Dynamical properties of hybrid power filter with single tuned passive filter
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1 Dawid BUŁA, Maria PASKO Silesia Uiversity of Techology, stitute of Electrical Egieerig ad Computer Sciece Dyamical properties of hybrid power filter with sigle tued passive filter Abstract. The paper has bee iteded to preset the aalysis of hybrid power filter (HP) dyamical properties. The hybrid power filter with sigle tued passive filter has bee take ito cosideratio. The preset paper deals with ifluece of cotrol algorithm ad its compoets o dyamical properties of HP. Simulatio ad experimetal results of trasiet states have also bee icluded i the article. Streszczeie. W pracy zaprezetowao zagadieia związae z właściwościami dyamiczymi hybrydowego eergetyczego filtru aktywego (HEA) w kofiguracji z filtrem pasywym jedej harmoiczej. Skupioo się a wpływie parametrów algorytmu sterowaia a właściwości dyamicze układu HEA. Przedstawioo wyiki badań symulacyjych oraz laboratoryjych w staach przejściowych pracy układu. (Właściwości dyamicze eergetyczego filtru hybrydowego z filtrem pasywym dla jedej harmoiczej). Keywords: hybrid power filters, harmoics, trasiet states. Słowa kluczowe: eergetycze filtry hybrydowe, harmoicze, stay przejściowe. troductio Oe of the methods to reduce harmoic distortio i power systems is usig hybrid power filters [, 2, 3, 4, 5]. Hybrid power filters combie two solutios i.e. active power filters with passive filters. Hybrid filters are usually used i medium voltage systems, where applyig of pure active power filter is uecoomical ad usig passive filters is isufficiet. There are also applicatios with hybrid filters i low voltage systems e.g. cofiguratios with reduced passive filters ad small rate active filters [6, 7, 8]. The developmet of power-electroic techology causes that characteristics of moder oliear loads have bee chagig. ast variatios of loads are the reaso why dyamical properties of the used solutio for harmoics filtratio have become importat. Both i active power filters ad i hybrid filters dyamical properties i great measure deped o cotrol strategy [, 5] ad its parameters. The paper is a cotiuatio of previous author's papers cocerig hybrid power filter with sigle tued passive filter [9, 0] ad is focused o dyamical properties coected with cotrol algorithm. Some of the preseted dyamical problems, e.g. stability problem, are typical for hybrid filter ad its feedback cotrol. is possible by suitable modificatio of the cotrol algorithm. Hybrid solutio allows to decrease the active power filter power ratig. O the other side reductio of passive part causes decrease of device weight ad size. Passive filter i this case is tued to 7th harmoic frequecy ad is smaller ad lighter tha the filter tued to the 5th-harmoic frequecy. Moreover impedace of 7th harmoic filter for 5th harmoic as well for th harmoic frequecy is still relatively low (fig. 2). t causes the small rate active part to be sufficiet to compesate these harmoics. ig.2. The magitude of impedace of 7th harmoic passive filter Cotrol priciple Active power filter voltage i shut hybrid filter is usually proportioal to higher harmoics of source curret (i Sh ) [, 2, 5]: () V j K j Sh t causes improvemet of atteuatio characteristic i compariso to pure passive filter [2, 4]. The active power filter voltage for selected harmoics i this case is also depedet o harmoics of load curret (i Lh ): (2) V j KSh j Kj Lh j 5,,3... ig.. System with the discussed hybrid power filter Cofiguratio of the system Shut hybrid power filter [2, 3, 5] usually cosists of a passive filter tued to the most ofte occurrig higher harmoics (i.e. 5th, 7th, th). the case cosidered the passive filter has bee reduced to a sigle tued filter [6, 7, 8, 9]. However, filtratio of other (selected) harmoics where: K(jω) frequecy trasfer fuctio of filter for -th harmoic, umber of selected harmoics. Atteuatio factor [2] i this case is give by: (3) (j) Sh Lh j j j Kj 5,,3... j j K S PREGLĄD ELEKTROTECHCY (Electrical Review), SS , R. 87 R /20 9
