EFFECTIVE HARMONIC MITIGATION TECHNIQUES USING WAVELETS BASED ANALYSIS

Transcription

1 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) EFFECTIVE HARMONIC MITIGATION TECHNIQUES USING WAVELETS BASED ANALYSIS R.KAMESWARA RAO 1 Electrcal and Electroncs Engneerng Departent, Jntu College Of Engneerng, Kaknada, Andhra Pradesh, Inda rkaeswara@gal.co G.RAVI KUMAR Electrcal and Electroncs Engneerng Departent, Bapatla Engneerng College, Bapatla, Andhra Pradesh, Inda gol.ravkuar@yahoo.co S.S.TULASI RAM 3 Electrcal and Electroncs Engneerng Departent, Jntu College Of Engneerng, Kaknada, Andhra Pradesh, Inda rasankara@gal.co Abstract - The haronc currents are generated by sngle phase nonlnear loads. The rror surplus haronc elnaton ethod s used ostly because of ts less coputaton. The Selectve Haronc Elnaton Pulse Wdth Modulaton (SHEPWM) based ethods can provde theoretcally the hghest qualty output aong all the PWM ethods. In ths paper SHEPWM odel of a ultlevel seres connected voltage source nverter s developed whch can be used for an arbtrary nuber of levels and swtchng angles. Ths paper descrbes the analyss of haronc elnaton ethods wth wavelet transfor ethod. For the analyss of haronc coponents Wavelet bor6.8 verson s used. The haroncs ust be reduced n order to reduce the sze of the flters. Selectve haronc elnaton ethod totally elnates a partcularly selected haronc ether of lower order or hgher order, there by Total Current Haronc Dstorton (THD) can be reduced to a large extent. Keywords: THD; SHEPWM; PWM; OMTHD; OHSW 1. Introducton Dstrbuted sngle phase power electronc loads are very sgnfcant source of haroncs n electrc power dstrbuton syste. The haronc currents generated by sngle phase nonlnear loads such as desk top coputers and florescent laps cause apprecable dstorton n dstrbuton feeder when consder ore n nuber. The rror surplus haronc elnaton ethod s used ostly because of ts less coputaton. The SHEPWM based ethods can provde theoretcally the hghest qualty output aong all the PWM ethods. In ths paper SHEPWM [1] odel of a ultlevel seres connected voltage source nverter s developed whch can be used for an arbtrary nuber of levels and swtchng angles. 1.1 Prograed PWM technque In 1973, the selected haronc elnaton ethod for PWM nverters was ntroduced for sngle-cell (two and three-level) nverters. Ths ethod s soetes called as prograed PWM technque. It llustrates the general quarter-wave syetrc trple-level prograed PWM swtchng pattern. The square wave s chopped tes per half cycle. Owng to the syetres n the PWM wavefor, only odd haroncs exst. The Fourer ISSN : Vol. 3 No. 8 August

