or drect dgtal pulse programmng technque [2], carrer-based PWM methods provde a lnear relatonshp between the reference and output voltages wthn a lmted range. The lnear voltage range of a PWM-VSI drve s manly determned by the modulator characterstcs. Inverter blankng tme and mnmum-pulsewdth constrants can further reduce Manuscrpt receved September 17, 1996; revsed June 8, Recommended by Assocate Edtor, D. Torrey. A. M. Hava s wth Yaskawa Electrc Amerca, Inc., Northbrook, IL USA. R. J. Kerkman s wth Rockwell Automaton-Allen Bradley, Mequon, WI USA (e-mal: rjkerkman@meq1.ra.rockwell.com). T. A. Lpo s wth the Electrcal and Computer Engneerng Department, Unversty of Wsconsn, Madson, WI USA (e-mal: hava@cae.wsc.edu; lpo@engr.wsc.edu). Publsher Item Identfer S (98) the range of lnearty by a consderable amount. As a result, the voltage lnearty of a drve, for example, n the snusodal PWM (SPWM) case, can be lost at as low a value as 70% of the sx-step voltage. Fg. 2 llustrates the typcal lnear and nonlnear range modulaton waveforms of the SPWM method and swtchng devce gate logc sgnals. The porton of the modulaton wave havng a larger magntude than the trangular wave peak value remans unmodulated, and the gate sgnals reman on or off for a full carrer cycle leadng to a nonlnear reference output-voltage relatonshp. Operatng n the nonlnear modulaton range, or n more common terms, the overmodulaton range s problematc: 1) large amounts of subcarrer frequency harmonc currents are generated; 2) the fundamental component voltage gan sgnfcantly decreases; and 3) the swtchng devce gate pulses are abruptly dropped. In constant -controlled PWM-VSI nducton motor drves, operaton n ths range results n poor performance, and frequent overcurrent fault condtons occur. In current-controlled drves, n addton to the nherent modulator subcarrer frequency harmonc-dstortondependent waveform degradaton, current-regulator-dependent performance reducton results. The current regulators are heavly burdened by the feedback current subcarrer frequency harmoncs and regulator saturaton and oscllatory operatons result n addtonal performance degradaton. On the other hand, full nverter voltage utlzaton s mportant from cost and power densty mprovement perspectves. Also, a drve wth hgh-performance overmodulaton range operatng capablty s less senstve to nverter dc-bus voltage sag, whch often occurs n dode-rectfer front-end-type drves due to aclne voltage sag or fault condtons, hence, ncreased drve relablty. Recently, overmodulaton ssues have attracted the attenton of many researchers, and overmodulaton strateges for the two popular methods SPWM [3], [4] and space-vector PWM (SVPWM) [5], [6] have been developed. However, the overmodulaton characterstcs of many other carrer-based PWM methods have not been explored, nor has a comparatve study been reported. Ths study nvestgates the overmodulaton range voltagegan characterstcs and waveform qualty of several popular carrer-based PWM methods employng the tranglentersecton technque. The detaled comparatve study reveals the advantageous attrbutes of a dscontnuous modulaton wave PWM method, and a smple gan lnearzaton technque provdes modulator lnearty untl the sx-step mode. The theoretcal results are verfed by laboratory experments /98$ IEEE

2 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 675 Fg. 1. Man power converter structure of the wdely utlzed dode-rectfer front-end-type PWM-VSI drve. Fg. 2. SPWM modulaton waveforms and swtchng devce gate logc sgnals. Lnear modulaton range. Overmodulaton range. II. REVIEW OF CARRIER-BASED PWM METHODS There are two wdely utlzed carrer-based PWM mplementaton technques: the drect dgtal gate pulse programmng technque and the trangle-ntersecton technque. In the drect method, the gate sgnal on-state tmes and are calculated from the space-vector voltage equaton and drectly programmed. The space-vector PWM methods, whch vary dependng on the parttonng of two nverter zero states, generally employ the drect method [2], [7]. In the trangle-ntersecton technque [1], three reference modulaton waves and are compared wth trangular carrer waves to generate the swtch gate sgnals. In solated neutral-type loads, the freedom to add a zero-sequence sgnal to the modulaton waves leads to a large varety of modulaton waves, hence modulaton methods [8], [9]. As shown n Fg. 3, n the zero-sequence sgnal njecton method, the reference modulaton waves and are utlzed to compute a zero-sequence sgnal. Addng to the orgnal reference sgnals, the modfed reference sgnals and are obtaned, and comparng these sgnals wth the carrer wave yelds the gate sgnals. In addton to SPWM [1], several hgh-performance zero-sequence sgnal njecton methods such as the thrd-harmonc njecton PWM (THIPWM) [10], Depenbrock s dscontnuous PWM (DPWM1) method [11], [12], and the zero-sequence sgnal njecton method equvalent of the conventonal SVPWM method [13], [14] also employ the trangle-ntersecton technque. The tranglentersecton technque has been tradtonally mplemented by analog hardware. Recently, varous mcroprocessors ( P) and dgtal sgnal processor (DSP) chps wth bult-n fully dgtal trangle-ntersecton-based PWM capablty have been developed and found a wde range of applcatons n fully dgtal PWM-VSI drves. In ths study, trangle-ntersecton-based technques wll be consdered. Although the overmodulaton swtchng patterns of the drect dgtal mplemented PWM methods may be qute smlar to trangle-ntersecton mplementatons of PWM methods, the overmodulaton strateges of the drect dgtal method [5], [6] are qute dfferent and more complex. Wth smplcty and the degree of mprovement over the exstng methods as the man crtera, of the many methods developed, only a small number of modulaton methods have ganed wde acceptance [9]. Due to ts smplcty, the SPWM method has found a wde range of applcatons. The conventonal SVPWM, ts trangle-ntersecton mplementaton, and THIPWM methods are preferred n hghperformance drves due to the wder lnear range and reduced carrer frequency harmonc dstorton characterstcs they provde compared to the SPWM method. Two modulators wth dscontnuous modulaton waves, classfed as dscontnuous PWM (DPWM), Depenbrock s DPWM1 [11], and Ogasawara s DPWM2 [7] methods, have ganed recognton due to ther low harmonc dstorton at hgh-voltage utlzaton and the controllablty of the swtchng losses [8]. The frst mplementaton of DPWM2 employed the drect dgtal mplementaton technque, whle the trangle-ntersecton mplementaton and therefore the modulaton wave appeared n the followng years [15]. Fg. 4 shows the modulaton waves of the dscussed modulators at 72% of the sx-step voltage. In the fgure, unty trangular carrer wave gan s assumed, and the modulaton sgnals are normalzed to. Therefore, saturaton lmts correspond to 1. The overmodulaton voltage-gan characterstcs of these modulators wll be nvestgated n detal n ths paper.

