COMPUTER MODELLING OF FLICKER PROPAGATION
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1 OMPUTER MODELLING OF FLIKER PROPGTION T.Keppler N.R.Wtson J.rrillg University of nterury hristhurh, New Zelnd strt The time series of the voltges t the desired lotions re first omputed y EMTD simultion. These re then used to determine fliker informtion. omprison is mde with frequeny domin simultion for the prtiulr se when the fliker soure is periodi nd sinusoidl. The test results re in good greement for the se of symmetril fliker injetions. The use of zero sequene signls shows slightly lrger differene etween the time nd frequeny domins due to the different pproximtions mde in the return pth. Keywords: Digitl flikermeter, frequeny domin, EMTD INTRODUTION The min soure of fliker is the eletri r furne (EF), due to the voltge flutution used y the nonliner vrition of the r resistne during the furne melting yle. physil nlysis of the r length vrition is imprtil due to the vrying metl srp shpes, the errti eletromgneti fores nd the reletrode positions. Insted, the ehviour of the EF is normlly represented y simplified deterministi or stohsti models[] when ssessing the effet of fliker ompenstion tehniques, suh s the use of series retors [], SV's or STTOM's[]. In the generl se, voltge fliker is nondeterministi nd the fliker severity indies re sed on sttistil evlution of the time series of the instntneous fliker level(ifl). Fliker severity evlution, thus, inherently requires the time domin wveform of the IFL. The IFL derivtion is itself non-liner proess (inluding two squring opertions). This mens tht the IFLs t different nodes of the power system nnot e relted to eh other through the (liner) frequeny hrteristis of the network in the wy tht is done for hrmoni nlysis. This prolem lso pplies to the fliker severity indies Pst nd Plt, sine the former is derived from the IFL time series nd the ltter is sed on the former. Hene, the fliker severity t prtiulr us nnot diretly e omputed from Pst vlues mesured t other uses. Insted, the time series of the voltge must first e omputed t the desired lotion nd then used to otin the IFL nd Pst informtion. urrently, fliker informtion is only derived t the terminls of the non-liner omponent (normlly n r furne), the simultion rried out on simplified rdil iruit with the power soure represented y voltge in series with the short-iruit impedne. This pper disusses the sujet of fliker propgtion, n importnt feture in the predition of the tul fliker severity levels t points distnt from the soure (or soures) of fliker. FLIKER SIMULTION IN THE TIME DOMIN This setion disusses the inorportion of digitl flikermeters in time domin simultion progrms. Figure shows lok digrm of digitl flikermeter speilly developed for this purpose nd sed on the IE(Interntionl Eletrotehni ommission) speifition[]. Design detils n e found in referene[] omplemented y sttistil evlution this unit hs een implemented in the PSD/EMTD simultion pkge running under Unix. The inorportion of multiple flikermeter units in the progrm permits the study of fliker propgtion throughout the power system. Typilly PSD runs re set up for system simultions in the order of seonds, requiring from minutes to hours of omputer simultion depending on network omplexity nd the speed of the host omputer. However, when performing fliker nlysis, muh longer simultion times will e required. This is in prt due to the input voltge sling used in the flikermeter. The input signl is sled to its verge RMS vlue, whih involves time onstnt of 6 seonds nd, thus, requires n initil settling time of t lest minutes. However, this feture of the flikermeter n e disled in the omputer simultion nd the verge RMS entered mnully. The min reson for the long simultion times is the speified oservtion time for the Pst index, i.e. minutes; to omplete minutes of tul opertion for the nine us system desried lter typilly tkes hours of running time on n UltrSPR omputer input voltge nti-lis squring weighting V V weighting /D voltge dptor squring. khz.khz nti-lis Hz LP.Hz LP deimtor D6 D6 D. khz Hz Hz IFL humn visul pereption model Figure : lok digrm of the digitl flikermeter
