Three-Phase Low-Frequency Commutation Inverter for Renewables

Transcription

1 Three-Phase ow-frequency Commutaton Inverter for Renewables José Antenor Pomlo, Geomar M. Martns School of lectrcal and Computer ngneerng Unversty of Campnas C. P Campnas Brazl e-mal: Antenor@dsce.fee.uncamp.br Smone Buso, Gorgo Spazz Department of lectroncs and Informatcs Unversty of Padova Va Gradengo 6/a Padova Italy e-mal: gorgo.spazz@de.unpd.t Abstract - The connecton of dstrbuted power sources wth the utlty grd generally needs an electronc power converter for processng the locally generated power and njectng current nto the system. If the source provdes a DC voltage, the converter must be able to produce a lowdstorton, hgh-power factor AC current. The same aspects related wth the voltage and current dstorton produced by non-lnear loads can be consdered for the njecton of power nto the grd. In the absence of a specfc standard, ths paper takes as a reference the lmts for current harmoncs gven by the IC6--4 techncal report. The justfcaton for ths approach s that, from the resultng lne voltage degradaton, there s no dfference between njected and absorbed current. Ths paper presents a three-phase nverter usng low-frequency commutaton. An auxlary crcut s added to the nverter topology n order to reduce the output voltage dstorton, thus mprovng the current waveform. The man advantages of ths approach are the mnmzaton of the swtchng losses (.e. hgh effcency and the elmnaton of the MI (whch avods hgh-frequency flters necessary n hgh-frequency commutaton nverters. PWM converters can be used to produce any voltage or current waveforms. Ths modulaton technque has been used for many applcatons, ncludng the connecton of DC sources to the grd []. The man advantage of PWM nverters s the possblty of producng any current waveform, as shown n Fg.. Nevertheless these converters present some drawbacks especally related wth the MI generaton, due to the hghfrequency commutaton, and a relatvely low effcency, due to the power swtches losses [4]. A low-pass flter s necessary to attenuate the hgh-frequency components due to the swtchng process. I. INTRODUCTION The connecton of dstrbuted power sources wth the utlty grd generally needs an electronc power converter for processng the locally generated power and njectng current nto the system. If the source provdes a DC voltage, the converter must be able to produce a low-dstorton, hgh-power factor AC current. The same aspects related wth the voltage and current dstorton produced by non-lnear loads can be consdered for the njecton of power nto the grd. In the absence of a specfc standard, ths paper takes as a reference the lmts for current harmoncs gven by the IC 6--4 techncal report []. The justfcaton for ths approach s that, from the resultng lne voltage degradaton, there s no dfference between njected and absorbed current. The recommendatons proposed n [] are applcable to low-voltage sngle and three-phase systems wth nput current greater than 6 A per phase. The harmonc current lmts are a percentage of the fundamental component, measured at the rated power. For low-power applcatons, lke photovoltac panels and small fuel cells, a sngle-phase nverter (DC-AC converter can be used for connectng the alternatve source wth the grd [2]. But above a few kw t s more convenent to use three-phase nverters. Fg. Three-level PWM waveform and fltered resultng voltage. There are other converter topologes presented for grd nterfaces applcatons [5], but they also use hgh-frequency commutaton, thus MI flters are stll necessary f one s nterested n njectng a low-dstorton current nto the lne. Ths paper presents a three-phase nverter usng lowfrequency commutaton. The converter s based on the lowfrequency commutaton three-phase rectfer [6]. An auxlary crcut s added to the nverter topology n order to reduce the output voltage dstorton, thus mprovng the current waveform. The man advantages of ths approach are the mnmzaton of swtchng losses, whch ncreases the converter effcency, and the elmnaton of the MI flter. The crcut s conceved as an nterface between DC sources and AC lnes and does not present the capablty of compensatng local load current dstortons. A comparson among low and hgh frequency commutaton rectfers was presented n [7]. Most of the conclusons can be extended to DC-AC topologes. The most mportant aspects are that the swtchng losses ask for a hgh heat-snk volume and the lmtaton of the conducted MI needs a huge flter. In both cases the consequence s the reducton of the overall converter power densty.

