Improvement of the Shunt Actve Power Flter Dynamc Performance Krzysztof Potr Sozansk Unversty of Zelona Góra, Faculty of Electrcal Engneerng omputer Scence and Telecommuncatons Zelona Góra, Poland Abstract Ths paper descrbes the proposed actve power flter (APF) wth a modfed output nverter. When the value of load current changes rapdly, the APF transent response s too slow, the lne current suffers from dynamc dstorton. Ths dstorton causes an ncrease of harmonc content n the lne current, whch s depent on a tme constant. The APF control current dynamcs s depent on the nverter output tme constant consstng of APF output nductance and resultant mpedance of load and mans. Accordng to ths modfcaton the APF dynamcs are mproved. The Matlab smulaton results of the modfed APF are also presented n the paper. As an example a control crcut for a three-phase 75 kva parallel actve power flter (APF) s used. I. INTRODUTION Shunt actve power flters (APF) are one of the best devces for compensatng the harmoncs and asymmetres of the mans currents caused by nonlnear loads. A harmonc compensaton crcut wth current-fed actve power flter wthout feedback (wth unty gan) s depcted n Fg., where Z S represents the mans power lne mpedance, Z represents nonlnear load, u S mans power lne voltage. The shunt actve power flter njects A power current to cancel the man A harmonc content. The lne current S s the result of summng the load current and the compensatng current = +. () S A smplfed lock dagram of the actve power compensaton crcut (bult by a team n our Insttute) wth the parallel APF for a power of 75 kva s depcted n Fg. a. The crcut conssts of a power part wth a three-phase IGBT power transstor brdge IPM (ntellgent power module) connected to the A mans through an nductve flterng system composed of nductors,, 3. The APF crcut contans D energy storage, ensured by two capactors and. The control crcut s realzed usng the dgtal sgnal processor ADSP-364 (EZ-KIT te). The actve power flter njects the harmonc currents,, 3 nto the power network and offers a notable compensaton for harmoncs, reactve power and unbalance. The APF control current dynamc s depent on the nverter output tme constant, tself resultng from APF output nductance and resultant mpedance of load and A Mans Power 3x4V e ZS e e3 ZS ZS3 3 N PE 4.8 mf 4.8 mf u 3 u u S S S3 3.6 mh f 3uF f 3uF f3 3uF 3.6 mh 3*PM3D SA 3 P (4Hz).6 mh ADSP-364 (EZ-KIT te) u, u Nonlnear oads Z Z Z3 Power System Actve Power Flter Nonlnear oad Z S S u S APF ontrol rcut Z Fgure.. Harmonc compensaton crcut wth current-fed actve power flter wthout feedback (wth unty gan) Fgure. lasscal three-phase shunt actve power flter: tests crcut, expermental waveforms of actve power flter n steady-state wth the resstve load: load current (red), lne current S (blue).
mans power lne (Fg.. When the value of load current changes rapdly, as n current n Fg. b, the APF transent response s too slow [4], [3] the lne current S suffers from dynamc dstorton. Ths dstorton causes an ncrease of harmonc content n the lne current, whch s depent on a tme constant. In the APF shown n Fg. the THD rato s ncreased by about %. The loads can be dvded nto two man categores: predctable loads and nose-lke loads. Most loads belong to the frst category. For ths reason t s possble to predct current values n subsequent perods, after a few perods of observaton [5], [6]. Possble solutons for mprovement of APF dynamc are shown n Table I. TABE I. DISUSSION ABOUT POSSIBE SOUTIONS For predctable loads. Typcal APF wth non-causal control algorthm. Typcal APF wth repettve control algorthm For unpredctable loads. Hgh speed APF. Set of two APFs: - hgh power low speed APF, - low power hgh speed APF. 3. APF wth modfed output nverter In ths paper s descrbed APF wth modfed output nverter sutable for both types of loads. II. APF OUTPUT INVERTER A dagram of a smple power nverter model connected to the mans power s shown n Fg. 3a, where s an output flter capactance, for dumpng modulaton components. In ths crcut the tme constant s manly depent on nductor value. Therefore when the transstor swtchng perod T s =/f s s much less than the crcut tme constant τ t s possble to smplfy the crcut (Fg. 3 to the crcut shown n Fg. 3b. The crcut resultant resstance R s the sum of R Q, the resstance of transstor Q n the swtched-on state, and R, the resstance of nductor R = R + R + R. () Q For swtchng state S =, S = compensatng current can be calculated by formula R t R t u Dp S = e + ( ) t e Rc and