Complete Harmonic-Domain Modeling and Performance Evaluation of an Optimal-PWM-Modulated STATCOM in a Realistic Distribution Network

Transcription

1 Internatinal Schl n Nnsinusidal Currents and Cmpensatin LagH', Pland, 08 Cmplete Harmnic-Dmain Mdeling and Perfrmance Evaluatin f an Optimal-PWM-Mdulated STATCOM in a Realistic Distributin Netwrk H. Valizadeh Haghi l and M. Tavakli Bina l,*, Senir Member, IEEE 1 Faculty felectrical Engineering, K. N. Tsi University ftechnlgy * Dr M. Tavakli Bina, Seid Khandan, P. O. Bx , Tehran Iran Tel: 98(21 ) , Fax: 98(21 )884666, tavakli@kntu.ac.ir Abstract-Pwer systems use STATCOM fr cmpensating purpses that is subjected t the high switching frequencies. Varius PWM techniques make selective harmnic eliminatin pssible, which effectively cntrl the harmnic cntent f vltage surce inverters. On the ther hand, distributin systems have t supply unbalanced nnlinear lads, transferring scillatins t the DC-side f the cnverter in a realistic perating cnditin. Thus, additinal uncharacteristic harmnics are mdulated thrugh the STATCOM at the pint f cmmn cupling (PCC). This requires mre attentin when switching angles are calculated ffline using the ptimal-pwm technique. This paper suggests a harmnic-dmain mdel in rder t realistically evaluate the injected harmnics at the PCC. This mdel prperly takes int accunt the DC capacitr effect, effects f ther pssible varying parameters such as vltage unbalance as well as netwrk harmnics, and effects f perating cnditins n the STATCOM harmnic perfrmance. The mdel is prgrammed, and can be easily run with ther algrithms such as Mnte Carl sim ulatin. Further, a semi-stchastic methd is prpsed t predict and simulate the three-phase vltage unbalance, leading t an analytical tl fr predictin f harmnic perfrmance f STATCOM. The predictive methd is develped based n the measured data btained frm a lw-vltage distributin netwrk. Finally, the mdeled STATCOM is linked with the distributin substatin, applying the prpsed vltage unbalance mdeling t evaluate aggregate harmnics f the lad. I. INTRODUCTION A STATCOM cnsists f a vltage surce cnverter (VSC), a dc capacitr and a cupling transfrmer. It may be seen as a basic building blck with which several pwer system bjectives can be achieved. A variety f applicatins include imprving pwer quality prblems in lw-vltage distributin netwrks, vltage regulatin and reactive pwer cntrl. Reference signals, cntaining these bjectives, are then mdulated by PWM switching frequencies that are much higher than the synchrnus frequency. In practice, as with any VSC-based applicatins, STATCOM will act as a surce f prducing harmnics fr pwer systems. It culd als interact with pssible harmnic distrtins and unbalances fthe pwer netwrk (e.g. distributed systems are cined with many pwer electrnic lads). These interactins wuld be cmplex, making the analysis f steady-state harmnic levels and full assessment f their dynamic behavir challenging tasks. This is necessary since STATCOM can be better designed, and pwer quality prblems are mre efficiently treated. Thus, it is required t pursue evaluatin f these harmnic interactins thrugh a suitable cmbinatin f practical measurements and analytical studies [1], [2]. Varius mdulatin techniques and tplgies are suggested fr STATCOM t effectively remve the generated lw-rder characteristic harmnics, including multi-mdule PWM techniques, selective harmnic eliminatin and multilevel tplgies [3], [4]. An ptimal pulse-width mdulatin (OPWM) uses pre-calculated switching angles based n assuming an ideal fixed DC bus vltage. This methd presents several advantages in cmparisn t the cnventinal carrier-based sinusidal PWM schemes [5]. On the ther hand, lad-terminal harmnics and unbalance f distributin systems impse distrtin n bth DC and AC sides [2, 12], intrducing additinal uncharacteristic harmnics generated by STATCOM. Cnsidering the OPWM, the pre-calculated chpping angles will nt then be ptimal under these cnditins. Hence, the amunt f uncharacteristic harmnics that is injected t a distributin system depends n several factrs such as ratings and perating cnditins