Selective Harmonic Mitigation Technique for Cascaded H-Bridge Converters with Equal DC Link Voltages

Transcription

1 Selectve Harmonc Mtgaton Technque for Cascaded H-Brdge Converters wth Equal DC Lnk Voltages B. Subba Reddy, G. Surendra Abstract Multlevel converters are very attractve for applcatons n medum-voltage hgh power range snce they are capable of producng the hgh qualty output waveform wth low swtchng frequency. The multlevel topology s obtaned by the cascaded H-brdge converter (CHB) whch s formed from the seres connecton of H-brdge cells. A new method to generate swtchng three-level pulse wdth modulaton (PWM) patterns to meet specfc grd codes s presented. Studyng of all harmoncs and total harmonc dstorton s the global problem n multlevel converters. The proposed method s the selectve harmonc mtgaton PWM s used to preprogrammng the harmonc output waveform. Ths fact leads to the reducton of bulky and costly grd connected tuned flters. Ths method s developed by the nterpolaton of dfferent set of angles. The smulaton results are presented for the proposed control method. Index Terms Harmonc dstorton, multlevel systems, optmzaton methods, pulse wdth modulaton converters. I. INTRODUCTION One mportant applcaton of multlevel converters s focused on medum and hgh power converson [1]. At present research s gong on the development of new and optmzed technques for ths type of converters to mprove the qualty of the output waveform. The avalable multlevel topologes are the neutral pont clamped, flyng capactor, and cascaded H-brdge converters (CHB) [2]. The cascaded H-brdge converter constructed from a seres cascade of three-level H-brdges. Ths cascaded connecton of the converter makes t to produce hgh qualty, hgh voltage waveforms by utlzng low or medum voltage swtchng devces. Ths functonalty makes ths converter an desrable opton for grd connected applcatons such as unnterruptble power supples, statc reactve volt ampere compensators, seres and shunt compensators, etc.[3]-[]. B. Subba Reddy, Electral and Electroncs Engneerng, Sree Vdyankethan Engneerng College, Trupat, Inda. G.Surendra, Electrcal and Electroncs Engneerng, Sree Vdyankethan Engneerng College, Trupat, Inda. The use of low-voltage nsulated-gate bpolar transstors at hgh-power levels usually demands a reducton n swtchng frequency n order to make sure that losses caused by the mperfect nature of practcal swtchng devces does not sgnfcantly reduce the converter effcency. Selectve harmonc elmnaton (SHE-PWM), total harmonc dstorton mnmzaton, and selectve harmonc mtgaton (SHM-PWM) methods are used to produce waveforms wth low swtchng frequency and to mprove the waveform qualty. As the frst approxmaton of the harmonc dstorton avodance, the selectve harmonc elmnaton pulse wdth modulaton (SHEPWM) technque, whch was frst ntroduced n 1973, s an effectve technque for the elmnaton of low order harmoncs n two-level hgh-power nverters. For these methods, mathematcal functons can be derved usng the Fourer analyss, whch may be solved to meet a certan predefned objectve n the waveform [5]-[6]. The waveform objectves may nclude the complete elmnaton (SHE-PWM) or reducton (SHM-PWM) of certan harmoncs n the output waveform n order to meet a partcular harmonc code for a certan applcaton [7]. The derved functons are transcendental and nonlnear n nature, can be solved for a range of modulaton ndces usng dfferent methods. The solutons are stored n lookup tables (LUTs) for use wth an approprate converter control scheme. In CHB based nverters, t may be sure that each cell of the nverter has to draw equal energy form the dc source connected. Ths can be acheved over a sngle or several fundamental cycles. Ths would ensure that these sources dscharge at the same rate and that each cell of the cascade s utlzed evenly. In applcatons due to the pattern of the swtchng angles and the unequal duty cycle of each devce, dstorton may be present n the converter waveform. To attan the optmal harmonc performance, t was found that a large number of dfferent waveform solutons are requred to nfluence the power flow through a CHB converter [9]. By decouplng the cells and ndependently controllng the modulaton ndex of each cell separately reduces the need of large number of solutons. Regrettably, ths reducton n the number of solutons potentally reduces the waveform qualty of the CHB converter because the degrees of freedom avalable n the multlevel converter waveform are not fully utlzed. ISSN: All Rghts Reserved 201 IJSETR 2353

