Simulation of Electric Arc Furnace Characteristics for Voltage Flicker study using MATLAB .pdf

174

2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering

Simulation of Electric Arc Furnace Characteristics for Voltage Flicker study using MATLAB

D. C. Bhonsle Electrical Engineering Department

CKPCET, Gujarat Technological University Surat, INDIA

[email protected]

R. B. Kelkar Electrical Engineering Department

Faculty of Technology, M S University of Baroda Vadodara, INDIA

Abstract—Power quality is becoming a more concern of today’s power system engineer due to the rapid growth of non-linear loads, such as power electronic control equipments and electric arc furnace (EAF). Harmonics and voltage flicker are the power quality problems which are introduced to the power system as result of non-linear behavior of the electric arc furnace operation. Electric arc furnace model is needed to analyze the power quality. There are numbers of arc furnace models. This paper presents a time domain model called exponential-hyperbolic for electric arc furnace using MATLAB. The model is used to study its behavior on the power system using MATLAB. To analyze the method, several characteristics for different operating conditions are investigated.

Keywords-Power quality, flicker, EAF, MATLAB.

I. INTRODUCTION The EAF is inherently non-linear and time-variant loads

and it can cause power quality problems such as harmonics and voltage flicker. Odd and even harmonic currents are generated by EAF operation. These harmonic currents, when circulated in the electric network can generate harmonic voltages which in turn can affect other users. Flicker is the sensation that is experienced by human eye when subjected to changes in the illumination intensity. The maximum sensitivity to change in illumination is in the frequency range of 5 to 15 Hz. As EAF is a large source of flicker, causes voltage fluctuation in the connected electric network. Hence, modeling of EAF has attracted attention of power system engineers to solve these problems pertaining to EAF.

The important issue in the modeling of the arc is the simulation of arc. There are several methods used to describe the electric arc [1]. The balanced steady state equations are used in. The time domain methods based on the differential equations are also presented. Other methods such as frequency response, V-I characteristic are employed to analyze the behavior of the EAF [2]. Comparison of EAF modeling in time domain and frequency domain shows that he time domain is more useful in studying the EAF[1-2].

In the above explained methods, there are some limitations such as initial conditions for the differential equations, balanced situation of thee phase currents and use of complicated mathematical equation for the modeling of EAF.

This paper presents simulation of the EAF model in the time domain using MATLAB. The main feature of the proposed model is modeling of the explained method with a good approximation without need of initial conditions of the EAF. Also, the proposed method can be used to describe different operating situations of the EAF and its effect of the connected electric network.

II. SUPPLY NETWORK Figure 1 shows a simple single phase electric network of a

source which supplies an EAF [2].

Figure 1. Electric network supplying an EAF

In Fig. 1, the system impedance is represented as Zs, bus PCC represents the point of common coupling, and bus AF is the low voltage side of the transformer whose impedance is given by Zt. The system parameters are tabulated in Table 1.

TABLE I. ELECTRIC SYSYTEM AND EAF MODEL PARAMETERSABLE

Item(s) Parameters

System

V=415 V

f=50 Hz

Zs=(0.0528+j0.468) mΩ

Zt=(0.3366+j3.22) mΩ

EAF

Vat=200 V

C=19 kW

D=5 kA

I0=20 kA

Vat0=200 V

978-1-4577-2149-6/11/$26.00 © 2011 IEEE

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III. MODELING OF EAF AS LOAD In this part, the modeling of EAF is performed using the

estimation of the voltage and current of the electric arc. This modeling is based on Fig. 2, which shows the actual VIC and piecewise linearization in reference [1, 2, 3, and 5].

Figure 2. The actual V-I characteristic of EAF

As can be seen from Fig. 2, the electric arc consists of four major parts as tabulated in Table 2 [3]:

TABLE II. MAJOR PARTS OF AN ELECTRIC ARC CHARACTERISTIC

Area Condition Equation No.

Area 1 (di/dt)>0, v & i>0 (1)

Area 2 (di/dt)<0, v & i>0 (2)

Area 3 (di/dt)<0, v & i<0 (3)

Area 4 (di/dt)>0, v & i<0 (4)

According to Table 2, Eq. 1 is similar to Eq. 4 and Eq. 2 is also similar to Eq. 3. However, the sign of voltage and the current in the similar ones are opposite. Thus the arc voltage can be expressed as a function of the arc current in their region.