for state S =, S = can be calculated by formula where: If t s assumed that R t R t Dn S = e + ( ) t e Rc, (3), (4) τ =. (5) R f s >> and fs >>, (6) τ T where: T M mans perod, durng the swtchng perod T s, and voltages u S, u Dp, u Dn are constant, and that average current s constant too, then the output current can be calculated by smplfed equatons: for state S =, S = u + and for state S =, S = Dp S = t, (7) n M Dn S = p + t, (8) where: t t swtch-on tme for S, t -t swtch-on tme for S. A tme dagram of dealzed compensatng current s shown n Fg. 4. Output rpple can be calculated by the equaton u Dp S R u S Δ u ( t ) Dp S Dn S = t = t. (9) u Dn S Fgure 3. Dagrams of APF output nverter connected to the mans power: smplfed crcut, smplfed nverter model connected to the mans power, used for current rpple calculaton The voltage value at capactors and s stablzed by a voltage controller and s equal to u D; ths s why t s possble to descrbe u D = u Dp = u Dn. To acheve low dynamc dstorton the output current slew rate must be hgh. The slew rate can be calculated by the formula
Fgure 4. Tme dagram of dealzed compensatng current d dt ( t) ± u ( t) D S =. () urrently IGBT transstors are mostly used as swtchng elements n the nverters. For the ordnary IGBT the maxmum swtchng frequency s equal to khz and around 6 khz for fast IGBT. The transstor swtchng power losses can be approxmately descrbed by the formula P tot fkek + P on, () where: E k energy lost n sngle swtchng cycle, P on power losses n swtched-on state. So t s possble to assume that transstor power losses are proportonally depent on swtchng frequency. Accordng to the above-mentoned problem of choosng the rght value of nductor s very dffcult. Dscusson about selectng rght value of APF output nverter nductor s shown n Table I. For a hgher value, the tme constant s hgher and dynamc dstorton s bgger, whle for a lower value, crcut dynamc dstortons are smaller, but the value of compensatng current rpple s hgher. One of the ways to decrease the dynamc dstorton and keep current rpple at a reasonable value s to ncrease transstor swtchng frequency, but n ths case there are ncreased swtchng losses and nfluence from the swtchng transton. Dscusson about choosng rght value of nductor s shown n Table II. be neffectve. Therefore, the author s proposng an nverter output stage (Fg. 5) wth two sets of transstors (fast and slow) and nductors. The crcut has common D bank (, ) for both part of nverter. The smplfed verson of ths proposton s shown n Fg. 6. The crcut conssts of two output stages [4], [7]: one wth swtches S s, S s and nductor s, and a second wth swtches S f, S f and nductor f. The frst works contnuously wth the slowest swtchng frequency f p. The value of nductor s s desgned to acheve a low current rpple. In the second, swtches S f, S f work wth a several-tmes hgher frequency only n the case when output current changes very quckly (typcally % of mans power perod). The value of nductor f was desgned to acheve a fast response n the output current. At the begnnng a hysteress dgtal modulator was desgned for controllng the modfed nverter. Taken nto consderaton durng the smulaton analyss were the modfed nverter and classcal nverter. The smulaton parameters are: f =.5 mh, s =.5 mh, u D = 39 V, f p = 5 Hz, f p = 56 Hz. Smplfed dagram of the modfed nverter smulaton crcut s shown n Fg. 7. The control algorthm of two hysteress dgtal modulator wth addtonal condtonal control logc mplemented n Matlab s shown n stng I. Step responses for modfed nverter and classc nverter are shown n Fg. 8. The classc nverter response tme s about 4 μs, and s near 7 μs for the modfed nverter. The hysteress dgtal modulator s one of the smplest and safest, especally at the early expermental stage, but t has a lot of dsadvantages, especally for dgtal mplementaton [], therefore durng future nvestgatons other modulator control algorthms wll be desgned and mplemented. TABE II. DISUSSION ABOUT VAUE OF INDUTOR Bgger value of nductor ower value of nductor Postves Negatves Postves Negatves - low current rpple, - lower transstor swtchng frequency. - slow transtons response, - bgger cost and weght. - fast transtons response, - lower cost and lower weght. - hgher value of current rpple, - hgher swtchng frequency, - bgger nfluence from the swtchng transton. Fgure 5. Sngle-phase actve power flter wth modfed nverter, test crcut III. APF WITH MODIFIED OUTPUT INVERTER Gven that hgh dynamc performance s necessary only for approxmately % of the tme n the mans power perod, ncreasng the swtchng tme to 6 khz seems to Fgure 6. Smplfed dagram of modfed nverter model connected to the mans power