2 (MHz). lthough the RTDS (Rel Time Digitl Simultor) n e of gret ssistne in this respet, t present the RTDS does not permit the ddition of User omponents, suh s the tul fliker metering, whih must, therefore, e inorported y the equipment mnufturers. Post-nlysis of the RTDS lulted voltges is possile option, ut the lrge file sizes involved re prohiitive. The simultion of the power trnsmission system usully requires smpling rtes of khz or more, generting huge mounts of dt (out 9 Myte/min for 8 hnnels). Furthermore, the speed gined from prllel proessing in the RTDS would e lost during post-nlysis. key feture of the RTDS is tht externl devies n e interfed diretly vi its nlogue inputs nd outputs. Hene it should e possile to onnet the tul flikermeters to perform fliker monitoring "online"; however, in the present stte of RTDS the digitl to nlogue onverters only offer -it quntistions, whih is insuffiient for ontinuous rel time three-phse monitoring [6]. STEDY STTE FLIKER ESTIMTION The IE stndrd speifies periodi sinusoidl nd retngulr fliker test signls for the lirtion of the flikermeter. Under these onditions the IE instrument reltes fliker severity nd mgnitude linerly, reltionship tht n e exploited to estimte the fliker severity index throughout the power system with the help of frequeny domin tehniques. Moreover, y identifying the dominting frequeny omponents of the fliker soure the frequeny domin n e extended to ny fliker soure. With periodi urrent injetions the resulting voltges re onstnt provided tht the network is liner nd time invrint. Under suh ondition the voltge spetr t every us n e lulted using hrmoni penetrtion progrm. The modultion mgnitudes re then estimted from the lulted voltges nd, finlly, the Pst index is found y multiplition with ertin ftor, sed on the type nd frequeny of the fliker wveform. The proportionlity ftors n e predetermined y mens of time domin simultion (e.g. using MTL) for eh type of wveform. The ove proedure is sed on the ssumption tht the modultion wveform remins onstnt s the disturne propgtes throughout the power system. lerly, this will not e the se in prtie. Depending on the frequeny hrteristis of the system, the originl disturing urrent wveform will pper in more or less distorted form s the modultion wve of the voltge wveform. For exmple sinusoidlly modulted urrent will not neessrily led to sinusoidlly modulted us voltge, euse the mplitude modulted(m) urrent onsists of three spetrl omponents tht propgte differently depending on their respetive frequeny dependent impednes. The sensitivity of the fliker distortion to this effet is investigted in Setion. Thus for the se of periodi fliker, estimting fliker severity diretly from the voltge spetrum redues the prolem of "fliker severity estimtion" to the prolem of determining the voltge. Figure illustrtes the proess of estimting the Pst index with the help of hrmoni penetrtion progrm (suh s HRM)[6]. The us voltges re found through superposition of the voltge modultion used y the urrent injetion (HV.DT) nd the nominl voltges, supplied either from time domin dt vi the Fst Fourier Trnsform or produed from lod flow progrm. The next stge is to use the pproprite proportionlly ftor tken from look-up tle to onvert these voltges into the orresponding Pst vlues. For instne, using the ftors for sinusoidl fliker, shown in Figure, modultion mgnitude of perent ourring t Hz yields Pst of units of severity.. Derivtion of the modultion ftor The modultion mgnitude is est mesured using squring nd low pss loks, suh s in the flikermeter. For this purpose, however, the time series of the voltge would hve to e reonstruted from its spetrl omponents, whih is undesirle. Insted, n nlytil pproh is used here. The three spetrl omponents tht onstitute the M wveform re depited in the phsor digrm of Figure. For V l = V u nd ϕ l - ϕ = - (ϕ u - ϕ ) the resulting signl represents sinusoidlly modulted sinewve. However, due to the frequeny dependent hrteristis of the system, the mgnitudes nd ngles will in prtie devite from the idel M wveform. The length of the resultnt phsor V r = V + V l + V u orresponds to the envelope of the M voltge wveform, whih fter some lger redues to: V r() t = [ V + Vl + Vu + VV l os( ϕ ϕl + ωmt) + VV os( ϕ ϕ ω t) u u m + VV os( ϕ ϕ ω t)] PSD l u l u m system dt file SYS.DT norml us voltges HRM us voltges HV.DT Mtl urrent injetion file Pst index Figure : Use of HRM to estimte the Pst index () Mtl look-up tle