3 676 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 Fg. 3. Trangle-ntersecton technque-based generalzed zero-sequence njecton PWM dagram. Fg. 4. Modulaton waveforms of the popular PWM methods (M =0:72). The voltage lnearty, harmonc dstorton, and overmodulaton range performance characterstcs of a modulator are manly dependent on the voltage-utlzaton level,.e., modulaton ndex. At ths stage, a modulaton ndex defnton s requred. For a gven dc-bus voltage, the rato of the fundamental component magntude of the lne to neutral nverter output voltage to the fundamental component magntude of the sx-step mode voltage s termed the modulaton ndex [9] Usng ths defnton, full voltage utlzaton (sx-step operatng mode) occurs at. Normalzng the trangular wave peak-to-peak sgnal magntude to, t follows that SPWM s lnear modulaton range ends at, a modulaton ndex of. The voltage lnearty of a modulator can be sgnfcantly ncreased by njectng a zero-sequence sgnal. The theoretcal lmt of SVPWM can be easly calculated by evaluatng the modulaton sgnal at the 60 pont, where the zero-sequence sgnal becomes zero and ths (1) calculaton yelds. The theoretcal lnearty lmt of all the dscussed zero-sequence njecton PWM methods s equal to ths nverter theoretcal lmt. Wthn the lower porton of the lnear modulaton range, SPWM, SVPWM, and THIPWM demonstrate better performance characterstcs than the two dscontnuous PWM methods, whle n the hgh-modulaton regon, the opposte s true [8]. In addton, wth the dscontnuous PWM methods, the modulator characterstcs have sgnfcant nfluence on the nverter swtchng losses: under the same nverter average swtchng frequency crtera, DPWM1 has reduced losses for unty power factor loads [15], and DPWM2 has reduced losses for 30 laggng loads [7], [15] compared to SPWM and SVPWM. Therefore, the lnear modulaton range performance of a PWM-VSI drve can be enhanced by selectng SPWM, THIPWM, or SVPWM n the low-modulaton range, and DPWM1 or DPWM2 n the hgh-lnear-modulaton range. However, at ths pont t s not clear whch modulator has better performance n the overmodulaton range. Also, the nfluence of nverter nondealtes such as blankng tme and mnmum pulsewdth (MPW) control on the lnearty lmt

4 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 677 of a modulator s not quantfed. From the perspectve of optmzng the overall performance, the overmodulaton range performance characterstcs of these modulaton methods must be evaluated. Ths paper s dedcated to a detaled study of the overmodulaton regon. III. OVERMODULATION RANGE VOLTAGE-GAIN CHARACTERISTICS In the trangle-ntersecton technque, when the modulaton wave magntude becomes larger than the peak of the trangular wave, swtchng durng that carrer cycle ceases and the correspondng swtch remans locked to the nverter pole wthn the carrer cycle. In the begnnng of the overmodulaton regon, dependng on the modulator type, one or two of the three modulaton waves are smultaneously saturated. As the modulaton ndex ncreases, the saturated segments of each modulaton wave and the number of smultaneously saturated phases ncrease accordng to the waveform characterstc of each modulator untl the sx-step mode s reached. When saturaton occurs, the reference per carrer cycle average voltage cannot be matched by the nverter, and a voltage-gan reducton results. Ths nonlnear voltage-gan relaton can be analytcally modeled by Fourer analyss of the saturated modulaton wave ndependently of the carrer frequency. The voltage gan calculated wth ths method s hghly accurate. Detaled computer smulatons ndcated for, the relatve gan error s less than 0.5% and the error sgnfcantly decreases wth ncreasng. Snce the wdely utlzed PWM-VSI drves employng nsulated gate bpolar transstor (IGBT) devces typcally have hgh values, the model successfully represents most nverter drves. Utlzng the modulaton ndex defnton, general formulas can be derved ndependent of the nverter voltage. Except for the SPWM method, the voltage-gan formulas of the carrer-based PWM methods have not been reported, nor has a detaled gan characterstc study been conducted [4], [16]. In the followng, the gan formulas of the dscussed modulators are derved, and a comparatve evaluaton follows. The fundamental component voltage gan of a modulator s the rato of the output-voltage fundamental component peak value to the reference modulaton wave fundamental component peak value. Utlzng the modulaton ndex and reference modulaton ndex defntons, t can also be expressed n terms of the modulaton ndexes as The gan formulas developed below have the followng applcatons: 1) fundamental component VSI overmodulaton modelng; 2) lnearzng the nverter gan block n the controller; 3) they provde smple tools for gan analyss and comparsons of modulators. A. Snusodal PWM The fundamental component of the saturated snusodal modulaton wave can be calculated by employng Fourer (2) Fg. 5. SVPWM trangle-ntersecton method modulaton waveforms n the overmodulaton regon. Regon I. Regon II. analyss, and the result can be expressed n terms of the modulaton ndex relatons n the followng [4], [16]: Snce the output-voltage fundamental component s dfferent from the reference voltage, the output modulaton ndex has a dfferent value from the reference modulaton ndex. Utlzng the defnton of (2), the fundamental component voltage relaton can be expressed by the followng gan functon: B. Space-Vector PWM Generatng the modulaton wave of conventonal SVPWM method s qute smple. Of the three snusodal modulaton waves, the one wth the smallest magntude s multpled by a coeffcent of to generate the zero-sequence sgnal [14]. Addng ths sgnal to all the reference waves results n a modulaton wave whch s very smlar to THIPWM modulaton wave. The overmodulaton range characterstcs of the tranglentersecton mplementaton of the SVPWM, therefore, can be closed-form modeled n the same manner as SPWM. As llustrated n Fg. 5, the overmodulaton regon conssts of two subregons. Regon I has two ntersectons between the saturaton lne and the modulaton waveform per quarter wave whle Regon II has only one ntersecton. Employng Fourer analyss, the fundamental component modulaton ndex and voltage-gan relatons of overmodulaton Regon I are found as follows: (3) (4) (5) (6)

