Arc Furnce Modeling in ATP-EMTP E. A. Cno Plt, Member, IEEE, nd H. E. Tcc, Member, IEEE Abstrct The use of the rc furnce nd its influence on the power system is being studied. A set of models tht llows for the evlution of the electricl behvior during stedy stte is presented in this pper. These models hve different levels of complexity; strting by tking into ccount ll the non-linerities of the rc furnce circuit, pssing through neglecting the nonlinerities of the trnsformer rectnce nd supposing tht the wve shpe of the voltge-current chrcteristic in the rc is piece wise liner. Experimentl results re presented nd used to vlidte them. Index Terms-- Hrmonics, power qulity, EMTP simultion, wvelet trnsform, instntneous power. I. INTRODUCTION t is recognized tht one of the min sources of hrmonic, I flicker nd unblnce re found in rc furnce. These three phenomen re problems of power qulity tht ffect our dily lives. These problems hve their origins in the non liner linking of the lod tht is connected to the power system. The utilities nd their potentil users tht hve this type of equipment should hve method tht permits the evlution of this type of problem. As the behvior of the rc furnce from the electromgnetic view point is not strictly periodic, it cnnot be nlyzed with precision using the Fourier series nd hrmonics []. Sometimes they cn be considered s trnsient lods for which the flicker is greter problem thn the hrmonics [4]. For this reson this pper will be using the electromgnetic trnsient progrm ATP []. This pper will ttempt to cover the study of the rc furnce from the power qulity point of view nd for this reson three models will be present. First, the complete model is presented. In this model, the most importnt non-linerities of the rc furnce systems re represented. These re the sturtion nd hysteresis effect on the trnsformer, the power cble, nd the rc phenomenon inside the furnce. An itertive method is needed to ggregte rndom signl (resistnce prmeter in this pproximtion. Then simpler, qusi-empiricl model is proposed in order to obtin n esy method to nlyse the rc furnce by wy of nlyticl expressions. The second model is intended to be simpler option. This simplifiction is chieved supposing the trnsformer rectnce to be liner. So, the sturtion nd the hysteresis effect on the trnsformer re not tken into ccount in this model; then nlyticl expressions will be chieved nd the study is quick nd esy. A deeper simplifiction is mde with regrd to the lst model. The wve-shpe of the rc voltge-current is supposed to be piece-wise liner nd the resistnce of the impednce is neglected. In this wy the third pproximte model is shown. In the models specil ttention is pid to the current nd power in the rc becuse they re closely relted to the flicker nd hrmonic study. The results for ech model re compred with rel rc furnce; pqat[-3] is being used in order to get vlidtion method. II. ARC FURNACE CIRCUIT The min furnce elements re shown in Fig.. These re: Trnsformer rectnce, power cble nd rc source (the electrodes. This work ws supported in prt by the Ntionl University of Colombi nd Deprtment of Electronics, Engineering Fculty t the University of Buenos Aires. E.A. Cno Plt is with Ntionl University of Colombi, Mnizles, Colombi, A.A. 7 (e-mil: ecno@fi.ub.r. H. E. Tcc is with the Deprtment of Electronic Engineering, University of Buenos Aires, Buenos Aires - Argentin, C.P. 63, Pseo Colón 85 piso. (e-mil: htcc@fi.ub.r. Presented t the Interntionl Conference on Power Systems Trnsients (IPST 5 in Montrel, Cnd on June 9-3, 5 Pper No. IPST5-67 Fig. Arc furnce equivlent circuit. This circuit hs strong non-liner behvior in sttionry stte, s shown in Fig.. The rc nd the oscilltory movement of the power cble re the min cuse of the distorted voltge shpe. Thus the cble nd rc re the most importnt non-linerities in the circuit. The hysteresis nd the sturtion in the iron core trnsformer re other non-linerities tken into ccount for the rc furnce study.