2 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) coeffcents of odd haroncs n trple level prograed PWM nverters wth odd swtchng angles are gven by 4 E j b [cos cos.. ( 1) 1 n n1 n cos n j n (1)... cos n ] Where n s haronc order. Any haroncs can be elnated by solvng equatons obtaned fro settng above equaton equal to zero. Usually Newton teraton ethod [] s used to solve these non-lnear equatons, the condton [3] ust be satsfed s () Each cell of such a sngle-phase nverter swtches and produces a three-level {-1, 0, 1} PWM wavefor. Ths results n a fve-level -, -1, 0, 1, nverter output. Theoretcally, odd haroncs can be elnated fro the nverter s spectru whle keepng the fundaental coponents of both cells equal to each other. The swtchng angles ust be obtaned fro the followng syste of nonlnear transcendental equatons: ( 1) 1 cos M ( 1) cos M ( 1) cos 3 ( 1) cos ( 1) cos(4 3) ( 1) cos (4-3) (3) Where α s the swtchng angle of the frst cell, β s the swtchng angles of the other cell, and M s the odulaton ndex. Ths paper explctly requres an even fundaental power sharng aong cells. The Convergence of nuercal procedures used to solve (3) s senstve to the startng values of swtchng angles and requres consderable coputaton 1. Mrror surplus haronc PWM technque Elnaton of low-order haroncs fro only one cell, whch wll be called a general SHEPWM ethod, can be obtaned by solvng a syste of equatons. 1 ( 1) cos 4 1 M 1 ( 1) cos ( 1) cos( 1) 0 (4) 1 The frst sgnfcant surplus haronc fro ths cell has apltude A +1. If t s desred to elnate A +1 fro the output spectru of the sngle-phase nverter, the other cell ust produce the +1 haronc of apltude -A +1. To preserve the elnaton -1 of the low-order odd haroncs and to set the apltude +1 of the haronc to -A +1, the nuber of swtchng angles n the second cell ust be ncreased by one to +1. The swtchng angles of the second cell fulfll the followng syste of +1 equaton: ISSN : Vol. 3 No. 8 August

3 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) ( 1) ( 1) ( 1) cos 4 cos 3 0 M cos( 1) 0 ( 1) (5) 1 1 ( 1) cos( 1) A An unexpected beneft of such a +1 haronc cancellaton s that the whole frst cluster of sgnfcant haroncs fro the second cell becoes nearly a rror age of the frst cluster of sgnfcant haroncs fro the frst cell. Thus, the soluton of (4) and (5) approxates very closely the soluton of (3). Slar odels can be developed for three-phase systes. The dfference between sngle- and three-phase calculatons s that for a three-phase syste trplen haroncs need not be ncluded n the set of haroncs selected for elnaton. The cancellaton of haroncs usng (4) and (5) wll be called a rror surplus haronc PWM technque. Ths cancellaton has been checked for several values of and for a wde range of the odulaton ndex M. Snce the syste of equatons as n (4) do not have analytcal solutons, t s dffcult to fnd a theoretcal explanaton for the proposed ethod. It wll be an portant topc for future research. Nevertheless, the proposed approach s a practcal way of fndng an approxate soluton to (3) and hence the haronc suppresson n double-cell seres-connected nverters. The an advantage of ths ethod s that the proposed approach s a practcal way of fndng an approxate soluton of prograed PWM technque equatons and hence haronc suppresson s acheved n double cell seres connected nverters. 1.3 Optal nzaton of total haronc dstorton technque The basc dea for ths ethod s to adjust swtchng angles n order to nze the output voltage THD. To nze the THD, t s necessary for ts partal dervatve to be zero wth respect to each swtchng angle. Ths ples that the partal dervatve of ts square s also zero because the value of THD s always postve. After developent and soe atheatcal splfcatons, the square THD of the chosen ult-level generalzed wavefor (perodc wth odd quarter-wave syetrc characterstc) s gven by: THD S Vk 1V 1 j k 1 8 S k 1 S j V j V cos k k V j1 j 1 V 1 (6) It s assued that the dc sources were all equal. It s also notced that there s no control on the fundaental coponent of the output voltage. Ths eans that Optzed Method of THD (OMTHD) technque s appled only for THD nzaton wth no constrant on the value of fundaental coponent; where as, the prary objectve n any ethod of nverter control s the adjustent of the fundaental coponent to the desred value. OMTHD technque s appled to the cascaded ult-level nverter wth unequal dc sources to nze THD whle producng the desred fundaental coponent at the output. On the other hand, the fundaental coponent ust have the desred value V f. Ths ples that swtchng angles ust also satsfy the followng equaton: V 1dc cos ( 1) Vdc cos ( )... VSdc cos ( S ) a (7) ISSN : Vol. 3 No. 8 August

