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EFFECT OF DIFFERENT ARC FURNACE MODELS ON VOLTAGE DISTORTION Elham B. Makram IEEESenior Member

Tongxin Zheng

IEEE Student Member

Adly A. Girgis IEEE Fellow

Electrical and Computer Engineering Department Clemson University

Clemson, SC 29634-0915

ABSTRACT In this paper, different arc fumace methods are reviewed for the purpose of harmonic analysis. In general, these models may be classified into time domain method and frequency domain method. The difference between these two methods is discussed and evaluated. In this paper, six typical arc furnace models from the time domain and frquency domain methods are selected to study their effects on harmonic analysis. Simulation results are also provided. Comparisons between these results show the effects of different arc furnace models on voltage waveform and percentage of harmonic components distribution. which provides a discussion of the differences between time domain and frequency domain methods. finally, recommendations are made for the application of some of these models.

KEYWORDS:Arc Furnace, Nonlinear Load,Harmonic Analysis

I.

INTRODUCTION

An A.C. arc fumace is an unbalanced, nonlinear and time varying load, which can cause many problems to the power system quality. An arc fumace load may cause unbalance, harmonic, interharmonics and voltage flicker. The dynamic property of arc fumace has also resulted in chaotic characteristic [11. It is necessary to develop an accurate three-phase arc furnace model for the purpose of harmonic analysis and flicker compensation. Since the arc melting process is a nonstationary stochastic process, it is difficult to make an accurate deterministic model for an arc furnace load. The factors that affect the arc fumace operation are the melting or refining materials, the electrode position, the electrode arm control scheme and the supply system voltage and impedance. Thus, the description of arc fumace load depends on the following items: arc voltage, arc current and arc length (which is determined by the position of electrode). Current research efforts on arc fumace models consider the above parameters and their interrelationship. At present time, there are many methods for three-phase arc fumace load modeling. In general, they can be classified into time domain and frequency domain analysis methods. For detail, the arc fumace models may be classified as: (1) V-I Characteristic Method [26] (2) Time Domain Equivalent Nonlinear Circuit Mode1[7-8] (3) Harmonic Voltage Source Model [9-101 (4) Harmonic Domain Solution of Nonlinear Differential Equation [1I] (5) Random Process Method [2-51.[12-14] The V-I Characteristic method given in the reference [2-6) is

simple and direct, it can satisfy a certain operating condition, and the simplification of V-I Characteristic is the main factor of accuracy. The time domain equivalent circuit method is based on the V-I characteristic, more simplification is made than the V-I characteristic method (reference [7-81). Harmonic voltage source method mentioned in reference [9-101is based on the harmonic study of a certain kind of the arc voltage waveform. The problem is that under this voltage waveform, the arc furnace system is not operating at the maximum power transfer condition. A method in reference [11J presents good results of arc fumace simulation, but it is based on an experimental formula. The harmonic domain solution of nonlinear differential equations depends on system topology and operating condition. Random process can reflect the operation of arc furnace system, but this model is mainly for voltage flicker analysis. In order to compare the difference of different arc fumace models, six models from time and frequency domain methods are discussed and presented in section 11. Numerical results from an actual arc fumace system are presented in Section IJI. In section IV, the differences between the arc fumace models are discussed. The conclusions are drawn in section V.

II. 1.

ARC FURNACE MODELS

TIME DOMAIN ANALYSIS METHOD

Time domain method is one of the two basic methods for the study of arc fumace system. For the harmonic analysis, FFT is applied to the actual waveforms to get the harmonic components in the frequency domain method. It can be classified as V-I CharacteristicMethod and Equivalent Circuit Method. V-I CHARACTERISTIC IVIC) METHOD VIC Method utilizes the numerical analysis method to solve the differential equation (which is used to describe the arc fumace system) with nonlinear VIC. Since different VIC's will result in different arc voltage waveform, in this paper different VIC's are entitled as different models.