The power cbles re rndomly oscillting by phse; picture of the distorted resistnce phenomen is constructed.,a 5-5 e(t i(t -.5..5..5.3.35.4 u(t 4 3 u(t - - oltge current chrcteristic 5-5 oltge - Current Chrcteristic - -3 - - 3 Fig.. oltge nd current wveforms In the following models ll prmeters re obtined from the mesurement on 35MW rc furnce t 5Hz of power frequency. III. MODEL I In this prt, the step to get simultion method for the rc furnce is depicted by using the Myr s model []. First, description nd modeling of the different elements re mde. The study of rectnce, power cble nd rc hve been emphsized, becuse these re the min non-liner elements. 8 6 u(t 4 - -4-6 oltge - current Chrcteristic -8 - -5 5 ka i(t Fig. 3 Mesured (U=45, rc furnce, chrcteristic -I curve. The non-linerity prevents direct solution from the Myr [] model of rc. The power in the rc is the result form of this nlysis. The flicker is derivtion of the rc phenomenon nd the interction with non-liner rectnce nd power cble. A -3-4 -6-4 - 4 A 6 i(t Fig. 4 oltge-current chrcteristic of the rc, pproximte model I. A. Model Description In this section the rc model, trnsformer rectnce model nd the power cble model re depicted, becuse they re the min non-linerities of the rc furnce circuit. As is shown in Fig., the rc model is derived from Myr s model. In this wy, n esy model for computer implementtion is obtined. The close form of the model shows tht current []: i = I sinωt ( cuses n rc voltge tht is expressed s follows: v sinω t = sin( ω t + ψ ( + (ωτ where p = r I ; tn ψ = ω τ τ is the rc time-constnt, is the most importnt prmeter tht governs the -I chrcteristic, nd p r the rc column power t the moment of the interruption []. The trnsformer impednce is the following non-liner element for the modeling. The model must cover the coil resistnce nd the sturtion nd hysteresis effect in the iron core. A series resistnce is used to model the coil resistnce (Fig. 5. The sturtion effect is modeled by non-liner inductnce, nd it hs the following eqution [5]: i( t = kφ ( t + kφ ( t (3 where φ (t is the flux in the iron core, i (t is the current cross the trnsformer inductnce, nd k, k re constnts. Next, resistnce prllel to the non-liner inductnce represents the hysteresis. Its vlue cn be clculted from the eqution [-3]: ω Rh = φmx (4 d i
where φ mx is the mximum flux, ω is the fundmentl frequency of the source nd d i is one hlf of the hysteresis width t φ =. As result, the model of the trnsformer impednce is obtined []. Finlly, the power cble model hs been included. The trnsient behvior of cbles hs been discussed in detil in mny textbooks nd ppers [,3,]. ATP includes routines to compute prmeters nd to simulte cble trnsients [3]. Series impednce nd shunt susceptnce mtrices re clculted from cble prmeter computing routines bsed on the multi-port theory. Also, boundry conditions (like cble trnsposition or erth setting my be included. Finlly, there re two options vilble for trnsient simultion: To use lumped-prmeter models (cscded π circuits or distributed prmeter models. Simultion of cscded π sections, computed t fixed frequency [3], results re computtionlly fst. Although these models do not include frequency dependent prmeters, the wnted frequency behvior is chieved by cscding the π circuit sections. Unfortuntely, lumped circuits re not good enough to model distributed prmeter effects. If the prticulr cse involves high frequencies, greter number of π sections must be used. Then, numericl errors could pper due to gret mgnitude differences between the π circuit prmeters nd the network prmeters. When cble fetures ffect the trnsient behvior of the system, the cble length nd its geometry become very importnt. The trnsient propgtion speed is function of both the inductnce nd the cpcitnce of the cble: v = m / s (5 LC where, L is inductnce in henry per meter nd C is cpcitnce in frd per meter. The cble wve impednce is: L Z o = ohms (6 C The mgnitude of the reflected wve t the electrodes depends on the reflection coefficient: Z m Z o = (7 Z m + Z o where is the reflected voltge, is the incident voltge, Z m is the equivlent rc impednce (which depends on the rc furnce lod nd Z o is the wve impednce of the cble. In the cse of multi-phse cbles, these prmeters must be computed for ech propgtion mode, using the bove mentioned ATP routines. By mens of the susceptnce nd impednce mtrices, the propgtion modes my be determined by [-4]. Eq. 7 is simple wy to understnd how the trnsient overvoltge mgnitude vries