International Journal of Scientific & Engineering Research, Volume 7, Issue 5, May ISSN

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1 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN Mathematcal Modelng of Electrc Arc Furnace to Study the Flcker Goyal R. Awagan Department of Electrcal Engneerng Govt. College of Engneerng, Aurangabad (M.S.), Inda A. G. Thosar Assocate Professor, Head of Electrcal Engg. Dept. Govt. College of Engneerng, Aurangabad (M.S.), Inda Abstract- Electrc arc furnaces (EAF) are used n the meltng and refnng of metals such as copper, lead, alumnum, hgh grade alloy steel, etc. The producton of steel by EAF technology s ncreasng n emergng economes. Today, Inda ranks second n the world n EAF-based steel producton. As the popularty and use of the EAF n the ndustry ncrease, so does the power qualty problems as a result of ths progress. The EAF operaton causes harmoncs, nterharmoncs, voltage flcker and strongly varyng reactve power demand, whch affect the power qualty adversely. Utltes and customers are concerned about these effects and try to take precautons to mnmze them. Therefore, obtanng the tme response of an electrc arc furnace becomes mportant n nvestgatng the mpact of these nonlnear, tme varyng loads on the power qualty of the overall power system. Hence, developng an accurate and easy to use arc furnace model has been an mportant and qute a challengng task for several researchers n the past. Ths paper attempts to study the power qualty ssues related to EAF partcularly flcker usng the Casse-Mayr arc furnace model. Index Terms- Power Qualty, Electrc Arc Furnace, Flcker, Harmoncs, Casse-Mayr arc model, Snusodal varaton, Random varaton v Arc voltage (V) Arc current (A) g Arc conductance (mho). NOMENCLATURE E θ P V at m Constant steady-state arc voltage (V) Arc tme constant (µs) Constant power loss (W) Threshold arc voltage (V) Modulaton ndex w f Flcker frequency (Hz) N ( t) Band lmted whte nose (Hz) 6

2 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN INTRODUCTION Electrc arc furnaces are wdely used n steel ndustry for meltng and refnng of ron. They are also used n the smeltng of nonferrous metals. The prncple of operaton of EAF s that the ar n the ar gap gets onzed under the nfluence of electrostatc forces and becomes conductng medum on the applcaton of hgh voltage across an ar gap and the current flows n the form of a contnuous spark, called the arc. Dependng on the formaton of arc, the EAFs are classfed as drect arc furnace, ndrect arc furnace and submerged arc furnace. Drect arc furnace s manly employed for makng alloy steels such as stanless, hgh speed steel. Indrect arc furnace s used for meltng nonferrous metals. Submerged arc furnace s used for the producton of Ferro-chrome and Ferromanganese. Though the arc furnace s becomng popular n the metallurgcal ndustry, t has become a cause for concern among the power system engneers. EAFs are characterzed by rapd changes n absorbed powers that occur manly n the ntal stage of meltng process, durng whch the crtcal condton of a broken arc may become a short crcut or an open crcut. Owng to the very complex arc phenomenon, the voltage-current characterstc of the arc s hghly non-lnear, whch causes harmonc currents whch n turn produce harmonc voltages when crculatng by the electrc network. Generaton of harmoncs results n equaton representng a general dynamc arc model s based on the prncple of conservaton of energy. Ths method makes use of emprcal formulas that relate arc radus/length, arc voltage and current but dd not drectly ncorporate the quas-stochastc nature of EAF operaton. S. Varadan [3] presents a tme doman controlled voltage source model for an arc furnace. The model s based on the pece wse lnear approxmaton of the v characterstc of the arc. Omer Ozgun [4] presents an arc furnace whch s modeled usng both chaotc and determnstc elements. The Chua s chaotc crcut s used to represent the flcker effect and a dynamc model s obtaned usng the dfferental equaton. A revew of the varous power qualty ssues n the arc furnace usng dfferent arc models s dscussed n [5]. However the above models