3 Multiplition ftor Fliker frequeny [Hz] Figure : Proportionlity ftors relting modultion mgnitude nd fliker severity for sinusoidl fliker. where V, V l, Vu re the mgnitudes of the fundmentl nd the lower nd upper sidend omponents, nd ϕ, ϕ l, ϕu their respetive phse ngles. The modultion ftor follows from the mximum nd minimum length. lthough the mximum nnot e solved for nlytilly, simple pproximte formul n e derived to estimte the modultion mgnitude. The modultion of the resultnt V r (t) is of the following form: V r ( t) = + f ( t) = + f ( t) / () where represents the onstnt terms (i.e. V + V l + Vu ) nd f(t) the time dependent terms of eqution. The mgnitudes of the sidend omponents V l nd V u re smll ompred to the fundmentl V, so tht f(t)/ <<. In this instne Tylor expnsion for the squre root (i.e. n e used, + x = + x x + 8 where the qudrti nd higher order terms my e negleted, thus V r () t = ( + f())/ t () fter removing the d ontent nd sustituting the pproprite terms for nd f(t) the modulting wveform eomes: V () t = (VV os( ϕ ϕ + ω t) r l l m + VV u ϕ ϕu ωmt V + Vl + Vu os( ))/( ) One gin Vl nd V u n e negleted ginst V in the denomintor s well s V l V u ginst V V l nd V V u, whih llows the following further simplifition: () V r ( t) = Vl os( ϕ ϕl + ωmt) + Vu os( ϕu ϕ + ωmt). () This result represents the projetion of two phseshifted phsors tht rotte with the sme speed onto the rel xis. Their sum (the mplitude of the modulting wveform) is otined from Pythgors' theorem nd the modultion ftor m follows fter multiplition y /V : m = Vl + Vu + V lvu os( ϕl + ϕu V ϕ ) (6) FLIKER PROPGTION The nine us system of Figure is used to illustrte fliker propgtion using the PSD model s desried erlier. The running time for the simulted ses mounted to severl dys!. To simplify the desription nd provide verifition y hrmoni penetrtion progrm, sinusoidlly vrying mplitude modulted urrent is used s the fliker soure. The injetion, t us, onsists of three urrent soures tht operte t the system fundmentl frequeny of Hz nd the frequenies ± f Hz. The voltges t the lod uses nd t the kv uses re monitored y 8 identil flikermeters. To redue simultion time, the oservtion period for the Pst evlution is set to ten seonds insted of the onventionl ten minutes. This should not ffet the results if the disturne is mintined onstnt.. Test system results Figure 6 displys the fliker severities throughout the test system due to symmetril three-phse positive sequene injetion t us. The Pst indies derived y the PSD model nd those otined from the frequeny domin solution re in good greement. The fliker severities re highest t the injetion us s expeted. ompring grphs () nd (e) nd (d) nd (f) respetively, it n e seen tht for the positive sequene Im ϕ ω V ω m V u V u + V l ϕ u ϕ l V l Figure : Phsor digrm showing the fundmentl nd two sidend omponents onstituting the pproximtely sinusoidl fliker. ω m Re
4 Mnpouri Roxurgh Tiwi urrent injetion Inverrgill Inv Rox 6 Figure : Test system for the nlysis of fliker propgtion. injetion the fliker propgtes lmost unttenuted from the trnsmission grid to the lod uses. However, onsidering the highly symmetril nture of the EF non-liner impednes, it is importnt to test the fliker propgtion model with zero sequene injetions, s well. The results in Figure 7 show slightly lrger differenes etween the PSD nd HRM solutions s ompred with the symmetril se. This my e explined y the pproximtions mde in the representtion of the erth return pth. In the PSD studies the trnsmission lines were represented y the defult option(i.e. logrithmilly sped smples