Keywords: Shunt active power filter, Space vector modulation, Sliding mode control, Synchronous reference frame.

Transcription

1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 12, No. 2, June 2015, UDC: /.27: DOI: /SJEE C Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero Sequence Current, Compensatng Harmoncs and Reactve Power wth Fxed Swtchng Frequency Al Chebabh 1, Mohammed-Karm Fellah 1, Mohamed-Fouad Benkhors 2, Abdelhalm Kessal Abstract: In ths paper, the four leg nverter controlled by the three dmensonal space vector modulaton (D SVM) s used as the shunt actve power flter (SAPF) for compensatng the three phase four wre electrcal network, by usng the four leg nverter wth D SVM advantages to elmnated zero sequence current, fxed swtchng frequency of nverter swtches, and reduced swtchng losses. Ths four leg nverter s employed as shunt actve power flter to mnmzng harmonc currents, reducng magntude of neutral wre current, elmnatng zero sequence current caused by nonlnear sngle phase loads and compensatng reactve power, and a nonlnear sldng mode control technque (SMC) s proposed for harmonc currents and DC bus voltage control to mprove the performances of the three phase four wre four leg shunt actve power flter based on Synchronous Reference Frame (SRF) theory n the dq0 axes, and to decouplng the four leg SAPF mathematcal model. Keywords: Shunt actve power flter, Space vector modulaton, Sldng mode control, Synchronous reference frame. 1 Introducton The ncreasng development of the ndustry has led research n the feld of semconductors and n partcular power electroncs. The results of these researches are very mportant n the ndustral and mproved sgnfcantly the process performances, whch explans the hgh use of statc converters n the ndustry, these great benefts are not wthout dsadvantages, the man dsadvantage s the statc converters are nonlnear loads absorb reactve power and non snusodal current, whch s very bad for the network, as a degradaton of the current and voltage waveform qualty [1 ]. Today, many actve 1 ICEPS Laboratory (Intellgent Control & Electrcal Power Systems), Djllal Labes Unversty of Sd Bel Abbes, Algera; E-mals: chebabhal@gmal.com; mkfellah@yahoo.fr 2 IREENA Laboratory (Insttut de Recherche en Energe Electrque de Nantes Atlantque), Unversty of Nantes at Sant Nazare, France; E-mal: Mohamed-Fouad.Benkhors@unv-nantes.fr Faculty of Technology, Unversty of Bordj Bou Arrerdj, Algera; E-mal:abdelhalm.kessal@yahoo.fr 205

2 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal compensators, or also called actve flters are proposed and studed, they dffers n how they connect to the network (seres or shunt), by ther functonalty (current or voltage compensatng) and the electrcal structure of the power crcut (voltage or current nverter) [ 5]. These actve flters have, as man objectve, to nject harmonc currents or voltages n the electrcal network, equal to that absorbed by the non-lnear load and n phase opposte, consequently t mprove the powers qualty and power factor [6 8]. The three leg shunt actve power flters for three phase three wre and four wre dstrbuton systems have already been presented [9 10]. These three leg shunt actve power flters can compensate the harmonc current generated by nonlnear three phase loads; however they are not preferable to compensate the harmonc current due to nonlnear sngle phase loads connected to the four wre dstrbuton systems and the ampltude of the zero sequence current s not reduced. To remedy these problems t wll be necessary to provde a four leg shunt actve power flter [11 14]. The four leg shunt actve power flter topology, Fg.1, can reduce zero sequence current and the harmonc currents cussed by nonlnear sngle phase loads n three phase four wre electrcal network. Ths topology based on four leg nverter, whch s the most common one because of ts good effcency. Its performance depends on the adoptve control approaches, for ths, there are four major parts of an actve power flter controller. The frst s the reference sgnal generate technques, the second s the swtchng sgnals generate technques, the thrd s the harmonc currents and DC bus voltage control, and the fourth s the four leg nverter. In ths paper, the synchronous reference frame theory n the dq0 axes for the reference sgnals generate s applyng, and we use the D SVM technque for generatng the swtchng sgnals, [1 19], and also the nonlnear sldng mode control (SMC) s used to harmonc currents and DC bus voltage of four leg SAPF controller, because the advantages of robustness and stablty under unbalanced or large loads varatons, decouplng the nonlnearty of these four leg SAPF mathematcal model, elmnated the DC bus voltage overshoot, mnmzng the harmonc currents, smple to obtan, and has been wdely appled to electrcal power systems and electrcal machne drves [20 27]. 2 Structure and Modelng of the Three Phase Four Wre Four Leg SAPF The three phases four wre four leg shunt actve power flter topology presented n ths paper s shown n Fg. 1 [, 12 1]. The man crcut contans a three phase power source wth three seres mpedance L S R S and a three sngle phase nonlnear loads composed of three flters characterzed as L l R l wth three sngle phase rectfer supplyng a three R ch L ch loads, ths 206