MODEL 1 Figure 1 shows the actual VIC and its piecewise linearlization in reference 121. The assumption is that the arc ignition voltage Vi8 and the arc extinction voltage V , are determined by the arc length during arc furnace operation. Let R , and R, be slopes of line OA and line AB, thus, the positive half cycle of VIC is expressed as,

Paper accepted for presentation at the t?' Intenrdinal Conference on Harmonics and Quality of Power ICHQP '98,jointly organized by IEEEIPES and NTUA, Athens, Gmce, October 1416,1998 0-7803-5105-3/98/$10.00 0 1998 IEEE

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[R,i

i e i, and increasing or i e i, and decreasing

I

i > i, and increasing V,, + (i - i2)R2 i e i, and decreasing V, + (i - i3)R3 Where, R I , R, and R, are the coressponding slopes of each section, and

I

C

In this model, the mean voltage level V,,,which is a function of the arc length, is used to reflect the operating condition, Vig , V,,

Figure 1:V-I Characteristic of Model 1

and V , are also considered to be proportional to V,,, .

MODEL 2 Another type of simplification on VIC [4]is shown in Figure 2, which is refered to as model 2. Since the arc voltage changes its polarity very fast, this model neglects the voltage rising time, which results in a sudden change in the arc voltage when the arc current is at zero crossing. Thus, the positive half cycle of VIC is expressed

as,

[

V = sig(i). V,,,+

-

(2)

D:H]

Let 1 be the arc lengtb, A and B are the coefficients from experimental formula, then V, z A - k B . 1 (3) Where V,, reflects the arc fumace operatingcondition.

400

-0.5

0 CU~C.N(A)

0.5

IW

1

Figure 3: V-I Characteristic of Model 3 With different VIC's, the arc fumace system is described by a set of nonlinear differential equations. Because of the nonlinearlirity. the time domain solution can be divided into the Direct VIC method and Voltage Source Method. (A) Direct VIC Method (DVIC) For a simple arc fumace system, the arc fumace system can be expressed as following,

-- 1

-0.5

0 Cunmt(A)

0.5

1

Figure 2 V-I Characteristic of Model 2

MODEL 3 Figure 3 shows the nonlinear approximationof VIC [6]. In this model, the arc melting process is divided into three sections. In the first section, the arc is from extinction to reignition. The voltage magnitude increases from extinction voltage -V, to ignition voltage Vig ,the arc fumace acts as a resistance, and the arc current

Where, V, and I, are the arc voltage and current, V, is the supply voltage. R and L are the equivalent resistance and inductance. The numerical method may be used for the time domain solution of differential equation. Supposing Euler method is applied to approximate the differential operator, the discrete form of equation ( 5 ) may be expressed as 2L 2L V, ( t )=V,(t) +-I,,,(t - At) - (-+ R)14( t )

I

I,(t

changes its polarity from -i, to i, . The second section is the beginning of arc melting process. There is a sudden voltage drop across the electrode, thus the arc voltage decreases from Vig to V ,, and the arc current has a little increase from i, to i, . In this approximation, the voltage drops in an exponential way. The third section is the normal arc melting process, the arc voltage drops slowly and smoothly from V,, to Vex. Since the melting process spans most of the half cycle, the mean value is assummed to be V,,, . Because the arc current increases to its maximum before it drops i, , the VIC is divided into current increasing and decreasing parts in this section. After approximating each section of VIC, it can be expressed by equation (4),

At

At

- At) = (V,( t - At) - R I ,

(t

- At)-V,

(I-

At))-

At

2L

(6)

.

v, 0)= f(I. ( 1 ) ) Thus, at each time step the differential equation changes to a set of nonlinear algebraic equations. The solution of this set of equations results in the arc voltage and current at the same time step. (B) Voltage Source Method In the DVIC method, it is difficult to solve the nonlinear algebraic equations. Since the voltage waveform is changing continuously, the arc voltage value changes slightly between two successive samples. Thus, a voltage source method can be formed to solve the equation approximately. First, the initial values of arc