re lulted in the rnge from. Hz- MHz). It is knowledged, however, tht numer of prmeters n e hnged in the PSD trnsmission line model to ontrol the qulity of the representtion, nmely the frequeny rnge used in the urve fitting nd the mximum order of the rtionl funtion. further study ws rried out in whih the time series of the voltges derived with PSD were sujeted to FFT nlysis to extrt the orresponding spetr, nd the ltter were then proessed in the sme wy s the output from the HRM progrm. The Pst indies estimted in this wy nd those given y the flikermeter virtully oinide, whih mens tht the differenes oserved in Figures 6 nd 7 must e ttriuted to inonsistenies in the modelling of the system omponents y PSD nd HRM. Moreover, these results lso vlidte the use of eqution (6) to estimte the modultion mgnitudes. For the speil se of periodi fliker, the liner reltionship etween fliker mgnitude nd the Pst index nd the ft tht the system is in stedy stte n e tken dvntge of. The fliker mgnitudes follow from frequeny domin simultion of the power system, whih n then e relted diretly to the orresponding Pst indies. The proportionlity ftors relting fliker mgnitude nd fliker severity still hve to e determined in time domin simultion for eh type of fliker wveform. oth methods hve een ompred for the prtiulr se of sinusoidl fliker nd the results show good greement. The test results re in good greement for the se of symmetril fliker injetions. The use of zero sequene signls shows slightly lrger differene etween the time nd frequeny domins due to the different pproximtions mde in the return pth. REFERENES [] Montnri, G.., Loggini, M., vllini,., Pitti, L. & Zninelli, D.(99), r furne model for the study of fliker ompenstion in eletril networks, IEEE Trns. on Power Delivery, V9(), 6-6. [] isih, l., mpestrini,. & Mlguti,.(99), Tehnil nd opertionl experienes for mitigting interferenes from high pity r furnes, IGRE, Pris. [] Woodford, D. (),Fliker redution in eletri r furnes, Mnito HVd Reserh entre Journl, V(7). [] IE -- (99), Eletromgneti omptiility. Prt : Testing nd mesurement tehniques- Setion : Flikermeter- Funtionl nd design speifitions. [] Keppler, T.(998), Fliker mesurement nd propgtion in power systems, Ph.D. thesis, University of nterury, New Zelnd. [6] rrillg,j, Wtson,N.R. nd hen,s., (), Power System Qulity ssessment(ppendix II), John Sons, hihester, U.K. [7] rrillg, J., Smith,., Wtson, N.R. & Wood,.R.(997), Power System Hrmoni nlysis, John Wiley nd Sons, hihester, U.K. ONLUSIONS In generl, fliker severity needs to e determined y flikermeter from the time series of the voltge. Therefore, to determine the Pst indies t vrious nodes of power system time domin simultion must e rried out to produe the voltges t those nodes. The fliker metering n e rried out t the sme time or off-line. However the simultion times re extremely long due to the Pst evlution over ten minutes intervls.
5 [units of fliker severity]... [units of fliker severity]... 6 Frequeny [Hz] () Mnpouri kv 6 Frequeny [Hz] () Roxurgh kv [units of fliker severity] [units of fliker severity] Frequeny [Hz] () Tiwi kv Frequeny [Hz] (d) Inverrgill kv [units of fliker severity] [units of fliker severity] Frequeny [Hz] (e) Roxurgh kv Frequeny [Hz] (f) Inverrgill kv Figure 6: omprison of Pst indies resulting from positive sequene urrent injetion t us of the test system (PSD results re shown s solid lines for phses,, nd HRM results s dsh-dotted lines for phses,,).
6 .. [units of fliker severity].. Frequeny [Hz] () Mnpouri kv [units of fliker severity].. Frequeny [Hz] () Roxurgh kv.. [units of fliker severity] 7.. [units of fliker severity] 7... Frequeny [Hz] () Tiwi kv. Frequeny [Hz] (d) Inverrgill kv.8.8 [units of fliker severity].6.. [units of fliker severity].6.. Frequeny [Hz] (e) Roxurgh kv Frequeny [Hz] (f) Inverrgill kv Figure 7: omprison of Pst indies resulting from zero sequene urrent injetion t us of the test system (PSD results re shown s solid lines for phses,, nd HRM results s dsh-dotted for phses,,).
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