For this purpose in the following, the equations of EAF are analyzed using three different models based on the VIC of the electric arc.

A. Model 1: Hyperbolic Model In this model, the VIC of the EAF is considered to be in the form of V=V (I) and it can be described as:

( ) iDCViV at +⎟⎠⎞

⎜⎝⎛+= (5)

Where V and i are arc voltage and arc current per phase. Vat is the threshold magnitude. Vat is the magnitude of the voltage threshold to which the voltage approaches as current increases. This voltage is dependent on the arc length which is defined by constants C and D taking care of arc power and arc current respectively.

B. Model 2:ExponentialModel In this model, the VIC of the EAF is approximated by exponential function as:

( ) ( )( ) ( )isignumeViV Iiat ⋅−= 01 (6)

In this equation a current constant (I0) is employed to model the steepness of positive and negative currents.

C. Model 3:Combined Model of Model 1 & 2 This model is proposed in [5]. The VIC of the electric arc

is described as:

( )( ) ( )⎪

⎩

⎪⎨

⎧

>≥⋅−

>≥+⎟⎠⎞

⎜⎝⎛+

=001

00

0 ianddtdiforisignumeV

ianddtdiforiDCV

iVIi

at

at

(7) The combined model has the capability of describing the

EAF behavior in time domain. Also the combined model can explains various operating conditions of the EAF such as initial melting, mild melting and refinement.

The various circuit constants utilized in the various models are tabulated below.

IV. SIMULATION The EAF along with the electric system shown in Fig. 1 has

been modeled using the Simulink/MATLAB shown in Fig. 39. The EAF is modeled as a non-linear time varying voltage controlled source using Embeded program function/MATLAB. The arc current is taken as the input parameter to this function and the output is non-linear time varying voltage. MATLAB file of the same is shown in Figure 39.

Dynamic EAF model is required for real time analysis of the effect of the arc. The dynamic arc characteristic is simulated by varying arc conductance. In general the variation is of random nature. However two types of variation are considered for the study-sinusoidal and random.

In order to study the effect of voltage flicker on the system of EAF, Vat is varied sinusoidally and randomly. In this regard Vat is modulated as follows:

The sinusoidal variation is assumed as:

( ) ( )[ ]tmVtV fatat ωsin10 ⋅+= (8) where m is modulation index and ωf is a flicker frequency. For random flicker generation Vat is modulated with a random signal having the mean of zero with the frequency band in the rage of 4-14 Hz [3]. Thus vat is written as:

176


( ) ( )[ ]tNmVtV atat ⋅+= 10 (9) where, N(t) is a band limited white noise with zero mean and variance of one. MATLAB simulation file for equations (8) & (9) are shown in Figure 40 (a) & (b).

V. SIMULATION RESULTS The simulated results are presented as a comparison of three models of EAF-hyperbolic, exponential and combined. The values used in the equation (5), (6) and (7) are tabulated in Table 1[3].

A. Steady State Characteristics 1) Arc Current

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-300

-200

-100

0

100

200

300

Time (S)

Arc

Cu

rren

t (A

)*25

0

Arc Current of Model 1 (Static)

Figure 3. Arc Current of Hyperbolic Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-400

-300

-200

-100

0

100

200

300

400

Time (S)

Arc

Cu

rren

t (A

)


Arc Current/250

Figure 4. Arc Current of Exponential Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-400

-300

-200

-100

0

100

200

300

400

Time (S)

Arc

Cu

rren

t (A

)


Arc Current/250

Figure 5. Arc Current of Combined Model

This group represents steady state characteristics of three models of EAF i.e. arc length is kept constant, which demonstrates refining condition of an EAF. In this condition, the level of molted material is constant and melting is uniform

in the furnace. Hence behavior of VIC is also uniform. This condition do not produces any flicker at PCC.