with the rc lod nd the instlltion fetures of the loction system. Power cble modeling in EMTP-ATP - Cble prmeter computtion by Ametni routine: In this cse, impednce nd susceptnce mtrices re computed using the multi-port theory. Boundry conditions, like cble trnsposition or grounding, re included. Finlly, two options for presenttion re vilble, set of prmeters to model the cble s cscded π circuits, or distributed prmeter dt to pply the Jmrti or Semlyen routines [3]. Cscded π model It uses the π coupled circuits of the EMTP progrm. Although this model does not include frequency dependent prmeters, frequency dependent behvior is chieved by the cscded connection. However, the distributed prmeter effects re not well represented by this lumped circuit model. If the prticulr problem involves high frequencies, greter number of π circuits will be required. In such cse, simultion my fil due to numericl errors cused by excessive differences between the π section prmeters with respect to the network prmeters. In distributed prmeter models, the frequency dependence nd the distributed effects of the cble prmeters re tken into ccount [,3]. However, the vlidity of these models re restricted becuse modl trnsformtion mtrices re ssumed to be rel nd constnt. The effect of the rndom oscilltion of the cble due to the electromgnetic forces in the electrodes in three-phse rc furnce ws replced by dynmic model in the resistnce prmeter. In the cse of skin effect, the resistnce of the power cble ws defined by bnd-limited white noise vrition tht ws defined by: R ( t R + BLW (8 = where R is constnt obtined from Ametni s routine for given geometricl cble nd BLW is bnd-limited (4-6Hz[4] white noise with zero men. I. MODEL II Model I will be clled the Complete Model; it ws present in detil for the EMTP simultion. However, the model cn be simplified to chieve fst simultion process. In model II two simplifictions re mde: pure sine wve three phse voltge nd blnced resistive lod: First, the rectnce is supposed to be liner. Thus, its model is n R-L combintion, neglecting the hysteresis nd sturtion effects. Second, the power cble is deprecited nd considerble increse in the resistnce of the bove-mentioned R-L circuit will be mde. The equivlent circuit with the bove simplifictions is
shown in fig. 6. The source tht represents the Myr s rc model, is time domin controlled voltge source, using TACS from ATP- Electromgnetic trnsients progrm []. In this cse, the finer resolution levels do not llow the detection of ny chnges. This curve will be used s reference in comprison with other lods in the system. It will pper s dotted line on ech of the testing cses. Fig.6: Approximted model II, the voltge is modeled using Myr s rc, eq. (. Using the circuit in fig. 6, the sttic rc furnce model II ws simulted. Fig. 7 shows the voltge-current chrcteristic. The power loss, represented by the enclosed re of the v-i chrcteristic of model II in comprison with the mesurement shown by fig. 3 suggest tht implementtion is successful. R i= ex ig ( ( R ir i i R + v = ir ig, i < i < i ( R ( / d i( t i i e p ro t τ, < dt where ex nd ig re the extinction nd ignition voltge respectively, i nd i re the currents corresponding to the ignition nd extinction voltges respectively, nd the therml inerti is modeled using the lst prt of the Myr s model, with the time constnt τ in the first qudrnt of the v-i chrcteristic shown in fig. 8 4 -I Chrcteristic, simultion using model II 3 - - -3-4 -3 - - 3 Fig. 7: Simultion obtined from model II. A x 4 Fig 8: Mesured nd piece-wise liner pproximtion of -I chrcteristic of n rc furnce lod. 4 -I Chrcteristic, simultion using model III For the bove figure, the -I chrcteristic is obtined over five full periods of the ATP simultion. 3. MODEL III A simpler model, it ws simulted using the rc furnce model proposed in [4]. This model is bsed on piece-wise liner pproximtion of the rted v-i chrcteristic of the lod nd includes the power consumed by the rc furnce lod s n input prmeter. In this cse, the rted v-i chrcteristic is ltered in such wy tht the power consumed by the lod is tht specified by the user nd the therml inerti is expressed by n exponentil expression. In this wy it hs three regions: ig i = (9 R - - -3-4 -3 - - 3 A x 4 Fig. 9: -I Chrcteristic obtined from simultion using rc furnce model III. It is to be observed tht the prt of this model ws proposed in [4]; the difference with respect to reference [4] is in the exponentil dely tht is typicl in the plsmtic chnnel [].