deal wth some propertes of EAF. Some of them deal wth snglephase model useful for the study of flcker effect other wth statc model useful for harmonc studes. Therefore, t s necessary to develop a mathematcal model capable of representng both the statc and dynamc behavor of the electrc arc furnace load wth enough accuracy. Ths paper presents a Casse-Mayr method to model the electrc arc furnace that s formulated from the classcal Casse and Mayr models used n the past to study the arc phenomenon n hgh voltage crcut breakers. The structure of the paper s organzed as follows. Secton 3 deals wth the prncple of electrc arc furnace. Secton 4 descrbes further flcker problems. Thus, EAF s one of the the mathematcal modelng of varous electrc arc responsble sources for deteroratng the power furnaces. Secton 5 descrbes the mathematcal qualty n the connected network. modelng of electrc arc furnace usng Casse-Mayr Wth the ncreasng use of EAFs many power method. Secton 6 descrbes the smulated electrc qualty problems are ntroduced n the power arc furnace model usng the Casse-Mayr system. In order to study the power qualty ssues related to arc furnace, there s a need to develop an equatons. The statc and dynamc characterstcs of the arc furnace model are dscussed n secton 7. accurate electrc arc furnace model whch can represent the furnace operaton wth accuracy. Lterature revew reveals some of the methods for 3. PRINCIPLE OF ELECTRIC ARC modelng and predctng the behavor of electrc FURNACE arc furnaces. R.C.Dugan [] developed an The physcal model of the electrc arc furnace s electronc arc model based on analog approach shown n Fg. [6]. It conssts of three electrodes whch smplfed the study of harmonc that are moved vertcally up and down wth phenomena n arc furnace power systems on a transent network analyzer (TNA). TNA s a specal-purpose analog computer whch s well hydraulc actuators. The ore s melted wth a huge power surge from the electrodes. The actual product s denser than the scrap and thus falls to suted for solvng swtchng and harmonc the bottom of the furnace creatng the matte. transent problems. The arc model s based on the Above the matte les the slag where the electrode smplfcaton of the v characterstc of the arc. tps are dpped. The tremendous heat created by The developed model s a prmtve one and the tme varyng characterstc of the arc s neglected. Early EAF models based on explct mathematcal these electrodes causes the ore to lquefy and separate. Thereupon more raw materals are placed n the furnace and the process repeats tself. equatons are reported n []. The dfferental 6

3 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN Fg. Physcal model of arc furnace The phenomenon of arcng takes place when the electrodes are moved above the slag. As the electrode approaches the slag, current begns to jump from the electrode to the slag, creatng electrc arcs. Dependng on the magntude of the nput voltages of the electrodes, the arcng dstance can vary. Usually, arcng occurs n a regon wthn centmeters of the slag (approxmately -5cm) [6]. Electrc arc furnaces marked ther begnnng durng the dscovery of carbon arc by Sr Humphrey Davy [7]. The arc voltage waveform for carbon s shown n Fg. [] and the correspondng v characterstc s shown n Fg.3 []. Fg.. Typcal carbon arc voltage Fg.3. Typcal carbon arc v characterstc The voltage s a mult-valued functon of current. Just after the regnton of arc at a voltage E, a negatve resstance s dsplayed untl the arc extngushes agan when the arc voltage falls below E e []. The dfferental equaton representng a general dynamc arc model based on the prncple of conservaton of energy s found n []. The power balance equaton for the electrc arc s p = + p p3 () where p s the power transmtted n the form of heat to the external envronment, p s the power whch ncreases the nternal energy n the arc, thus affectng ts radus, and p 3 s the total power developed n the arc and converted nto heat. It s assumed that the coolng effect s a functon of the arc radus r only n equaton (). Therefore, p s wrtten as n p = kr () The coolng effect s also a functon of the arc temperature. However, n