2 the ideal case trasfer fuctio of filters for selected harmoics amouts oe, whereas for other harmoics it is equal to zero. t produces the effect that umerator of (3) for particular harmoics equals zero. Cotrol strategy Block diagram of cotrol algorithm for referece voltages computatio has bee preseted i fig. 3. The cotrol algorithm is a implemetatio of cotrol strategy give by (2) for three phase system. The preseted algorithm ca be divided ito two parts the upper with feedback cotrol, which ca realize fudametal algorithm, () ad the lower with feedforward cotrol, which is resposible for filtratio of selected harmoics i.e. 5th, th ad 3th i this case. Both parts use Clarke ad Park trasformatios with suitable filters to determie the required compoets of source ad load currets. G j matrix correspodig with Park trasformatio ad low pass filter (LP) i feedback cotrol (used for computatio egative sequece of source currets): (0) G j D ( j) (j ) (-2) D j) D ( ), j) ( ) ( j (3) j ( (4) K j (j) / D (j) LP G 2, j matrixes coected with Park trasformatio ad low pass filters (LP ) i feedforward cotrol: 2, (5) G j D (j) (j ) (6-7) D ( j) D ( ), ( j) ( ) j (8) j (9) K j (j) / D (j) LP (20-23) 5,, 3, 5 5,, 3 3 ig.3. Diagram of the cotrol system Based o circuit from fig. ad diagram from fig. 3 frequecy model for higher harmoics has bee prepared (fig. 4). the preseted frequecy model executio part (voltage coverter) ad DC-voltage cotroller have bee omitted. By usig the prepared model oe ca obtai: Sα j j S j (4) j j KG j G j G2j s 5,,3 where: 2 x 2 idetity matrix, j impedace, Sj gai, j Lα L j j passive filter source impedace, K hybrid filter G matrix coected with Park trasformatio ad high pass filter (HP) i feedback cotrol [5, ]: matrix coected with passive filter impedace for -harmoic: (24) Re m j m j j Re j There is couplig betwee α o β compoets. Therefore it is ot possible to obtai Sα / Lα ad Sβ / Lβ filterig characteristics, but after trasformatio to positive/egative sequece accordig to: P j α (25) 2 - j β it is possible to determie SP / LP ad S / L filterig characteristics, which have bee show i fig. 5. (4) G j D( j) ( j ) j (5-8) D ( j) D( ), ( j) ( ), j ig.4. requecy model diagram of the discussed system (9) K j (j) / D(j) HP 92 PREGLĄD ELEKTROTECHCY (Electrical Review), SS , R. 87 R /20
3 where G P, (jω) is trasfer fuctio for positive ad egative sequece is give by: (27) G P (j) 0 0 G (j) j [ G 2 - j - j j G j] j ig.5. ilterig characteristics of the hybrid power filter for differet hybrid filter gai Sigal filters Sigal filters used i cotrol algorithm are elemets with sigificat ifluece o dyamical properties of the whole hybrid power filter. O the oe had lower cut-off frequecy of filters causes better filtratio properties (fig. 6), o the other, it brigs about extesio of step respose trasiet time. Example set of frequecy ad step resposes for 2d order Butterworth filters with differet cut-off frequecy has bee show i fig. 7. Whe frequecy characteristic of filtered sigals are kow, filter parameters ca bee chose. or low pass filter (LP) 6 Hz cut-off frequecy has bee established. or other filters cut-off frequecy has bee set at 25 Hz. Secod order Butterworth filters have bee chose i all cases. t should be oticed that filters i feedback cotrol (LP, HP) also have sigificat ifluece o stability