4 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST). Haroncs A haronc s a sgnal or wave whose frequency s an ntegral (whole-nuber) ultple of the frequency of soe reference sgnal or wave. For nstance, wth a fundaental frequency of 60Hz, the 3rd haronc frequency s 180Hz (3 x 60Hz). Fg.1. Haronc wavefor The current drawn by non-lnear loads s perodc but not snusodal. Perodc wavefors are descrbed atheatcally as a seres of snusodal wavefors that are sued together. Snusodal coponents are nteger ultples of the fundaental frequency whch s 60 Hz n the Unted States. Haroncs are ultples of the fundaental frequency, as shown n Fgure 1. Total haronc dstorton s the contrbuton of all the haronc frequency currents to the fundaental. The total haronc dstorton, or THD, of a sgnal s a easureent of the haronc dstorton present and s defned as the rato of the su of the powers of all haronc coponents to the power of the Fundaental frequency..1 Selectve Haronc Elnaton Method Ths ethod totally elnates a partcularly selected haronc ether of lower order or of hgher order; thereby THD can be reduced to a large extent [4]. Ths provdes the hghest qualty output to the syste when copared to the other ethods and a pure snusodal wave can be obtaned. Ths ethod can be appled to dfferent nverters of ult levels. Ths paper focuses on seres-connected voltage-source PWM nverters. The Selectve Haronc Elnaton pulse wdth odulaton (SHEPWM) based ethods [5] can theoretcally provde the hghest qualty output aong all the PWM ethods. The SHEPWM ethod presented n ths paper offers the sae nuber of control varables as the nuber of nverter levels. The results gven n are only for a fve-level nverter allowng up to seven swtchng angles wthout takng nto account that nverter cells should equally share the output power. The SHEPWM odel of a ultlevel seres-connected voltagesource nverter s developed whch can be used for an arbtrary nuber of levels and swtchng angles. 3. Mult Level Inverter MULTI-LEVEL nverter [6] and [7] s recently used n any ndustral applcatons such as ac power supples, statc VAR copensators, drve systes etc. One of the sgnfcant advantages of ult-level structure s the haronc reducton n the output wavefor wthout ncreasng swtchng frequency or decreasng the nverter output power. The output voltage wavefor of a ult-level nverter s coposed of a nuber of levels of voltages, typcally obtaned fro capactor voltage sources. The so-called ult-level starts fro three levels [8]. As the nuber of levels ncreases, the output THD approaches zero. The nuber of achevable voltage levels, however, s lted by voltage unbalance probles, voltage clapng requreent, crcut layout, and packagng constrants. Therefore an portant key n desgnng an effectve and effcent ult-level nverter s to ensure that the total haronc dstorton (THD) n the output voltage wavefor s sall enough. The total haronc dstorton of the output current decreases as the nuber of levels of the generated output voltage ncreases. The ult level starts fro 3 levels. The an advantage of ult level structure s the haronc reducton n the output wavefor wthout ncreasng swtchng frequency or decreasng the nverter output power. As the nuber of levels ncreases, the output THD approaches zero. 4. Wavelet Analyss In atheatcs, wavelets, wavelet analyss and the wavelet transfor refers to the representaton of a sgnal n ters of a fnte length or fast decayng oscllatng wavefor known as other wavelet. ISSN : Vol. 3 No. 8 August