order to keep the model smple, ths dependence s assumed to be less sgnfcant and s therefore gnored. Thus, only the arc radus r appears as a state varable. If the envronment surroundng the arc s hot, the coolng of the arc may not depend on ts radus at all, so that n ths case n =. If the arc s long, then the coolng area s manly ts lateral surface area, so that n ths case n =. If the arc s short, then the coolng s proportonal to ts crosssectonal area at the electrodes, so that n ths case n =. The term p s proportonal to the dervatve of the energy nsde the arc whch s proportonal to r, dr p = kr (3) dt Fnally, p k 3 rm 3 v = = (4) r In equaton (3), the resstvty of the arc column s assumed to be nversely proportonal to r m, where m =., to reflect the fact that the arc may be hotter n the nteror f t has a large radus. Substtutng equatons (), (3) and (4) nto () gves the dfferental equaton of the arc: k r dr k + k r = (5) dt r n 3 m+ The arc voltage s gven by v k3 = = (6) g r m + where g s defned as arc conductance and s gven by 6

4 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN m+ r g = (7) k 3 For statc arc model, equaton (6) gves m+ n+ = const r (8) So that n equaton (6) k v = (9) (9) q wth m + n q = () m + + n The values of q do not vary much wth m. The statc characterstc depends manly on the coolng and lttle on the varaton of resstvty wth temperature. n the arc furnace were notced to be chaotc n nature [9]. Therefore, chaos theory was used for modelng arc furnace. Some of the researchers used both chaotc and stochastc elements to model the arc furnace [4]. Most of the efforts were put to model the electrc arc furnaces ether from harmoncs or from flcker pont of vew. The lterature shows some models wth the combnaton of both flcker and harmoncs as well. In [3], the arc furnace load s modeled as a controlled voltage source, and the model s based on a pece-wse lnear approxmaton of the rated v characterstcs of the load. Dependng on the arc resstance varatons, ths model represents both statc and dynamc characterstc. The random operaton of the arc has been modeled by stochastcally modfyng ts v characterstcs. Ths model ncludes the power consumed by the arc furnace load as an nput parameter. Fg.4. shows the typcal v characterstc of an arc furnace load []. 4. MATHEMATICAL MODELING OF ELECTRIC ARC FURNACE There are several approaches for modelng and predctng the EAF behavor. The methods of electrc arc furnace modelng can be broadly classfed as tme doman and frequency doman methods. The frequency doman model represents the arc voltage and arc current by ts harmonc components. The electrcal arc s a tme varyng and nonlnear phenomenon. Therefore descrpton of arc behavor s easer n tme doman than frequency doman. Tme doman methods are Fg.4. Actual and pece-wse approxmaton of v the basc methods for flcker study n EAF. Tme characterstcs of an arc furnace load doman methods can be further classfed as v characterstc (VIC) and equvalent crcut method The pece-wse lnear approxmaton of the v (ECM) []. VIC method utlzes the numercal characterstcs can be defned n the frst quadrant analyss method to solve the dfferental equaton of the v plane as n equaton (3) whch s wth nonlnear VIC. Ths method s wdely used defned n terms of equaton () and (). for modelng the statc and the dynamc operaton V of EAF. The ECM methods can be obtaned from g = () arc operaton; the perodc varaton of arc voltage R and the resstance that arc shows can be used to develop the arc furnace model. Another method to R analyze the arc model n the tme doman s based = Vex Vg () on the Casse-Mayr equaton. In ths method R Casse and Mayr equatons are employed for the low and hgh current of the arc, respectvely. R, The prevous studes reveal that most of the v = R + V g R (3), R < stochastc deas are used to capture the tmevaryng, a-perodc, and nonlnear, behavor of arc furnaces [8]. The use of the chaos theory n arc where, v s the voltage, s the current, R furnace modelng s almost a new compared to the and R are the slopes of segments OA and AB stochastc deas. The electrc fluctuatons occurrng respectvely, Vg and Vex are the gnton and 6