of hybrid filters. Hybrid power filter gai K ad delay τ also have ifluece o stability of the system. Stability aalysis has bee made assumig that τ = 00 μs [, 2] ad gai K = 30. yquist plots of feedback trasfer fuctio (25) for positive ad egative sequece have bee preseted i figure 8b. Theoretical critical gai equaled 69 i this case. ig.8. Stability aalysis: a) block diagram used for the aalysis b) yquist plots ig.6. ilterig characteristics of the hybrid filter for differet cut-off frequecy of sigal filters i cotrol algorithm DC-voltage cotrol Block diagram of the DC-voltage cotrol is show i fig. 9a. Example step resposes for the DC-voltage cotrol are also preseted i fig. 9b. Parameters of P cotroller ca be calculated assumig T itegral time ad critically-damped respose (dampig ratio = [8]) i which o voltage oscillatio occurs i trasiet states. Based o these assumptios T = 40 ms ad K P = 0.2 have bee assiged. ig.7. requecy ad step resposes of 2d order Butterworth filter Stability aalysis eedback cotrol ad delays i real cotrol system [2] may cause stability problem. The diagram used for stability aalysis has bee preseted i fig. 8a. eedback trasfer fuctio i this case ca be expressed as: (26) H P, KG (j) -j P, je j j S ig.9. DC-voltage cotrol: a) block diagram b) step resposes Simulatio results The discussed hybrid power filter has bee simulated usig SLPS iterface (SimuLikPSpice). SLPS makes it possible to carry out simulatio of complex hardwaresoftware systems simultaeously i two simulatio PREGLĄD ELEKTROTECHCY (Electrical Review), SS , R. 87 R /20 93
4 eviromets: Capture-PSpice ad MATLAB-Simulik. Simulatio tests have bee made with the followig parameters: E,2,3 = 230 V, L S = 0.5 mh, L 7 = 4.0 mh, C 7 = 52 μ, R 7 = 0.4 Ω, K = 30 Ω, U DC = 60 V, C DC = 4700 μ, f PWM = 25 khz. The first test was made for balaced oliear load ad cosisted i step chagig of load from 3.5 kw to 5 kw. Simulatio results have bee preseted i fig. 0. Trasiet state observable i source curret waveforms lasts about 20 ms. t is clearly visible i fig. where the selected cotrol sigals waveforms have bee showed. ext test demostrates the case with large delay i cotrol, τ = 350 μs. Uder these coditios the system loses stability which has bee show i waveforms i fig. 2. The last of the preseted tests shows results (fig. 3) for step chagig of ubalaced load. ig.3. Simulatio results for ubalaced load. Load currets i L,2,3 ad source currets i S,2,3 ig.4. Laboratory model of the hybrid power filter a) ig.0. Simulatio results for balaced load. Load currets i L,2,3 ad source currets i S,2,3 waveforms b) ig.5. Experimetal results for balaced load: a) steady state, b) trasiet state ig. Simulatio results for balaced load. Source currets i S,2,3, u dc voltage ad selected cotrol sigals waveforms ig.2 Simulatio results for balaced load with large delay i cotrol system. Load currets i L,2,3 ad source currets i S,2,3 waveforms. Delay τ = 350 μs, K = 30 Experimetal results Experimetal tests for the discussed hybrid power filter have bee made with the same parameters as i simulatio tests. Pictures of laboratory model, that was used i the experimetal tests, have bee preseted i fig. 4. Experimetal results of the two cases for dyamical properties verificatio have bee preseted i fig. 5 ad fig. 6. The first test was made for balaced oliear load ad cosisted i step chagig of load from 3.5 kw to 5 kw. The secod oe cosisted i coectig 2 kw ubalaced liear load to a 3.5 kw balaced oliear load. Experimetal results for steady states after load chage have also bee show i fig. 5 ad 6. Total harmoic distortios of source currets after load chage have bee show i tab.. t ca be oticed that the trasiet time i i S source curret waveforms was about 20 ms ad i u DC voltage 94 PREGLĄD ELEKTROTECHCY (Electrical Review), SS , R. 87 R /20
