Simulations on Harmonic Analysis of Arc Furnace

Simulations on Harmonic Analysis of Arc Furnace

Electrical Arc Model

Zhao Hui

School of Electrical Engineering Tianjin University of Technology

Tianjin, China

E-mail: zhaohui3379@https://www.360docs.net/doc/4015643422.html,

Tang Wei

School of Electrical Engineering

Tianjin University of Technology

Tianjin, China

E-mail: tangwei87110@https://www.360docs.net/doc/4015643422.html,

Yue You-jun

School of Electrical Engineering

Tianjin University of Technology

Tianjin, China

E-mail: bakeryueyj@https://www.360docs.net/doc/4015643422.html,

Abstract—Harmonic problems are highlighted, when the electric arc furnace work steadily. Because the characteristics of an arc resistance is highly nonlinear, time variability and uncertainty, harmonic analysis and suppression is difficult. In this paper, a MATLAB/Simulink simulation model of the AC electric arc furnace system had been built on the basis of the parameters analysis of time-varying arc resistance. The new model simulated the electrical characteristics of an electric arc furnace which is operating steadily on the basis of the physical mechanism. This model is used for FFT harmonic analysis of electric arc furnace voltage and current. Simulation results of EAF in a steel plant show that the odd harmonics is the obvious main reason which caused the power voltage and current distortion. This Model is effective and easy to use; it's proposed to lay the foundation for the harmonic suppression.

Keywords-Arc furnace; Electric system; Harmonic analysis; MATLAB Simulation)

I.I NTRODUCTION

AC electric arc furnace is equipment which uses arc energy to smelt metal, its optimum smelting quality and low cost advantages of investment make it be widely used in the metallurgical industry. Modern large-scale high-power electric arc furnace steel-making, because of its large capacity, is the big power; EAF has a decisive impact on the grid. It has a low power factor, large and rapid changing reactive power fluctuation in load, these result in power quality deterioration with harmful high harmonic currents, serious unbalanced three-phase load negative sequence current and other adverse factors on the grid [1]. It is not only reducing the efficiency of power transmission and the utilization ratio of electrical equipment, but also make electrical equipment overheat, vibrate and noise, age insulation, diminish life and even failure or fire, these will jeopardize distribution and the large number of users, affect the quality of production of electric furnace itself, make power and electrode consumption increases. These factors make electric arc furnace become one of the main power grid pollution.

Electric arc furnace will produce the following run-time behaviors: ①As the arc resistance of nonlinear and transient generated high harmonics; ②As the arc asymmetry generated negative phase sequence current; ③As the electrode movement, the role of electromagnetic force to produce irregular fluctuations in arc length, this will result arc current amplitude in a similar random fluctuations, and thus affect the power grid of fluctuation [2].Therefore, the harmonics and fluctuations of electric arc furnace system are interrelated and the solution to the problem has a great deal of difficulties.

From the perspective of the system, EAF is a typical non-linear, time-varying and distributed parameter, three-phase multi-input, multi-output and coupling system. Its parameters are or unknown, or with random noise [3]. For this reason, in theory, harmonic analysis and simulation on the electric arc furnace system has been slow. But regarding the needs of evaluation the voltage harmonics and voltage fluctuation, or in terms of effective control measures for flicker compensation, there has a need to establish the precise model of arc furnace load as the basis for numerical simulation.

In this paper, the harmonic problems caused by arc furnace are simulated. According to the arc model provided by literature, based on arc characteristics, the AC arc furnace model for harmonic analysis is created by MATLAB/ Simulink software. Model is used for harmonic analysis of the simulation study and provides a method for the suppression of such undesirable volatility.

II.MODEL OF AC ELECTRIC ARC FURNACE

A.Single-phase arc furnace model

Electric arc furnace generally includes the following sections: power distribution systems, electric transformers, short nets and arc [4]. Except arc, the rest of the system could replace by using the linear time-invariant circuit elements. So, one side of the furnace transformer can be read out circuitry converted to the secondary side. The three-phase parameters of distribution system, electric transformers, and short net of the high-pressure electric arc furnace are exactly the same. Ignore the impact of furnace transformer magnetizing circuit and does not take into account the role of reactive power compensation

capacitors, Single-phase equivalent circuit is shown in Fig.1.