5 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN extncton voltage of the arc respectvely, and The dynamc load model takes nto account are the currents correspondng to the gnton and both perodc and stochastc changes of the arc extncton voltages respectvely n the frst resstance about the value R found n equaton quadrant of the v characterstc shown n Fg.4. (4) for a gven loadng condton and not the arc Snce the power consumed by the arc furnace s radus as there s a drect relatonshp between the equal to the area under the pece-wse lnear v arc resstance and arc radus. Ths model s based characterstcs, the arc resstance R, can be on representaton of the v characterstcs usng obtaned n terms of the power consumed by the two dfferent varatons for the arc resstance about arc furnace load as the value R found n equaton (4).e. snusodal varaton and band lmted whte nose varaton. V The arc resstance n the case of snusodal g R = (4) varaton s defned as V g Vex P + R ( t) = R [ + sn( ω f t) ] (5) R R and n the case of band lmted whte nose varaton s defned as However, f we assume that the quanttesv g, Vex and R R do not change wth the load operatng ( t) = R + BLW (6) condtons, then for any other gven power consumpton, P, t s possble to obtan a smlar v where characterstcs wth a dfferent slope R new n R s a constant obtaned n equaton (4) terms of the new power P new as n equaton (4). for a gven power consumpton, The statc load model for the arc furnace load can ω f s the flcker frequency, and be obtaned from the combnaton of equatons (3) BLW s band lmted (4-4 Hz) [] whte and (4) at any gven power consumpton gven nose wth zero mean. the rated v characterstcs. The expected value of R ( t) s equal to R as n By consderng the v characterstc of the arc n (7) over a perod such that the total nput power detal, a more accurate non lnear approxmaton requrement of the arc furnace s satsfed. model s developed n Fg.5 []. ξ [ R ( t) ] = R (7) Dependng on the type of study to be performed, the statc or the dynamc load model can be used. Bascally the statc model s used for harmonc studes whle the dynamc model s used for voltage flcker studes. As an alternatve to the stochastc models, n [9] determnstc chaos s used n the characterzaton of arc current s a-perodc behavor. Chaos, also called strange attractor, has no generally accepted precse mathematcal defnton. From a practcal pont of vew, t can be defned as bounded steadystate behavor that does not fall nto the categores Fg.5. Nonlnear approxmaton of v characterstc of the other three steady-state behavors,.e., The arc meltng process s broadly dvded nto equlbrum ponts, perodc solutons and quasperodc solutons [3]. The arc furnace load s three parts n ths model. In the frst part, the voltage magntude ncreases from extncton modeled usng a dynamc and mult-valuedv voltage Vex to gnton voltagev g. The arc acts characterstc obtaned by solvng the as a resstor and the arc current changes ts polarty correspondng dfferental equaton (5), whose from 3 to. In the second part, the arc begns to parameter s the arc length and the forcng melt and the voltage across the electrode drops functon s the arc current []. In order to represent exponentally fromv g to V st and the arc current the flcker effect, a low frequency chaotc sgnal s ncreases from to. In the thrd part, the modulated wth the arc voltage. The model s normal arc meltng process takes place and there s connected to the system as a controlled voltage a lnear, slow and smooth drop n voltage from V source [4, ]. st tov ex. The mean value s assumed to be V m as the The chaotc component of the arc furnace meltng cycle spans for most of the half cycle [] voltage s suppled from the well known chaotc 6