3 Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero SAPF s shunt connected to a three phase four wre electrcal network n a pont called the Pont of Common Couplng (PCC) on the loads sde through a flter featured as L f R f. Ths s necessary for elmnatng current rpples due to swtchng []. vs1 Rs Ls s1 v l1 l1 Rl Ll L ch R ch vs2 s2 v l2 l 2 vs s v l l sn ln fn f f 2 f 1 Rf Lf K1 K 2 K 4 K v f 1 v f 2 v f Vdc v fn K1 K 2 K K4 Fg. 1 Four leg shunt actve power flter connected n Parallel to a three phase four wre electrcal network. The four leg nverter s composed by four legs, each leg of the nverter s composed of two swtches, and each swtch s consttuted by a transstor wth ant-parallel dode, and DC sde capactor s used to store the necessary reactve energy Fg. 1. The neutral current sn and zero sequence current o are gven by 1 1 o sn ( s 1 s2 s ), (1) where s 1, s2, s are source currents. Equaton (2) expresses the nverter output voltages. These output voltages are expressed as a functon of the voltage (V dc ), and of the swtchng functons S j [12, 15, 18] vf 1 ( S1 Sn) Vdc vf 2 ( S2 Sn) Vdc, (2) vf ( S Sn) Vdc 207

4 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal where v f are phase-to-neutral voltages ( = 1, 2,, n), S s swtchng state and V dc s DC bus voltage. The nput current d of the four leg nverter s calculated as (). d S 1 f1s2f 2 Sf Snfn () The vector tenson of the four leg nverter s represented by: v v v j v k, (4) f f f f 0 where vf, vf, vf 0 are the projectons of vector v f n the 0 axes. That gves [15]: v f v f1 2 vf vdc 0 vf (5) v f 0 v f V V dc 2V V dc V V dc V 0 V V dc 2V V dc 2V V dc Fg. 2 Space vector dagram showng swtchng states of four leg nverter. The space vector dagram of a four leg nverter s showed n Fg. 2. They are 16 possble swtchng vectors: fourteen actve vectors and two null vectors of four leg nverter. The four leg SAPF mathematcal model n the dq0 axes s gven by [1]. 208

5 Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero dfd Rf 1 1 v v dt L L L dfq Rf 1 1 fq fd v fq v lq, dt L L L d 1 1 f 0 Rf f 0 v f 0 v l0 t Lf Lf Lf d fd fq fd ld f f f f f f dvdc 1 dt C dc.,, (6) The Three Dmensonal Space Vector Modulaton (D SVM) In three dmensonal space vector modulaton (D SVM), there are 16 possble swtchng vectors: fourteen actve non zero vectors and two null vectors [7 8]. Sx prsms n the D space vector dagram can be dentfed and numbered as Prsms I through VI, each of these sx prsms s decomposed nto four tetrahedrons are labeled T 1 T 4. Wthn the selected prsm, there are sx none zero swtchng state vectors and two zero swtchng state vectors [1]. Ths method s represented and studed n detal as [15 19]. 4 Sldng Mode Control The three phase load currents, l1, l2, l, based on Clark transformaton, are used to obtan synchronous reference frame load currents, ld, lq, l0, accordng to the followng equaton. 2 2 cos( ) sn cos ld l lq sn( ) sn sn l 2. (7) l0 l Based on the SRF theory [28, 29], the currents ld and lq can be expressed as the sum of two components, one drect and the other s alternatve, such as: ld ld ld (8) lq lq lq 209