2 It s not possble, wthout a specfc study, to conclude whch converter would present the hghest power densty, but one should not prevously dscard the low frequency commutaton alternatve. II. TH PROPOSD TOPOOGY Fg. 2 shows the proposed converter topology. The brdge swtches are controlled so as to apply at the nverter termnals a voltage that results n a quassnusodal lne current. ach brdge swtch operates at the lne frequency, whle the auxlary swtches at twce ths frequency, as shown n Fg.. The fundamental component of the nverter voltage (v nv must be adjusted to produce the desred current through the output nductor. The desgn procedure s orented to select the mnmum nductance value that smultaneously allows generatng the rated power and complyng wth the current harmonc lmts. The nductor voltage v must lead by 9 the respectve lne voltage to mnmze the RMS lne current, as shown n Fg. 4. Ths procedure maxmzes the resultng power factor. Fg. Typcal swtches command sgnals. v δ v nv v v an S S 4 S 2 S 5 S S 6 S a S a2 S a Fg. 4 Phasoral representaton of the voltages on phase a Wthout the auxlary crcut operaton, the nverter lneto-lne output voltage presents a three level waveform whle the lne-to-neutral voltage has four levels, both waveforms wth sharp edges, as shown n Fg. 5. The current harmoncs wll depend on the voltage components of the lne-to-neutral voltage, dvded by the respectve reactance. The effect of the auxlary crcut, as shown n Fg. 6, s to smooth the edges, thus reducng the harmonc components of the nverter output voltage and allowng reducng the nductance needed to comply wth the standard. n Van Vbn Vcn Statc swtch... ocal load a v b c S S2 S V nv S 4 S 5 S 6 S a C S a2 S a C 2 v c2 DC to DC converter FC Possble bdrectonal swtch mplementaton (S a Fg. 2 Three-phase nverter and the b-drectonal swtch.

3 V ne - to - lne voltage ne - to - neutral voltage Grd voltage Fg. 5 Inverter output voltages, wthout the auxlary crcut. v nv (nverter output voltage θ θ 2 θ θ 4 θ 5 π π+θ π+θ2 π+θ π+θ4 π+θ5 2π θ Fg. 6 Inverter output voltages wth the auxlary crcut. The nductor voltage s the dfference between the lne and the nverter voltage: v ( θ = v ( θ V snθ nv p The current njected nto the grd s: = θ θ ω v ( d ( The peak-to-peak capactor voltage varaton s V r.. Ths value can vary from (for a complete excurson to (for a nfnte capactance or null resonant nterval. In the next analyss the resonant nterval s approxmated as a snusodal varaton. In fact t s not, due to the harmonc currents, but as wll be shown, the results are qute smlar. For <θ<θ v nv = (2 θ = Vp ( cos( ( + θ ( ω + For θ <θ<θ 2 v + sn[ α( θ θ ] nv = (4 2 6 = ( θ + ω V 2 + Vp α r ( θ θ 6 cos( θ { [ ] } cos α( θ θ (5 For θ 2 <θ<θ 2 v nv = (6 2( θ θ2 = Vp ( cos( cos( 2 + ( θ2 + θ θ ω (7 For θ <θ<θ 4 v + sn[ α( θ θ ] nv = = (8 2 6 ( θ + ω α ( θ θ + V cos( θ p { cos[ α( θ θ ] } (9 For θ 4 <θ<θ 5 v nv = ( ( θ θ ω 4 = + V cos( θ + ( θ ( p 4 4 For θ 5 <θ<π vnv = { 2sn[ α( θ θ5 ]} (2 ( ( θ θ5 + Vp cos( θ cos( θ5 = ( θ + { [ ] } ( 5 ω 2 + cos α( θ θ5 α Durng the negatve sem-cycle: For π<θ<π+θ v nv = (4 ( θ = Vp ( cos( + ( π + θ + (5 ω For π+θ <θ<π+θ 2 + sn[ α( θ θ ] v nv = (6 2 6 V r + ( θ θ + Vp cos( θ 2 6 = ( θ + { [ ] } ω + cos α( θ θ α (7 For π+θ 2 <θ<π+θ 2 v nv = (8 2( θ θ 2 = + ( θ (9 ω + Vp cos( θ 2 2 For π+θ <θ<π+θ 4 + sn[ α( θ θ ] v nv = (2 2 6 ( θ θ 2 6 = ( θ + + Vp cos( θ { [ ] } (2 ω cos α( θ θ α For π+θ 4 <θ<π+θ 5 v nv = (22