Fig. 9 showed the -I chrcteristic in this model. I. POWER QUALITY ANALYSIS TECHNIQUE PQAT- A. Devition Qulity Index It is defined s the noise/signl reltion using the wvelets coefficient t the levels j nd j o, clculted by the multiresolution lgorithm [,3]. The dispersion mesurement with respect to curve which represents the best of power trnsfer under conditions free of contmintion of ny kind, define the qulity of the system with regrd to the curve. Commentry: The stndrd devition is mesurement of dispersion, which when pplied to the wvelet coefficients, represents the energy of the signl, for which its men vlue is zero. The dispersion of these coefficients in reltion with resistive nd pure liner lods, produces reltive degree of qulity. With the temporl frme in mind, the reltive qulity index is defined s follows : ξk ( t ξk ( t ξk ( t ξk ( t Qulityk = ξk ( t ξk ( t, ( Where ξ k is the mximum dmissible vlue for the prmeter, ξ k is the best trjectory nd ξ k is the mesured dt. A projection of ( in the trnsformed frme leds to the next definition Definition : The prticulr index of the devition of qulity is defined s: sdt( d std( d Re sistivo PDQI = std( d, (3 where std represents the symbol of stndrd devition, d represents the vlue of the wve coefficients in level for the power mesurement on tht level nd d Resistivo represents the vlue of the wvelet coefficients for power consumed by resistive lod on the sme level. This estblishes n importnt difference with other definitions of the power qulity index [6, 8, nd 9]. With ll this, the std_msd curve [-3] my be trced. The rc furnce models re nlyzed using pqat [] bsed on the following rules:. Mesurement of v, vb, vc nd i, ib, ic..trnsformtion to i, v in the wvelet domin. t t 3. Rel nd imginry power clcultion []. 4. std_msd, the stndrd devition vector formtion nd visuliztion of p, q 5. PDQI, qulity index devition clcultion by (3. B. Arc furnce Anlysis In fig. nd the rel power is mesured in 5ms. The solid curve corresponds to the rel system while the dotted curve corresponds to the simulted one; the pproximte model I is being used. All of the models were being used with power system of 5Hz. 8 x 4 Arc Furnnce Rel Instntneus Power Mesured 7 6 5 4 3 Simulted model I.5..5..5 Fig. Rel nd zero sequence power, in n rc furnce system. wtts 6 x 4 Rel nd zero power 5 4 3 ( Mesured ( Simulted (System Frequency (flicker - 3 4 5 6 7 nivel Fig. Multi-resolution nlysis of the rel nd zero sequence power. The mesured dt presented in fig., shows tht the flicker phenomen (typicl of this kind of lod is chrcterized t level 7 (low frequency n dc component. The next representtion shows the simplicity of the models in the simultion process using ATP. These simultions re depicted in fig. 3; it is the noise/ signl representtion. Stndrd devition.5.45.4.35.3.5..5..5 DQI Power Qulity Noise/signl reltion Model II Mesured Model I Model III 3 4 5 6 Level Fig. 3: std_msd curve of ech model simulted is compred with the mesurement cse. II. CONCLUSIONS The results of mesurements on 35 MW rc furnce under the sme conditions s the simultion models re included (Fig. nd 3. The nlysis of the simultion results presented in bove figures leds to the following conclusions: The complete Model (Model I represents the most