6 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal wth ld and lq are the drect components, the ld and lq are alternatve components of ld and lq respectvely. To obtan the drect and alternatve current components of the reference state varable vector x, the ld current s extracted based on the SRF theory [28, 29] by the low pass flter (LPF) to calculated the reference component fd (alternatve components). The lq and zero sequence currents l0 are used as reference components fq and f 0 [14, 22]. The model (6) s a mult-nput mult-output nonlnear system [21 24], n the three phase four wre four leg shunt actve flter wth sldng mode control, the outputs flter fd, fq, f 0 and V dc are the daxs, qaxs and the zero sequence axs SAPF currents and the DC bus voltage respectvely, the control varables v fd, v fq, v f0 are the reference voltages. Ths model can be wrtten nto the followng state space general form: [14, 22] where: X AX Bu D, (9) x1 fd x 1 fd ud v fd d 2 fq, X x X x2 fq, u u q v fq dt, x f 0 x f 0 u o v f 0 1 vld Rf L f Lf 1 1 A, B, D vlq, R L f Lf f L f 1 vl 0 Lf kd 0 0 kd 0 0 K 0 kq 0, K 0 kq k k 0 Equaton (10) represents the three sldng surface of the flter currents fd, fq and f 0 where: : S( X) K( X X) K ( X X)dt, (10) 210

7 Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero x 1 fd ld dc X x2 fq lq. (11) x f 0 l0 The current dc at the output of DC bus voltage controller used to compensated the losses power of four leg nverters and to conserved the necessary reactve energy stored n the DC sde capactor s calculated as follow [11]: uv dc c1x4y1 c2x5y2, (12) where y 1 and y 2 are swtchng functons x4 ev d dc V,, dc Vdc x5 x x6 x4 t, 1, xs 4 x4 0 y1, (1) 1, xs 4 x4 0 y 2 1, xs 5 x4 0. (14) 1, xs 5 x4 0 The sldng surface S(x 4 ) of the DC bus voltage s gven by (15) [2] and c k, c are postve constants. S x S V V c x x c x, 4 dc dc k d Sx4 ckevdc evdcc evdcd t dt The three sldng surface of the three flter currents fd, fq, f 0 fd d fd fd d fd fd fq q fq fq q fq fq f 0 0 f 0 f 0 0 f 0 f 0 S k k d, t S k k d, t S k k d. t Durng the sldng mode, we have fd fq f 0 fd fq f 0 The control varables are gven by: S S S 0, S S S 0. are (15) (16) (17) 211

8 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal v u v u u v f 0 fd fq ds eq. (18) Solvng (9) gves the expresson of the equvalent command as follows: ueqd 1 ueq KB K X X KX AX D u eqq. (19) u eq0 If the trajectores are dfferent from the state of the sldng surface, the dscontnuous control ensures decrease the dstance between the state trajectory and the sldng surface [22, 26]. Ths command s selected to ensure the convergence of the path to ts reference [14]. In our case, we chose the dscontnuous control functon as: udsd u uds dsq sgn S X U u ds0 max, U max U U U d max q max 0max (20) 5 Smulaton Results The SmPower Systems and S-Functon of MATLAB are used for mplemented the three phase four wre four leg shunt actve power flter controlled by nonlnear sldng mode technque Fg.. The components, parameters, and condtons consdered for smulaton are lsted n Table 1 and 2. Table 1 System parameters for smulaton and load specfcatons. Capactance of the capactor Couplng mpedance R f, L f The source voltage and frequency Source mpedance R s, L s Lne mpedance R ch, L ch Load mpedance R l, L l 5 mf 0.2 mω, 0.15 mh 220 V, 50Hz 1 mω, 1 mh 1 mω, 1 mh 5Ω, 10 mh 212