The project was supported by National High-tech R&D Program (863

Program) (2007AA041401)，09JCZDJC23900, 10JCZDJC23100), and

University Science and Technology Development Foundation of Tianjin

(2006ZD32, SB20080069).

978-1-4244-7941-2/10/$26.00 ?2010 IEEE

Figure 1. Single-phase equivalent circuit diagram of arc furnace

In the figure, R =R 1+R 2, L =L 1+L 2. R 1, L 1 represent the single-phase equivalent resistance and inductance of the transformer from the furnace out of the circuit depends on conversion to the second side. R 2, L 2 is on behalf of equivalent resistance and inductance which belongs to single-phase short network. The circuit equation can be listed by the Kirchhoff theorem as following:

()dt

di L

i R R e a a a a +?+= (2-1)

Considering the role of reactive power compensation

capacitors, single-phase equivalent circuit is shown in Fig.2.

Figure 2. Single-phase equivalent circuit diagram affected by the

compensation of electric capacity

The circuit equation can be listed by the Kirchhoff theorem as following:

()???

???

?+?+=+?+?+?=dt di L i R R u u dt

u d C L dt du C R i R e a

a a c c c c a a 2222111(2-2) For the equation above, as long as the relationship of arc

resistance R a , R b , R c could be made sure over time, the equation can be solved to get the circuit voltage and current response. B. Resistance modal

As arc features are very complex, it is very difficult to get the general form of the arc model. However, as far as the analysis of the electric arc furnace system is concerned, the people just want to know the influence of arc to harmonics, electrical work characteristics of the system. Therefore, from the view of circuit point, as long as a component whose external features are the same as outside characteristics of the arc can be found, you can use it to reflect the arc of the system.

As the arc resistance is highly nonlinear, electric arc furnace in the smelting process will produce a large number of harmonics; algebra of short-circuit reactance and the harmonic reactance is operating reactor [5]. That is, the operation reactance of electric arc furnace is greater than short-circuit reactance arc resistance was mainly due to harmonics generated caused by non-linear reactance, so arc modeled it can deal as a purely resistive.

Professor Liu Xiao-he get the model through systematic analysis of electrical arc furnace system, the arc model is given as follow:

()()[]

θω++?+=D t B A CLe L t R 2cos 11

, (2-3) Type in: C for the constant of proportionality, reflect the impact of the arc column radius on the resistance; L for the arc length; I is arc current RMS; ω is the angular frequency of external excitation; A = T L /α, reflecting the lowest temperature value of arc column arc resistance, the smaller A is, the greater the resistance R , the more obvious the zero off. B = (T H -T L ) / α, reflecting the impact of arc temperature on the value of the resistance. Due to the impact of B , R had decreased rapidly to a lower value after the maximum point , the current arc the drop close to zero from a higher value , the resistance rapidly increased; D reflects the impact of gas thermal inertia on resistance, due to the presence of D , making the maximum value of resistance does not appear in the current zero-crossing time, and there exist a lag angle; T L is the minimum temperature for the arc column; T H is the highest critical temperature of arc column; α is the electrical conductivity of arc column, under the conditions of atmospheric pressure open arc, α is a constant, and α = 3.323×104.

From the circuit point of view, this model treats arc as a nonlinear time-varying resistance, reflects the effect of the AC current in the electric arc furnace system as a whole, meets the out characteristics of AC arc, and further from the physical mechanism, seize the main physical characteristics of the object.

C. Resistance model parameter estimation

1) Estimates of A, B

Known by the A = T L /α, B = (T H -T L )/α, on A , B 's estimate is on the T L , T H estimates. T L is the minimum arc column temperature; its value should ensure that the arc column arc area is always plasma zone. According to reference [6], the value of T L is between 7000 ~ 8000K. T H is the maximum temperature of arc column. The following formula shows us the relationship between electric arc furnace operating current and the arc temperature:

()()∫?=

t

T t t

T

d i T t I ττ1 (2-4)

Actual measured the arc current and arc temperature in a

steel factory is as shown in Table 1.