f bth STATCOM and distributin netwrk. Therefre, the fllwing steps shuld be perfrmed t btain a mre reliable harmnic perfrmance evaluatin fstatcom: Develping a cmprehensive mdel which takes int accunt relevant factrs and interactins in harmnic generatin such as DC capacitr scillatins, capacitance limitatin, and unbalance f the grid system. This mdel will prvide accurate and efficient analytical capability. Simulating a realistic distributin system under unbalance and distrted situatin. The envirnment shuld be als capable f integrating deterministic and stchastic appraches, ifnecessary. Making the simulatin cmpnents efficient and fast t avid unnecessary iterative prcedures that slw dwn cmplementary simulatins such as Mnte Carl methd. The first step is a challenging tpic that has been devted a nticeable amunt f research wrk ver the last few years [6-14]. A detailed verview f harmnic mdeling methds can be fund in [15]-[17]. Generally speaking, there are three philsphies in mdeling f devices, netwrk and their interactins. The methds are embedded in time-dmain, frequency-dmain, and harmnic-dmain. The time-dmain frmulatin cnsists frelevant differential equatins representing the dynamic behavir fthe intercnnected pwer system cmpnents. The resultant set f equatins is nrmally slved using numerical methds as dne in typical simulating sftware /08/$ IEEE

2 - Internatinal Schl n Nnsinusidal Currents and Cmpensatin Lagw, Pland, 08 + Cupling TransKmrer C [>A... a5 7t-a5... 7t-a l Figure 1: Three-phase vltage surce cnverter cnnected t the pwer system thrugh a transfrmer. such as PSCAD/EMTDC, PSpice, and SABER. Harmnic infrmatin is then btained using the fast Furier transfrm (FFT) in steady state [2]. This requires cnsiderable cmputatin steps even fr relatively small systems [18]. Other prblems attached t the time-dmain algrithms fr harmnic. studies are the difficulty f describing distributed r frequency-dependent parameters [15], their inflexibility related t the advanced stchastic algrithms, and the needed delay t cnverge steady state. Meanwhile, a mdel is suggested in [10, 11] based n the switching functin, intrducing a direct slutin fthe steady state in a clsed frm. The presented algrithm requires a peridic steady state t be quantified in the time-dmain. Thus, this cnstraint implies similar situatin when FFT analysis is perfrmed n the resulting wavefrms frm the time-dmain simulatins. Als, nnlinearity cannt be well-perfrmed by the clsed-frm slutin fthe steady state. Anther direct slutin fr the effect f an individual harmnic (r frequency) is discussed in [15] in the frequency-dmain, excluding the harmnic interactin between the netwrk and the nnlinear cmpensatr. When the harmnic injectin frm each surce depends n thse fther surces alng with the state variables f the system, accurate results can nly be btained in harmnic-dmain. The harmnic-dmain is a restricted frequency-dmain, while all nn-linear interactins are mdeled [19]. While sme research wrks take the effects f cntrl system int accunt [7, 14] in the harmnicdmain, anther methd wrks n harmnic pwer flw [6]. These are nt relevant t evaluatin f steady state harmnic perfrmance f STATCOM. In [8], mdeling f STATCOM is carried ut by representing switching functins by their Furier spectra. This apprach ptentially ffers an accurate slutin, cnsidering all harmnics and their interactins. This mdel is extended and imprved in this paper using harmnic-dmain techniques. This paper intrduces a mre realistic evaluatin f harmnic penetratin f STATCOM cnnected acrss a distributin substatin. The structure and mdeling f STATCOM fr harmnic analysis is presented, where harmnic perfrmance fstatcom using the OPWM is investigated by means f a harmnic-dmain mdel. A detailed semi-stchastic mdeling is then prpsed at the PCC fr the vltage unbalance. The suggested techniques are extensins f the prpsed methds in [, 21]. Then, this realistic representatin f the PCC is applied t the mdel f STATCOM. Resultant utcmes shw the maximum uncharacteristic harmnic injectin by the OPWM-STATCOM. This can be easily perfrmed with ther mdulatin techniques