Aalborg Unverstet Pulse Pattern-Modulated Strategy for Harmonc Current Components Reducton n Three-Phase AC DC Converters Davar, Pooya; Zare, Fruz; Blaabjerg, Frede Publshed n: I E E E Transactons on Industry Applcatons DOI (lnk to publcaton from Publsher): 10.1109/TIA.2016.2539922 Publcaton date: 2016 Document Verson Early verson, also known as pre-prnt Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Davar, P., Zare, F., & Blaabjerg, F. (2016). Pulse Pattern-Modulated Strategy for Harmonc Current Components Reducton n Three-Phase AC DC Converters. I E E E Transactons on Industry Applcatons, 52(4), 3182-3192. DOI: 10.1109/TIA.2016.2539922 General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: august 26, 2018
Pulse Pattern Modulated Strategy for Harmonc Current Components Reducton n Three-Phase AC-DC Converters Pooya Davar Member, IEEE Department of Energy Technology Aalborg Unversty 9220 Aalborg, Denmark pda@et.aau.dk Abstract -- Generated harmonc current as a consequence of employng power electroncs converter s known as an mportant power qualty ssue n dstrbuton networks. From ndustry pont of vew complyng wth nternatonal standards s mandatory, however cost and effcency are two other mportant features, whch need to be consdered n order to be compettve n the market. Therefore, havng a flexblty to meet varous requrements mposed by the standard recommendatons or costumer needs s at most desrable. Ths makes the generated harmonc current mtgaton a challengng task especally wth three-phase dode brdge rectfer, whch stll s preferred n many power electronc systems. Ths paper addresses a novel current modulaton strategy usng a sngle-swtch boost threephase dode brdge rectfer. The proposed method can selectvely mtgate current harmoncs, whch makes t sutable for dfferent applcatons. The obtaned results at expermental and smulaton levels verfy and confrm the robustness of the proposed approach. Index Terms--Selectve harmonc mtgaton, three-phase rectfer, current control, modulaton, electronc nductor. I. INTRODUCTION AC to DC converson s an nevtable stage n most power electronc systems, but t s responsble for generatng lne current harmoncs especally f the conventonal topologes such as sx-pulse dode rectfer are employed. The level of generated current harmoncs of ths converson stage s of sgnfcant mportance as t can easly deterorate the supply network qualty [1]- [6]. Although the power electroncs technology has brought new nsght n many applcatons, however controllng ther generated harmoncs at certan levels s not achevable wthout addtonal cost and crcutry. The basc topology for AC to DC converson has started by utlzng a dode brdge rectfer due to many reasons such as smplcty, relablty, robustness, and beng cost-effectve compared to other complex systems such as actve front end systems. However, the dode rectfers mpose a hgher level of lne current harmoncs. Over the past years, many approaches have been studed and ntroduced from absolutely passve up to fully actve methods [1], [4]- [10]. A majorty of these methods have targeted pure snusodal waveform generaton, and as a consequence cost and complexty have been sgnfcantly ncreased. Of course havng a low Total Fruz Zare Senor Member, IEEE Danfoss Power Electroncs A/S 6300 Gråsten, Denmark fza@danfoss.com Frede Blaabjerg Fellow, IEEE Department of Energy Technology Aalborg Unversty 9220 Aalborg, Denmark fbl@et.aau.dk Harmonc Current Dstorton (THD ) mproves the system effcency but ths s of nterest for specfc applcatons such as space and arborne ndustry, where the cost of the power converter s not the man concern. But wth most applcatons such as ndustral Adjustable Speed Drves (ASDs), swtch mode power supples, home applances and etc, the key of success s to perform a trade-off between effcency and cost snce many manufacturers are competng n the market. Therefore, as long as the power electronc system comples wth the recommended standards there s no need to obtan a pure snusodal current waveform. Moreover, due to the cost, power densty and components lmted power ratngs many of the pror-art approaches are not applcable at medum and hgh power levels. Wth the rapd growth of power electroncs applcatons, the standard recommendatons such as IEC61000 are contnuously updatng and becomng more strngent. In addton, the demands on varous power level and costumer needs are extendng. These brng the absolute nterest of havng a flexble system whch can be adapted wth vared stuaton as t can reduce the cost of the system sgnfcantly. Ths paper proposes a novel current modulaton strategy to reduce low order harmonc current components. The objectve of the proposed method s to address a flexble selectve harmonc mtgaton technque sutable for varous applcatons. One of the man ams n ths study was to apply an actve flterng method as an ntermedate crcut to the conventonal three-phase dode-rectfer. Ths way, no major modfcatons s requred for the systems whch are equpped wth the three-phase dode rectfer. Therefore, the proposed current modulaton strategy s appled to a sngle-swtch boost topology operatng n Contnuous Conducton Mode (CCM). Consderng ths stuaton ts only counterpart harmonc mtgaton methods wth boost capablty whch are appled to the conventonal dode rectfer are Δ-rectfer and boost converter operatng n Dscontnuous Conducton Mode (DCM) [5]. The Δ-rectfer prncple s based on phasemodular Power Factor Correcton (PFC), meanng that threephase dode rectfers wth boost converter at ther DC-lnks are appled to each phase. Its advantage s ablty to sgnfcantly mprove the nput current qualty; however the 1