5 678 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 Fg. 6. THIPWM waveforms n the overmodulaton regon. Regon I. Regon II. Regon II begns at, and the modulaton ndex and gan relatons n ths regon are calculated as follows: C. Thrd-Harmonc Injecton PWM The zero-sequence sgnal of THIPWM can be algebracally defned as [10]. The overmodulaton voltage-gan relatons of ths method are qute smlar to the SVPWM methods. As shown n Fg. 6, n Regon I, the modulator waveform ntersects wth the saturaton lne twce per quarterfundamental cycle. The ntersecton angles are calculated from the followng transcendental equaton: The above equaton can be easly solved by teratve methods. Utlzng the ntersecton angle values, the reference output-voltage relatonshp can be computed by the followng formula establshed by the Fourer analyss of the modulaton wave: (7) (8) (9) Fg. 7. DPWM1 method overmodulaton waveforms. packages. Once the modulaton ndex values are calculated, the gan can be easly computed from (2). The thrd-harmonc njecton PWM method wth a slghtly better lnear modulaton regon waveform qualty than the above method ( [17]) loses lnearty at, and ts overmodulaton gan characterstc can be evaluated followng the same algebrac steps descrbed n ths secton. The gan characterstc of ths modulator s very smlar to the conventonal THIPWM method, and further detals can be found n [18]. D. Depenbrock s Dscontnuous PWM Method (DPWM1) In ths farly old method [11], [12], the zero-sequence sgnal generaton steps are smple. Of the three reference snusodal modulaton waves, the one wth the largest magntude determnes the zero sequence. The dfference between the dc-bus ral wth the same polarty as ths modulaton wave and the modulaton wave s equal to the zero-sequence sgnal. Assume that s the sgnal wth the largest magntude. Then,. Addng such a zero sequence to the reference sgnals, dscontnuous modulaton waves wth two 60 saturated segments result. As shown n Fg. 7, once n the overmodulaton range, the saturated segments ncrease beyond the 60 value of the lnear modulaton range, and the modulaton wave s upward shfted by an amount dependent on the modulaton ndex value. Fourer analyss of the saturated wave yelds the followng: (10) The above formula s vald untl the reference modulaton ndex value of and then Regon II begns whle n Regon II, only one ntersecton pont exsts and can be calculated from (9). Fnally, the modulaton ndex can be calculated from the Fourer analyss derved formula as follows: (12) (11) Although the above formulas are dependent on the ntersecton angles and dffcult to completely wrte n full closed form, they can be easly evaluated by smple numercal software (13)

6 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 679 Fg. 8. DPWM2 method overmodulaton waveforms. Regon I. Regon II. E. Ogasawara s Dscontnuous PWM Method (DPWM2) In ths method, the zero-sequence sgnal s generated n a manner smlar to DPWM1. The three reference snusodal modulaton waves are phase shfted by 30 (laggng), then the sgnal wth the maxmum magntude defnes the nverter leg to be unmodulated. The zero-sequence sgnal s the dfference between the orgnal modulaton wave defned by the maxmum magntude test and the saturaton lne wth the same polarty as ths modulaton wave. The resultng modulaton wave s not quarter-wave symmetrc, hence, the overmodulaton voltagegan equatons are complex compared to the prevous cases. As shown n Fg. 8, the overmodulaton regon s dvded nto two subregons. In the frst subregon, as shown n Fg. 8, the modulaton wave has four saturated segments per fundamental cycle. Employng Fourer analyss and utlzng the ntermedate varables and, the voltage relatons n the frst regon can be calculated from the followng: (14) Fg. 9. The overmodulaton regon voltage-gan characterstcs of the popular modulators. (15) (16) (17) The second subregon begns at. Shown n Fg. 8, the modulaton wave heavly saturates, and on each sde two saturated segments merge, leadng to only two saturated segments per cycle. Introducng the varable, the coeffcents and can be calculated as follows: (18) (19) (20) Once the above coeffcents are known, the reference outputvoltage relatons can be calculated from (17) and the voltage gan can be calculated n both subregons from the defnton of (2). IV. VOLTAGE-GAIN COMPARISONS In ths secton, the voltage-gan characterstcs of all the dscussed modulators are comparatvely evaluated. The comparsons are provded n terms of the voltage gan and modulaton ndex relatons. Utlzng the gan functons derved n the prevous secton, the gan characterstcs of the canddate modulators are calculated and llustrated n Fg. 9. The mprovement n the lnearty range of all the zero-sequence njecton methods compared to SPWM s obvous from the fgure. More mportantly, the graph reveals the unusual gan characterstc of Depenbrock s DPWM1 method: the gan of ths modulator drops at a sgnfcantly smaller rate than all the other modulators, and the mnmum value, whch occurs at the sx-step operatng pont, s. All the other modulators have a rapd drop n gan, and eventually the gan becomes practcally zero at the sxstep operatng pont. The smlarty of ther gan characterstcs wth respect to each other s also obvous from the fgure. Shown n Fg. 10 and llustrated n terms of the modulaton ndexes, the nput output-voltage relatons provde more specfc nformaton. Except for DPWM1, all the modulators