under a realistic perating 0.2>-- B(rad) 1_- lj L.lI_--I-'-.J...I J Harmnic Order Fiure 2: A typical selective harmnic eliminatin (5 th, 7 th, 11 th, and 13 1) based n quarter-cycle symmetry: the wavefrm and its harmnic spectra. cnditin. Further, a real case study is arranged in which the vltage unbalance and backgrund harmnics are simulated at a distributin substatin. This substatin is chsen frm part f Tehran nrth-east distributin system. Als, a STATCOM will be cnnected acrss this real substatin. It is eventually examined uncharacteristic harmnics prduced by STATCOM that is subjected t the interactin with the realistic mdel f the PCC. The btained cnclusins are finally discussed and evaluated. II. STATCOM STRUCTURE AND MODELING Here it is presented briefly the OPWM, fllwed by a prpsal n mdeling f STATCOM fr harmnic analysis and perfrmance evaluatin. A. The OPWM mdulatin technique A three-phase VSC, using IGBT switches, is shwn in Fig. 1. Like ther PWM schemes, the DC-link vltage is mdulated by the cnverter using the prgrammed harmnic eliminatin technique, Le. the OPWM. Bth switching instants and duratins are pre-calculated ff-line such that certain chsen harmnics are eliminated; als, a desired value is assigned t the fundamental cmpnent f the utput. A typical wavefrm is shwn in Fig. 2 in which it is prgrammed t eliminate nn-triple dd harmnics up t 17. The quarter-wave symmetry is cmmnly used t reduce the cmplexity f the resulting equatins. A general technique is als prpsed withut this assumptin in [22]. Nrmally, a set f slutins fr a certain range f fundamental vltage magnitudes is precalculated and stred in a lk-up table fr n-line implementatins. Detailed discussins n implementing the OPWM can be fund in [23]. B. STATCOM Mdelingfr Harmnic Analysis Frequency-dependent apprximate representatin f AC/DC cnverters already used fr small levels f distrtin using transfer functin apprach [15]. Apprximatins can be avided by mdeling the cnverter in the time-dmain in the expense fthe slutin speed. It is nticeable, hwever, that advanced prbabilistic /08/$ IEEE 2

3 Internatinal Schl n Nnsinusidal Currents and Cmpensatin Lagw, Pland, 08 PCC a Figure 3: Suggested three-phase mdeling fr a STATCOM in the harmnic-dmain that is cnnected t adistributin substatin. analysis and Mnte Carl simulatin needs fast and flexible prcedures. Hence, building n the wrk f [8], this paper prpses a Thevenin equivalent mdel fr STATCOM in the harmnic-dmain. This mdel, shwn in Fig. 3, prvides a fast prcedure with sufficient accuracy in additin t the flexibility in prgramming capabilities. Cnsidering a pulse train fr the cnverter's switches, assume Sa, Sb and Se are the three-phase switching functins. Three cmbinatins Sab= Sa-Sb, Sbe= Sb-Se and Sea= Se-Sa are defined based n the three switching functins f the PWM cnverter (e.g. see Fig. 2). Then, the fllwing equatins can be btained in harmnic-dmain: [ Van] V [ de V = V 1 0 bn = V en ][Sab] Sbe 1 Sea Where the cnverter utputs Yam Vbm V en are the phase vltages, all represented as cmplex harmnic vectrs, and Sab, Sbe, Sea are cnvlutin matrices cnstituted f the harmnic cefficients fthe Sab, Sbe and Sea at a certain harmnic. Als, Vde is the harmnic-dmain vectr f the DC-side vltage. Cnsidering Fig. 1, the DC current can be intrduced as: Where cnverter currents la' I b and Ie are the cmplex harmnic vectrs f the line currents, and Ide is the harmnic-dmain vectr fthe DC-side vltage. Equatin (2) culd als be presented in matrix frm f An integral frmula relates bth DC quantities in the timedmain (see Fig. 1) as fllws: t V de (I ) = Jide (I )dl +v de (0+). Assuming the DC-side harmnics are riginated frm harmnic cntent f the ide(t), Ede is the pure DC vltage (1) (2) (4) a Figure 4: STATCOM equivalent impedance matrix structure implying the phases a, band e cmpnents crss cupling fr harmnics bigger than 0.02 P.D. up t 50 th. and Zeap is the DC-link impedance. Then, the fllwing relatinship can be established based n (4): Substituting lile and V de frm (3) and (5) in (1), bth the Thevenin equivalent vltage (Et,,) and impedance (Zt") f the cnverter can be represented as belw (shwn in Fig. 3 in which v,,, is the resultant equivalent cnverter utput vltage): b (5) V=Zthl+Eth (6) Zth = st Zeap S, E th = [E tha E thb E the ] t = E de S S =.!.