2 Ths paper presents a SHM-PWM control method based on multlevel waveforms whch allows the requred control of power flow n a CHB converter by fully utlzng the waveform degrees of freedom. The proposed method uses the nterpolaton of LUT-based solutons for a number of mbalances thus reduce the need of very large LUTs apparent n prevous methods to control the power flow through the H-brdges asymmetrcally. defnte set of angles must be calculated for each possble mbalance scenaro for the converter, and therefore a very large number of LUTs and a complex LUT selecton scheme would be requred to practcally mplement the method. Ths paper presents a method whch may overcome ths dsadvantage by attemptng to nterpolate between LUTs. III. SHM-PWM PRINCIPLE A. Three-Level Converters Three-Cell Converters Fourer analyss can be used to study a typcal three level waveform wth k swtchng angles α( = 0,..., k 1) (Fg. 2). The ampltude of each harmonc can be obtaned usng the followng expresson where Hj s the ampltude of the jth harmonc: k1 H j [(_ 1) sn(j )] (1) j 0 (1) Fg. 1. Fve-level cascaded H-brdge converter based on the seres connecton of two three-level power cells. II. CASCADED H-BRIDGE CONVERTERS Hgher number of output voltage levels can be observed by the seres connecton of several three-level generated sngle full H-brdge as can be observed from Fg. 1. The number of seres connected sngle full H-brdge s depends on the number of output levels requred for partcular applcaton. In usual, f n power cells havng the same dc voltage are connected n seres to buld the converter, the number of levels that can be obtaned s 2n + 1. Ths topology s named the n-cell CHB converter, and t presents a hgh level of modularty and redundancy as well as an ablty to produce hgh qualty output voltage waveforms. In the applcatons of the multlevel converter t s necessary to avod the overheatng of the swtchng devces by sutable power flow among all the cells equally n order to extend the lfetme of all the elements n the converter [9]. In the topology of the multlevel converter the other, more complcated, CHB-based converter structures may requre the power flow to be controlled asymmetrcally through the converter cells. In both cases, assumng that the current s undstorted, the power flow from each cell of the converter can be decded by take n to account that the fundamental frequency component of each cell only. It s feasble to operate SHE-PWM and SHM-PWM technques to control the power flow through a CHB converter as was shown n [9]. The method reflects the use of a low swtchng frequency SHE-PWM to control power flow through the cells of a CHB converter whle stll producng hgh qualty waveforms. The dsadvantage of ths approach presented n [9] s that a Fg. 2. Three-level preprogrammed PWM swtchng pattern wth fve swtchng angles (α0, α1, α2, α3, α). Typcal output waveform of the top power cell represented n Fg. 1. By usng ths expresson a specfc value to each harmonc ampltude can be set usng the swtchng angles as degrees of freedom. The well known SHE-PWM technque s based on ths theory,.e., the ampltude of fundamental harmonc and cancel of a specfc set of harmoncs are obtaned by usng these swtchng angles [5]-[6]. The relatonshp between the dc lnk voltage of the converter and the ampltude of the generated fundamental component s called the modulaton ndex (Ma) and can be defned as Ma = H1π/Vdc.As a result of half wave symmetry n the waveform, even harmoncs have zero ampltude so the chosen harmonc orders would be 3, 5, 7,... and up to k 1 harmoncs can be cancelled usng k swtchng angles. In balanced three-phase topologes wthout a neutral connecton, the trplen harmoncs are also cancelled, and so t s possble to elmnate a very hgh number of the low-order harmoncs wth a low swtchng frequency. Summarzng, the SHE-PWM technque for three-level converters s based on solvng the followng system of equatons where q s the hghest harmonc order that wll be ISSN: All Rghts Reserved 201 IJSETR 235