f R + s s u_cf=; f e>h u_cs=u_dp-u_s(n); u_cs=u_dn-u_s(n); R + s Fgure 7. Smplfed block dagram of the output nverter smulaton crcut I [A] I [A] 4 - -4.99....3.4.5.6 6 4 - -4.99....3.4.5.6 Tme [s] Fgure 8. Step responses of two nverters: classcal nverter cref (t) red, c (t) blue, modfed nverter cref (t) red, c (t) blue, cf (t) green, cs (t) black ISTING I. MATAB PROGRAM OF TWO HYSTERESIS MODUATORS e=_cref(n)-_c(n)*kr; e_s=_ref(n)-_cs(n)*kr; f u_cs>= f e_s>kh*h u_cs=u_dp-u_s(n); f e<-h&&u_cf>= u_cf=u_dn-u_s(n); f e>h&&uc_f<= u_cf=u_dp-u_s(n); u_cf=; f blad<-h u_cs=u_dn-u_s(n); u_cs=u_dp-u_s(n); %u_cs < f e_s<-kh*h uc_s=u_dn-u_s(n); f e<-h&&u_cf>= u_cf=u_dn-u_s(n); f e>h&&u_f<= u_cf=u_dp-u_s(n); APF Smulaton Results A block dagram of the control crcut for the consdered APF s presented n Fg. 9. The control algorthm uses sldng DFT [], [5], [6] for the load current frst harmonc detecton. In respect to sldng DFT characterstcs control crcuts have to be synchronzed to lne voltages u (t), u (t), u 3 (t). Ths s why the synchronzaton unt s one of the most mportant parts of the control crcut. The dgtal control crcut s synchronzed wth the mans voltage by a synchronzaton unt. It conssts of a low-pass flter and phase-locked loop crcut (P). Fgures and show the smulaton waveforms n the same steady-state condtons, for classcal crcut (Fg. ) and for crcut wth modfed nverter (Fg. ). Depcted are the followng waveforms: load currents, compensatng currents, lne currents S. Usng the modfed nverter t s possble to decrease the harmonc contents n power lne currents from about THD=5% to about THD=5%. The results of the smulaton analyss confrm good dynamc performance of the modfed nverter used n a shunt actve power flter. urrently beng bult at our Insttute s a three-phase modfed nverter for a 75 kva shunt actve flter. Ths APF wll be used for testng APF control algorthms. The presented soluton wll be employed together wth the non-causal algorthm descrbed, whle for predctable loads there wll be used only a workng non-causal algorthm, but for unpredctable rapd change of load current the fastest part of the modfed nverter wll be workng. For assumed smulaton parameters current rpples are hgher when the fastest part of the nverter s swtchedon, but the resultant value of THD s less f compared to the classcal nverter. ONUSION For nose type nonlnear loads (such as n an arc furnace) where the load currents are non perodc and stochastc, the proposed APF wth mproved dynamc performance s good soluton. REFERENES [] E. Jacobsen, R. yons, "The sldng DFT", Sgnal Processng Magazne, IEEE, Vol., No., March 3. [] M. Kazmerkowsk,. Malesan, urrent ontrol Technques for Three-Phase Voltage-Source onverters: A Survey, IEEE Transactons on Industral Electroncs, vol.45 N 5, October, 998. [3] S. Marethoz, A. Rufer, Open oop and losed oop Spectral Frequency Actve Flterng, IEEE Transactons on Power Electroncs, vol.7, N 4, July,.
[4] K. Sozansk, The Shunt Actve Power Flter wth Better Dynamc Performance, Power Tech 7 onference, ausanne, Swtzerland, 7. [5] K. Sozansk, Harmonc ompensaton Usng the Sldng DFT Algorthm, 35rd Annual IEEE Power Electroncs Specalsts onference - PES '4, Aachen, Germany, 4. [6] K. Sozansk, Sldng DFT ontrol Algorthm for Three-Phase Actve Power Flter, rd Annual IEEE Appled Power Electroncs onference - APE '6, Dallas, Texas, USA, 6. [7] S. Watanabe, P. Boyagoda, H. Iwamoto, M. Nakaoka, H. Takano, Power converson PWM amplfer wth two paralleled four quadrant chopper for MRI gradent col magnetc feld current trackng mplementaton, Power Electroncs Specalsts onference, 999. PES 99, 3th Annual IEEE Volume, Issue, 999 Page(s):99-93 vol.. Fgure 9. Block dagram of APF control algorthm 5 5 d) -5.4.5.6.7.8.9... 5 5-5.4.5.6.7.8.9... I S (f) [A] c) S 5 5-5.4.5.6.7.8.9... t [s] 5 5 5 3 f [Hz] Fgure. Smulaton waveforms of sngle-phase actve power flter n steady-state wth the resstve load, classcal nverter: load current, compensatng current, c) lne current S, d) frequency spectrum of lne current S 5 5 d) I -5.4.5.6.7.8.9... 5 5 I I S (f) [A] -5.4.5.6.7.8.9... c) 5 5 I S -5.4.5.6.7.8.9... t [s] 5 5 5 3 f [Hz] Fgure. Smulaton waveforms of sngle-phase actve power flter wth modfed output nverter n steady-state wth the resstve load, modfed nverter: load current, compensatng current, c) lne current S, d) frequency spectrum of lne current S