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Journal of Applied Mathematics, Islamic Azad University of Lahijan Vol.3, NO.10, Autumn 2006

A SIMULINK Study of Electric Arc Furnace Inactive

Power Compensation by Using STATCOM

Abdolreza Tavakoli a, Mehdi Ehsan

b, Seyed Mohammad Tagie Batahiee

c

aIslamic Azad University-Science and Research Branch, Tehran, Iran bSharif University of technology, Tehran, Iran

cKhaje Nasir Toosi University of technology, Tehran, Iran

Abstract

The nonlinear and time varying nature of electric arc furnaces (EAFs) create flicker, harmonics, and

voltage/current unbalances. Nowadays high-speed compensators like STATCOM can improve the

performance of EAFs and the power quality problems of electrical systems around them. This paper

uses a time domain model for electric arc furnaces and a new model of STATCOM respectively for

creating mentioned power quality problems and inactive power compensation. In this paper, we

investigate and simulate electric arc furnace and STATCOM using SIMULINK/PSB. Then, we

simulate a network including them completely. The proposed model takes into account arcing

conditions and some power quality effects improvement.

Keywords: Electric Arc Furnace, STOTCOM, SIMULINK, Power Quality.

1. Introduction

Study of power quality problems caused by EAFs requires a general and accurate model for

EAF. Different arc furnace modeling, both in time and frequency domain, is as following:

1- The V-I characteristic method.

2- Time-domain equivalent nonlinear circuit model.

3- Harmonic voltage source model.

4- Harmonic domain solution of nonlinear differential equation.

5- Random and stochastic process method.

6- Use of actual recorded terminal quantities use in current injection models.

7- Use of electric arc furnace power balance equation.

8- Use of combined Cassie/Mayr model.

In this paper combined Cassie/Mayr model, a three-phase arc furnace model, which can

simulate all the mentioned power quality indices, is used. This model enables us to investigate

different design alternatives for the secondary current conductors, study the effects of EAFs

circuit parameters on electric states, and rationalize furnace conditions in service [1, 2 and 3]. Also in this modeling, the furnace transformers tap effect and the mutual inductance between the

flexible cables of the secondary side of the furnace transformer has been considered.

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This model is in the time domain and in addition to generating power quality parameters, can

investigate the effect of different feed systems designs on performance of furnace. The basic

methodology for flicker mitigation can be categorized into three types:

1- Regulating the EAF passive components, such as source impedance [4].

Although, to some extent, the increasing series reactance can mitigate the flicker, it reduces

power supply and therefore decreases EAF productivity.

Moreover, it is also expensive and laborious to control upstream transformer reactance or

series reactor in the firmer deregulation power system [5].

2- Compensation through the combination of thyristor and passive components, such as the

well-known SVC1. SVC can not only improve power quality of nearby system, but also

increase EAF productivity and bring additional economic benefits. However, it cannot catch up

the fast-varying flicker (1Hz~20Hz) very well with the inherent limit of relatively low

bandwidth and hence its dynamic performance for flicker mitigation is limited.

3- The state-of-the-art solution is the STATCOM2 based on high frequency VSC

3 [5, 6].

2. Simulation of the Electrical arc furnace

In simulating the following electrical circuit, phase parameters and arc equation are used [4]:

Fig 1

A simplified electrical circuit for EAF simulation

RL1=0.0004Ω ,RL2=0.0004Ω ,RL3=0.0004Ω , Rs=0.1mΩ

L1=15.97 mH, L2=15.97 mH, L3=15.33 mH, Ls=1mH M12=4.58 mH, M13=3.89 mH, M23=4.58mH,

)dt

dgθ

p

i))(

i

i - (exp(

E

vi))

i

i - exp(-(1gg

0

2

2

0

2

2

0

2

o

2

min −++=

In order to determine the arc static model the arc has the following parameters:

( 0θ =0.000110 or 0θ =0.000510), Eo=200V, α =0.0005,

1θ =0.000100; po=100; io=10; gmin=0.008

The above-mentioned mathematical model has been simulated in the form of a program in the

MATLAB /SIMULINK Software, and is presented in Fig. 2. The selection of different time

constants for the arc has taken place because the information processing related to the melting

processes shows that the arcs time constant increases from 80 to 100 microseconds in the initial

stages of melting to 500 to 550 microseconds in the final and refining stages.