4 ( θ θ4 = Vp 4 + ω 4 (2 For π+θ 5 <θ<2π v nv = { 2sn[ α( θ θ5 ]} (24 ( θ θ5 = + Vp cos( θ5 + π + ( θ5 (25 ω 2 { cos[ α( θ θ5 ] } α cos( θ + ( θ The selected nductance value wll be determned by the resonant angle that results n untary dsplacement factor (DF. Through numercal smulatons t s possble to determne the relatonshp between the resonant angle, θ r, and the angle δ (that results DF=, and the RMS value of the nverter voltage fundamental component. As can be seen, the K factor s almost constant all over the resonant angle range and ts average value s.48 mv -. θ r =. 5 δ (26 V = V K (27 nv III. DSIGN PROCDUR For a gven maxmum current, assocated wth the rated power, and n order to mnmze the nput nductance, t s nterestng to reduce the phase-shft δ. However, whle the fundamental component of the current depends on the dfference between the grd and the nverter voltages, the harmoncs depend only on the nverter waveform. Theoretcally, consderng only the fundamental component, the nput nductance could tend to zero. In such a stuaton the harmoncs would tend to nfnty! Fg. 7 shows the necessary nductance for each harmonc component, as a functon of the resonant nterval duraton expressed n degrees. Notce that typcally, for a wder resonant nterval, the necessary nductance reduces, due to the reducton of the harmonc components. For the fundamental component the rated current s consdered, whle for the harmoncs the lmts are gven by []. The best soluton s the mnmum nductance that allows njectng the nomnal current whle guaranteeng an acceptable harmonc content. In Fg 7, for a DC voltage of 5 V and a rated power of kw, selectng the nductance determned by the fundamental component the harmoncs wll comply wth the lmtatons for any resonant nterval. Inductance [H] st K [/kv],6,5,4, Resonant Angle ( Fg. 8 Parameter K for dfferent resonant angles. The nput data are: lne voltage, V, and rated power (per phase, P max. For P max the capactor voltage excurson n complete (V r =. Based on numercal calculus, fnd the mnmum DC lnk voltage,, for whch the nductance assocated wth the fundamental component are always hgher than the values calculated for the harmoncs, as done n fg stmate the nverter voltage fundamental component: Vnv = V K Known V and V nv, determne V e δ V δ = a cos Vnv V = V tan( δ (28 4 Determne θ r. 5 Determne accordng to Fg. 7 (specfc for each set of parameters. 6 Numercally, determne the average current durng the nterval θ 5 to π (Im and evaluate the capactor value: Im θr C = 2 ω (29 Resonant angle (degrees Fg. 7 Mnmum nductance for complance wth []. 5th IV. SIMUATION RSUTS Fg. 9 shows the current waveform and the respectve spectrum, at rated power. In ths smulaton, for a 27/22 V grd, the component values are: 5.9 mh nput nductance, 6 µf resonant capactance. The rated power njected nto the grd s kw, correspondng to 26 A RMS. The DC voltage s 5 V. The Total Harmonc Dstorton (THD of the current