2) Arc Voltage

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-250

-200

-150

-100

-50

0

50

100

150

200

250

Time (S)

Arc

Vo

ltag

e (V

)

Arc Voltage of Model 1 (Static)

Figure 6. Arc Voltage of Hyperbolic Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200

-150

-100

-50

0

50

100

150

200

Time (S)

Arc

Vo

ltag

e (V

)

Arc Voltage of Model 2 (Static)

Figure 7. Arc Voltage of Exponential Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-250

-200

-150

-100

-50

0

50

100

150

200

250Arc Voltage of Model 3 (Static)

Time (S)

Arc

Vo

ltag

e (V

)

Figure 8. Arc Voltage of Combined Model

3) VIC

-300 -200 -100 0 100 200 300-300

-200

-100

0

100

200

300

Arc Current (A)*250

Arc

Vol

tage

(V

)

V-I Characteristic of Model 1 (Static)

Figure 9. VIC of Hyperbolic Model

Typical waveforms of arc current, arc voltage VIC and arc conductance are presented in Figure 3 to 17 for three models of EAF.

177


-300 -200 -100 0 100 200 300-200

-150

-100

-50

0

50

100

150

200

Arc Crrent (A)

Arc

Vo

ltag

e (V

)

V-I Characterisic f Model 2 (Static)

Figure 10. VIC of Exponential Model

-300 -200 -100 0 100 200 300-250

-200

-150

-100

-50

0

50

100

150

200

250

Arc Current (A)

Arc

Vo

ltag

e (V

)

V-I Characteristic of Model 3 (Static)

Figure 11. VIC of Combined Model

4) Arc Voltage and Arc Current

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-300

-200

-100

0

100

200

300

Arc Current and Arc Voltage (Static)

Time (S)

Arc

Cu

rren

t (A

)A

rc V

olt

age(

V)

Arc Current/250

Arc Voltage

Figure 12. Arc Voltage and Arc Current of Hyperbolic Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-400

-300

-200

-100

0

100

200

300

400

Time (S)

Arc

Cu

rren

t (A

) A

rc V

olt

age

(V)

Arc Current and Arc Voltage of Model 2 (Static)

Arc Current/250

Arc Voltage

Figure 13. Arc Voltage and Arc Current of Exponential Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-400

-300

-200

-100

0

100

200

300

400

Time (S)

Arc

Cu

rren

t (A

)A

rc V

olt

age

(V)

Arc Current and Arc Voltage of odel 3 (Static)

Arc Current/250

Arc Voltag

Figure 14. Arc Voltage and Arc Current of Combined Model

5) Arc Conductance

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

50

100

150

200

250

300

350

Time (S)

Co

ndu

ctan

ce (

Mh

o)

Arc Conductance of Model 1 (Static)

Figure 15. Arc Conductance variation of Exponential Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1100

150

200

250

300

350

400

450

Time (S)

Arc

Co

ndu

ctan

ce (M

ho

)


Figure 16. Arc Conductance variation of Combined Model

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

50

100

150

200

250

300

350

400

450

Time (S)

Arc

Co

nd

uct

ance

(M

ho

)


Figure 17. Arc Conductance variation of Combined Model

Power consumption during EAF operation is also one of the important features to look upon. It helps in designing process of filters to mitigate harmonics and voltage flickers for EAF power quality improvement. Due to constant length of arc, active and reactive power consumption during steady state is also constant. It can be seen from Figures 18 & 19 that active power consumption is more in case of Exponential Model than the Hyperbolic Model. More ever, reactive power demand is more in the Hyperbolic Model than the Exponential Model.

178


0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.51

2

3

4

5

6

7

8

9x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active and Reactie Power (PQ) (Static)

P

Q

Figure 18. PQ of Hyperbolic Model

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

4

6

8

10

12x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active Power and Reactive Power of Model 2 (PQ) (Static)

P

Q

Figure 19. PQ of Exponential Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2

4

6

8

10x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active Power and Reactive Power (PQ) of Model 3 (Static)

P

Q

Figure 20. PQ of Combined Model

Also it is observed that the active and reactive power variation range is higher in case of Hyperbolic Model than that of Exponential Model.

B. Dynamic Characteristics The effect of voltage flicker on the system with EAF can be

studies using voltage variation with reference to time. As described in section IV, the effects of two types of flicker on the dynamic characteristic of the EAF are studies.

Results of the simulation are obtained using equations (8) & (9) with values given in Table 1[5].