1 Static VAR Compensation 2 Static synchronous Compensator 3 Voltage-Source-Converter

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Journal of Applied Mathematics, Islamic Azad University of Lahijan Vol.3, NO.10, Autumn 2006

The arc voltage versus current has been seen in Fig. 3. The corresponding arc conductance,

voltage, and the comparative voltage/current for phase an are shown in figures (4) to (6). In continuation of the topic, investigation of the arcs dynamic characteristics is done. As was

explained, for creating the flicker effect, it is necessary to modulate the arc voltage-current

characteristic with sinusoidal and random signals. With the assumption for balanced working conditions

for the electric arc furnace and the sinusoidal variation law for the arc effective voltage, the different

quantities wave shape in the furnace system are shown in figures in figures (7) to (10).

With the assumption of balanced working conditions for the furnace and random time

variations, for E (for a, b, c ), different quantities have been drawn in figures (11) to (14). For the

unbalanced performance of electric arc furnace, the voltage values at different phases have

been chosen as follows:

0θ =0.000510, Eoa=200V, Eob=180V, Eoc=250 α =0.0005

Figures (15) to (18) show static characteristics of different quantities at the furnace different

point in its unbalanced performance.

Fig 2 Fig 3

The Electric Arc Furnace Simulated in SIMULINK Voltage/current characteristic seen at phase a

Fig 4 Fig 5

Electric Arc Conductance Related to Phase a Phase a Arc voltage Curve

Fig 6 Fig 7

Phase a voltage/current comparative curve the phase current curve with the 10Hz sinusoidal balanced flicker

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Fig 8 Fig 9

Electric arc conductance with the balanced 10Hz flicker Electrical arc voltage-current characteristic seen at phase a

Fig 10 Fig 11

Phase a s voltage and current comparative curve Arc voltage

Fig 12 Fig 13

Electric Arc Conductance Voltage characteristic and the Electric Arc current Seen at phase a

Fig 14 Fig 15

Phase as voltage and Current Comparative Curve Phase A’s Current in Unbalanced conditions

Fig 16 Fig 17 Voltage/Current Characteristic Seen at phase a the phase a Arc Voltage Curve

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Journal of Applied Mathematics, Islamic Azad University of Lahijan Vol.3, NO.10, Autumn 2006

Fig 18

Arc voltage and current comparative curve

3. Distribution Static Synchronous Compensator (DSTATCOM)

The power circuit of the three-phase DSTATCOM with time varying arc furnace load has

shown in Fig. DSTATCOM comprised of a voltage source inverter that has a capacitor at its

DC side. A transformer usually does the inverter outlet connection to the network. In the no-

load state, the DSTATCOM output voltage and the networks voltage are the same and as a

result, no current is injected to the network. In the capacitive state, the DSTATCOM voltage

amplitude is more than the network voltage. As a result, in facts it is a capacitive Inactive

current to the network. In other words, DSTATCOM acts like a capacitor, and generates

reactive power. In the inductive state, DSTATCOM’s voltage amplitude is less than the

network voltage and as a result receives an inductive current from the network. In other words

DSTATCOM acts like an inductor and consumes reactive power. In this way by changing the

DSTATCOM output voltage amplitude that’s done by controlling the implemented pulses to

the gate switches of the semiconductor, we can control the consumed or generated reactive

power by it [7, 8].

The different applied flicker reducing methods in DSTATCOM can briefly be listed below:

1-Direct methods of controlling the current and direct control of power have a good

performance in compensating voltage flicker but because they are based on measuring the

loads current, they are only usable when only compensating the flicker duo to a specific load is

intended.

2- Voltage positive sequence component control method and positive and negative sequence

Components simultaneous control method.

Fig 19

The power circuit of the three-phase DSTATCOM with time varying arc furnace load

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Table 1

COMPARISON OF DIFFERENT CONTROLLING METHODS OF DSTATCOM IN ORDER TO COMPENSATE VOLTAGE FLICKER

4. Power system Description

Modeling the sample power system with STATCOM & its controller and the electric arc

furnace EAF by using MATLAB/SIMULINK has given in Fig. 20.

In this paper a completely new model of STATCOM for improving electric arc furnace

power quality in the time domain & a power system is simulated. This simulation is done by

using the MATLAB/SIMULINK and the PSB4. In this simulation, STATCOM has made

equivalent to an instantaneous inactive power compensator with an active consumer (for

showing the switching loss). Also the suggested control method is based on the generalized

instantaneous power theory that was expressed the first time in the year 1996 is valid for the

three phase systems in the sinusoidal, non-sinusoidal, balanced and unbalanced conditions and

has generality compared to the previous methods [9].