3 cancelled: k1 H1 k1 [( 1) sn( )], 0 [( 1) sn(j )] 0 j 0 Where j=3,5,7,9,11,.,q (2) The SHM-PWM technque was presented n [7] says that t s not necessary to completely cancel the harmoncs n the converter ac waveform. Instead, they just have to be reduced to levels where they can be consdered allowable. The maxmum harmonc content for a grd-connected nverter can be obtaned from the lmts specfed n the actual grd codes (Lj represents the lmt for the jth harmonc). The extra flexblty gven by the SHM-PWM prncple can be used for dfferent objectves, for example reducng the THD, consderng a hgher number of harmoncs usng the same number of swtchng angles, or extendng the modulaton ndex range for the same set of vald solutons. B. Extenson to Converters wth a Hgher Number of Levels Consderng, for nstance, a waveform smlar to the pattern shown n Fg.3 but wth N levels and k swtchng angles α ( = 0,..., k 1). The SHE-PWM can be appled wth ths knd of waveform. Agan, solvng the equatons, the fundamental harmonc can be set to the desred value and k 1 harmoncs can be reduced to zero (Hj = 0 where j = 3, 5, 7, 9, 11,..., q). In order to assure that all the cells are sharng the same power ths system of equatons needs to be altered. Instead of usng the fundamental harmonc of the global waveform, the fundamental component generated by each cell s forced to be equal to the desred value. Ths way, for a N-cell converter workng wth k swtchng angles per cell only N(k 1) extra harmoncs can be cancelled. The new system of equatons can be formed wth (3) and () consderng that n () t s assumed that the angles of all the cells are reordered to generate the approprate multlevel global waveform. The SHM-PWM technque can also be appled to converters wth more than three levels. Fg. 3. Nne-level preprogrammed PWM swtchng pattern wth ten swtchng angles (α, = 0,..., 9). The waveform s symmetrcal n order to elmnate the even harmoncs. k1 H1 ( 1) sn( celln ) 0 where n=1,2,3, N (3) k1 0 (Vsn( 1 0) [V [sn(j ) sn(j 1)]]) j 1 where j=3,5,7,9,11, q () There are several optmzaton methods such as Tabu Search, Ant Colony, or Partcle Swarm [10] can be used to optmze the system. As n prevous work, n ths paper, the well known Smulated Annealng optmzaton method has been chosen because t can be adapted very easly to problems wth many dfferent constrants. In any case, t has to be observed that snce the solutons are calculated only once and then are stored n LUTs for use wth the power converter, the optmzaton method tself s of lttle mportance. IV. SHM-PWM FOR BALANCING Under mbalance condtons, t s necessary to use a strategy to adjust the modulaton ndex n order to share the power among all the cells. In [9], a method was presented based on the SHE-PWM technque that could endure any mbalance stuaton by decouplng all of the cells of the converter. Ths requred a sngle table of solutons, whch could be appled to each H-brdge of the converter to ndependently control the power flow. The dsadvantage of ths method s that t elmnates lower number of harmoncs compared wth the use of global multlevel solutons snce t does not use the multlevel waveform of the converter durng angle calculaton. In the case of ths paper, the global output waveform of the converter s used n order to ncrease the number of consdered harmoncs. Consequently, a hgher number of harmoncs can meet the grd code requrements ncreasng the qualty of the output waveform. In ths paper, three swtchng angles have been consdered for CHB converters wth two and three cells. Consderng a multcell cascaded converter, specfc LUTs can be prevously obtaned for dfferent unbalancng condtons. When the dc voltages of each cell are normalzed, the mbalance of each cell can be referred as an ncrement or decrement wth respect to the theoretcal mean value. In the rest of the paper, the followng nomenclature wll be used to defne the condtons of each LUT: (X1,X2,..., Xn) where Xn represents the mbalance of cell n, n percent, of the average desred voltage (perfect balanced stuaton). For example, consderng a two-cell converter wth a maxmum tolerable mbalance of 3%, two LUTs, S1(0, 0) and S2( 3, 3) are requred. Interpolaton between the elements of these two LUTs can be used n order to fnd the requred swtchng angles, whch acheve the requred waveform objectves over ths 0 3% mbalance range. For hgher mbalance condtons, extra LUTS could be added to extend the range. For example, the range could be extended to endure an mbalance of up to 6% usng S3( 6, 6), or 9% usng S( 9, 9), etc. The lnear nterpolaton between the swtchng angles ISSN: All Rghts Reserved 201 IJSETR 2355