man drawback of ths topology s the presence of hgh number of power swtches, hgh complexty and lower effcency comparng wth a sngle-swtch boost converter. The DCM sngle-swtch boost converter requres three nductors at the AC-sde of the dode rectfer. More mportantly ths topology suffers from the large EMI (Electromagnetc Interference) flterng effort (.e., due to the DCM operaton) and for effectve harmonc mtgaton ts output voltage should be boosted above 1 kv (.e., for grd phase voltages of 220 or 230 Vrms) [5]. Ths paper s structured as follows. Secton II provdes detaled analyss of selectve harmonc mtgaton usng the proposed current modulaton strategy. In Secton III, practcal desgn consderatons wth respect to the boost nductor and modulaton sgnal generaton are ponted out. The obtaned expermental results that are summarzed n Secton IV valdate the performance of the proposed method. Secton V recalls a bref overvew on the perspectves of the proposed method n mult-pulse rectfer systems based on comparatve numercal smulaton results. Fnally, concludng remarks are gven n Secton VI by hghlghtng the man achevements and provdng suggestons for further studes. II. PROPOSED CURRENT MODULATION STRATEGY A. Prncple of the Proposed Method In order to understand the basc prncple of the proposed method, let s frst consder the crcut dagram depcted n Fg. 1. As t can be seen, the current source at the DC-lnk sde of the rectfer draws a constant current whch s equal to I 0. Therefore, the nput current wll be a square-wave wth 120 degrees conducton due to the fact that at each nstant of tme only two phases conduct and crculate DC-lnk current through the man supply. Due to the nature of a three-phase system (120 o phase shft), the correspondng phase shft for any trple harmonc would be a multple of 360 o and snce the currents at each nstant are dentcal wth opposte ampltude, the sum of lne currents a, b, and c s zero at all nstants of tme, whch makes them to be free from trple harmoncs n a balanced system. The currents are also vod of even harmoncs because of the half-wave symmetry of the waveforms whch as a matter of fact makes the most promnent harmoncs n ths system to be the ffth, seventh, eleventh, and thrteenth [11]. The proposed dea s based on addng (or subtractng) phase-dsplaced current levels to the square-wave current waveform n order to manpulate the current harmonc components [12], [13]. To keep the above mentoned propertes (free of trple and even harmoncs) the new added pulse should be repeated 1/6 of the perod. For nstance, Fg. 1 depcted two sectors of 1 and 2, where at each sector a s crculated through one of the other phases current. Now, f the new level s added at sector 1 t should be exactly repeated n sector 2 (see Fg. 2(a)). Ths means that the frequency of the added pulse at the DC-lnk should be sx tmes of the fundamental frequency so t can be repeated at each phase current. Fg. 2(a) llustrates detaled analyss of the proposed dea for only one new level added to a constant square wave. As can be seen the proposed current waveform s comprses of three square-wave sgnals wth dfferent magntudes and pulse wdths. The frst current waveform has the magntude of I 0 wth the conducton phase angle of 30 o, whch s defned based on the normal operatng modes of a three-phase dode rectfer and the conducton phase angle cannot be altered. The second current waveform has the magntude of I 1 wth the conducton phase angle of α. The thrd current waveform has the magntude of I 1 but wth a dfferent conducton phase angle (α ). These current waveforms can be analyzed based on a perodc square-wave Fourer seres n whch the fundamental nput current magntude and ts harmoncs can be calculated as follows: 4 n I0 cos( n30) I1cos( n1 ) I1cos( n11 ) (1) n Equaton (1) shows that the fundamental current can be (a) Fg. 1. Smplfed crcut dagram of a three-phase dode rectfer wth a controlled DC-lnk current, (a) deal three-phase nput currents, (b) systems schematc. (b) 2
defned by selectng the varables I 0, I 1, 1 and 11 but a man consequence wll be on harmonc magntudes. Accordng to the lne current waveform depcted n Fg. 2(a) the followng condton should be vald: 11, where 1 (2) 2 6 Consderng (1) and (2) and havng 1 and 11 as the swtchng angles, up to two selected low order harmoncs ( h and j ) can be cancelled out. The mathematcal statement of these condtons can be expressed as (3). Ths s a system of three transcendental equatons wth three unknown varables I 0, I 1, 1: 4 2 1 I0 cos I1 cos1 I1 cos 1 M 6 3 4 2 h I0 cos h I1 cosh1 I1 cosh 1 0 h 6 3 4 2 j I0 cos j I1 cos j1 I1 cos j 1 0 j 6 3 (3) The proposed method can be further extended to a multlevel current waveform. Fg. 2(b) llustrates a generalzed pulse modulated current waveform, where m s the number of swtchng angles. By extendng (3) and usng Fourer seres, the ampltude of any odd n th harmonc of the stepped current waveform can be expressed as: n 4 m 1 2 I0 cos n Ik cos( nk ) Ik cos n k 6 n k 1 3 (4) Accordng to Fg. 2(b), 1 to m must satsfy the followng condton: 1 2 3 m (5) 6 2 From (5) t can be seen that the degree of freedom n manpulatng the current waveform s only 60 o, whch makes the control of the harmonc components a dffcult task. Therefore, to gve more flexblty to (4) the new added levels should not necessarly have same ampltude. In addton, the ampltude could be postve or negatve, whch totally depends on the targeted harmoncs and the desred modulaton ndex M a (fundamental harmonc content). As the equatons are nonlnear, numercal solutons are requred to fnd proper values for these varables. B. Optmum