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voltage and current are assumad to be known. ?hen, the initial guess of arc voltage at time step n is assumed to be the arc voltage at time step n-I,and the arc Current at time n is calculated from the first part of equation (6). Finally, the arc voltage is calculated from the nonlinear VIC expression. This method is simple and direct, but the convergence depends on the initial values of the arc voltage and current, and the VIC expression. If the arc voltage has a sudden change in VIC, this method will produce more errors than DVIC. TIME DOMAIN EOUNALENT CIRCUIT (TDEC) Unlike the VIC method, the TDEC method forms an equivalent circuit constructed by voltage source and resistors, after studying the VIC, arc voltage and current waveform. In fact, TDEC makes so many simplifications on VIC that the accuracy is affected.

classified as Harmonic Voltage Source and Harmonic Domain Solution of Nonlinear Differential Equation Technique.

HARMONIC VOLTAGE SOURCE (HVS) METHOD MODEL 6

H V S method first applies Fourier transform to the arc voltage waveform to obtain its harmonic components, then the current harmonic components are calculated through the arc voltage harmonic components [9]. Since the arc voltage changes its polarity very fast, reference [9] considered the arc voltage to be a square wave with the magnitude of U,. Let 0 be the system frequency and u,(t) be the arc voltage, then the fourier series of

with k = 1.3,5,7.....

U,,(t) = x-sinkwr wd

MODEL 4

k 4

Reference [7]provides a timing-switch model. Since there is a foamy slag across the arc furnace, the equivalent circuit in reference [7] is changed to the one shown in Figure 4. At time tl, the arc extincts and the current changes its polarity, the arc voltage is the voltage across the foamy slag, When the voltage on the foamy slag increases to the melting voltage at time t2, the arc begins to melt and keeps the constant arc voltage U,, Because the diference between currents at time tl and tz is very small.the current is asuumed to be zero, which is called current gap. ntus, at time tl arc voltage is assummed to change polarity and at time t2 arc melting process is assummed to be activated. This forms a timing-switch arc furnace model. The voltage level U, depends on the arc length, which reflects the operating condition. In this model, the approximation of arc voltage U, and the estimation of switch time tl and t2are the main factors of acuracy. n

U,(t) may be expressed as : (7)

Idc

Let the source voltage V, =fiEsin(wt+a)

Zkk

and let system

at the kth harmonic frequency. Assuming the

impedance be

current to be zero when voltage change its polarity, the fundamental frequency component of the arc voltage is expressed as U,,= 6,Esin(#, -a) (8) where, 1 sing, -=Z1-&--wher k = 1,3,5.7 ..... (9)

-

k-1

' 1

Moreover, the phase angle of source voltage is calculated by assuming the maximum power transfer in the fundamental frequency. Thus,

From above calculation, an equivalent circuit for the fundamental frequency component can be represented as an equivalent arc resistance and a reactance. The equivalent circuit is shown in Figure 6.