4 stored n the two LUTs can be acheved usng the followng equaton on each element of the two LUTs: A. Two Cell Converters () A () B () (5) LUT1 LUT2 Ths nterpolaton method s benefcal when compared wth other methods consdered n lterature as t lmts the number of requred LUTs that are needed to acheve the waveforms objectves n the presence of a dc mbalance. For example, usng the LUTs descrbed above, for an mbalance of 1%, the constants would be A = 1/3 and B = 2/3. The next sectons show some examples for both two and three-cell CHB converters. V. SIMULATION RESULTS Ths secton presents the smulaton results that have been obtaned usng the SHM-PWM technque n a two and a three-cell CHB converter. In order to obtan solutons, whch could be easly mplemented n a real converter, real power semconductors have been consdered. A mnmum safe margn of 0.01 radans has been taken between two consecutve swtchng angles. In the computng process the lmts specfed n the EN and CIGRE WG grd codes have been consdered but any other could have been chosen. These standards nclude specfc lmts for each harmonc up to 9 th harmonc the waveform THD calculated up to 0th harmonc. Table I shows the harmonc lmts specfed n these standards. Fg. shows the swtchng angles for a two-cell topology per H-brdge. Four extra harmoncs are consdered n the global waveform, and a maxmum mbalance of 10% has been consdered n the computng process. Table. I Grd code EN50160 requrements+ Qualty grd code CIGRE WG Odd Non Trplen Odd Trplen Even Harmoncs Harmoncs Harmoncs Orde r (n) Lmt (L) Order (n) Lmt (L) Order (n) Lmt (L) 5 6% 3 5% 2 2% 7 5% 9 1.5% 1% % % % 13 3% % >10 0.2% 17 2% >21 0.2% % % % > / n Fg.. SHM-PWM swtchng angles for the case of two cells and three angles per cell n the Ma range from 0.20 to 0.80 for a balanced stuaton (black), an mbalance of 5% (blue) and an mbalance of 10% (red). In Fg.5, the harmonc content obtaned for an mbalance of 3% for the complete modulaton ndex range from 0.2 to 0.8 n steps of 0.01 can be observed. It can be seen that n all the cases the lowest harmoncs are fulfllng the grd code. The bars on ths fgure represent the lmts specfed n the grd code. The trangular waveforms show the ampltude of the correspondng harmonc component for each value of Ma n the whole range. A detaled plot showng the lowest order harmoncs s presented n Fg.6. Fg. 5. Global harmonc content and THD (on the rght) generated by the converter for each modulaton ndex value for a ( 3, 3) mbalance and 0.20 < Ma < 0.80 (more detaled n Fg. 6). Fg. 6. Detal of the low-order harmonc ampltudes generated by the converter. ISSN: All Rghts Reserved 201 IJSETR 2356

5 Fg. 7. Voltage of both cells and current(bottom) of two cell cascaded converter. B. Three Cell Converters Ths secton presents smulaton results obtaned usng a three-cell converter. Fg.8 shows the swtchng angles correspondng to a set of mbalance condtons of (0, 0, 0), ( 2, 2, ) and (, 2, 2) for the three cells. Fg. 10. Global output waveform and current(bottom) of three cell cascaded converter. It must be noted that ths strategy can be very useful to tolerate low unbalancng condtons because a hgh number of harmoncs can be controlled usng a lower number of swtchng angles. Usng a three-cell topology and three angles per cell, t s possble to set the ampltude of the fundamental component and to control up to sx undesrable harmonc components. In comparson wth the decoupled technque presented n [9], a hgher number of harmoncs can be controlled usng a lower number of swtchng angles. Ths technque could however be used n conjuncton wth the decoupled technque presented n [9], for use n systems