Harmonc Reducton To target more harmonc components the number of the current levels need to be ncreased, but on the other hand t a 3 (a) (b) Fg. 2. Detaled analyss of the proposed current modulaton technque wth: (a) one new added level, (b) generalzed m-level pulse modulated. reduces the feasblty of practcal mplementaton snce the new added levels and swtchng angles depends on the trackng performance of the power electroncs unt and ts controller. Therefore, n order to keep the number of the added current levels to mnmum whle obtanng desrable outcome an optmzaton needs to be performed. The basc prncple of the appled optmzaton s to consder the maxmum permssble harmonc levels allowed by the applcaton or the grd code. In other word, nstead of fully nullfyng, the harmonc components could be reduced to acceptable levels by addng sutable constrants (L n ) to the set of the above mentoned equatons. The problem s now descrbed as an optmzaton functon (F n ) that searches a set of m and I m values over the allowable ntervals. F M L 1 a 1 1 n Fn Ln, where n 5, 7,11,13, 1 Based on (6) an objectve functon needs to be formed to obtan a mnmum error. The objectve functon (F obj ) plays an mportant role n leadng the optmzaton algorthm to the sutable set of soluton. Here F obj s formed based on squared error wth more flexblty by addng constant weght values (6)
(W n ) to each squared error functon [14]. The value of the W n n the objectve functon prortzed the ncluded functons as follows: 2, where 1,5,7,11,13, (7) F W F L n obj n n n III. IMPLEMENTATION DETAILS AND HARDWARE SETUP To control the DC-lnk current shape and magntude followng the waveforms shown n Fg. 2, a boost converter topology based on electronc nductor [12], [13], [15]- [19] concept s employed. Fg. 3 depcts the overall system structure and the mplemented hardware setup. Usng the conventonal boost topology has the advantage of boostng the output DC voltage whch s sutable when the DC-lnk s fed to an nverter. Moreover, as the DC-lnk current s controlled based on the load power t has the advantage of keepng the THD ndependent of load profle. Fg. 3(b) shows the mplemented prototype. Here, one SEMIKRON-SKD30 was used as a three-phase brdge rectfer and one SEMIKRON-SK60GAL125 IGBT-dode module s employed n the boost topology. A Texas Instrument TMS320F28335 s used for control purposes and LEM current and voltage transducers are used as measurement unt. To synchronze the current controller wth the grd a Second-Order Generalzed Integrator (SOGI) based phase locked loop (PLL) system s adopted [20]. As Fg. 3(a) depcted, for the smplcty, one lne-to-lne voltage s fed to the PLL and therefore the result wll have 30 o phase shft regardng to the phase voltage, whch should be corrected wthn the reference current generator algorthm. In order to obtan a dscrete-tme ntegrator for PLL and PI controller, the trapezodal dscretzaton method s used. A. Boost Inductor Selecton of the boost nductor s a challengng task as t contrbutes to the system loss, power densty and current rpple. To better understand ths, the nductor current n a steady-state CCM s analyzed. Here the swtchng frequency s consdered to be hgh enough so that the rectfed voltage and output voltage are constant durng one swtchng cycle. Therefore, the nductor value can be calculated as, V D(1 D) 1 1 Ldc where f f I T T T o sw, avg sw, avg L, pk pk sw on off where V o s the output voltage, f sw,avg s the average swtchng frequency, I L,pk-pk s the peak to peak nductor current rpple and D s the steady-state duty cycle of the boost converter. Usng (8) the mnmum requred swtchng frequency (f sw,avg ) can be selected by consderng the maxmum peak to peak nductor current rpple (D = 0.5) as, Vo fsw, avg (9) 4Ldc IL, pk pk,max (8) (a) (b) Fg. 3. The mplemented three-phase AC-DC system wth the proposed selectve harmonc elmnaton method, (a) overal system schematc and control structure, (b) photograph of the mplemented hardware setup. Followng (8) and (9) the optmum swtchng frequency can be selected by makng a tradeoff among the system effcency, sze and cost [21]. For example the system effcency can be optmzed by mnmzng the swtchng frequency by allowng more rpple current for hgh power applcatons and t wll result n lower swtchng losses. As mentoned before the THD can be ndependent of the load profle. Equaton (10) can be rewrtten based on the output average current as L dc V D(1 D) I I (1 D) f k I I I 2 o L, pk pk L, pk pk where krpple sw, avg rpple out L out (10) wth k rpple beng the peak-to-peak rpple factor, I L the average nductor current and I out the average output current. Hence, keepng the rpple factor as a constant value wll make the nput current qualty ndependent of the load profle. However, careful selecton of the rpple factor s needed as t 4
