Voltage Sag mitigation in Electric Arc Furnace with - International ...
Voltage Sag mitigation in Electric Arc Furnace with - International ...
Voltage Sag mitigation in Electric Arc Furnace with - International ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>International</strong> <strong>Electric</strong>al Eng<strong>in</strong>eer<strong>in</strong>g Journal (IEEJ)<br />
Vol. 2 (2011) No. 2, pp. 536-542<br />
ISSN 2078-2365<br />
<strong>Voltage</strong> <strong>Sag</strong> <strong>mitigation</strong> <strong>in</strong> <strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong><br />
<strong>with</strong> D-STATCOM<br />
<br />
Abstract— <strong>Arc</strong> furnace represents one of the most <strong>in</strong>tensive<br />
and disturb<strong>in</strong>g loads <strong>in</strong> the electric power system. Utilities are<br />
concerned about these effects and try to take precautions to<br />
m<strong>in</strong>imize them. Therefore, an accurate model of an arc furnace<br />
is needed to test and verify proposed solutions to this end. This<br />
paper, presents the results of a study, where furnace arc is<br />
modeled us<strong>in</strong>g both chaotic and determ<strong>in</strong>istic elements. <strong>Voltage</strong><br />
fluctuations (<strong>Sag</strong>), is captured us<strong>in</strong>g the well-studied circuit<br />
whereas a dynamic model <strong>in</strong> the form of differential equation is<br />
used for the electric arc. Simulation of developed model is done<br />
<strong>in</strong> Sim-Power-System environment of the MATLAB 7.1<br />
Version.<br />
Index Terms— <strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong>, Simul<strong>in</strong>k, <strong>Voltage</strong><br />
Flicker<br />
I. INTRODUCTION<br />
<strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong> (EAF) is a widely used device <strong>in</strong><br />
metallurgical and process<strong>in</strong>g <strong>in</strong>dustries. It is a nonl<strong>in</strong>ear time<br />
vary<strong>in</strong>g load, which can cause many problems to the power<br />
system quality such as unbalance, harmonic <strong>in</strong>ter harmonic<br />
and voltage flicker. Thus study of electric arc furnaces has<br />
potential benefits for both customers and utilities. An accurate<br />
model<strong>in</strong>g of an EAF will help <strong>in</strong> deal<strong>in</strong>g <strong>with</strong> the problems<br />
caused by its operation. M<strong>in</strong>imization of the undesirable<br />
impact of EAFs can improve electric efficiency and reduce<br />
power fluctuations <strong>in</strong> the system.<br />
The description of an arc furnace load depends on the<br />
follow<strong>in</strong>g parameters: arc voltage, arc current and arc length<br />
(which is determ<strong>in</strong>ed by the position of the electrodes). Based<br />
on the study of above essential parameters, many models are<br />
set up for the purpose of harmonic and flicker analysis. In<br />
general, they may be classified as follows, a) Time doma<strong>in</strong><br />
analysis method (Characteristic Method, Time Doma<strong>in</strong><br />
Equivalent Nonl<strong>in</strong>ear Circuit Method), and b) Frequency<br />
Saji Chacko, Shri Shankaracharya College of Eng<strong>in</strong>eer<strong>in</strong>g &<br />
Technology, Department of <strong>Electric</strong>al & Electronics, Junwani, Bhilai (CG)<br />
490020, INDIA. e-mail: chackosaji68@gmail.com, Ph: +919893174845<br />
Naveen Goel, Shri Shankaracharya College of Eng<strong>in</strong>eer<strong>in</strong>g &<br />
Technology, Department of <strong>Electric</strong>al & Electronics, Junwani, Bhilai (CG)<br />
490020, INDIA. e-mail: ngoel_18@rediffmail.com. Ph: +917828699244<br />
Saji Chacko, Naveen Goel<br />
Doma<strong>in</strong> analysis method (Harmonic <strong>Voltage</strong> Source Model,<br />
Harmonic doma<strong>in</strong> Solution of nonl<strong>in</strong>ear differential<br />
equation). Each method has its own advantages and<br />
disadvantages. Comparison and commendation of different<br />
arc furnace models were presented <strong>in</strong> [1]. Most of the exist<strong>in</strong>g<br />
models make some k<strong>in</strong>ds of approximation on the<br />
characteristic of arc. There have been two general approaches<br />
to the problem of arc furnace model<strong>in</strong>g: stochastic and<br />
chaotic. In most of the previous studies, stochastic ideas are<br />
used to capture the periodic, nonl<strong>in</strong>ear, and time-vary<strong>in</strong>g<br />
behavior of arc furnaces [2]–[4]. In [2], the arc furnace load is<br />
modeled as a voltage source. The model is based on<br />
representation of the V-I characteristics us<strong>in</strong>g s<strong>in</strong>usoidal<br />
variations of arc resistance and band limited white noise. Here<br />