[Sab -Sea Sbe -Sab Sea -Sber (6a) 3 This is the cnverter mdel f STATCOM that is cnnected thrugh an equivalent inductance t the PCC. The phase cmpnents crss cupling structure fthe Zth has been pltted in Fig. 4 fr harmnic interactins up t the 50 th harmnic that are bigger than 0.02 P.U. It is nticeable that the matrix excludes cntrl system transfer elements because f steady state analysis (all sub-matrices are diagnal). III. HARMONIC BEHAVIOR OF STATCOM The harmnic perfrmance f STATCOM can nw be established using the develped mdel in (6) under ideal perating cnditins. Als, the OPWM scheme assumes ideal switching transitins (having n tum-n r tum-ff delays). Further, assume the balanced system parameters are Iv1 = 1 P.U., Zs= jo.1561 P.U., Zt= jo.5612 P.U. at 50 Hz. Simulating the presented mdel f (6) results in the vltage and current wavefrms shwn in Fig. 5 (Harmnics up t the 100 th are cnsidered). In fact, the fundamental and harmnic cntents are btained directly frm the equivalent circuit f Fig. 1. Then, the time-dmain wavefrms in Fig. 5 are analyzed thrugh an inverse Furier transfrm. This is different /08/$25.00 (g08 IEEE 3

4 Internatinal Schl n Nnsinusidal Currents and Cmpensatin Lagw, Pland, 08 In\erter Current Harmnic Spectra -: 8 >-= -/._ '----- > : Time (sec) Figure 5: Simulatins f the mdel (6) under balanced cnditin when STATCOM supplies 1 P.U. reactive pwer t the PCC; pictures frm the tp ne are the Thevenin vltages (EIII and VII,), the PCC vltage at phase a (Vpcc), and the cnverter current at phase a (Iinv) all in P.U. frm a nrmal prcedure when a time-dmain simulatin is taken place. The OPWM is ptimized such that selective harmnics (5 th, 7 th, 11 th, 13 th and 17 th ) are eliminated. Figure 6 shws the harmnic spectra f the cnverter phase vltage and current. Nte that the STATCOM current spectra exclude the third harmnics. Recently, a detailed study n the harmnic perfrmance f STATCOM is intrduced in [2] using an OPWM switching pattern under realistic perating cnditins. While that methd can be examined with the prpsed theretical mdeling in harmnic-dmain (see (6)), but a mre realistic case is investigated here in which an additinal system examinatin is perfrmed with regard t the degrees f unbalance and distrtin. This culd be useful when cmmissining study f a distributin system fcuses n the levels f uncharacteristic harmnic prduced by a STATCOM at a distributin substatin. IV. MODELING AND SIMULATION OF SYSTEM UNBALANCE Operatin f STATCOM under three-phase unbalanced vltages affects nticeably the penetratin f uncharacteristic harmnics which are nt usually targeted by the engaged mdulatin technique [2]. The prper predictin f the level f vltage unbalance culd be useful in applying further measures t the OPWM, influencing the harmnic perfrmance f STATCOM. Here an imprved and enhanced versin f simulatin apprach in [21] is utilized fr statistical predictin f vltage unbalance. A. Case study: System Descriptin and Measuements A data lgger is installed at the distributin substatin f Mavad that is lcated in nrth-east f Tehran. The measured data is gathered during a week in September 02. Figure 7 shws single-line diagram f the lcal distributin system in which the transfrmer T3 crrespnds t the substatin f Mavad ( kv/400 V, 1 MVA). Figure 8 demnstrates the recrded active and reactive pwers f the three phases at this substatin fr ne week. Als, Fig. 9 intrduces phase vltages f the c 1 :-- C Q) I I -g 0.5 l.2 '0!?f Figure 7: 40 In\erter Phase Vltage Harmnic spectra m Type C TypeC THO = Sheyda 0 kya 1 L"L""'''.''''''''' ,132_1 1 Figure 6: Harmnic Order Harmnic spectra f Vtl, and I inv. Single-line diagram fthe distributin netwrk under study Figure 8: Recrded three-phase active and reactive pwers by data lgger that is installed at 400 V substatin fmavad. substatin transfrmer (at 400 V-end), which are btained using a three-phase lad flw prgram in MATLAB. B. Vltage Unbalance Simulatin The fllwing prcedure is suggested t be used here fr predictin and simulating vltage unbalance: 1) Active and reactive pwers are split int tw parts: prbabilistic and deterministic cmpnents. This is perfrmed using the wavelet transfrm. Als, the analysis is managed separately fr tw categries fwrking days and week-end like thse f the lad frecasting algrithms. 2) The apprximatin parts (btained frm the wavelet transfrm) are then directly predicted as the average daily pwer curve. 3) The detail parts f the wavelet transfrm are mdeled using a Gaussian linking functin which /08/$ IEEE 4