has drect mpact on the rpple current, whch as stated n (9) can affect the nductor sze, system effcency and cost [21]. Dependng on the applcaton requrement the converter may operate n partal loadng condtons such as n ASD applcatons. In partal loadng condton the DC-lnk current L can become dscontnuous whch adversely affect the harmonc reducton performance of the proposed method. However, by sutable selecton of the converter parameters, the converter can cover wde range of loadng condtons. Therefore, n order to guarantee CCM operaton of the converter the parameters (.e., f sw, L dc, ΔI L ) should be calculated based on the mnmum ntended output power. Ths condton based on Boundary Condton Mode (BCM) operaton (I L = ΔI L,pk-pk /2) s, 6 o 1 rm rm 1 60 2 2 D1 D Vo K o Ldc wth K 1 1 60 2 fsw,avgpo mn 1 rm 6rM o 1 60 1 rm (11) wth r M beng the rato between the calculated current levels r M = I 1 /I 0, and K a coeffcent factor whch depends on the appled modulaton type as depcted n Fg. 4. As t can be seen from Fg. 4, three dfferent modulatons can be consdered. The frst type s when a new current level s added to the square-wave waveform (.e., α 1 < 60 o ). The second type s conventonal square-wave (.e., α 1 = 60 o ). The thrd type s when a new current level s subtracted from the square-wave current (.e., α 1 > 60 o ). In order to guarantee the CCM operaton the mnmum appled current level should be consdered. Ths condton s reflected usng the calculated K factor n (11). Therefore, consderng the mnmum ntended output power level the converter parameters should be selected based on the appled current modulaton type. For nstance under same condton, the frst and second types of modulaton can operate n CCM operaton at lower power levels comparng wth the thrd modulaton type whch the current becomes dscontnuous at hgher power levels. B. Modulaton Sgnal As Fg. 3(a) llustrates, the reference current s formed by multplyng the voltage controller output by a preprogrammed modulaton sgnal. Fg. 5 depcts the basc concept n generatng the modulaton sgnal (.e., M ) followng Fg. 2(a). As t can be seen, M can be generated based on the sum of absolute values of three-phase nput currents. The llustrated swtchng parameters (.e., I 0, I 1 and 1 ) at both grd sde and DC-lnk currents helps to better understand ths relaton. As t can be seen the perod of the modulaton sgnal M s 1/6 of the nput currents abc. Therefore, the smplest way to generate and synchronze the modulaton sgnal nsde the controller s to compare t wth a snusodal sgnal (.e., sn(3ω 0 t) ) usng the PLL estmated angular frequency (ω 0 ). Comparng the swtchng angles wth 5 Fg. 4. Detaled analyss of the three dfferent modulaton types: (a) proposed current modulaton wth one new added level, (b) conventonal flat current modulaton, (c) proposed current modulaton wth one new subtracted level. the snusodal waveform yelds the followng smple condtons: f ( sn(3 0t) sn(3 )) M I0 I1 1 11 : else M I0 f ( sn(3 0t) sn(3 )) M I0 I1 1 11 : else M I0 (12) Here, based on the fact that the proposed method s addng or subtractng phase-dsplaced current levels, two condtons have been consdered, whch results n dfferent modulaton sgnals. It can be known from Fg. 2(a) that addng a phasedsplaced current level requres to have α 1 < α 11. However to reduce a specfc set of harmonc components, phase dsplaced current level needs to be subtracted. Therefore, for those stuatons α 1 should be set above α 11 (α 1 > α 11 ). The above equaton can easly be extended to mult-level stuaton by applyng (12) to each swtchng parameters and summng up the correspondng modulaton sgnals. As t s mentoned, the reference trackng performance of the current controller has an mportant role n the harmonc mtgaton performance. Therefore, the bandwdth of the
Fg. 5. Synthess of the modulaton sgnal (.e., M ) at the DC-lnk based on three-phase nput currents. current controller should be hgh enough to accurately follow the appled mult-pulse pattern modulaton. For the tradtonal PWM-based PI current controller the control loop bandwdth needs to be less than 1/5 of the swtchng frequency (.e., n the case of usng Tustn or Trapezodal dscretzaton method). Ths may result n havng a hgh swtchng frequency, whch can ether exceeds the power swtchng devce lmts or ncrease the swtchng losses. Hence, employng a fast current control method lke hysteress or dead-beat are recommended. Here, the hysteress current control method s used. Notably, usng the hysteress current control n the proposed method wll not result n a well-known sgnfcantly dspersed frequency spectrum as the nput voltage s a rectfed voltage wth a small rpple as shown n Fg. 1 (.e., 0.9069V r v r 1.0472V r ). Consderng the boost converter CCM operaton, steady-state duty cycle D and rectfed voltage V r, the swtchng frequency s changng wthn the followng range, 0. 0494 1. 0966D 0. 0844 0. 8225D Vr fsw Vr (13) LI LI To better understand ths small varaton, the consdered system parameters n ths paper (Table I) s appled to (8), Vr Vr 0. 241 f sw 0. 302 LI LI IV. RESULTS (14) In ths secton the crcut operaton and the proposed current modulaton scheme are verfed through dfferent smulaton and experments usng the mplemented prototype (Fg. 3(b)). Here the flexblty of the proposed method by targetng dfferent set of harmonc components s llustrated. The system parameters are lsted n Table I. Notably, for all of the harmonc reducton cases, smulaton results are also carred out to show ts close agreement wth the measured expermental results. For the sake of comparson, the conventonal square-wave (flat) current modulaton has been consdered as the frst case. Fg. 6 shows both the smulated and obtaned measured results along wth the harmonc dstrbuton of the nput current at phase a. 6 TABLE I PARAMETERS OF THE SYSTEM Symbol Parameter Value v abc Grd phase voltage 220 V rms f g Grd frequency 50 Hz L g, R g Grd mpedance 0.18 mh, 0.1 Ω L dc DC lnk nductor 2 mh C dc DC lnk capactor 470 µf V o Output voltage 700 V dc K p, K PI controller (Boost converter) 0.01, 0.1 HB Hysteress band 2 (A) P omax Rated output power = 5 kw Fg. 6. Obtaned results for sqaure-wave modulaton usng hysteress current control at V o = 700 V dc and P o = 3kW (P o = 60%): (a) smulaton results of three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a), (b) measured expermental results of three-phase nput currents wth FFT of the nput current ( a).