whch may present hgher mbalance stuatons. Fg. 8. Swtchng angles for a set of mbalance condtons of (0, 0, 0) n black, ( 2, 2, ) n red and (, 2, 2) n blue. Fg. 9. Output spectrum for an mbalance of ( 1.2, 1, 1.5) and 0. < Ma < It can be observed from the above fgures that for all the values of Ma the lower harmonc components are below the lmts specfed n the grd code. For three-cell converters, the smulaton results obtaned usng the presented swtchng angles gve very low theoretcal fnal mbalance for all the condtons consdered n the computng process. VI. CONCLUSION A new method named SHMPWM to generate preprogrammed swtchng patterns to meet grd codes has been presented. The proposed SHMPWM technque adapts the power system s behavor n the new scenaro, where hgh qualty s demanded by the electrcal utltes and grd codes have to be fulflled. The proposed method s based on the calculaton of three-level PWM swtchng patterns by usng optmzaton methods, takng nto account grd codes and technologcal mplementaton requrements of the power devces. All the harmoncs and the THD are consdered as a global problem to optmze the behavor of the complete system, fulfllng specfc and actual grd codes. The proposed SHMPWM method deals wth the problem as a global optmzaton random search over the contnuous space, where all the harmoncs and the THD are taken nto account and are bounded by the appled grd code. In ths way, they are mtgated to be below the lmt mposed by the appled grd code. An example of applcatons, whch may beneft from such a scheme, s n a multlevel UPS. Dfferent smulaton results for two and three-cell converters have been ncluded to show the vablty of the technque. REFERENCES [1] S. Kouro, M. Malnowsk, K. Gopakumar, J.pou, L.G. Franquelo, B. Wu, J. Rodrguez, M. A.Perez, and J. I. Leon, Recent advances and ndustral applcatons of multlevel converters, IEEE Trans.Ind. Electron., vol. 57, no. 8, pp , Aug [2] J. Rodrguez, L. G. Franquelo, S. Kouro, J. I. Leon, R. C. Portllo, M. A. M. Prats, and M. A. Perez, Multlevel converters: An enablng technology for hgh-power applcatons, Proc. IEEE, vol. 97, no. 11, pp , Nov [3] H. Akag, S. Inoue, and T. Yosh, Control and performance of a transformerless cascade PWM STATCOM wth star confguraton, IEEE Trans. Ind. Appl., vol. 3, no., pp , Jul./Aug ISSN: All Rghts Reserved 201 IJSETR 2357

6 [] A. I. Bratcu, I. Munteanu, S. Bacha, D. Pcault, and B. Rason, Cascaded dc-dc converter photovoltac systems: Power optmzaton ssues, IEEE Trans. Ind. Electron., vol. 58, no. 2, pp ,Feb [5] H. S. Patel and R. G. Hoft, Generalzed technques of harmonc elmnaton and voltage control n thyrstor nverters: Part I harmonc elmnaton, IEEE Trans. Ind. Appl., vol. IA-9, no. 3, pp , May [6] H. S. Patel and R. G. Hoft, Generalzed technques of harmonc elmnaton and voltage control n thyrstor nverters: Part II voltage control technques, IEEE Trans. Ind. Appl., vol. IA-10, no. 5, pp , Sep [7] 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. 5, no. 6, pp , Dec [8] L. M. Tolbert, J. N. Chasson, Z. Du, and K. J. McKenze, Elmnaton of harmoncs n a multlevel converter wth nonequal DC sources, IEEE Trans. Ind. Appl., vol. 1, no. 1, pp , Jan./Feb [9] A. J. Watson, P. W. Wheeler, and J. C. Clare, A complete harmonc elmnaton approach to DC lnk voltage balancng for a cascaded multlevel rectfer, IEEE Trans. Ind. Electron., vol. 5, no. 6, pp , Dec [10] K. Sundareswaran, K. Jayant, and T. N. Shanavas, Inverter harmonc elmnaton through a colony of contnuously explorng ants, IEEE Trans. Ind. Electron., vol. 5, no. 5, pp , Oct B. Subba Reddy receved B.Tech degree n Electrcal and Electroncs Engneerng from JNT Unversty Hyderabad and M.Tech degree n Power System Operaton and Control from S.V.Unversty, Trupat. Presently workng as Assstant Professor n Sree Vdyankethan Engneerng College, Trupath. Hs research areas are power system operaton and control and Specal Machnes. G. Surendra receved B.Tech degree n Electrcal and Electroncs Engneerng from JNT Unversty Anantapur and pursung M.Tech degree n Electrcal Power System n Sree Vdyankethan Engneerng College, Trupath, my research areas are power system operaton and control. ISSN: All Rghts Reserved 201 IJSETR 2358