7 680 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 requre large reference sgnals n order to penetrate the overmodulaton regon. In partcular, DPWM1 requres a reference sgnal wth a magntude of, whle the other modulators requre sgnals wth very large magntudes. Ths result s extremely mportant from an mplementaton perspectve: the smaller the gan range, the better the accuracy of the modulaton sgnal and the smaller word length requrement of a sgnal processor (or the sgnal range n an analog mplementaton). Therefore, DPWM1 utlzes the sgnal range of a processor wth hgh resoluton and abrupt pulse droppng, and the consequent overcurrent fault condton s avoded. The unusual gan characterstc of DPWM1 s not dffcult to explan. In the overmodulaton range, the zero-sequence sgnal of ths modulator s effectvely a square-wave functon wth an ncreasng magntude as the sx-step operatng pont s approached. Therefore, n ths method, the modulaton wave s vertcally and horzontally forced to approach the sx-step mode, whle the other zero-sequence njecton methods force the modulaton wave to expand manly horzontally untl the sx-step mode s generated. Ths characterstc of DPWM1 can be clearly observed n Fg. 11, where DPWM1 and SVPWM modulaton waveforms are compared for a set of reference modulaton ndex values. It s apparent that as the reference modulaton ndex ncreases, the SVPWM modulaton wave saturates heavly, whle the DPWM1 modulaton wave easly approaches the square wave. Fg. 10. Overmodulaton regon M = f(m 3 ) characterstcs. lmt. The lowest modulaton level at whch ths problem occurs can be easly calculated. When the modulaton sgnal s postve, the narrow pulse occurs when the upper nverter leg swtch s the off state wth a duraton calculated as follows: (21) V. INFLUENCE OF BLANKING TIME AND MINIMUM PULSEWIDTH ON MODULATOR GAIN Inverter blankng tme s the tme nterval that both swtches of an nverter leg are open followng a change n the gate logc reference sgnal value. It s provded for protecton aganst the dc-bus short crcut. As shown n Fg. 12, the blankng tme crcut delays the reference gate sgnals by the blankng tme and results n loss of gate sgnal symmetry (ncreases the uncharacterstc harmoncs) and also a reducton n the output-voltage value. Typcally, a gate-pulse-correcton (compensaton) algorthm s employed n order to restore the symmetry and volt-second balance [19]. As shown n Fg. 12(c), n the exact compensaton method, f the polarty of the phase current of the correspondng nverter leg s postve (negatve), the reference gate sgnal on the trangle sde wth negatve (postve) slope s advanced (delayed) by the blankng tme, leadng to the correct output-voltage pulse. When a modulator operates near ts theoretcal lnearty lmts, as shown n Fg. 12, narrow gate pulses are generated. When the wdth of such pulses becomes smaller than, the compensaton algorthm fals to correct the pulses properly. In Fg. 12(c), ths condton corresponds to and correct compensaton requres nterference wth the modulaton sgnal n the prevous half-carrer cycle. Snce n the conventonal dgtal PWM methods the reference modulaton sgnal s generated only at the postve and/or negatve peak ponts of the trangular carrer wave (regular samplng), correct compensaton of such a narrow pulse s not possble. Hence, voltage-gan reducton occurs before the theoretcal lnearty Substtutng the modulaton wave peak value of the modulator under nvestgaton n the above formula and selectng the mnmum pulse wdth equal to, the practcal maxmum lnear modulaton ndex can be found as follows: (22) In the above formula, s the theoretcal lnearty lmt of the modulator. The coeffcent dstngushes the dscontnuous PWM methods from the contnuous-wave modulaton methods. Its value s for the DPWM methods and for the modulators wth contnuous modulaton wave. The small coeffcent of the DPWM methods ndcates that DPWM methods have a wder voltage lnearty range than SPWM, SVPWM, and other contnuous-wave PWM methods. Ths result s a consequence of the dfferent dstrbuton of the nverter zero states n the two dfferent modulaton groups. The dscontnuous PWM methods generate only one nverter zero state per carrer cycle ( : all the lower nverter swtches are n the on state or : all the upper swtches are n the on-state), whle the contnuous PWM methods generate two zero states (for SVPWM ). Snce the total zero state tme s not a functon of the zero-sequence sgnal, but the lne lne reference voltage, for the same lne lne output voltage and carrer frequency value, the gate pulses of the DPWM methods are wder than the gate pulses of the modulators wth contnuous modulaton waves. Therefore, the narrow pulse problem occurs at a hgher modulaton ndex wth DPWM methods than contnuous PWM methods.