5 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) Ths wavefor s scaled and translated to atch the nput sgnal. In foral ters, ths representaton s wavelet seres, whch s the coordnate representaton of square ntegrable functon wth respect to a coplete, orthonoral set of bass functon for the Hlbert space of square ntegral functons. The word wavelet s due to Morlet and Grossan n the early 1980s. They used the French word ondeletteeanng sall wave. A lttle later t was transfored nto Englsh by translatng ondo nto wave -gvng wavelet. Wavelet analyss [9] represents a next logc step descrbng a wndowng technque wth varable szed regons. The Wavelet analyss allows the use of longte ntervals when ore precse low-frequency nforaton s needed and shorter regons when hgh frequency nforaton s needed. Wavelet analyss does not use a te-frequency regon, but rather a te-scale regon. Wavelet theory s applcable to several other subjects. All wavelet transfors ay be consdered to be fors of te-frequency representaton and therefore are, related to the subject of haronc analyss. Alost all practcally useful dscrete wavelet transfors ake use of flter banks contanng fnte pulse response flters. The wavelets forng a Contnuous Wave Transfor (CWT) are subject to Hesenberg s uncertanty prncple and equvalently, dscrete wavelet bases ay be consdered n the context of other fors of the uncertanty prncple The prncpal dfference between the CWT and the Dscrete Wave Transfor (DWT) s that CWT operates over every possble scale and translaton whereas DWT uses a specfc subset of all scale and translaton values. There are nuber of ways of defnng a wavelet (or a wavelet faly). 4.1 Scalng flter: The wavelet s entrely defned by the scalng flter g a low pass pulse response (FIR) flter of length of length N and su1. In Borthogonal wavelets, separate decoposton and reconstructon flters the te reverse of the decoposton. Daubeches and Sylet wavelets can be defned by the scalng flter. 4. Scalng functon: Wavelets are defned by the wavelet functon Ψ (t) (.e; the other wavelet) and scalng functon Φ (t) (also called father wavelet) n the te doan. The scalng functon flters the lowest level of the transfor and ensures that the spectru s covered. For a wavelet wth copact support, Φ (t) can be consdered fnte n length and s equvalent to the scalng flter g. Meyer wavelets can be defned by scalng functons. 4.3 Wavelet functon: The wavelet only has a te doan representaton as the wavelet functon Ψ (t). Mexcan hat wavelets can be defned by a wavelet functon. The contnuous wavelet transfor was developed as an alternatve approach to the short te Fourer transfors to overcoe the resoluton proble. ISSN : Vol. 3 No. 8 August

6 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) 5. Sulaton Results The fgures.4, 8 and 1 shows the sulaton dagras,fg.5, 9 and 13 show the coparatve analyss of THD usng FFT Fg. 6,10,11,14,15 show the haroncs analyss usng wavelet. 5.1 Sulaton Of Frst Cell Of Sngle Phase Double Cell Seres Connected PWM Inverter Fg: 4 Scheatc dagra of frst cell for sngle phase double cell seres connected PWM nverter. Fg 5: sngle phase spectra and wave fors for frst cell (a) output voltage wavefor (b) frequency spectra ISSN : Vol. 3 No. 8 August

7 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) Fg 6: Wavelet Analyss of sngle phase spectra and wave fors for frst cell output voltage wavefor detaled coeffcent spectra. Fg 7: Wavelet Analyss of sngle phase spectra THD wave fors for frst cell output voltage wavefor detaled coeffcent spectra. 5. Sulaton Result For Second Cell Of Sngle Phase Double Cell Seres Connected PWM Inverter Fg 8: Scheatc dagra of a sngle phase double cell seres connected PWM nverter. 5.3 Sulaton Result For Sngle Phase Double Cell Seres Connected PWM Inverter ISSN : Vol. 3 No. 8 August

8 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) Fg 9. (a) Inverter output voltage (b) Frequency spectru Fg 10: Wavelet analyss of a sngle phase double cell seres connected PWM nverter. Fg 11: Wavelet analyss of a sngle phase double cell seres connected PWM nverter THD Analyss. ISSN : Vol. 3 No. 8 August

9 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) 5.4 Sulaton Result For Optzed Haronc Stepped Wavefor (OHSW) Fg 1: Scheatc dagra of OHSW Technque. Fg 13: Haronc spectra of OHSW Fg 14: Wavelet analyss of OHSW Technque. ISSN : Vol. 3 No. 8 August