6 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN crcut of Chua [4, 5]. In order for an autonomous crcut consstng of resstors, capactors, and nductors to exhbt chaos, t has to contan the followng [4]:. At least one locally actve resstor,. At least one nonlnear element,. At least three energy storage elements. Chua's crcut [4, 5], s the smplest such crcut that satsfes the above condtons; moreover t s the only physcal system for whch the presence of chaos has been proven. These two propertes of ths crcut motvated ts use as a chaos generator. One more useful property of ths crcut s ts ablty to generate chaotc sgnal at any frequency by scalng the values of the energystorage elements.fg.6 shows the Chua's crcut that ncludes two capactors (C, C), a resstor (R), an nductor (L) and a nonlnear resstor (NR) (a par of negatve resstors). v and v Fg.6. Chua s crcut The electrc arc voltage s obtaned from the smultaneous soluton of (8), and the lowfrequency chaotc sgnal that s generated by the smulaton of Chua s chaotc crcut. Modulaton of these two sgnals produces the fnal arc furnace s gven by equaton () as voltage, whch s the output of the model. The current absorbed from the power system bus s njected as the nput to the model. The model behaves as a controlled source, namely t takes the system current as an nput and assgns the termnal voltage value at each tme step. 5. MATHEMATICAL MODELING OF ELECTRIC ARC FURNACE USING CASSIE-MAYR METHOD A Casse-Mayr electrc arc furnace model capable of representng both the statc and dynamc behavor of the electrc arc furnace load wth enough accuracy has been studed n [6]. The relatonshp between the arc voltage and arc current s hghly nonlnear due to the very complex arc phenomena. The characterstcs of the arc depends on a number of factors such as electrode materal, geometry of electrodes, separaton between the electrodes, poston of the electrodes, type of gas and the gas pressure. Accordng to Nottngham, an atmospherc arc of constant length could be represented by equaton (8) as follows. B v = A + (8) (8) n where, v s the arc voltage, s the arc current, n s the exponent whch depends upon the absolute bolng pont temperature of the anode and also on the type of gas n whch the arc burns. The v characterstc of the arc can also be explaned by takng nto account the mode of heat loss from the arc. For ths a smple arc model s consdered wth a constant current densty and constant heat loss per unt area of the cylndrcal surface of the arc. The crcumference of the arc column and therefore the heat loss v s proportonal to the arc radus. For a constant current densty, the arc radus s proportonal to the square root of the arc current. The relatonshp between v, and arc conductance g s gven by equaton (9) as g (9) Ths model gves the v characterstc of the arc n the low-current range. For the hgh-current range, the current densty s kept constant. The loss s assumed to be proportonal to the cross-sectonal area of the arc. Here, v remans constant and the arc conductance g () Ths model represents the arc n the hgh-current range. The Casse model, whch s a sutable representaton of an arc for hgh currents, and the Mayr model, whch yelds good results for arcs wth low currents are usually expressed n conductance rather than arc resstance because of the extremely low values for arc resstance. A qualtatve understandng of the phenomena determnng arc strkng or extncton of the energy-balance type can be acheved by the smple Casse and Mayr dfferental equaton models, based on smplfcatons of prncpal power-loss mechansms and energy storage n the arc column. Wth the arc conductance g as the dependent varable, the Casse equaton s gven by g v E = dg θ dt () where E s the constant steady-state arc voltage, θ s the arc tme constant= energy stored per unt 6

7 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May-6 69 ISSN volume/ energy loss rate per unt volume and the Mayr equaton by g = P dg θ dt () where P s the constant power loss The Casse equaton s more vald for hgher current regons whle the Mayr equaton s more representatve of zero and low-current regons, an arc may be smulated by the combnaton of () and (). In order to combne () and () nto a sngle arc model we have defne a transton current I such that the arc conductance s gven by v dg g = θ E dt dg g = θ P dt, f > I, f < I (3) therefore g s domnated by Casse conductance g C. However, when the arc s absent between any two electrodes there has to be a fnte though very small amount of conductance, g mn whch depends on the dstance