8 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 681 Fg. 11. Overmodulaton regon modulaton wave profles of SVPWM and DPWM1 for fve dfferent M 3 values. Notce that n both contnuous and dscontnuous PWM cases, the lnearty boundares depend on the rato of the blankng tme to the carrer cycle. Snce the ncreasng carrer cycle practcally mples ncreasng nverter power and ncreasng blankng tme, the rato s at least a few percent n most PWM-VSI drves. As a result, n most applcatons the lnearty range of a modulator s reduced by a nonneglgble amount. In ether modulaton method, once beyond the boundary of lnear modulaton range, the output voltage s reduced by an amount whch depends on the overlap tme shown n Fg. 12(c). As a result, the gan begns to decrease at a lower modulaton ndex than the theoretcal lnearty lmt and decreases more rapdly than the theoretcal gan characterstc. Compared to the modulator theoretcal gan reducton, the gan reducton of the DPWM methods due to the blankng tme s farly small and can be gnored for nverters wth a few klohertz swtchng frequency and blankng tme less than a few mcroseconds [18]. In the gate-turn-off (GTO) swtchng-devce-based PWM-VSI applcatons, the effect s more emphaszed due to the long blankng tme. In certan applcatons, the narrow voltage pulses whch occur at hgh-modulaton levels may damage the drve or load. In such cases, the blankng tme correcton algorthm yelds to a MPW control algorthm. For example, the swtchng devce turn-on and/or turn-off speed capabltes of a GTO may not be suffcent to generate such narrow pulses. In order to avod commutaton falure of GTO-based drves, such narrow pulses are ether elmnated or fxed at an acceptable level. Narrow voltage pulses can also cause overvoltage related motor nsulaton falure. State-of-the-art PWM-VSI drves utlze the modern thrd-generaton IGBT devces wth very small turnon and turn-off tmes. Feedng motors wth long cables from such PWM-VSI drves, sgnfcant overvoltages are generated across the motor termnals due to voltage reflecton. As a result, the motor termnals experence excessve overvoltages contrbutng to nsulaton falure. When such PWM-VSI drves operate at hgh-modulaton levels and narrow pulses are generated, the voltage-reflecton problem s exacerbated: overvoltages n excess of twce the dc-bus value can appear across the termnals of a motor connected to a drve through as short a cable as 30 m [20]. Therefore, narrow voltage pulses are problematc n many PWM-VSI drves. These problems can be elmnated by ether employng passve solutons such Fg. 12. Regular samplng PWM reference and gate sgnals. The reference gate sgnal at hgh-modulaton level. No compensaton results n asymmetrc gate sgnal (for as > 0). (c) Sgnal after exact compensaton. as nsertng reactors between the drve and the motor, or actve solutons such as MPW control whch only requres modfcaton to the PWM algorthm of a drve. The actve soluton s more economc, compact, and mantenance free. When employed, MPW control algorthms affect the modulator voltage gan and reduce the lnear modulaton range notceably. The pulse elmnaton method (PEM) omts pulses narrower than a desrable lmt and ncreases the modulator gan. The pulse lmtng method (PLM) lmts the wdth of the pulses to the mnmum allowable pulse wdth lmt and reduces the gan. However, as the modulaton ndex ncreases, the modulator theoretcal gan characterstcs domnate, and n both cases the gan decreases rapdly, therefore, the gan curves follow the gan curves of Fg. 9 closely. In ether method, the lnearty lmt of a modulator becomes smaller than the theoretcal lmts. In a proper desgn, the MPW pulses are wder than, therefore, the blankng tme controller has no nfluence on the modulator lnearty n ths case. When MPW s appled, the practcal voltage lnearty lmt of an nverter can be found from (22) by substtutng the mnmum pulse tme nstead of. Snce n ths algorthm both sdes of the trangle are affected whle n the blankng tme compensaton case only one sde of the trangle has ncorrect gate sgnal, the effect of MPW control has more nfluence on the gan characterstc of a PWM- VSI. In partcular, n GTO-based hgh-power PWM-VSI s whch employ GTO s wth large MPW values ( s), MPW control starts at very low-modulaton depths, and the nonlnear gan characterstcs domnate the drve behavor at a low-modulaton depth. Although less sgnfcant, (c)

9 682 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 the effect cannot be underemphaszed n the modern IGBT devce-based PWM-VSI drves. In order to avod the abovementoned overvoltage problem, MPW tmes as large as 8 16 s are requred [20]. Snce the carrer frequency s at least a few klohertz, the nfluence of MPW control on the gan characterstcs of such drves s sgnfcant. The MPW-controlled modulator gan formulas can be closed-form calculated by modfyng the theoretcal modulator gan formulas [18]. For example, when employng PEM, the modulaton ndex relatons of the DPWM1 method become as follows [18]: (23) In the above equaton, s the output-voltage modulaton ndex and s the theoretcal modulaton ndex value wthout MPW control whch s gven by (12). The ntermedate varables and are calculated as follows: (24) (25) Fg. 13 shows the closed-form-calculated gan characterstcs of PEM-controlled PWM-VSI for both SVPWM and DPWM1 [18]. Both modulators employ khz and s. As the fgure llustrates, the nfluence of the MPW algorthm has a nonneglgble effect on the voltage gan of SVPWM. The nonlnearty s notceably smaller n the DPWM1 case. On the same fgure, the blankng-tmedependent gan characterstc of DPWM1 s shown for s. Notce the blankng tme has very lttle nfluence on the lnearty compared to MPW. The gan curves of the PEM-controlled drve clearly ndcate the lnearty range of DPWM methods s sgnfcantly wder than SVPWM, and n the overmodulaton regon, DPWM1 s the only modulator that mantans a hgh gan. Therefore, DPWM1 can be most benefcal to hgh-power PWM-VSI drves and all the PWM- VSI drves wth large rato whle operatng n the hgh-modulaton range. VI. VOLTAGE-GAIN LINEARIZATION As llustrated n Fg. 14 n block dagram form, n the overmodulaton regon the VSI output voltage s dfferent from the reference voltage due to gan nonlnearty. PWM-VSI drves whch employ PLM and drves whch do not employ any MPW control algorthm always experence gan reducton, whle those employng PEM experence gan ncrease n the entrance of the overmodulaton regon and gan reducton as the overmodulaton regon s further penetrated. On the other hand, t s mportant to program the reference fundamental component voltage value correctly so that the drve performance does not degrade. For example, n ac motor drve applcatons the stator flux value (or equvalently the value) must be mantaned at a proper level to obtan hgh effcency. Fg. 13. SVPWM and DPWM1 theoretcal M = f(m 3 ) characterstcs and the magnfed vew n the low end of the overmodulaton regon. 