IL L I @+

RI Figure 4 Equivalent Circuit of Model 4

MODEL 5 Reference [8] presents another equivalent circuit of an arc fumace load, which is shown in figure 5. This circuit is based on the same VIC as MODEL 1. Arc voltage is considered to be a square-wave voltage source (whose magnitude is U, that is called the arc clamper) with a negative resistor during arc melting process. In this model, since the time-shift of ac clamper starting point has much influence on the arc current waveform, its approximation is the main factor of simulation accuracy.

~~~~

~

Figure 6:Fundamental Frequency Equivalent Circuit Where,

6,Z, sin(4, -CY) 6,cos#, sin($, - a) Figure 7 shows the equivalent circuit for the calculation of kth harmonic components, where U, is the harmonic voltage source. RNL

-

= cos(#, -a)

RI Figure 5: Equivalent Circuit of Model 5 2.

FREQUENCY DOMAIN ANALYSIS

The frequency domain analysis method represents the arc voltage and current by their harmonic components. It can be

Figure 7: Harmonic Voltage Source Circuit In this model, it is assumed that the arc fumace load draws the maximum power in the fundamental frequency, which is not always true for the actual arc fumace operation. This constitutes the main source of error.

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HARMONIC DOMAIN SOLUTION DIFFERENTIALEOUATION (HDSNDE)

OF

With these parameters shown in table 1, the six models are studied. and the results are shown in Figure 9-14 respectively. The source voltage, voltage at PCC, arc voltage and arc current are shown in each figure. Comparisons of these results are summarized in the following comments, (1) The six models result in different arc voltage waveforms. Arc voltage waveforms of model 1 , 2 and 3 have the same pattern. They have transient at the beginning of arc melting process, but the arc voltage goes up when the arc begins to extinct, which is not the case in fact. Arc voltages of models 4 and 6 are similar with the squarewave pattern, but these phenomenon such as the transient and the voltage drop at the beginning and the end of arc melting process, are not presented. The arc voltage magnitude of model 4 is higher than that of model 6. The arc voltage waveform of model 3 is more accurate than that of other models, since it is consistent with the actual measurement, (2) There are minor differences in the arc current waveforms. The current waveforms of models 1,2.3,4 and 5 have the same pattern that the current increases slowly before arc melting. While the arc current of model 6 does not have the current gap phenomenon, and has few hannonic components. (3) The voltage waveforms at PCC have little difference among each model. They all look like sinusoidal, the only difference is the voltage distortion in the period between arc extinction and arc reignation. The percentage harmonic components of arc voltage, arc current and voltage at PCC are summarized in Table 2. Comparison between them shows the following, (1) The arc voltage of model 1 has the largest percentage harmonic components. Although the percentage harmonic components of the six models are close to each other, model 6 has the smallest fundamental frequency component. (2) The arc current of model 2 has the largest percentage harmonic components, while those of model 1,3.4 and 5 are close to each other. However, the arc current waveform of model 6 has less distortion than that of others, since the fundamental frequency component is too

NONLINEAR

Reference [111 provides a harmonic domain solution method of nonlinear differential equation. In this model. the arc fumace load model is developed from the energy balance equation, which is actually a nonlinear differential equation of arc radius and arc current. The arc radius waveform can be calculated from the given current waveform, and the method used here is the Harmonic Newton-Raphson method. As a function of the arc current and the arc radius with analytical expression, the arc voltage can also be calculated. This model uses some experimental parameters to reflect the arc fumace operation, but it neglects the influence of its supply system. Since this method depends on the experimental formula, which is different with different arc fumace loads, the simulation of this model is not provided in this paper.