5 Internatinal Schl n Nnsinusidal Currents and Cmpensatin Lagw, Pland, Figure 9: Measured phase vltages f the transfrmer T3 (Mavad) during a week. generates six crrelated randm variables crrespnding t active and reactive pwers fthe three phases. 4) Time-dmain active and reactive pwers (mdeled during the previus steps) are recnstructed by applying the inverse wavelet transfrm. 5) The recnstructed pwers are then used t predict the three-phase vltages thrugh a three-phase lad flw prgram using the Mnte Carl simulatin. The IEC vltage unbalance factr (VUF) is calculated frm the btained vltages in step 4. This prcedure prvides a mre realistic insight int the VUF at the PCC. It is als cmpatible with the Mnte Carl simulatin prgram and statistical evaluatins. Wavelet transfrm presents suitable filtering characteristic. This enables the prcedure t intrduce the pwer as a deterministic cmpnent (apprximatin parts) \vith a quite stable mean and standard variatin as shwn in Fig. 10 (a). Als, the prcedure intrduces a nearly Gaussian distributed prbabilistic cmpnent (detail parts) as shwn in Figs. 10 (b)-(c). Assuming the Daubechies (db5) mther-wavelet, up t the furth filtering level is used t determine apprximatins and details. It is nticeable that the prbabilistic cmpnent in Fig. I0 (b) can be mdeled using a Gaussian linking functin that describes dependencies amng variables, prviding a way t crrelate multivariate data [24, 25]. In a practical distributin system, active and reactive pwers f the three phases shw mderate crrelatin characteristics, which can be mdeled using the Gaussian functin in large netwrks. The suggested prcedure is applied t the studied distributin substatin (Mavad). Simulatins are shwn in Fig. II ver a week. The vltage unbalance percent (VUF%) f the substatin f Mavad is calculated at the lw-vltage side (400 V) f the transfrmer T3 using MATLAB. Simulatins are depicted in Fig. II(a) fr a ne week perid, varying within [0.38%, 1.58%]. T validate the suggested algrithm, the prbability distributin functins are btained frm bth the prpsed unbalance algrithm and field measurements. Bth POFs are shwn in Fig. II(b). Cmparing the exact cllected data (dtted line) with thse fthe prpsed methd (slid line), it can be seen that the suggested algrithm prvides an accurate simulatin funbalance variatin at the PCC. V. STATCOM HARMONIC PERFORMANCE UNDER UNBALANCE OPERATION A realistic vltage unbalance case is studied using the freging suggestin at a distributin substatin. It is als shwn that the distributin system may perate under :,'-I _., --L LJ (a) (b) ' Calculated prbabilistic cmpnent f P a (W) X 10 5 (c) Figure 10: Applicatin f the wavelet transfrm t active pwer, (a) real (blue trace) and apprximated (red trace) lgged data fr ne week, (b) the difference between the apprximated and the exact data, and (c) the distributin f active pwer vs. Gaussian distributin functin. certain vltage unbalance percent (see Fig. II(a)). It can nw be studied the effects f vltage unbalance n the harmnic perfrmance f the OPWM-STATCOM. The prpsed mdel fr STATCOM (see (6) alng with Fig. 3) is linked with the Mnte Carl simulatin f the calculated unbalance percent (VUF%) in Fig. II(b). Assume the capacitance f the DC-link capacitr f STATCOM is I mf. Then, the resultant THD% is calculated fr all data as shwn in Fig. 12. Backgrund harmnics are represented by vltage harmnic surce btained frm field measurements. It can be seen frm Fig. 12 that a realistic vltage unbalance wuld nt dramatically mdifies the uncharacteristic THD f STATCOM AC current (THOS) except fr situatins that STATCOM supplies r absrbs relatively small amunts f reactive pwer. Figure 12(a) prvides a qualitative evaluatin f the prpsed methd. Als, t validate quantitatively the suggested methd, Figs. 12 (b)-(e) cmpare the prbability distributins f the THOS fr realistic VUF% when fur different reactive pwer are supplied by STATCOM. It can be seen frm Figs. 12 (b) (e) that reactive pwers f -0.8 P.D and 0.9 P.U. alng with realistic VUF% give a relatively small range f the THDS variatins arund I% and 0.96%, respectively /08/$ IEEE 5