10 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) Fg 15: Wavelet analyss of OHSW Technque THD analyss. 6. Concluson A ore effectve ethod of haronc suppresson s descrbed. Mrror surplus haronc elnaton PWM technque s the effectve ethod to elnate selected lower order haroncs copared to other pulse wdth odulaton technques wth added advantage of elnatng the selected haroncs copletely. In the selected two haronc elnaton ethod angles were found to generate pulses to the nverter and observed that THD reduced and also notced that selected lower order haroncs were elnated effectvely, at output stage n rror surplus technque and t requred only two cells to elnate any nuber of haroncs. Ths s an added advantage for ths ethod where as n OHSW technque the THD was reduced effectvely. As seen fro the above observatons Wavelets wll support n a ore effectve way to analyze haroncs n current and voltage wavefors. References [1] P. M. Bhagwat and V. R. Stefanovc. (1983). Generalzed structure of a Multlevel PWM nverter, IEEE Trans. Ind. Applcant., vol. IA-19, pp [] Tjallng J. Ypa, (004). Hstorcal developent of the Newton-Raphson ethod, SIAM Revew 37 (4), , Do: / P. Deuflhard, Newton Methods for Nonlnear Probles. Affne Invarance and Adaptve Algorths. Sprnger Seres n Coputatonal Matheatcs, Vol. 35. Sprnger, Berln, ISBN [3] Carrara, D. Casn, S. Gardella, and R. Salutar. (1993). Optal PWM for the control of ultlevel voltage source nverter, n Proc. 5th European Conf. Power Electroncs and Applcatons, vol. 4, Brghton, U.K., pp , Sept [4] Multlevel Selectve Haronc Elnaton PWM Technque n Seres-Connected Voltage Inverters, (000). IEEE Transactons on Industry Applcatons, vol. 3, no. 1, pp , [5] Ajay Maheswar, Kha D. T. Ngo, (1993). Synthess of 6-step PWM wavefors wth Selectve Haronc Elnaton, IEEE Transactons on Power electroncs, Vol.8, No.4, pp [6] M. Marcheson and M. Mazzucchell. (1993). Multlevel converters for hgh power ac drves: A revew, n Proc. IEEE Int. Syp. Industral Electroncs, pp [7] Prasad N. Enjet, Meber, IEEE, Phovos D. Zogas, Senor Meber, IEEE, and Jaes F. Lndsay, Senor Meber, IEEE, A Current Source PWM Inverter wth Instantaneous Current Control Capablty, Industry Apllcatons Socety Annual Meetng, Conference record of the 1988 IEEE. [8] J. S. La and F. Z. Peng. (1996). Multlevel converter-a new breed of power converters IEEE Trans. Ind. Applcat., vol. 3, pp [9] Aara Graps, An Introducton towavelets, (1995). IEEE Coputatonal Scence and Engneerng, Vol., No., also avalable on the Web at wth a varety of otherwaveletsresources. ISSN : Vol. 3 No. 8 August

11 R.Kaeswara Rao. et al. / Internatonal Journal of Engneerng Scence and Technology (IJEST) Bography R. Kaeswara Rao receved B. Tech and M.Tech degrees n Electrcal Engneerng fro JNTU College of Engneerng, Kaknada. He s presently workng as Assocate professor n Electrcal and Electroncs Engneerng departent n the sae college. Hs areas of nterest nclude Power qualty and Haroncs analyss. G.RavKuar graduated fro Andhra Unversty College of Engneerng, Vsakhapatna, Inda and receved M.Tech fro JNTU College of Engneerng, Kaknada. He s currently workng as Assocate professor n EEE Departent at Bapatla Engneerng College, Bapatla, Inda. Hs areas of nterest are Power Syste operaton and Control, Power Syste Protecton. Dr.S.S.Tulas Ra receved B. Tech, M.Tech and Ph.D degrees n Electrcal Engneerng fro JNTU College of Engneerng, Kaknada. He s currently workng as professor of Electrcal and Electroncs Engneerng n the sae college. Hs areas of nterest nclude hgh voltage engneerng, Power syste analyss and control. ISSN : Vol. 3 No. 8 August