empirical formulas related to the arc<strong>in</strong>g process are used.<br />
Recent study shows that, the electrical fluctuations <strong>in</strong> the<br />
arc furnace voltage have proven to be chaotic <strong>in</strong> nature. Some<br />
chaos-based models reported <strong>in</strong> specialized literature [5]–[6]<br />
have been applied to simulate ac [7]-[8] and dc arc furnaces<br />
[9]. In [7] the Lorenz chaotic model has been used to<br />
represent the highly vary<strong>in</strong>g behavior of currents <strong>in</strong> an ac arc<br />
furnace and a tun<strong>in</strong>g procedure is applied to obta<strong>in</strong> the model<br />
parameters.<br />
In this work <strong>in</strong>stead of us<strong>in</strong>g s<strong>in</strong>gle valued piece-wise<br />
l<strong>in</strong>ear V-I characteristics of the arc furnace load, a dynamic<br />
and multi-valued V-I characteristics are obta<strong>in</strong>ed by us<strong>in</strong>g<br />
correspond<strong>in</strong>g differential equations [8]. The output of<br />
dynamic model developed is modulated <strong>with</strong> low frequency<br />
chaos signal to produce the arc furnace model. The model<br />
developed is connected to sample power system to study the<br />
voltage fluctuation.<br />
II. ARC FURNACE OPERATION<br />
<strong>Electric</strong> arc furnaces are available <strong>in</strong> both alternat<strong>in</strong>g current<br />
(AC) and Direct current (DC) models. A transformer directly<br />
energizes furnace electrodes <strong>in</strong> a high current circuit <strong>in</strong> arc<br />
furnaces, whereas dc furnaces employ a controlled rectifier to<br />
supply dc to the furnace electrodes. <strong>Arc</strong> furnace operation<br />
may be classified <strong>in</strong>to stages, depend<strong>in</strong>g on the status of the<br />
536
Saji et al. <strong>Voltage</strong> <strong>Sag</strong> <strong>mitigation</strong> <strong>in</strong> <strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong> <strong>with</strong> D-STATCOM<br />
melt and the time lapse from the <strong>in</strong>itial energization of the<br />
unit.<br />
Consider the case of the process<strong>in</strong>g of scrap steel <strong>in</strong> an ac<br />
EAF. Dur<strong>in</strong>g the melt<strong>in</strong>g period, pieces of steel create<br />
momentary short circuits on the secondary side of the furnace<br />
transformer. These load changes affect the arc characteristics,<br />
caus<strong>in</strong>g fluctuations of current. The current fluctuations cause<br />
variations <strong>in</strong> reactive power, which cause a momentary<br />
voltage drop or flicker, both at the supply bus and at nearby<br />
buses <strong>in</strong> the <strong>in</strong>terconnected system. The arc currents are more<br />
uniform dur<strong>in</strong>g the ref<strong>in</strong><strong>in</strong>g period and result <strong>in</strong> less impact on<br />
the power quality of the system. <strong>Arc</strong> furnaces also create<br />
harmonic load currents and asynchronous spectral<br />
components. Harmonics represent an important power quality<br />
issue, because they may cause undesirable operat<strong>in</strong>g<br />
conditions such as excess losses <strong>in</strong> transformers maloperation<br />
of drive controllers etc.[12]. Figure.1 shows typical<br />
<strong>in</strong>stallation of EAF.<br />
Substation transformer EAF transformer<br />
Transmission system<br />
xsc HV/MV<br />
MV/LV<br />
Generat<strong>in</strong>g source<br />
Xe Re<br />
<strong>Electric</strong> arc furnace<br />
Fig. 1 Typical <strong>in</strong>stallation of EAF<br />
III. CHAOTIC DYNAMICS IN ELECTRIC ARC FURNACES<br />
Chaos, also known as the strange attractor, does not<br />
generally have an accepted precise mathematical def<strong>in</strong>ition.<br />
Usually from a practical view po<strong>in</strong>t, it can be def<strong>in</strong>ed as the<br />
bounded steady-state behavior that does not fall <strong>in</strong>to the<br />
categories of the other three steady-state behaviors i.e. the<br />
equilibrium po<strong>in</strong>ts, periodic solutions, and quasi periodic<br />
solutions [6]. The equilibrium po<strong>in</strong>ts are zero dimensional<br />
and periodic solutions are one dimensional ,where as strange<br />
attractors are more complex and their dimension is a fraction.<br />
A chaotic system is a determ<strong>in</strong>istic system that exhibits<br />
random movement and it is a nonl<strong>in</strong>ear system that exhibits<br />
extreme sensitivity <strong>in</strong> the state trajectory <strong>with</strong> respect to the<br />
<strong>in</strong>itial conditions. It has been observed that the electric<br />
fluctuations <strong>in</strong> an arc furnace are chaotic <strong>in</strong> nature.<br />
The chaotic component of the arc furnace voltage is<br />