Et. SIMULATION RESULT To show the comparison of different arc &ace models, a simple arc fumace system is studied in single phase. The system configuration is shown in Figure 8. Pcc

Z

2.

AF

I

The parameters of this system are obtained from an actual system provided in reference 161. There is a foamy slag in parallel with the arc fumace. The rated power of the arc fumace is 55 MW. In figure 8, the system impedance is represented as 5, bus PCC represents the Point of Common Coupling and bus AF is the low voltage side of the transformer whose impedance is given as Z,. The system parameters and the parameters of each model are presented in Table 1.

I

1

Table 1. System and Arc Fumace Model Parameters Parameters Items I 1 E=566V f =6OHz R, =50& System

Model 1 Model 2 Model 3 Model 4 Model 5

Model 6

I

I

Z, = 0.0528+ jO.46-

Vi, = 350.7N

V, = 289.79'

high.

I

Z, = 0.3366 + j 3 . 2 W

R, = 5 0 4 i, = 7.02kA R, = 4 . 7 6 n R i, = 80kA

v,, = 289.79 c = 1.68MW

(3) The voltage distortion at PCC has slight difference, except that fundamental freauencv ComDonent of model 6 is a little bit small. (4) Model 6 has the largest power consumption with 17MW and the highest power factor, which is caused by the maximum power transfer assumption .

I

.

Iv. DISCUSSION

D = 20.65kA

Table 3 summarizes the differences between each arc furnace model that are mentioned above in section 11. it reveals the Vi,= 350.79 V, = 320.73' V, = 289.7511 V, = 30% following: DVIC method is simple and direct, it is not influenced by the =289-75V R2 =-0*76mR i2 =80kA supply system parameter (such as distorted source voltage and system impedance) and the initial value of differential equation. It can achieve higher accuracy than other methods and has no U, =3ON w, = 28.72" + k r ox, =37.16' +krc convergence problem. However, by depending upon the operating condition, VIC changes with arc length, it is difficult to get a U, = 320.2N precise approximationof VIC. VS method has no difference from R, = 50mQ R2 = -0.572mn a =39.04" DVIC but convergence problem which depends on the initial value of differential equation. High error will exist if there is a sharp U, = 245.01V a = 41.4" 6,= 0.8152 voltage change in VIC. Normally TDEC method can not achieve good results like DVIC, because it depends on the simple XNL=16mR RNL=3mCL Uk=312/nsin(ka) approximation of VIC. In addition. the structure of equivalent

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-- SOllrceVdtagc -.-

-- Sourcevoltage -.-

.

VdtageatpcC

-400. -Arc

t\.

CY

0.005

0

600

Time(=)

Figure 1 2 Voltage and Current Waveform from Model 4

-- sourcevoltage --- VoltageatpcC . I

200. h

3

-200

0"'-

600-

= :? ',!

+x

--

sourcevoltage

-.-

VoltageatpcC .

j I! I/ I Ii !.,

+\ . I.---,\..\J;./i

\\

g 1-

\'

"."._ Arc current -6co

VoltageatpcC .

/---a I?.,

-400. -ArcVoltage

-600

SOllrceVdtage

-./

-200-

-400. -ArCVoltage

-4

r?

-

-0

-400. -Arcvoltage

-600 0

.

a\=:/ AJ

Voltage

-.."...Arcanrent 0.01 0.015 0.02 Timc(sec) Figure 9: Voltage and Current Waveform from Model 1

VottageatKX

0.005

0.01 Time(=)

0.015

0.02

Figure 11: Voltage and Current Waveform from Model 3

Note: All the current waveforms in the above figures are scaled to 200, in order to mach the voltage waveform.

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Time Domain Method

I

I”

Harmonics Fund (V) . .

7th(%) 9th(%) 1Ith 1%) .,

3 I

2

O

2

L

’

’

Fund (U) 3rd(%) . .

I I

51.99

Model3 278.73 33.60 1957 13.55 9.90 7.36 53.88 15.73 5.49 2.71 1.53 0.93 380.80 3.13 1.82 1.25 0.91

Equivalent Circuit Model4 I Model 5 274.46 268.13 35.13 33.20 19.77 19.92 13.04 13.97 10.71 8.98 8.63 6.24

1

55.02

I

I

Model 6 220.56 33.30 19.94 14.20 11.00 8.96 74.85 8.91 3.21 1.64 0.99 0.66 370.64 2.52