Fg. 7. Obtaned results for the proposed 7 th and 13 th harmoncs cancellaton usng hysteress current control at V o = 700 V dc and P o = 3kW (P o = 60%): (a) smulaton results of three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a), (b) measured expermental results of three-phase nput currents wth FFT of the nput current ( a). [wth I 0 = 1, I 1 = 0.618, 1= 42 o ]. Fg. 8. Obtaned results for the proposed 5 th and 13 th harmoncs cancellaton usng hysteress current control at V o = 700 V dc and P o = 3kW (P o = 60%): (a) smulaton results of three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a), (b) measured expermental results of three-phase nput currents wth FFT of the nput current ( a) [wth I 0 = 1, I 1 = 0.653, 1= 70 o ]. Fg. 9. Calculatng nput current 5 th and 7 th harmoncs magntude (normalzed wth I 0 = 1) versus swtchng angle α 1 α 1 < 90 o and new added current level I 1 (0 < I 1 < 0.8) for two-level current modulaton (.e., transton between frst and thrd modulaton types as llustrated n Fg. 4) at DC-lnk followng (1), where zero magntudes ( n = 0) are the possble harmonc elmnaton solutons. As the second case, addng one current level to the DClnk current was consdered to target two low order harmoncs. Hence, the cancellaton of 7 th and 13 th harmonc orders have been consdered by solvng (3) usng MATLAB functon fsolve. Fg. 7 llustrates the obtaned results. As t can be seen from Fg. 7, 7 th and 13 th harmonc components have been sgnfcantly reduced. In the thrd case as depcted n Fg. 8, 5 th and 13 th harmoncs have been targeted. However, the obtaned results n Fgs. 7 and 8 clearly show that the consequence of cancelng 7 th harmonc s the ncrease of the 5 th harmonc order and vce versa. Ths results n hgher THD and power factor (λ) comparng wth the conventonal square-wave case. To better understand ths relaton, Fg. 9 llustrates the possble nput current magntudes regardng to both 5 th and 7 th harmoncs orders as a functon of swtchng angle (α 1 ) and new added current level (I 1 ) when a two-level current modulaton s appled to the DC-lnk. As can be seen, the solutons for elmnatng 5 th harmonc attaned when the swtchng angle s wthn the range 65 o < α < 90 o whch s n contrary to 7 th harmonc, where 40 o < α < 55 o makng t mpossble to elmnate these two harmoncs at the same tme. A proper selecton of the harmoncs to be reduced or elmnated depends on the applcaton needs. To exemplfed, n the second scenaro addng two levels to the square-wave current s consdered followng (4) and 7 th, 11 th and 13 th harmonc orders are targeted to be half of ther values comparng to the square-wave current. Here, followng (7) an 7
Fg. 10. Obtaned results for the proposed 7 th, 11 th and 13 th harmoncs cancellaton usng hysteress current control at V o = 700Vdc and P o = 3kW (P o = 60%): (a) smulaton results of three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a), (b) measured expermental results of three-phase nput currents wth FFT of the nput current ( a) [wth I 0 = 1, I 1 = 0.7328, 1= 38.3 o, I 2 = 0.7328, 2= 51.5 o ]. TABLE II COMPARATIVE EXPERIMENTAL RESULTS AT OUTPUT POWER LEVEL OF 3 KW Harmonc Mtgaton Strategy 7 th, 13 th harmonc cancellaton (Fg. 7(b)) 5 th, 13 th harmonc cancellaton (Fg. 8(b)) 7 th,11 th,13 th harmonc cancellaton (Fg. 10(b)) Conventonal method (square-wave) (Fg. 6(b)) Harmonc Dstrbuton and THD (%) a,5 a,1 a,7 a,1 optmzaton needs to be performed, whch has been done usng a MATLAB genetc optmzaton algorthm. It s mportant to apply a sutable restrcton followng (5) and (6). As Fg. 10 shows the three harmonc orders of 7 th, 11 th and 13 th have been reduced whch as explaned before results n ncrease of the 5 th harmonc. Table II summarzes the obtaned results based on the targeted harmonc orders and THD for both the proposed and the conventonal squarewave methods. As can be seen for all cases the obtaned results slghtly dffer from what expected whch s due to the presence of grd mpedance, and consequently affects the calculated angles. As t was dscussed n Secton III.A, dependng on the a,13 a,1 a,13 a,1 THD 32.7 0.5 9.4 0.8 35.3 0.93 2.1 38.5 25.4 1.5 48.6 0.88 38.4 8 4.5 3.4 41.1 0.91 21 13 8.9 7 29 0.94 λ 8 Fg. 11. Smulated nput current a for the proposed 7 th and 13 th harmonc reducton at dfferent power levels: (a) nput current waveforms wth correspondng THD and λ (b) FFT of the nput current ( a). applcaton requrement the converter may operate at dfferent partal power. In fact, ths s qute common n applcatons such as ASD