between the electrodes, geometry of the electrodes, type of gas and temperature. Thus, the complete Casse-Mayr arc model s gven by exp I + exp I dg. θ. P dt and = gv (7) In general form, θ should be a functon of because when an arc s gntng or extngushng, the energy stored per unt volume s large compared wth the energy loss per unt volume. However, when the arc stablzes, error of I s small and can represented by θ = θ.exp + θ ( α. ) (8) where α > and θ >> θ When the arc s gntng or extngushng, s small andθ θ. When s large, θ θ. The seven parameters together wth g mn, I, E and P characterze the arc furnace model. Ths model s n tme doman and n addton to generatng power qualty parameters, can nvestgate the effect of dfferent feed system desgns on performance of furnace. In order to allow for smooth transton between 6. SIMULATION OF ELECTRIC ARC () and (), a transton factor σ ( ) s defned, FURNACE MODEL USING CASSIEwhch s a functon of arc current such that the arc conductance s gven by g = [ σ ( ) ] g C MAYR METHOD The three phase arc furnace smulated n ths paper + σ ( ) g M (4) s modeled usng the Casse-Mayr model that has where gc and g M are the conductance gven the real tme modelng capablty of the dfferent by () and (), respectvely. states of the furnace. Ths model s helpful to study σ ( ) vares between zero and unty and should the statc characterstcs and also to smulate flcker be a monotonc decreasng functon when dsturbance caused by the electrc arc furnace. ncreases. The transton factor s gven by, Fg.7 shows complete smulaton of three phase electrc network supplyng an EAF. The model ( ) = exp conssts of 5 kv, MVA, 5Hz three phase σ (5) source block feedng through a three phase I transformer to an electrc arc furnace. In order to When s small, the value of σ s close to unty provde an adequate voltage level to the arc and g s domnated by Mayr conductance g M. furnace two step-down transformers are used. The When s large, the value of σ s neglgble and, EAF s connected to the utlty through a (HV/MV) [/3.8 kv] transformer (T) and s fed by a (MV/LV) [3./.55 kv] transformer (T). Fg.8 shows three smulated equaton sets of Casse- Mayr for three phases. EAF s modeled as a nonlnear tme varyng voltage controlled source usng subsystem. The arc current s taken as the nput parameter to ths functon and the output s nonlnear tme varyng voltage. The XY graph s used to montor the voltage-current characterstc of the v. arc. Fg.9 shows detaled smulaton of Casseg = g mn. + Mayr equatons (6) to (8). Table shows the E values of parameters assocated wth Casse-Mayr (6) EAF model useful for the determnaton of arc statc model [7] 6

8 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May-6 69 ISSN TABLE PARAMETERS FOR CASSIE-MAYR EAF MODEL Parameter Descrpton Parameter Value Mnmum arc conductance g mn.8 Transton current I A Momentarly constant steady E 5 V state arc voltage Momentarly power loss P W Tme Constant θ µ s Tme Constant θ µ s Constant α.5 Fg.9. Casse-Mayr EAF equaton Smulaton Fg.7.Complete SIMULINK model of three phase electrc network supplyng an EAF Fg.8. Three phase EAF Smulaton Durng the meltng process, there are fast varatons n the current whch are connected wth the arc-length varatons caused due to metal-scrap adjustments, electrodynamc forces and arcelectrode varable dsplacement [8]. These current fluctuatons causes a momentary voltage drop or flcker both at the supply bus and at nearby bus n the nterconnected system. Thus, EAF exhbts dynamc characterstcs durng the meltng cycle. The arc currents durng the refnng perod are more unform and have a very less mpact on the system. Durng the refnng cycle the level of molted materal s constant along wth unform rate of meltng n the furnace. The arc length s almost constant durng ths cycle resultng nto unform v characterstc [9]. Thus, there s no flcker at the PCC. However, due to the ntrnsc non-lnearty of the arc characterstc, voltage and current harmoncs are present at PCC. Thus, EAF exhbts steady state characterstc durng the refnng cycle. The refnng stage contrbutes harmoncs n current and voltage, whle scrap meltdown stage yelds voltage flcker at PCC. Therefore, real tme analyss of power qualty demands dynamc model of EAF. In order to brng the statonary arc-model to gve rse to voltage fluctuatons, cause of flcker, the v characterstc must undergo tme varatons whch correspond to a tme dependence of the arc length as n equaton (9) [8] = + (9) V at A B l where, V s the threshold arc voltage at A s the constant representng the sum of anode and cathode voltage drops B s the voltage drop per unt arc length l s the arc length n centmeters There are two tme-varaton laws for 6