1.44

1lth (%)

0.85 380.24 3.37 1.93 1.28 0.91

0.67

0.64

0.67

0.79

0.56

0.68

14.35 0.85 16

14.02

14.37 0.8618

14.43 0.8541

14.78 0.8665

17.19 0.9390

.

.

5th(%) 7th(%) ab(%) 1 Irh (a) Power (MW) Power Factor

2

I

I

I

0.8515

Time Domain Method V-I CharacteristC DVIC

I

arc

length I

I

I

I

The most accurate one if Not acuuate when the arc VIC is approximated P d l Y

I

I

I

I

1.08

380.15 3.05 1.82 1.28 0.99

I

1.51

1.08 0.83

Frequency Domain Method

vs

No influenceon VIC and No influeme on VIC and the solluion procedure the. solluion procedure

15.00 5.37 2.72 1.63

57.47 14.84 5.06 2.37 1.27 0.73 379.01 3.17 1.80 1.18 0.81

Frequency Domain

9th(%)

I

\

54.84 16.36 5.59 2.64

I

17.40 6.01 2.81 1.54 0.93 381.80 3.33 1.91 1.25 0.88

0

8

Modell 274.47 36.16 20.69 13.77 9.75 7.12

V-I Characteristic 1 Model2 I 282.84 35.29 20.25 13.18 9.07 6.44 I

TDEC

HVS

HDSNDE

Equivalent circuit changes with arc length

No Influence

As a variableto be solved in the n o n l i m differential equation

I

I

key

Depends on TDEC

I

Influencesequivalent circuit parameter

I

No consideration

Influencesequivalent circuit parameter

Influencesthe solution of differential equation

Not accurate becaw of the maximum power

Dependson the experimental formula of

transfer assumption

the arc length

Converge

Not Necessary

-

AbsolutelyConverge

Depends on the initial value, may have

Converge

oscillation

FET is applied on the timedomainwaveform

FIT is appliedon the tim domain waveform

FIT is appliedon the time domain waveform

Available by assuming VIC changes with arc

Availableby assuming VIC changeswith arc length

Available by assuming TDECparameteras random variables

length

DNot Available

Direct Solution

Not Available

Increasethe accuracy of Includethe network VIC approximationand of iterattion is needed when Changeequivalent circuit Eleminate the maximum differetial equation and Increasesthe a? VIC approxmwon to satisfy more precise VIC power transfer assumption improveexperimental thereexista sudden fomular changeof arc voltage

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1

circuit changes with VIC and some of TDEC's parameters are determined by the system parameter, although this method is simple for circuit analysis. HVS is straightforward for harmonic analysis without convergence problem. However, HVS method determines the parameter of equivalent circuit through the supply system parameter with the assumption of maximum power transfer, which can not reflect the arc fumace operating condition. FDSNDE can achieve good resblt if the experimental formula is accurate. But this method only studies the differential equation of the arc furnace load, which neglects the interaction between the supply system and arc furnace load operation.

V. CONCLUSION This paper presents several typical arc fumace models in the time domain (TD) and the frequency domain (FD) for the harmonic analysis. Results of six models from an actual arc fumace system are presented and compared. The differences between each model are also discussed and summarized. From the simulation procedure, it shows that TD method is more accurate than FD method, since it can represent the nonlinearity easier in TD than in FD. However, the FD method is more efficient than TD method, because it can represent the variable directly in the harmonic domain.

VI. REFERENCE G. T. Heydt, E. ONeill Canillo and R. Y. Zhao, 'The Modeling of Nonlinear Loads as Chaotic Systems in Electric Power Engineering", North American Power System Symposium, Oct. 1997, pp. 704-9. Srinivas Varadan, Elham B. Makram and Adly A. Girgis, "A New Time Domain Voltage Source Model For An Arc Furnace Using EMTP", IEEE Trans. on Power Delivery, Vol. 11, No. 3. July 1996, pp. 1685-90. Adly A. Girgis. Brian D. Moss and Elham B. Makram. "Reactive Power Compensation and Voltage Flicker Control of an Arc Fumce Load". Proceeding of the 7th International Conference on Harmonics and Quality of Power(ICHQP), at