TABLE I. R ELATIONS BETWEEN ELECTRIC ARC MAXIMUM TEMPERATURE

AND ARC CURRENT

arc current （KA） 15 20 24 28 30 arc temperature （

1000K） 15.5 20.8 25.0 28.329.4arc current （KA） 32 36 40 44 50 arc temperature （

1000K）

30.1

30.4

30.6

30.8

31.0

corresponding T H can be found by Gaussian fitting

Interpolation. This method can reduce the error to the extent permitted. Fitting results are shown in Fig.3.

.

Figure 3. Gaussian interpolation

2)

Estimates of C

Since L is usually difficult to obtain, so we took C 0= C*L , divided the period T into N deciles, took N = 60. ()

∑=???

??

???????+?+?≈

N

K D N K B A e

r

ctg L N C 1

4cos 11

'0

π?ω (2-5)

L' is the decoupling and simplification of the equivalent inductance. r is the equivalent resistance of the net short and electric arc furnace transformer. According to the above formula, we obtained the value of C 0 is 3.027×10-4. 3) D estimates Electric arc furnace is used to operate a large arc current, high arc column temperature, more fully ionized. According to the results of several simulation practices, to determine the values of D at -8 ~ -12 degrees would be more appropriate [7]. It is very difficult to study the harmonic of electric arc furnace system, because the arc resistance is a random variable. In this article, the arc resistance added into the whole circuit as a time-varying model, then obtain the U-I characteristic curve through simulation, and finally analyzed harmonic through the FFT algorithm. Time-varying arc resistance curve is shown in Fig.4.

Figure 4. Time-variable curve of arc resistance

III.

SIMULATION AND ANALYSIS OF RESULT

A. Main parameters of the system

The electric arc furnace parameters in this paper: Rated capacity of electric arc furnace transformer is: when Se =12500KVA and U k %=8%，then R T ≈0?，X T ≈7.3984×10-4

?; Short Net: R 0=0.0011?，X 0=0.0037338?; arc: T L =8000K ，T 1=28000K, C =1.01×10-4, L =25cm ，cos φ=0.8，r c =0.45cm ，D +θ=-2.4rad, through calculation A =0.241, B =0.3.

The main arc circuit is shown in Fig.5 [8]. Furnace receives the high voltage power line through short network, furnace transformers, reactors, circuit breakers and isolation switches. Generally, reactive power compensation capacitors should be added in the high side. Large-capacity electric arc

furnace are configured fast static var compensator in foreign.

Figure 5. Schematic diagram of electric arc furnace power supply system

B. Simulation and analysis

Based on the data above, we used Matlab7.0 to simulate

the system. Using module called Powergui, which is located in the library of Power System Blocks, analyze simulation waveform FFT. Powergui is a powerful tool that is provided by Power System Blockset. It can be used for harmonic analysis, convenient and fast.

The usage of Powergui is as follows: click the Simulink menu bar in Simpowersystem of module library, locate the Powergui module, add it to the model in the window which need to simulate, pop-up properties by double-click the Parameters dialog box. FFT Analysis tool can be used to simulate system by the Fourier analysis, to get the harmonic content. Results are generally displayed by bar charts and data table. Fig.6 is the AC arc V-I characteristic curve. From the diagram, a highly nonlinear variation between arc voltages and

currents could be found.

Figure 6. Ac arc V-I characteristic curve

Under the arc voltage and current relationships, we made V-I characteristics of arc shown in Fig.7. Simulation time is 0.1s, simulation step is 45. The random of arc voltage and current fluctuations can be seen from this graph.

Figure 7. Arc voltage, current curve

After fast Fourier decomposition, we get all the frequency spectrum of the harmonics as shown in Fig.8 and Fig.9 from the voltage and current waveforms which are showing us a simulation curve of single-phase arc voltage and

arc current.

Figure 8.

Simulated harmonic contents of voltage

Figure 9. Simulated harmonic contents of current

IV. C ONCLUSIONS

In this paper, arc model which is established for harmonic analysis based on detailed analysis of operating characteristics of electric arc furnace. A simulation of electric arc furnace steel plant shows that the model can reproduce the true arc voltage, current and voltage characteristics. So it can be used in the study of electrical characteristics. The harmonic analysis on this modal shows that, in the arc voltage and current: 3 to 7 harmonics occupy a large proportion. This study is conducive to the effective harmonic suppression measures, and it has a practical significance to carry out the research of the impact

that electric arc furnace brings to the electrical network for the future.

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