1: SVPWM, 2: DPWM1, 3: SVPWM wth MPW, and 4: DPWM1 wth MPW. The blankng-tme-dependent nonlnearty of DPWM1 s shown wth the 2 symbol. Therefore, fundamental component voltage lnearty must be retaned n the overmodulaton range also. Snce the dscussed modulaton methods have nonlnear gan characterstcs, to retan voltage lnearty, a gan compensaton technque must be employed. Gan compensaton technques are based on ether addng extra sgnals such as square waves to the reference modulaton waves or by ncreasng or decreasng the fundamental component magntude of the reference modulaton waves [3]. As shown n Fg. 14, n the latter approach the reference modulaton wave fundamental component sgnal s premultpled wth the nverse gan functon such that the nonlnearty s canceled. The former approach may alter the modulator harmonc characterstcs whle the latter does not. In ths work, the nverse gan method wll be nvestgated. In both gan lnearzaton methods, calculatng the gan compensaton functon s very dffcult. The dffculty of descrbng the gan functons n closed-form equatons has been overcome n the early stages of ths paper. However, closed-form calculaton of the nverse gan functon s very dffcult. Furthermore, on-lne computaton of such complex gan compensaton sgnals wth the state-of-the-art DSP or P devces s prohbtve. Instead, the gan functon and ts nverse can be numercally computed off lne, and the data can be utlzed to approxmate the gan compensaton functon by a lookup table and/or a smple curve-fttng method. Inverse gan compensaton-based gan lnearzaton of the SPWM method whch employs a table lookup approach was prevously reported, and the requrement for a large table sze and an effcent table search algorthm was ndcated [3]. The zero-sequence njecton PWM methods whch are dscussed n ths paper have a smaller gan range than SPWM, therefore, the memory requrements are less demandng. However, of all the dscussed methods, DPWM1 provdes an exceptonal mplementaton advantage due to ts sgnfcantly small gan

10 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 683 Fg. 14. Overmodulaton range voltage-gan block dagrams. Modulator nonlnear gan characterstc. The compensator cancels the nonlnearty by nverse gan multplcaton. reducton. The gan compensaton sgnal (nverse gan functon magntude) of DPWM1 s less than two unts whle the other modulators requre large sgnals rangng from 5 to 20 unts. Therefore, when employng DPWM1 n a fxed-pont dgtal platform, the word length of the P or DSP can be more effcently utlzed. The other methods requre a sgnfcant amount of data shftng to process the large nverse gan values such that overflow does not occur, and ths results n poor modulaton sgnal resoluton and ncreased computaton tme. The nverse gan functon data of DPWM1 can be easly ft nto several frst-order polynomals leadng to a smaller memory sze requrement and mproved accuracy. Near the sx-step operatng pont, the gan nverse coeffcents ncrease due to the rapd gan reducton and the nverse gan functon can be better modeled by several data entres. Employng the analytcal gan functon of DPWM1 and accountng for PEM-based nonlnearty [18], the nverse gan functon data can be accurately and easly computed from (23). Utlzng ths data to obtan a smple hybrd model consstng of several pecewse frst-order polynomal functons and several data entres s a straghtforward task. Compared to the drect dgtal PWM mplementaton, the trangle-ntersecton technque requres smpler overmodulaton algorthms. In the drect dgtal method, the overmodulaton condton s detected only after computng a zero-state tme length wth negatve sgn. Therefore, a back step for correctng the sgn s nevtable, and addtonal algorthms (often complex) must be employed to compensate for the gan loss [6]. Therefore, the DPWM1 trangle-ntersecton method requres the smplest overmodulaton algorthm and has superor performance when compared to all the other PWM methods reported. VII. WAVEFORM QUALITY AND SWITCHING LOSSES The lnear modulaton range harmoncs of carrer-based PWM methods (characterstc harmoncs) are concentrated at the carrer frequency and ts sdebands. In the overmodulaton regon, as the unmodulated portons of the modulaton waves ncrease, the characterstc harmoncs decrease. However, large amounts of subcarrer frequency harmoncs (5th, 7th, etc.) are generated, and as the sx-step mode s approached, these harmoncs become ncreasngly domnant n determnng the waveform qualty. In ths secton, the lnear modulaton and overmodulaton regon waveform qualty factor of the dscussed modulators s nvestgated. In the hgh end of the lnear modulaton range, the waveform qualty of DPWM methods s superor to SVPWM and other PWM methods wth contnuous modulaton wave, and the opposte s true n the low-modulaton range [8]. Therefore, a hgh-performance drve must select SVPWM n the lowmodulaton regon and make a transton to DPWM methods beyond a certan modulaton level. The proper transton modulaton ndex value can be found from the ntersecton pont of the modulaton ndex versus waveform qualty factor curves of the selected methods. Defned n the followng, the nverter output lne lne voltage weghted total harmonc dstorton (WTHD) factor s an approprate measure n determnng the modulator waveform qualty both n the lnear and overmodulaton range [18] WTHD (26) In most ac motor drve and utlty nterface applcatons, the WTHD functon s more meanngful than the conventonal voltage THD defnton n whch the weght factor s absent n the formula because the WTHD functon accounts for the low-pass flter characterstc of the load nductance automatcally. Hence, a better measure for the current harmonc dstorton. The WTHD functon s carrer frequency dependent, and the terms are typcally calculated by evaluatng the PWM-VSI lne lne output-voltage data for one fundamental cycle (obtaned by smulaton) through fast Fourer transformaton (FFT) analyss. In ths study, lne lne voltage WTHD curves for SVPWM and DPWM1 are calculated and compared. The nverter lne lne voltage data of a PWM-VSI drve whch employs the once per carrer regular samplng technque s generated by means of computer smulatons. The smulaton assumes a fundamental frequency of Hz. The carrer frequency s 5 khz n the DPWM1 case and 3.33 khz n the SVPWM case. Ths mples equal nverter average swtchng frequency n both methods. In order to llustrate the carrer frequency dependency of the WTHD functon, the SVPWM case s evaluated for 5 khz also. The harmonc voltages, accountng for all the domnant harmoncs (up to ), were calculated by evaluatng the 8192 data ponts by means of an FFT algorthm of the MATLAB numercal software package. The WTHD curves n Fg. 15 llustrate the advantageous waveform characterstcs of the DPWM1 method at hgh modulaton ncludng the overmodulaton range. Under the equal nverter average swtchng frequency crtera, the harmonc dstorton of DPWM1 s less than the SVPWM methods from to, where both curves merge. Under an equal carrer frequency crtera, whch mples a 50% ncrease n the average swtchng frequency n the SVPWM case, the waveform qualty advantage of SVPWM over DPWM1 s lost near.