Las Vegas, Oct. l6-18,1996, pp242-47. G. C. Montanari. M. Loggini A, Cavallini etl. "Arc Furnace Model For The Study of Flicker Compensation in Electrical Networks", IEEE Trans. on Power Delivery, Vol. 9. No. 4, October 1994. pp. 2026-33 Le Tang, Sharma Kolluri and Mark F. McGrangghan. "Voltage Flicker Prediction For Two Simultaneously Operated AC Arc Fumaces", IEEE Trans. on Power Delivery, Vol. 12, No. 2. April 1997, pp. 985-92. Juan Celada S. "Electrical Analysis of the Steel Melting Arc Fumace",,Iron and Steel Engineer, Vol. 70, May 1993 pp. 3539. H. Schau and D. Stade, "Mathematical Modeling of ThreePhase Arc Fumace", Proceedings of IEEE ICHPS VI, Bologna, Sep. 21-23, 1994, pp. 422-28. Roger C. Dugan, "Simulation of Arc Furnace Power Systems" IEEE Trans on Industry Applications Vol. 16, No. 6, 1980, pp. 8 13-18. J. G Mayordomo, R. Asensi etl. "A Frequency Domain Arc Fumace Model for Harmonic Power Flows Under Balanced Conditions" Proceeding of the IEEE 7th Intemational Conference on Harmonics and Quality of Power(ICHQP), at Las Venas, Oct. 16-18.1996, DD. 419-27. [lo] J. G. Mayordomo, L. F. Be&, R. Asensi. M. Izzeddine, L. Zabala and J. Amantegui. "A New Frequency Domain Arc Furnace Model For Iterative Harmonic Analysis", IEEE PES Winter meeting 1997, New York, PE-375-PWRD-0-12-1996.

[1I] E. Acha, A. Semlyen and N. Rajakovic, "A Harmonic Domain

Computational Package for Nonlinear Problems and its Application to Electric Arcs," IEEETrans. on Power Delivery, Vol. 5,NO.3, July 1990, pp. 1390-95. [I21 A. M. Dan and A. Mohacsi, "Computer Simulation of a Three Phase A.C. Electric Arc Fumace and its Reactive Power Compensation", Proceedings of IEEE ICHPS VI, Bologna, Sep. 21-23, 1994, pp. 415-21. [13] Rafael Collantes and Tomas Gomez, "Identification and Modeling of a Three Phase Arc Furnace for Voltage Disturbance Simulation", IEEE Trans. on Power Delivery, Vol. 12, N0.4, Oct. 1997, pp. 1812-17. [14] J.D. Lavers and B. Danai, "Statistical Analysis of Electric Arc Furnace Parameter Variations", IEE Proceedings, Vol. 132, R C , N0.2Mar. 1985, pp.82-93.

BIOGRAPHY Tongxin Zheng is a research assistant at Clemson University. He received his BS degree in 1993 from North China Institute of Electric Power, MS degree from Tsinghua University, China in 1996. Presently he is working towards the Ph.D. degree in Electrical Engineering at Clemson University, Clemson, SC. His research interests include power quality, power system analysis and optimization. Elham B. Makram (SM '82) was born in Assuit, Egypt. She received the B.S. degree in Electrical Engineering from Assuit University, Egypt in 1969. She received the M.S. and Ph.D. degrees from Iowa State University in 1978 and 1981 respectively. She is presently a Professor of Electrical and Computer Engineering at Clemson University, Clemson, SC. Dr. Makram is senior member, IEEE,member of ASEE, Sigma Xi, NSPE and CIGRE. She is a registered professional engineer. Her present research interests include. computer simulation of power systems, high impedance faults and power system harmonics. She is the recipient of the 1991 Alumni Research Award, the 1992 NSFFAW award, the 1993 S W E distinguished engineering educator award, the 1994 outstanding faculty award at Clemson University, and the 1996s Provost's Award for Scholarly Achievement. Adly A. Girgis (S'80-SM'81-F92) is a fellow of the IEEE. He received the B.S. (with distinction first class honors) and the M.S. degrees in Electrical Engineering from Assuit University, Egypt. He received the Ph.D. in Electrical Engineering from Iowa State University. He is currently Duke Power Distinguished Professor of Power Engineering in the Electrical and Computer Engineering Department and Director of the Clemson University Electric Power Research Association. His present research interests are real-time computer applications in power system control, instrumentation and protection, Signal processing and Kalman filtering applications in power systems.

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