9 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May-6 69 ISSN smulatng a flcker.e. snusodal law and whtenose law. Some models apply these tme-varaton laws to the arc resstance for a gven loadng condton [3]. Some models ncorporate both snusodal and stochastc tme varaton rules to vary the arc length by varyng the arc voltage drectly [8]. In order to represent the flcker effect, a low frequency chaotc sgnal s modulated wth the arc voltage [4]. However n ths paper, the mpact of voltage flcker on EAF s explaned usng threshold voltage, Vat whch s vared snusodally and randomly. In ths regard V at s modulated as follows: Snusodal Varaton The snusodal varaton s assumed as, Vat ( t) = Vat [ + m.sn w f. f ] (3) where, m s modulaton ndex w s a flcker frequency f The SIMULINK model for Sne Flcker s shown n Fg. 7. RESULTS AND DISCUSSION The electrc arc furnace s modeled usng the Casse-Mayr mathematcal equatons n MATLAB software. The statc and dynamc v characterstc of the arc along wth the respectve voltage and current waveforms are dscussed. The dynamc arc characterstc are smulated usng both the Fg.. SIMULINK Model for Sne Flcker snusodal varaton and band-lmted whte nose random tme varaton. Random Varaton 7. Statc Characterstcs of Arc The random varaton s assumed as, The Casse-Mayr statc arc model s smulated usng Vat ( t) = Vat [ + m. N( t) ] (3) the arc parameter where, N ( t) s a band lmted whte nose wth E = V, α =.5, θ = µ sec, θ = µ zero mean and unt varance The SIMULINK model for Random Flcker s shown n Fg. TABLE PARAMETERS USED FOR DYNAMIC CHARACTERISTICS Snusodal Varaton Parameter Parameter Descrpton Value Intal threshold V at V voltage Modulaton ndex m.9 w Flcker frequency f Random Varaton Parameter Parameter Descrpton 4 Hz Value Intal threshold V at V voltage Modulaton ndex m.9 Band lmted whte nose N ( t) 4-4 Hz Statc voltage/ current characterstc of the arc s depcted n Fg.. Correspondng arc voltage waveform and arc current waveform are shown n Fg.3 and Fg.4 respectvely. sec Fg.. SIMULINK Model for Random Flcker Table shows the parameters utlzed for snusodal varaton and random varaton [8]. Fg.. Voltage-current characterstcs of arc 6

10 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN Fg.6: Arc voltage waveform Fg.3: Arc voltage waveform Fgure.7: Arc current waveform Fg.4: Arc current waveform 7. Dynamc Characterstcs 7.. Snusodal Flcker Generaton The results for the dynamc arc model smulaton usng the snusodal varaton law for the arc effectve voltage s shown n ths secton. The flcker frequency was randomly chosen to be 4 Hz. The correspondng voltage-current characterstc, arc voltage waveform and arc current waveform are shown n Fg.5, 6 and Random Flcker Generaton Results pertanng to the dynamc model wth band-lmted whte nose random tme varaton are presented n ths secton. The voltage-current characterstc for random varaton s shown n Fg.8. The correspondng arc voltage and arc current waveforms are shown n Fg.9 and respectvely. Fg.8: Voltage-current characterstcs of arc Fg.5: Voltage-current characterstcs of arc The smulaton results obtaned shows that f the arc furnace generates snusodal flcker, the arc voltage and current are vared snusodally wth the flcker frequency. The flcker phenomenon s vsble for the electrcal bulbs that are rapdly changng the lght ntensty. Also, the sde effects of the flcker are vsble for the modern computaton technque that could be damaged by the voltage varatons. The results obtaned for random varaton of arc furnace shows that the arc voltage and current are vared randomly. Thus, we see that the furnace load flcker leads to a varaton n the voltage of the bus supplyng EAF and the nearby buses n the nterconnected system. Fg.9: Arc voltage waveform 6