systems [22]. Here, the frst modulaton type where 7 th and 13 th harmonc orders are targeted (Fg. 7) s consdered when the output power s changed n the range of 10% < P o < 100%. Notably, followng (11) the converter parameters have been re-calculated n order to obtan CCM operaton based on the mnmum power (.e., P o = 10%). Therefore, L dc and HB are changed to 4 mh and 0.5 A, respectvely. Fg. 11 shows the obtaned smulaton results of nput current at phase-a ( a ) at dfferent power levels along wth ther correspondng harmonc dstrbuton. As t can be seen from Fg. 11(b), although at all power levels same THD s obtaned, but notably at lower power levels (.e., P o = 10% and P o = 30%) 7 th and 13 th harmoncs of nterest are more reduced. Ths s due to the fact that n smulaton the lne mpedance s constant and at lower powers the effectve lne mpedance reduces and consequently ts effect on the current modulaton as a phase-shft error reduces as well. To further verfy the proposed method at dfferent power levels, same condton s appled to the hardware prototype and the obtaned expermental results at P o = 100% and 10% are llustrated n Fg. 12. As t can be seen from both smulaton and expermental results, the performance of the system n terms of THD and λ s almost constant regardless of the load power. Fnally, the start-up and shut-down dynamc behavor of the mplemented system are llustrated n Fg. 13. For the start-up phase of operaton, the nput voltage s already
Fg. 14. Extenson of conventonal 12-pulse rectfer system connected n parallel on DC sde applyng the proposed current modulaton strategy. (The leakage nductances of L 1 = L 2 = L 3 = 10 µh, wndng resstance of R 1 = R 2 = R 3 = 0.1 Ω, and wndng rato of n Δ/n y = 3 ). Fg. 12. Expermental results for the proposed 7 th and 13 th harmoncs cancellaton at dfferent power levels: (a) measured three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a) at 100% of rated power (P o = 5 kw) and (b) measured three-phase nput currents wth Fast Fourer Transform (FFT) of the nput current ( a) at 10% of rated power (P o = 500 W). [L dc = 4 mh, HB = 0.5 A] (a) (b) Fg. 13. Measured dynamc behavor of nput current a and output voltage V o at (a) startup and (b) shutdown at the nomnal operatng condtons. 9 appled, the load current s flowng and boost converter s n the off-state. Turnng on the DC-DC converter makes the controller to start the pulse pattern modulaton as seen from the nput current a and changes the output voltage V o from 515 V dc to 700 V dc wthout any large overshoot (Fg. 13(a)). The symmetrcal pulse patterns on the nput current after 100 ms valdate the PLL settlng tme. At shut-down phase of operaton the control crcut permanently turns off the IGBT swtch so t stops the current modulaton and the output voltage drops to 515 V dc (Fg. 13(b)). V. PERSPECTIVES The proposed concept gves the possblty to elmnate varous sets of harmonc components n a three-phase dode rectfer based on electronc nductor concept. Therefore, based on the applcaton requrement employng the proposed method can further mprove the nput current qualty by reducng the low order harmoncs. However, as stated before, targetng 5 th and 7 th orders harmonc smultaneously solely based on a sngle unt system s mpossble. In ths secton, one of the possble solutons based on combnaton of nonlnear loads [22]- [24] are brefly dscussed. Here, the proposed method s appled to a mult-pulse rectfer system [10]. Fg. 14 llustrates the applcaton of the proposed concept n a 12-pulse rectfer topology wth a common DC-bus. The comparatve smulaton results are shown n Fg. 15. Here, except the output power whch s set to 6 kw, same parameters for the system s appled as mentoned n Table I. Fg. 15(a) llustrates the total nput current waveform of a conventonal 12-pulse rectfer system. Bascally, the 12-pulse arrangement elmnates the 5 th, 7 th, 17 th and 19 th harmonc orders (see Fg. 15(d)). The mproved nput current harmonc dstorton for a 12-pulse rectfer system dependng on the output power level vares between 10% < THD < 15%. Hence, employng the proposed method applyng a two-level current modulaton strategy at the DClnk followng (1) and (3) can further mprove the nput current qualty by targetng the remanng 11 th, 13 th harmonc orders. Notably, here same modulaton pattern s appled to each converter. The obtaned results n Fgs. 15(b) and 15(d) show that the new 12-pulse rectfer system obtaned THD 5.7%, whch s comparable wth a conventonal 18-pulse rectfer system.