9 Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero Rs Ls s1 v l1 l1 Rl Ll Lch R ch L R s2 v l 2 l 2 s v l l sn ln fn f f 2 f 1 dc R f Lf v f 1 v l12 v f 2 v f Four Leg C V dc f 12 l12 PLL v fn Inverter abc dq ld lq V dc V dc ld LPF l fdq fd fq f Sldng Mode Control v fd v fq v fo dqo v f v f v fo V dc S1 S2 S Three Dmensonal Space Vector Modulaton D SVM Sn Fg. Schematc block dagram of shunt actve power flter wth Sldng Mode control technque. Table 2 The condtons consdered for smulaton. PI Sldng Mode The swtchng frequency: f s 14 khz 14 khz The reference voltage: V dcref 800 V 800 V The currents regulators frequency: f c k, k, u max =constant The voltage regulator frequency: f ds c k, c, c 1, c 2 =constant. 10 khz 4 Hz k k k 5 d q 0 5.5e 8 kd kq k0 2e u u u 800 dmax qmax 0max c k c 950 c c 2 5e 21

10 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal 5.1 Smulaton wth PI control Fg. 4 Performance of the three phases four wre four leg SAPF usng Synchronous Reference Frame theory (SRF) based D SVM control strategy usng PI control n the dq0 axes. (a) Fg. 5 Magntude Spectrum of Source Currents for the PI control: (a) before unbalanced load, (b) after unbalanced Load. 214 (b)

11 Sldng Mode Controller for Four Leg Shunt Actve Power Flter to Elmnatng Zero 5.2 Smulaton wth Sldng Mode Control Fg. 6 Performance of the three phase four wre four leg SAPF usng Synchronous Reference Frame theory (SRF) based D SVM control strategy usng SMC n the dq0 axes. (a) Fg. 7 Magntude Spectrum of Source Currents for the SMC: (a) before unbalanced load, (b) after unbalanced Load. (b) 215

12 A. Chebabh, M.K. Fellah, M.F. Benkhors, A. Kessal Fg. 4 and 6 llustrates the three phase four wre four leg SAPF performance wth the two controller (PI and SMC) under unbalanced loads, the source currents waveform s snusodal and n phase wth the correspondng voltage (the power factor s untary). The ampltude of the neutral wre current s n the range of ±6A wth PI controller and the range of ±A wth Sldng Mode controller, the DC bus voltage control presents good dynamc and statc characterstcs wthout overshoot. When the unbalanced loads, the voltage converges to the gven value wth a short tme adjustment. Fgs. 5 and 7 Illustrates the Harmonc spectrum of source current for the two theores, before unbalanced loads, total harmonc dstorton (THD) s 1.19% wth PI control and 0.87% wth SMC, when after a 1.91% wth PI control and 1.77% wth SMC. Table gves the THD and ampltude of neutral wre current comparson between the two control technques PI and SMC usng Matlab/ Smulnk. Table Comparson of the dfferent technques. Source current THD % The ampltude of the neutral current (A) Before unbalanced loads After unbalanced loads PI control SM control PI control SM control 1.19% 0.87% 1.91% 1.77% ±6A ± A 6 Concluson In ths work we studed and verfed wth the smulaton of a nonlnear sldng mode control technque for reference harmonc currents and DC bus voltage regulaton based on Synchronous Reference Frame (SRF) theory and three dmensonal space vector modulaton (D SVM), to generate reference harmonc currents and swtchng sgnals respectvely, for a four leg shunt actve power flter, have shown hgh performance of four leg shunt actve power flter to elmnated zero sequence current, fxed swtchng frequency, reduced magntude of neutral current, and power factor correcton n the three phase four wre network. The obtaned smulaton results of these SAPF wth sldng mode control shows the four leg shunt actve power flter under unbalanced loads s capable to compensate harmonc currents, reactve power, elmnated zero sequence current, and also shows better dynamc performance over conventonal PI controller. 216

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