1) Sinusoidal Flicker Results for sinusoidal flickers are presented in Figures 21 to

23, which shows the variation of arc voltage and arc current. It can be seen that if the furnace load generates sinusoidal

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-500

-400

-300

-200

-100

0

100

200

300

400

500Arc Current and Arc Voltage of Model 1 (Dynamic) 2

Time (S)

Arc

Cu

rren

t(A

)A

rc V

olt

ae (

V)

Arc Current/250

Arc Voltage

Figure 21. Arc Voltage and Arc Current for Sinusoidal Flicker of

Hyperbolic Model

0.1 0.2 0.3 0.4 0.5 0.6-500

-400

-300

-200

-100

0

100

200

300

400

500

Time (S)A

rc C

urr

ent

(A)

Arc

Vo

ltag

e (V

)

Arc Current and Arc Voltage for Sinusoidal Variaion of Model 2 (Dynamic)

Arc Current/250

Arc Vltage


Exponential Model

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-500

-400

-300

-200

-100

0

100

200

300

400

500

Arc

Cu

rren

t (A

)A

rc V

olt

age

(V)

Arc Current and Arc oltage for Sinusoidal Variatio of Model 3 (Dynamic) 2

Arc Current/250

Arc Volage


Combined Model

flicker, the arc voltage and arc current, are varied sinusoidally with the flicker frequency.

0 0.1 0.2 0.3 0.4 0.5 0.6-2

0

2

4

6

8

10x 10

6 Active and Reactive Power (PQ) (Dynamic)

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

P

Q


The active and the reactive power consumption pattern during sinusoidal flicker is shown in Figures 24 to 26.

179


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2

4

6

8

10

12x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active and Reactive Power for Sinusoidal Variation of Mode 2 (Dynamic)

P

Q


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4

6

8

10

12x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active Power and Reactive Power for Random Variation of Model 2 (Dynamic)

P

Q


Typical pattern is exhibited by active power and reactive power consumption waveforms. The active power consumption is more in case of Exponential Model than that of Hyperbolic Model. Vice versa is the situation for reactive power consumption.

2) Random Flicker

0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6-400

-300

-200

-100

0

100

200

300

400

500Arc Current and Arc Voltage for Random Varition of Model 1 (Dynamic)

Time (S)

Arc

Cu

rren

t (A

)A

rc V

olt

age

(V)

Arc Current/250

Arc Voltage

Figure 27. Arc Voltage and Arc Current for Random Flicker of

Hyperbolic Model

The simulation results for random flicker are presented in Figures 27 to 29. The pattern of the active and reactive power consumption for various three models has been shown in Figures 30 to 32. The active power consumption is more in case of Exponential model than the Hyperbolic Model and vice versa is the situation for reactive power consumption.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-600

-400

-200

0

200

400

600

800

Time (S)

Arc

Cu

rren

t (A

)A

rc V

ota

ge

(V)

Arc Current and Arc Voltage for Random Variation of Model 2 (ynaic)

Arc Current/250

Arc Voltage


Exponential Model

0.05 0.1 0.15 0.2 0.25 0.3-800

-600

-400

-200

0

200

400

600

800

Time (S)

Arc

Cu

rren

t (A

)A

rc V

olt

age

Arc Current and Arc Voltage for Random Vaiation of Model 3 (Dynamic) 2

Arc Current/250

Arc Voltage


Combined Model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-5

0

5

10x 10

6Active and Reactive Power (PQ) for Random Variation of Model (Dynamic)

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2

4

6

8

10x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q)

Active Power and Reactive Power for Sinusoidal Variation of Model 3 (Dynamic)

P

Q


The active power consumption is more in case of sinusoidally varying flicker than the randomly varying flicker for Hyperbolic Model as seen from Figures 31 & 34.