11 Internatonal Journal of Scentfc & Engneerng Research, Volume 7, Issue 5, May ISSN CONCLUSIONS Fg.: Arc current waveform In ths paper, an electrc arc furnace s modeled usng the Casse-Mayr arc equatons capable of representng the statc and dynamc characterstcs of the arc furnace load. There are current fluctuatons n the EAF durng the meltng process whch causes flcker phenomenon. The flcker effect s smulated usng snusodal and random sgnals n ths paper. The voltage-current characterstcs correspondng to snusodal and random varatons are shown n ths paper. The utltes are workng on how to mtgate the flcker effcently and economcally. The fast response of the dstrbuton statc compensator (DSTATCOM) makes t effcent soluton for mprovng the power qualty n the dstrbuton system. By usng the adequate control strategy we can compensate the load reactve power varatons, reduce the voltage flcker, mprove the power factor and stablze the voltage profle. REFERENCES [] R C. Dugan, Smulaton of Arc Furnace Power Systems, IEEE Transactons on Industry Applcatons, vol. IA- 6,no. 6, pp , Nov./Dec. 98. [] E. Acha, A, Semlyen, N. Rajakovc, A Harmonc doman Computatonal Package for Nonlnear problems and ts Applcaton to Electrc Arcs, IEEE Transactons on Power Delvery, vol. 5, no. 3, pp ,July 99. [3] S. Varadan, E. B. Makram, A. A. Grgs, A new tme doman voltage source model for an arc furnace usng EMTP, IEEE Transactons on Power Delvery, vol., no. 3, pp , July 996. [4] Omer Ozgun and Al Abur, Development of arc furnace model for power qualty studes, IEEE Transacton Power Delvery, vol. 7, No 3, Nov.999. [5] Goyal. R. Awagan and A. G. Thosar, Study of Power Qualty Issues Related to Electrc Furnaces: A Revew, Internatonal Conference on Innovatve Trends n Engneerng, Scence and Management, NICESM, Kumaracol, Taml Nadu, Feb 6. [6] B. Boulet, G. Lall and M. Ajersch, Modelng and Control of an Electrc Arc Furnace, Proceedngs of the Amercan Control Conference, Denver, Colorado, Jun. 3. [7] D. Knght, Humphry Davy, Scence and Power. Cambrdge, UK: Cambrdge Unversty Press, 99. [8] G. C. Montanar, M. Loggn, A. Cavalln, L. Ptt, and D. Zanell, Arc furnace model for the study of flcker compensaton n electrcal networks, IEEE Transactons on Power Delvery, vol. 8, pp. 6 36, Oct [9] E. O Nell-Carrllo, G. Heydt, E. J. Kostelch, S. S. Venkata, and A. Sundaram, Nonlnear determnstc modelng of hghly varyng loads, IEEE Transacton on Power Delvery, vol. 4, pp , Apr [] Omer Ozgun and Al Abur, Flcker study usng a novel arc furnace model, IEEE Transacton on Power Delvery, vol. 7, No 4, Oct.. [] T. Zheng, E. Makaran and A. Grgs, Effect of Dfferent Arc Furnace Models on Voltage Dstorton, 8 th Intrernatonal Conference on Harmoncs and Qualty of Power, Athens, Greece, Oct 998. [] G. Manchur, C.C. Erven, Development of a model for predctng flcker from electrc arc furnaces, IEEE Transactons on Power Delvery, vol. 7, pp , January 99. [3] H. Chang, C. Lu, P. P. Varaya, F. Wu, M. G. Lauby, Chaos n a Smple Power System, IEEE Transactons on Power Systems, vol. 8, no. 4, pp , November 993. [4] M. P. Kennedy, Three Steps to Chaos, Part l: Evoluton, IEEE Transactons on Crcut and Systems-I: Fundamental Theory and Applcatons, vol. 4, No., October 993, pp [5] M. P. Kennedy, Three Steps to Chaos, Part : A Chua's Crcut Prmer, IEEE Transactons on Crcut and System-I: Fundamental Theory and Applcatons, vol. 4, No., October 993, pp [6] K. J. Tseng, Y. Wang and D. M. Vlathgamuwa, An Expermentally Verfed Hybrd CASSIE-Mayr Electrc Arc Model for Power Electroncs Smulatons, IEEE Transactons on Power Electroncs, vol., No. 3, May 997, pp [7] H. Mokhtar, M. Hejr, A new three phase tme-doman model for electrc arc furnaces usngmatlab, Transmsson and Dstrbuton Conference and Exhbton : Asa Pacfc. IEEE/PES vol. 3, pp.78-83, Oct.. [8] R. Hooshmand, M. Banejad and M. Toraban, A New Tme Doman Model for Electrc Arc Furnace, Journal of Electrcal Engneerng, vol.59, No. 4, pp 95-, 8. 6

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