Fg. 15. Comparatve smulaton results of total nput current ( a) at P o = 6 kw: (a) conventonal 12-pulse rectfer (V o = 511 V dc), (b) proposed method wth two-level current modulaton at DC-lnk targetng 11 th and 13 th harmoncs (V o = 700 V dc) [wth I 0 = 1, I 1 = 1.932, 1= 45 o ], (c) proposed method wth threelevel current modulaton at DC-lnk targetng 11 th, 13 th, 23 th, and 25 th harmoncs (V o = 700 V dc) [wth I 0 = 1, I 1 = 1.88, 1= 50 o, I 2 = 1.97, 2= 40 o ], (d) THD of total nput current. As each current level n the proposed technque can contrbute to mtgaton of two low order harmoncs, extendng the number of the current level usng (4) can target larger number of harmoncs. Therefore, employng a threelevel current modulaton at the DC-lnk can target two more harmoncs of 23 th and 25 th n addton to 11 th and 13 th harmoncs. The obtaned total nput current waveform wth a unty power factor s depcted n Fg. 15(c) and the harmonc dstrbuton resultng n THD 3.8% s shown Fg. 15(d). In fact, the only remanng 35 th and 37 th harmoncs mply that applyng the proposed method wth three-level modulaton mproves the performance of a conventonal 12-pulse rectfer system to be comparable wth a conventonal 24-pulse rectfer system. Moreover, the output voltage can be ncreased to hgher voltage levels usng the boost topology; ths s benefcal when the DC-lnk voltage s fed to an nverter. Unlke the conventonal mult-pulse rectfer systems whch the performance of the system s dependent of the load profle, applyng the proposed concept can mantan the nput current THD and power factor regardless of the output power varaton. VI. CONCLUSION In ths paper a novel current modulaton technque has been proposed for a three-phase rectfer wth an electronc nductor at the DC-lnk sde. The proposed method modulates the DC-lnk current to control the fundamental current and to reduce the selected lne current harmoncs. Moreover, calculatons of the optmum swtchng patterns have been conducted based on applyng the mnmum number of current levels. A man advantage of the proposed method s that the relatve values of harmoncs wth respect to the fundamental 10 value reman constant regardless of load profle varaton. Applyng the proposed method to other confguratons such as 12-pulse rectfer can sgnfcantly mproves THD comparatve to a 24-pulse rectfer. The performance of the proposed method can be mproved by ncreasng the number of the levels n order to obtan optmum solutons for low order harmoncs whch completely depends on the swtchng frequency and nductor sze. REFERENCES [1] D. Kumar and F. Zare, "Harmonc analyss of grd connected power electronc systems n low voltage dstrbuton networks," IEEE J. Emerg. Sel. Top. Power Electron., vol. 4, no. 1, pp. 70-79, 2016. [2] J.W. Gray and F. J. Haydock, "Industral power qualty consderatons when nstallng adjustable speed drve systems," IEEE Trans. Ind. Appl., vol. 32, no. 3, pp. 646-652, May/Jun 1996. [3] F. Zare, "Harmoncs ssues of three-phase dode rectfers wth a small DC lnk capactor," n Proc. of PEMC, 2014, pp. 912-917. [4] C. Klumpner, F. Blaabjerg, and P. Thogersen, " Alternate ASDs: evaluaton of the converter topologes suted for ntegrated motor drves," IEEE Ind. Appl. Mag., vol. 2, no. 2, pp. 71-83, 2006. [5] J. W. Kolar and T. Fredl, "The Essence of Three-Phase PFC Rectfer Systems - Part I," IEEE Trans. Power Electron., vol. 28, no. 1, pp. 176-198, Jan. 2013. [6] B. Sngh, B. N. Sngh, A. Chandra, K. Al-Haddad, A. Pandey, and D. P. Kothar, "A revew of three-phase mproved power qualty AC-DC converters," IEEE Trans. Ind. Electron., vol. 51, pp. 641-660, 2004. [7] M. Lserre, F. Blaabjerg, and S. Hansen, "Desgn and control of an LCLflter-based three-phase actve rectfer," IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1281-1291, 2005. [8] M. Lserre, A. Dell'Aqula, and F. Blaabjerg, "An overvew of threephase voltage source actve rectfers nterfacng the utlty," n Proc. of Power Tech Conf., 2003, vol. 3, pp. 1-8. [9] H. Akag, "Modern actve flters and tradtonal passve flter," Bulletn of the polsh academy of scences techncal scences, vol. 54, 2006. [10] H. Akag and K. Isozak, "A hybrd actve flter for a three-phase 12- pulse dode rectfer used as the front end of a medum-voltage motor drve," IEEE Trans. Power Electron., vol. 27, no. 1, pp. 69-77, Jan. 2012.
[11] A. M. Trzynadlowsk, Introducton to modern power electroncs: John Wley & Sons, 2010. [12] P. Davar, F. Zare, and F. Blaabjerg, A smart current modulaton scheme for harmonc reducton n three-phase motor drve applcatons, n Proc. of EPE, 2015, pp. 1-10. [13] P. Davar, F. Zare, and F. Blaabjerg, Pulse pattern modulated strategy for harmonc current components reducton n three-phase AC-DC converters, n Proc. of ECCE, 2015, pp. 5968-5975. [14] L.G. Franquelo, J. Napoles, R.C.P. Gusado, J.I. Leon, and M.A. Agurre, "A flexble selectve harmonc mtgaton technque to meet grd codes n three-level PWM converters," IEEE Trans. Ind. Electron., vol.54, no.6, pp.3022-3029, Dec. 2007. [15] K. Mno, M. L. Heldwen, and J. W. Kolar, "Ultra compact three-phase rectfer wth electronc smoothng nductor," n Proc. of APEC, 2005, pp. 522-528. [16] J. Salmon and D. Koval, "Improvng the operaton of 3-phase dode rectfers usng an asymmetrcal half-brdge