11 684 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 Fg. 15. WTHD characterstcs of SVPWM and DPWM1. Ideal nverter model case. Magnfed vew wth MPW ( ) and wthout MPW (- - -) control algorthm. The blankng tme and MPW control-algorthm-dependent nverter nonlneartes can cause sgnfcant harmonc dstorton ncrease whch s modulator dependent. Fg. 15 llustrates the ncrease n the harmonc dstorton when a 12- s MPW control algorthm s employed n the above system. Although the harmonc dstorton ncreases n all the cases, the relatve ncrease n the DPWM1 case s sgnfcantly smaller than the SVPWM s. The data clearly ndcates that the harmonc dstorton of the SVPWM method sgnfcantly ncreases and the ncrease n the swtchng frequency worsens the harmonc dstorton. Therefore, accountng for the MPW nonlnearty, the superorty of DPWM1 over SVPWM begns at a sgnfcantly smaller modulaton ndex value than the deal case. Fg. 15 clearly ndcates that f the carrer frequency s kept constant and the modulaton method s swtched from SVPWM to DPWM1 beyond, no degradaton of waveform qualty wll be obtaned relatve to the SVPWM case. Furthermore, the swtchng losses are greatly reduced. Fg. 15 also ndcates the overmodulaton regon waveform characterstcs of DPWM1 are superor to SVPWM untl the pont where the 5th, 7th, etc., subcarrer frequency harmoncs totally domnate and both WTHD curves merge. Although n the low end of the overmodulaton range the WTHD factor s strongly dependent on the carrer frequency, nverter nonlneartes, and the modulaton method, n the hgh end t s domnated by the subcarrer frequency harmoncs, and t s weakly dependent on the carrer frequency and the modulaton method [18]. Snce the subcarrer frequency harmoncs do not play an mportant role n determnng the modulator waveform qualty, the performance evaluaton should manly be based on the low-end overmodulaton range waveform qualty, and clearly ths argument favors DPWM1 due to ts superor voltage-gan characterstcs. Fg. 16. Expermental and theoretcal M = f(m 3 ) characterstcs of SPWM and SVPWM. Full modulaton range. Magnfed vew of the nonlnear modulaton regon. 1: SPWM, 2: SVPWM, 3: SPWM wth MPW, and 4: SVPWM wth MPW. The expermental data s shown wth and 2 symbols, whle the contnuous curves correspond to the theoretcal formulas. In the hgh end of the lnear modulaton regon, the waveform qualty of DPWM2 s only slghtly better than DPWM1, therefore, the choce between the two modulators can be based on the swtchng loss mnmzaton crtera [8]. The swtchng losses of the drve can be reduced by selectng DPWM1 for near unty-power-factor loads and DPWM2 for near 30 laggng loads because wth ths modulator choce the unmodulated portons of each modulaton wave concde wth the largest current conductng ntervals of the correspondng drve phase. At the DPWM lnear modulaton lmt, regardless the load value, DPWM1 should be selected n order to obtan hgh-voltage gan n the overmodulaton regon. Snce the

12 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 685 Fg. 17. The expermental setup and the gan lnearzed DPWM1-based V -controlled motor drve block dagram. f overmodulaton range waveform qualty of all the DPWM methods s practcally the same, DPWM1 s nvarably the optmal overmodulaton modulator [18]. Generatng all the dscussed modulaton waves n fully dgtal trangle-ntersecton mplementaton-based dgtal platforms s an easy task. Programmng several modulators by employng the low-cost hgh-performance state-of-the-art DSP s or P s and on-lne selectng a modulaton method dependng on the modulaton ndex s a feasble approach. VIII. EXPERIMENTAL RESULTS In ths secton, the expermental voltage-gan characterstcs of SPWM, SVPWM, and DPWM1 are extracted, and ther waveform characterstcs are llustrated. For ths purpose, an expermental system whch conssts of a PWM-VSI drve and a 10-HP nducton machne has been utlzed. The nverter drve employs trangle-ntersecton technque-based PWM, and the carrer frequency s 5 khz. The blankng tme of the nverter s 4 s. The controller s fully dgtal, and t employs a 24-b fxed-pont DSP (Motorola ) wth 40-MHz clock frequency. For the purpose of voltage-gan measurement, operatng the drve n the constant mode s adequate, and the motor can be operated at no load. The algorthm and the modulaton waves are generated by the DSP. In partcular, generaton of all the dscussed modulaton waves, exact blankng tme compensaton, and requred MPW control are all smple tasks requrng only a few lnes of software code when employng a DSP. The dgtally mplemented trangular comparson hardware (PWM block) s also nsde the DSP chp provdng a compact ntegrated soluton. Frst, the SPWM and SVPWM method voltage-gan characterstcs were extracted by measurng the reference and output lne lne voltages from zero voltage untl the sxstep mode s reached. The nverter output-voltage fundamental component value was measured by a dynamc sgnal analyzer (HP35670A). The nverter dc-bus voltage was also measured n order to account for the utlty lne and load-dependent dc-bus voltage varatons. The test was conducted wth and wthout PEM-based MPW control algorthm. When employed, PEM elmnates (drops) the pulses whch are narrower than 12 s. Expermental results are shown n Fg. 16 along wth the analytcal results. As the fgure clearly ndcates, the theoretcal and expermental results match wth good accuracy. The SVPWM method has wder lnearty range than the SPWM method, and both methods requre very large reference sgnals n order to reach the sx-step mode. As the expermental data ndcates, PEM narrows the lnearty range of both modulators qute sgnfcantly. In the second stage, the gan characterstcs of DPWM1 were measured frst wthout PEM control and second wth 12- s PEM control. In the followng, an nverse gan algorthm was mplemented for the PEM-controlled case and gan data extracted. Selectng the MPW length as 12 s, the nverse gan functon data was computed from (23), and ths data was utlzed to extract the followng numercal approxmaton for the nverse gan compensated modulaton ndex functon: (27) The above numercal representaton provdes a straghtforward and hghly accurate approxmaton wth lttle computaton and memory requrements, sutable for the P or DSP mplementatons. In the gan-lnearzed case, a dc-bus voltage-dsturbance decouplng algorthm whch scales the reference modulaton ndex by was also mplemented n order to account for the dc-bus voltage varatons. The