6 I Internatinal Schl n Nnsinusidal Currents and Cmpensatin Lagw, Pland, ' 90 - (a) 0 50 :r: E--< I 1 I VI. I..1 1a I -+ -.",_.-: ;..rl'. -. l I,... I I I... I.'..,,..,. 7.. I e... a --, L.L,_L,_ ",_ VUF(%) (b) Figure 11: (a) The VUF% variatin ver the ne week perid at the lw-vltage side f T3 btained using the prpsed simulatin methd, and (b) cmparing the PDFs f VUF% btained frm field measurements (dtted line) and the prpsed algrithm (slid line). Hwever, fr reactive pwers equal t 0.04 and -0.1 P.U. alng with the same realistic VUF% result in a cnsiderable range f the THDS variatins arund 25% and 15%, respectively. It shuld als be nted that the THDS is affected by changing the DC-link capacitance. Als, the pwer system equivalent impedance influences the THDS under variatin f the vltage unbalance percent. This analysis can be easily extended t include ther realistic cnditins. It is theretically pssible t mdify the OPWM prcedure t remve uncharacteristic harmnics under unbalanced cnditins. Hwever, the analysis becme mre cmplex, it is nt purely deterministic and culd be difficult t implement nline. CONCLUSION This paper suggests a cmprehensive analysis related t the penetratin level f harmnics by STATCOM int pwer systems. Hence, starting with intrductin f a harmnic-dmain mdel fr STATCOM, an equivalent Thevenin circuit is established. This simplifies simulatin f the develped mdel, while it links certain harmnics t their cmplex values in a three-dimensinal representatin. A case study is arranged in which a data lgger gathers required data frm a kv/400 V distributin substatin lcated in Tehran fr a ne week perid. Analyzing the exact measured vltage unbalance f this substatin, a prbabilistic methd is suggested t predict the unbalance percent. Then, the Mnte Carl methd is linked with the STATCOM mdel. The resultant mdel is used t evaluate harmnic perfrmance f STATCOM under the suggested unbalanced predictin algrithm. Varius simulatins are perfrmed t verify the suggested mdel alng with the prpsed unbalance predictive algrithm r r SO , r-----r---,---_ 0 i Reactive Pwer (pu) (a)...50 i [1] 1. H. R. Enslin and P. 1. M. Heskes, "Harmnic interactin between a large number f distributed pwer inverters and the distributin netwrk," IEEE Trans. Pwer Electrn., vl. 19, pp , Nv. 04. [2] S. Filizadeh and A. M. Gle, "Harmnic perfrmance analysis f an OPWM-cntrlled STATCOM in netwrk applicatins," IEEE Trans. Pwer Del., vl., pp , Apr. 05. [3] R. W. Menzies and Y. Zhuang, "Advanced static cmpensatin using a multi-level GTO thyristr inverter," IEEE Trans. Pwer Del., vl. 10, pp , Apr [4] L. Ran, L. Hldswrth, and G. A. Purtus, "Dynamic selective harmnic eliminatin f a three-level inverter used fr static VAr cmpensatin," Prc. Inst. Elect. Eng., Gen., Transm., Distrib., vl. 149, pp , Jan. 02. [5] P. N. Enjeti, P. D. Zigas, and 1. F. Lindsay, "Prgrammed PWM techniques t eliminate harmnics: a critical evaluatin," IEEE Trans. Ind. Applicat., vl. 26, pp , Mar./Apr [6] Y. Sun, G. Zhang, W. Xu, and 1. G. Mayrdm, "A harmnically cupled admittance matrix mdel fr ac/dc cnverters," IEEE Trans. PwerSyst., vl. 22, pp , Nv O i O (d) TIIDS% (e) TIIDSO,/ Figure 12: (a) Penetrated THDS due t the 5 th, 7 th, 11 th, 13 th, 17 th and 19 th harmnics under varius VUF% and reactive pwer btained frm Mnte Carl Simulatin. (b)-(e) distributins f the THDS crrespnding t the reactive pwer ladings f 0.8 P.U., 0.9 P.U., 0.04 P.U. and -0.1 P.U., respectively. REFERENCES /08/$ IEEE 6

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