importnt representtion nd the instntneous power is very close to it, s shown in Figure. The other models do not differ much in the power consumed, but it hs minus relistic noise/signl representtion. Every one of the models in this pper ws developed using time domin controlled voltge source in ATP. The developed lod models re bsed on two pproches. First, one ws the Myr s rc model nd the second ws bsed on the -I chrcteristic modified by piece-wise liner nd time constnt of the -I chrcteristic. Finlly, PqAT ws the pplictor to compre the models nd it proved to be successful, s shown by comprisons done between the rel mesured dt nd other models presented in vriety of simulted cses. This new method (pqat offers mny ttrctive fetures: The evlution of the curve of coefficients, llows the right physicl chrcteriztion of the kind of rc furnce lod, which brnches fter the mesured section. III. REFERENCES [] A. E. Emnuel, J.A: Orr An Improved Method of Simultion of the Arc oltge-current Chrcteristic, 9 th interntionl Conference on Hrmonics nd Qulity of Power, Proceedings p.p. 48-5, October - 4,, Orlndo, Florid. [] E.A. Cno Plt, H. Tcc Power Lod Identifiction, Journl of the Frnklin Institute vol. 34, No., pp.97-3, Jnury 5. [3] E.A. Cno Plt, H. Tcc, Perturbtion Power, WSEAS Trns. On Circuits nd Systems vol 3, No 4, pp.996-3, June 4. [4] S. rdm, E.Mkrm nd A. Girgis A New Time Domin oltge Source Model for n Arc Furnce Using EMTP", IEEE Trnsctions on Power Delivery, ol., No.3, pp. 68569, July 996. [5] C.Crrillo nd J.Cidrás, Fluorescent Lmps Modelling for oltge Fluctutions ETEP.ol., No..pp 9-6, Mrch/April [6] C. Mucs, "Assessment of Electric Power Qulity: Indices for Identifying Disturbing Lods", Europen Trnsction on Power Systems, ETEP ol. 8, pp. 87 9, July/August 998 [7] IEEE Working Group on Non-sinusoidl Situtions: Prcticl definitions for powers in systems with non-sinusoidl wveforms nd unblnced lods: discussion, IEEE Trns. on Power Delivery, vol., pp. 3-34, Jnury 996 [8] L.Cristldi nd A. Ferrero A digitl method for the identifiction of the source of distortion in electric power systems. IEEE Trns. on Instrumenttion nd Mesurements, vol..44, pp. 83-89 Feb. 994. [9] G. Strng nd T. Nguyen, Wvelets nd Filter Bnks", Wellesley- Cmbridge Press, 996,p.69. [] A.M. Goud, M.M.A. Slm, M.R. Sultn nd A.Y. Chikhni, Power qulity detection nd clssifiction using wvelet-multiresolution signl decomposition, IEEE Trns. on Power Delivery, vol. 4, pp. 469-476, October 999. [] The MthWorks, MATLAB 5.3-999. [] Electromgnetic trnsient progrm (EMTP/ATP Reference Mnul. Leuven Center, Belgium, 987. [3] Hermn Dommel, EMTP "Theory Book", MicroTrn Power Systems Anlysis Corportion, ncouver, British Columbi 996. [4] H. Akgi, Y.Knsw & A. Nbe, Instntneous Rective Power Conpenstor Comprizing Switching Devices Without Energy Storge Components, IEEE Trns. on Industry Applictions, ol. IA-, No. 3, 984. IX. BIOGRAPHIES Edurdo A. Cno Plt (S 96, M 98 ws born in Neiv, Colombi, in 967. He received the B.Sc. nd Specilist Engineering degree in 99 nd 994 from Ntionl University of Colombi, Mnizles, both in electricl engineering. Between 996 nd 998 hd DAAD scholrship for postgrdute studies in electricl engineering t the Ntionl University of Sn Jun, Argentin. He is currently working towrd the doctorte degree in engineering in the University of Buenos Aires. Since 994 is n ssistnt professor t the Ntionl University of Colombi in Mnizles. Hernán E. Tcc (S 9-M 93 ws born in Argentin in 954. He received the B.E. degree in electricl engineering from the University of Buenos Aires, Argentin, in 98, the M.S. in 988 nd the Ph.D. degree from the University of Sciences nd Technologies of Lille, Frnce, in 993. In 998 he received the doctorte from the University of Buenos Aires. Since 984, he hs been with the Fculty of Engineering, University of Buenos Aires, where he is currently with the Dept. of Electronics, engged in teching nd reserch in the res of industril electronics, leding lbortory devoted to power electronics (LABCATYP. His reserch interests re in the fields of SMPS, UPS, bttery chrgers, soft-switching techniques, nd low-cost micro-controller control of power converters.