Fig.20 shows a STATCOM at the connection to a 138kv network. The feeding network has

shown with its equivalent there in network. While the dimension of the voltage is 1.06×138KV

and the short circuit of the network is 1000MVA with the ratio 5.2=R

X, and is connected to 2B

bus bar. The systems complete information has been mentioned in table (2) [10].

The power is applied to the dynamic compensator by noting the necessary signal controlling

strategy. So by considering B2 bus bar as the consuming bus bar and PCC bus bar as the

feeding bus bar the vector relations have been applied according to Fig.20 in the SIMULINK

environment. In which QL(t) and PL(t) are the furnaces instantaneous active and inactive power

and QS(t) and PS(t) are the feeder network instantaneous power and QL and PL are the furnaces

average power and QS and PS are the feeder network average powers.

Also abcV and abcI are the instantaneous voltages and currents at the STATCOM connection

to the utility and the load according to Fig 20.

4 Power System Blackest

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Journal of Applied Mathematics, Islamic Azad University of Lahijan Vol.3, NO.10, Autumn 2006

By defining an adequate function of f(q) we can define the STATCOM responsibilities for

improving power quality. For example whenever f(q) = q is defined then the injected power by

STATCOM will cause the furnace inactive power compensation. It is clear that in this case the

applied equipments in the STATCOM structure shall be able to tolerate a large value of the

current. If f(q)=q –qave5ohz is defined all of the nonnative power oscillating values except

components below the 50 Hz frequency will also be compensated. In figures (22) to (28), the

outputs resulting from this simulation is shown.

Fig 20

Schematic of the simulated circuit in SIMULINK

Table 2

THE COMPLETE SPECIFICATIONS OF THE SIMULATED SYSTEM

Fig 21

Simulated vector Relations in the SIMULINK Environment.

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Fig 22 Fig 23

Furnace voltage Furnace Current

Fig 24

Load, supply and STATCOM Instantaneous Inactive power

Fig 25 Fig 26

Load, supply and STATCOM Average Inactive power Supply Inactive and Active Instantaneous power

Fig 28 Fig 27

Supply Inactive and Active Average power Load, supply and STATCOM current

Also if f (q) is defined as the suitable function, of inactive power oscillating values are also

compensated at flickering frequencies. In other words Flicker will be eliminated from the

electric arc furnaces inactive power (with the least power from the elements forming

STATCOM), And because the amount of voltage value variations have direct relationship

with the variations of inactive power values, One can say a major portion of voltage Flicker

will be eliminated. Figures (29) to (31) are the outputs of simulation.

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Journal of Applied Mathematics, Islamic Azad University of Lahijan Vol.3, NO.10, Autumn 2006

Fig 29 Fig 30

Load Inactive and Active Instantaneous power Load Inactive and Active power

Fig 31

Supply Inactive and Active Instantaneous power

If STATCOM controlling function acts according to compensating q(t) and f(p) then

compensation reactive power and a lot of active power oscillations are also supplied by

STATCOM, And as a result the amount of passing current decreases on the supply side

(feeding) and a lot of non-sinusoidal components and generating flicker will be supplied by

this compensator.

5. Conclusion

In this paper , a three phase model of the electric arc furnace by depending on the

Cassei/Mayr model by using the MATLAB /SIMULINK toolboxes was introduced that has the

real time modeling capability of the different status of the furnace. Investigation of the results

obtained by simulating is briefly as follows.

1- Investigating the results obtained from simulation show that the noticeable frequencies in

the Flicker effect are usable by the cassie/Mayr model for the electric arc furnace.

2- In order to compensate the destructive effects resulting from the furnaces specially the

flicker one can use elements such as DSTATCOM and STATCOM. These elements can

completely compensate the loads reactive power variations at each frequency and their

response speed is very fast.

3- Here the equations of instantaneous active and inactive power have been used and have been

controlled with the necessary purpose fullness of STATCOM. In order to be clear regarding

this matter each of the intended goals of improving the network by STATCOM was addressed

and the obtained results show the success of STATCOM. By using the adequate control

strategy one can compensate the load inactive power, stabilize the voltage profile, reduce the

voltage flicker and improve the power factor.

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4- In this paper, a new model of STATCOM without depending on the elements of power

electronics and by using load dynamic models has been simulated. It shows the obtained results

of the very adequate model presented in compensating the electric parameters at the power

coupling point.

5- When improving the different parameters with a particular weighting factor is intended, the

intended improvement function is applicable to the Model. It is observed that using

STATCOM provides the connection capability of the arc furnace to the weak networks.

Acknowledgment

This work is sponsored by Islamic Azade University Science and Research branch and the

main author is a graduated PH.D student from it.

References

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