5 waveform was loger ad equaled eve 60 ms. Trasiet state i dc-voltage cotrol was ot visible i source currets waveforms. Table. Total harmoic distortio before ad after applyig of hybrid power filter Balaced load Ubalaced Load a) b) THDi S THDi S2 THDi S3 THDi S THDi S2 THDi S3 Before 24.8 % 24.6 % 24.7 % 4.0 % 2.4 % 25.3 % After 3.4 % 3.3 % 3.3 % 2. % 2.4 % 3.5 % ig.6. Experimetal results for ubalaced load: a) steady state, b) trasiet state Summary The preset paper deals with ifluece of cotrol algorithm ad its compoets o dyamical properties of hybrid power filter with sigle tued passive filter. or dyamical properties verificatio simulatio ad experimetal results of trasiet states have bee examied ad icluded i the article. While selectig cotrol system parameters for the discussed hybrid filter it is ecessary to compromise betwee excellet filtratio ad dyamical properties. However it is possible to obtai good characteristic of filtratio ad satisfactory dyamical properties, what has bee proved i the article. Selectio of cotrol system parameters should be preceded by a stability aalysis, because uder certai coditios system ca lose stability. Oe ca draw the coclusio that the preseted hybrid power filter ca be used i systems with fast-variable loads. This work was supported from resources for sciece i the years uder the project REERECES [] H. Akagi, E. H. Wataabe, M. Aredes, stataeous Power Theory ad Applicatios to Power Coditioig, Wiley-EEE Press, Series Power Egieerig, 2007 [2] S. Bhattacharya, P. Cheg, D. M. Diva, Hybrid Solutio or mprovig Passive ilter Performace High Power Applicatios, EEE Tras. o dustry Applicatios, vol. 33, o. 3, May/Jue 997, [3] M. Pasko, D. Buła, Hybrid Active Power ilters (i Polish), Przegląd Elektrotechiczy, o. 7/8, 2007, pp. -5. [4] D. Rivas, L. Mora, J. W. Dixo, J. R. Espioza, mprovig passive filter compesatio performace with active techiques, EEE Tras. o dustrial Electroics, vol. 50, o., 2003, 6-70 [5] R. Strzelecki, H. Suproowicz, iltratio of the harmoic i AC supply systems (i Polish), Toruń, Polad, Adam Marszałek Publishig House, 997/999 [6] H. Akagi, S. Sriathumrog, Y. Tamai, Comparisos i circuit cofiguratio ad filterig performace betwee hybrid ad pure shut active filters, Cof. Rec. EEE-AS A. Meetig, 2003, [7] S. Sriathumrog, H. Akagi, A medium-voltage trasformerless ac/dc power coversio system cosistig of a diode rectifier ad a shut hybrid filter, EEE Tras. o dustry Applicatios, vol. 39, o. 3, 2003, [8] W. Tagtheerajaroowog, T. Hatada, K. Wada, H Akagi, Desig of a Trasformerless Shut Hybrid ilter tegrated ito a Three-Phase Diode Rectifier, Power Electroics Specialists Coferece PESC '06, 37th EEE, 2006, -7 [9] Buła D., Pasko M.: Hybrid Active Power ilter with Sigle Tued Passive ilter (i Polish), Przegląd Elektrotechiczy, o 2, 2009, [0]Buła D., Pasko M.: Sesitivity Problem of Hybrid Active Power ilter with Sigle Tued Passive ilter, Przegląd Elektrotechiczy, o, 200, 59-6 [].. Peg, H. Akagi, A. abae, Compesatio Characteristics of the Combied System of Shut Passive ad Series Active ilters, EEE Tras. o dustry Applicatios, vol. 29, o., 993, [2] Buła D., Maciążek M., Pasko M., Optimizatio of time delays i Active Power ilter cotrol algorithm, 8th teratioal Workshop CPEE 2007, Przegląd Elektrotechiczy Koferecje, o. 2, 2007, Authors: mgr iż. Dawid Buła, dawid.bula@polsl.pl, prof. dr hab. iż. Maria Pasko, maria.pasko@polsl.pl, stytut Elektrotechiki i formatyki, ul. Akademicka 0, Gliwice PREGLĄD ELEKTROTECHCY (Electrical Review), SS , R. 87 R /20 95
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