13 686 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 4, JULY 1998 Fg. 20. Expermental DPWM1 modulaton wave, ts fundamental component, and the motor current waveforms for M 3 =0:75 value. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. Fg. 18. Expermental and theoretcal M = f(m 3 ) characterstcs of DPWM1 wth and wthout lnearzaton and the magnfed vew of the overmodulaton regon. 1: The theoretcal M = f(m 3 ) curve. 2: The theoretcal M = f(m 3 ) curve wth MPW. 3: Ideal lnear modulator lne. The expermental results are shown wth, 2, and 3 symbols. Fg. 21. Expermental SVPWM modulaton wave, modulaton sgnal prevous to MPW block, ts fundamental component, and the motor current waveforms for M 3 = 0:82. Note the low-frequency current harmonc dstorton. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. Fg. 19. Expermental SVPWM modulaton wave, ts fundamental component, and the motor current waveforms for M 3 =0:75. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. value was computed by a smple Taylor seres approxmaton nstead of straghtforward dvson whch consumes a sgnfcant amount of computatons. The complete block dagram of the system for ths case s shown n Fg. 17. Fg. 18 shows the theoretcal and expermental gan characterstcs of the DPWM1 method. The lnearty range of the DPWM1 method as the data ndcates s wder than the SVPWM case, and the nfluence of the MPW algorthm s sgnfcantly smaller. The gan compensator, as shown n the fgure extends the modulator lnearty untl near the sx-step operatng mode wth hgh accuracy. For the purpose of comparng the waveform qualty of DPWM1 and SVPWM, the motor currents for several modulaton ndex values are demonstrated along wth the modulaton waveforms. The modulaton sgnals were output from the DSP through a dgtal-to-analog (D/A) converter and the trangular wave gan s ( 10 V represent the postve/negatve dc ral clamp condtons). Fgs. 19 and 20 llustrate the motor current and modulaton waveforms of SVPWM and DPWM1 for. As the fgures ndcate, both modulators have good waveform qualty wthn the lnear modulaton range, and the rpple of SVPWM s slghtly less. However, as the modulaton ndex s ncreased and MPW control s appled, the SVPWM performance degrades sgnfcantly. Fg. 21 shows when a 12- s PEM s employed, the SVPWM method performance degrades at, a value sgnfcantly smaller than the theoretcal lnearty lmt (0.907). The modulator lnearty s lost at, and the current waveform contans sgnfcant low-frequency harmonc dstorton leadng to poor motor performance. As llustrated by the operatng pont n Fg. 22, DPWM1 mantans lnearty and low harmonc dstorton n a sgnfcantly wder modulaton range. As llustrated n Fg. 23 by the operatng pont, beyond, modulator lnearty s lost and the waveform qualty sgnfcantly degrades. A further ncrease n the modulaton ndex results n sgnfcant ncrease of the lowfrequency subcarrer harmonc content. Fg. 24 llustrates the near sx-step mode behavor of the nverter. Notce n all the fgures whch belong to the hghmodulaton regon that the PWM rpple current magntude appears to be practcally the same. Snce the carrer frequency s fxed at 5 khz for both SVPWM and DPWM1, the average swtchng frequency of DPWM1 s 33% less than SVPWM.

14 HAVA et al.: CARRIER-BASED PWM-VSI OVERMODULATION STRATEGIES 687 Fg. 22. Expermental DPWM1 modulaton wave, ts fundamental component, and the motor current waveforms for M 3 =0:855 value. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. Fg. 25. Termnal-voltage dc-bus voltage characterstcs for V1m 3 = 337 V. Fg. 23. Expermental DPWM1 modulaton wave, modulaton sgnal prevous to MPW block, ts fundamental component, and the motor current waveforms for M 3 =0:876. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. plng algorthms. The -controlled nducton machne was operated at constant nverter output-voltage reference value V( at V). Obtaned from a dode rectfer, the dc-bus voltage of the drve was slowly vared by adjustng the ac-nput voltage va an autotransformer, and the motor termnal voltage was measured. Fg. 25 llustrates the expermental nverter output-voltage dc-bus voltage characterstcs wth and wthout nverse gan compensaton and dc-bus voltage-dsturbance decouplng. As the fgure ndcates, the compensated case output voltage s mantaned at the commanded value untl the dc-bus voltage s sgnfcantly reduced, and the nverter operates n the sx-step mode. The uncompensated case output voltage sgnfcantly changes wth the dc-bus voltage varaton. The motor speed and torque devate from the normal operatng ponts, and poor drve performance results. Therefore, the compensated drve performance s nsenstve to the dc-bus voltage varatons for a wde range of dc-bus voltage varatons (utlty-lne voltage sag or surge condtons), whle the uncompensated drve experences dsturbances. Fg. 24. Expermental DPWM1 modulaton wave, modulaton sgnal prevous to MPW block, and the motor current waveforms for M 3 =0:964. Note near the sx-step mode the low-frequency subcarrer harmoncs are domnant. Scales: 2 ms/dv, 2 A/dv, and 5 V/dv. Therefore, DPWM1 has sgnfcantly reduced swtchng losses compared to SVPWM. Consderng the reducton n the swtchng losses and ncrease n the lnear modulaton range, the DPWM1 method clearly becomes the choce for operatng n the hgh-modulaton range. Fnally, the senstvty of the -controlled drve to dcbus voltage varatons s llustrated wth and wthout the nverse gan compensaton and dc-bus dsturbance decou- IX. CURRENT-CONTROLLED DRIVES Hgh-performance feld-orentaton-controlled (FOC) drves and voltage-source converter (VSC) utlty nterface applcatons generally employ hgh-bandwdth current-control algorthms and n such applcatons dynamc performance requrements are demandng. Although the conventonal hghperformance current controllers and the PWM methods have satsfactory lnear modulaton range performance, the overmodulaton range performance s poor. Snce n the overmodulaton range the feedback currents contan consderable amount of subcarrer frequency harmoncs, n addton to the nherent modulator/nverter subcarrer frequency harmoncs, feedback harmonc current-dependent harmoncs are generated. Performance degradaton s generally sgnfcant, and the overmodulaton operatng regon s often prohbted except for dynamc condtons.