180


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5

0

5

10x 10

6

Time (S)

Act

ive

Po

wer

(P

)R

eact

ive

Po

wer

(Q

)

Active Power and Reactive Power for Random Variation of Model 3 (Dynamic)

P

Q


3) VIC

-500 -400 -300 -200 -100 0 100 200 300 400 500-400

-300

-200

-100

0

100

200

300

400

Arc Current (A)

Arc

Vo

lag

e (V

)

V-I Characteristic of Model 1 (Dynamic)

Arc Current/250

Figure 33. VIC of Hyperbolic Model

-400 -300 -200 -100 0 100 200 300 400-400

-300

-200

-100

0

100

200

300

400

Arc Current (A)

Arc

Vo

ltag

e (V

)

V-I Characteristic for Sinusoidal Variation of Model 2 (Dynamic)

Arc Current/250

Figure 34. VIC of Exponential Model

-500 -400 -300 -200 -100 0 100 200 300 400 500-400

-300

-200

-100

0

100

200

300

400

Arc Current (A)

Arc

Vo

ltag

e (V

)

V-I Characteristic for Sinusoidal Variation of Model 3 (Dynamic)

Figure 35. VIC of Combined Model

The VICs of dynamic state for three models has been presented in the Figures 33 to 35.

4) Arc Conductance variation

0.4 0.5 0.6 0.7 0.8 0.90

500

1000

1500

2000

2500Arc Codctance for Random Variation of Model 1 (Dynamic)

Time (S)

Arc

Con

du

ctan

ce (

Mh

o)

Figure 36. Arc Conductance of Hyperbolic Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

500

1000

1500

2000

2500

3000

Time (S)

Arc

Co

nd

uct

ance

(M

ho

)

Arc Conductance for Random Variation f Model 2 (Dynamic)

Figure 37. Arc Conductance of Exponential Model

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

500

1000

1500

2000

2500

Time (S)

Arc

Co

nd

uct

ance

(M

ho

)

Arc Conductance for Random Variation of Model 3 (Dynamic)

Figure 38. Arc Conductance of Combined Model

The arc conductance variation for various models for random flicker are shown in Figures 36 to 28.

VI. CONCLUSIONS This study investigates the existing hyperbolic, exponential

and combined models for electric arc furnace. The combined model does not require any initial conditions for modeling the arc. The combined model describes most of the specifications of EAF. The combined model is useful for studying power quality aspects such as voltage flicker. The combined model can be used for studying effect of harmonics as well.

Sinusoidal and random-these two types of voltage flickers are been carried out. The combined model with its typical EAF characteristics is useful to design and to validate voltage flicker mitigation and harmonic mitigation techniques such as static var compensator, active filters, etc. to improve power quality at point of common coupling (PCC).

181


VII. REFERENCES

[1] Zheng T., Makram E. B. and Girgis A. A., “Effect of different arc furnace models on voltage distortion”, IEEE Transactions , International Conference on Harmonics and Quality of Power, 14-18 October 1998, Volume 2, pp. 1079-1085

[2] Golkar M. A and Meschi S., “MATLAB Modeling of arc furnace for flicker study” IEEE Conference on Industrial Technology (ICIT), 1-6, 2008.

[3] Rahmatallah Hooshmand, Mahdi Banejad and Mahdi Torabian Esfahani, “A New Time Domain Model for Electric Arc Furnace”, Journal of Electrical Engineering, Vol. 59, No. 4, 195-202, 2008.

[4] Mahdi Banejad, Rahmat-Allah Hooshmand and Mahdi Torabian Esfahani, “Exponential-Hyperbolic Model for Actual Operating conditions of Three Phase Arc Furnaces”, American Journal of Applied Scinces 6 (*):1539-1547, 2009.

[5] K. Anuradha, B. P. Muni and A. D. Raj Kumar, “Modeling of Electric Arc Furnace & Control Algorithms for voltage flicker mitigation using DSTATCOM”, IPEMC, 1123-1129, 2009.

Zs Zt

G

Varc

Iarc

Continuous

powergui

XY Graph

Vt

ivfcn

V-I Char

Scope

Vt

Flicker Generation Sin

Vt

Flicker Generation Ran

Divide

i+ -

s

-+

CVS

AC Source

Figure 39. Complete Simulink/MATLAB file of Simulation

1

Vt

0.8

m

200

Vt0

Product1

Product

1

Band-LimitedWhite Noise Add

1

Vt

0.8

m

200

Vt0

Sine

Product1

Product

1

Add

Figure 40. Simulink/MATLAB Simulation of (a) Random Flicker and (b) Sinusoidal Flicker

Simulation of Electric Arc Furnace Characteristics for Voltage Flicker study using MATLAB .pdf

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