DC-lnk actve flter," n Proc. of IAS Annual Meetng, 2000 vol. 4, pp. 2115-2122. [17] H. Ertl and J. W. Kolar, "A constant output current three-phase dode brdge rectfer employng a novel "Electronc Smoothng Inductor"," IEEE Trans. Ind. Electron., vol. 52, pp. 454-461, 2005. [18] C. Galea and L. Asmnoae, "New topology of electronc smoothng nductor used n three phase electrc drves," n Proc. of EPQU, 2011, pp. 1-6. [19] P. J. Grbovc, P. Delarue, and P. Le Mogne, "A Novel Three-Phase Dode Boost Rectfer Usng Hybrd Half-DC-Bus-Voltage Rated Boost Converter," IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1316-1329, 2011. [20] M. Cobotaru, R. Teodorescu, and F. Blaabjerg, "A New Sngle-Phase PLL Structure Based on Second Order Generalzed Integrator," n Proc. of PESC, 2006, pp. 1-6. [21] T. Nussbaumer, K. Raggl, and J.W. Kolar, "Desgn Gudelnes for Interleaved Sngle-Phase Boost PFC Crcuts," IEEE Trans. Ind. Electron., vol.56, no.7, pp.2559-2573, July 2009. [22] P. Davar, Y. Yang, F. Zare, and F. Blaabjerg, A mult-pulse pattern modulaton scheme for harmonc mtgaton n three-phase mult-motor drves, IEEE J. Emerg. Sel. Top. Power Electron., vol. 4, no. 1, pp. 174 185, 2016. [23] S. Hansen, P. Nelsen, and F. Blaabjerg, "Harmonc cancellaton by mxng nonlnear sngle-phase and three-phase loads," IEEE Trans. Ind. Appl., vol. 36, no. 1, pp. 152-159, Jan/Feb 2000. [24] Y. Yang, P. Davar, F. Zare, and F. Blaabjerg, A DC-lnk modulaton scheme wth phase-shfted current control for harmonc cancellatons n multdrve applcatons, IEEE Trans. Power Electron., vol. 31, no. 3, pp. 1837 1840, Mar. 2016. Fruz Zare (S 98-M 01 SM 06) receved hs Ph.D. n Power Electroncs from Queensland Unversty of Technology n 2002. He has spent several years n ndustry as a team leader and development engneer workng on power electroncs and power qualty projects. Dr. Zare won a student paper prze at the Australan Unverstes Power Engneerng Conference (AUPEC) conference n 2001 and was awarded a Symposum Fellowshp by the Australan Academy of Technologcal Scence and Engneerng n 2001. He receved the Vce Chancellor s research award n 2009 and faculty excellence award n research as an early career academc from Queensland Unversty of Technology n 2007. Dr. Zare has publshed over 150 journal and conference papers and techncal reports n the area of power electroncs. He s currently a Lead Engneer wth Danfoss Power Electroncs, Graasten, Denmark. He s a Task Force Leader of Actve Infeed Converters wthn Workng Group one at the IEC Standardzaton Commttee. Hs current research nterests nclude problem-based learnng n power electroncs, power electroncs topologes and control, pulsewdth modulaton technques, EMC/EMI n power electroncs, and renewable energy systems. Pooya Davar (S 11 M 13) receved B.Sc. and M.Sc. degrees n electronc engneerng from the Unversty of Mazandaran (Noushrvan), Babol, Iran, n 2004, 2008, respectvely and the Ph.D. degree n power electroncs from the Queensland Unversty of Technology (QUT), Brsbane, Australa n 2013. From 2005 to 2010 he was nvolved n several electroncs and power electroncs projects as a Development Engneer. Durng 2010-2014, he has desgned and developed hgh-power hgh-voltage power electronc systems for mult-dscplnary projects such as ultrasound applcaton, exhaust gas emsson reducton and tssue-materals sterlzaton. From 2013 to 2014 he was wth Queensland Unversty of Technology, Brsbane, Australa, as a Lecturer. Dr. Davar joned the Department of Energy Technology at Aalborg Unversty as a Postdoctoral Researcher n August 2014. Currently, he s an Assstant Professor wth Department of Energy Technology at Aalborg Unversty. He s awarded a research grant from Dansh Councl of Independent Research (DFF) n 2015. Hs current research nterests nclude actve front-end rectfers, harmonc mtgaton n adjustable speed drves, Electromagnetc Interference (EMI) n power electroncs, hgh power densty power electroncs, and pulsed power applcatons. 11 Frede Blaabjerg (S 86-M 88 SM 97 F 03) was wth ABB-Scanda, Randers, Denmark, from 1987 to 1988. From 1988 to 1992, he was a Ph.D. Student wth Aalborg Unversty, Aalborg, Denmark. He became an Assstant Professor n 1992, an Assocate Professor n 1996, and a Full Professor of power electroncs and drves snce 1998 at Aalborg Unversty. He has been a part-tme Research Leader wth the Research Center Rsoe workng wth wnd turbnes. In 2006-2010, he was the Dean of the Faculty of Engneerng, Scence and Medcne. Hs current research nterests nclude power electroncs and ts applcatons such as wnd turbnes, photovoltac systems, relablty, harmoncs and adjustable speed drves. Prof. Blaabjerg has receved 17 IEEE Prze Paper Awards, the IEEE Power Electroncs Socety (PELS) Dstngushed Servce Award n 2009, the EPE-PEMC Councl Award n 2010, the IEEE Wllam E. Newell Power Electroncs Award n 2014, and the Vllum Kann Rasmussen Research Award 2014. He was an Edtor-n-Chef of the IEEE TRANSACTIONS ON POWER ELECTRONICS from 2006 to 2012. He has been a Dstngushed Lecturer for the IEEE Power Electroncs Socety from 2005 to 2007 and for the IEEE Industry Applcatons Socety from 2010 to 2011. He s nomnated n 2014 and 2015 by Thomson Reuters to be among the most 250 cted researchers n Engneerng n the world.