5 s % and the harmoncs comply wth the recommended lmtatons. Inverter voltage Phase voltage V Current (x Fg. - Output voltage waveform for slandng condton. - V. XPRIMNTA RSUTS % A prelmnary prototype, operatng wthout the auxlary crcut has been tested n order to verfy the crcut behavor and the desgn procedure. The man waveforms are shown n Fg.. The DC voltage s V, the AC lne voltage s 55V RMS, and the nverter s connected wth the lne through a three-phase transformer bank. 2% Hz.2kHz.kHz 2.kHz Frequency Fg. 9 Voltage and current waveforms and normalzed current spectrum. For reduced power generaton there are dfferent possbltes: reducng the DC voltage, adjustng the phase shft between the grd voltage and the nverter voltage, modulatng the swtches' duty-cycle or even a combnaton of these. Another stuaton that must be consdered s the slandng. In ths case the lne must be dsconnected and the nverter wll supply the local load. It s necessary to ensure a local synchronsm and stablze the AC voltage. Usng a DC voltage next to the lne peak voltage, and mantanng the swtchng pattern, the resultng waveform wll be the same as shown n Fg. 9. The voltage THD s 22%. A lower dstorton can be obtaned by addng a capactve flter at the output, as shown n Fg.. The voltage waveform wll be mproved for a domnantly resstve load. The THD s 9.5%, the peak voltage s mantaned as compared wth the nomnal lne-to-phase voltage. For non-lnear loads (lke rectfers, the output flter resonance can degrade the waveform. When the lne voltage returns, t s necessary to guarantee synchronzaton before the reconnecton. Fg. Inverter voltage ( V/dv., ne voltage (75 V/dv. and lne current (5 A/dv.. Horz. 5ms/dv. VI. CONCUSIONS The proposed three-phase, low-frequency commutaton nverter presents some nterestng characterstcs f one s lookng for low-cost, good-qualty nverters sutable for dstrbuted generaton systems, based on DC prmary sources, connected wth the utlty grd. Takng as qualty parameter, the current dstorton lmts establshed by nternatonal standards, the current njected nto the grd by the topology presents low dstorton and hgh-power factor. As the crcut operates at the lne frequency, MI flters are not necessary, and the swtchng losses can be neglected, thus reducng the heatsnk area. The desgn procedure mnmzes the nductance and the DC voltage value. If t would be necessary to control the njected power, t could be done controllng the auxlary swtches conducton tme.

6 ACKNOWDGMNT Authors would lke to ackowledge the Fundação de Amparo à Pesqusa do stado de São Paulo FAPSP and Fundação CAPS by supportng of ths project. RFRNCS [] IC 6--4, Frst dton 998-, Commsson lectrotechnque Internatonale,, rue de Varembé, Genève, Swtzerland. [2] G. M. Martns, J. A. Pomlo, S. Buso: A Sngle- Phase ow-frequency Commutaton Inverter for Renewables, I ICON, Denver, USA, Nov/Dec 2. [] G. A. O Sullvan, Fuel Cell Inverter for Utlty Applcatons, CD-ROM of the I Power lectroncs Specalsts Conference, Galway, Ireland, June 2. [4] U.S. Departament of nergy et al., 2 Future nergy Challenge, Homepage UR: HYPRINK turenergychallenge [5] G. edwch and P. Wang, Smple Grd Interfaces for Renewables, Internatonal Journal of Renewable nergy ngneerng, vol., No. 2, August 999, pp [6] J. A. G. Marafão, J. A. Pomlo, G. Spazz, Improved three-phase hgh-qualty rectfer wth lne-commutated swtches, CD-ROM of the I Power lectroncs Specalsts Conference, Vancouver, Canada, June 2. [7] J. A. Pomlo, G. Spazz, S. Buso, Comparson among Hgh-Frequency and ne-frequency Commutated rectfers Complyng wth IC Standards, CD-ROM of the I IAS Conference, Rome, Italy, Oct. 2. [8] N6--2, mts for harmonc current emssons (equpment nput current up to and ncludng 6A per phase Frst dton 995, uropean Commttee for lectrotechncal Standardzaton, Brussels, Belgque. APPNDIX The techncal report IC 6--4 stablshes mtaton of emsson of harmonc currents n lowvoltage power supply systems for equpment wth rated current greater than 6 A per phase. The lmts shown n Table I are those called stage : current emsson values for smplfed connecton of equpment (S equ S sc /, reported n Table I. As we can see, each harmonc current lmt s specfed as a functon of the rated fundamental current (up to the 4 th harmonc. Ths fact allows to analyze the converter nput current normalzed to a unty fundamental current, so as to obtan results that are ndependent of the nput power. If the nput current s lower than 6 A, one should consder the constant lmts gven by N 6--2 [8], class A, shown n Table II. Table I - mts of techncal report IC 6--4: "Stage: current emsson values for smplfed connecton of equpment (S equ S sc /" Harmonc number n Admssble harmonc current I n /I * % ven 8/n or.6 Table II - N 6--2 mts for harmonc current emssons (equpment nput current up to and ncludng 6A Harmonc number Class A lmts n [A rms ] < n < /n < n < 4.84/n