obta<strong>in</strong>ed from the chaotic circuit of Chua [8]. To exhibit<br />
chaos, the circuit consist<strong>in</strong>g of resistors capacitors and<br />
<strong>in</strong>ductors has to conta<strong>in</strong> the follow<strong>in</strong>g:<br />
(i) At least one locally active reactor<br />
(ii) At least one nonl<strong>in</strong>ear element.<br />
(iii) At least three energy storage elements<br />
Chuas circuit satisfies the above requirements.<br />
The arc furnace model is composed of two ma<strong>in</strong> parts.<br />
The first po<strong>in</strong>t is about the use of dynamic multi valued<br />
voltage current characteristic of the electric arc. The second<br />
po<strong>in</strong>t makes use of the chaotic current.<br />
The dynamic V-I characteristics of arc furnace load is<br />
obta<strong>in</strong>ed by us<strong>in</strong>g a general dynamic arc model <strong>in</strong> the form of<br />
a differential equation derived as<br />
n dr k3<br />
2<br />
k1r k2r<br />
i m<br />
2<br />
dt r<br />
where r stands for the arc radius and is chosen as the state<br />
variable. The arc voltage is given by<br />
i<br />
v <br />
g<br />
where g is def<strong>in</strong>ed as arc conductance and is given by the<br />
follow<strong>in</strong>g equation<br />
m 2<br />
r<br />
g <br />
k<br />
IV. ARC FURNACE MODEL<br />
The development of general dynamic arc model <strong>in</strong> the form<br />
of a differential equation is based on the pr<strong>in</strong>ciple of<br />
conservation of energy. The approach is fundamentally<br />
different from those methods where some empirical relation is<br />
used to represents the electrical arc. In the dynamic model<br />
such relations which are implicit for steady state conditions<br />
are not pre def<strong>in</strong>ed and gives result for different conditions<br />
depend<strong>in</strong>g on both frequency and current magnitude. Here the<br />
arc furnace is modeled <strong>in</strong> two stages. First dynamic electric<br />
arc model<strong>in</strong>g is done and the obta<strong>in</strong>ed arc voltage is then<br />
modulated <strong>with</strong> chaotic signal to produce f<strong>in</strong>al arc furnace<br />
model.<br />
The power balance equation for the arc is<br />
p p <br />
1<br />
2<br />
Where, p1 represents the power transmitted <strong>in</strong> the form of<br />
heat to the external environment, p2 represents the power,<br />
which <strong>in</strong>creases the <strong>in</strong>ternal energy <strong>in</strong> the arc, and which<br />
therefore affects its radius, and p3 represents the total power<br />
developed <strong>in</strong> the arc and converted <strong>in</strong>to heat. The above<br />
equation can be represented <strong>in</strong> the form of differential<br />
equation [10] of the arc:<br />
n dr k3<br />
2<br />
k1r k2r<br />
i m<br />
2<br />
dt r (2)<br />
Here ―r‖ stands for the arc radius which is chosen as a state<br />
variable <strong>in</strong>stead of tak<strong>in</strong>g arc resistance or conductance. The<br />
arc voltage is then given by<br />
i<br />
v (3)<br />
g<br />
Where g is def<strong>in</strong>ed as arc conductance and given by the<br />
m 2<br />
equation<br />
r<br />
g (4)<br />
k3<br />
It is possible to represent the different stages of the arc<strong>in</strong>g<br />
process by simply modify<strong>in</strong>g the parameters of m and n <strong>in</strong> (2).<br />
The complete set of comb<strong>in</strong>ation of these parameters for<br />
different stages of electric arc can be found <strong>in</strong> [7].<br />
3<br />
p<br />
3<br />
(1)<br />
537 | P a g e
<strong>International</strong> <strong>Electric</strong>al Eng<strong>in</strong>eer<strong>in</strong>g Journal (IEEJ)<br />
Vol. 2 (2011) No. 2, pp. 536-542<br />
ISSN 2078-2365<br />
N<br />
Source<br />
A<br />
B<br />
C<br />
Discrete ,<br />
Ts = 5e-005 s.<br />
A<br />
B<br />
C<br />
RL<br />
A<br />
B<br />
C<br />
RLC Load<br />
A<br />
B<br />
C<br />
A<br />
B<br />
C<br />
Vabc<br />
Measurement 1<br />
A<br />
B<br />
C<br />
a<br />
b<br />
c<br />
Sequence Analyzer 2<br />
a<br />
b<br />
c<br />
Breaker1<br />
abc<br />
Mag<br />
Phase<br />
-C-<br />
a<br />
b<br />
c<br />
A<br />
B<br />
C<br />
Measurement<br />
A<br />
B<br />
C<br />
N<br />
Vs<br />
a2<br />
b2<br />
c2<br />
a3<br />
b3<br />
c3<br />
Transformer 1<br />
Transformer<br />
Fig. 3 Control Scheme and test system us<strong>in</strong>g MATLAB/ Simul<strong>in</strong>k<br />
stics of electric <strong>Arc</strong> <strong>Furnace</strong><br />
a<br />
b<br />
c<br />
A<br />
B<br />
C<br />
Fig. 2 Dynamic characteri<br />
Conn 1<br />
Conn 2<br />
Conn 3<br />
In 1<br />
DSTATCOM1<br />
A<br />
Vabc<br />
Iabc<br />
B a<br />
C<br />
b<br />
c<br />
Measurement 2<br />
Iarc<br />
A<br />
B<br />
C<br />
Breaker<br />
a<br />
b<br />
c<br />
Ia<br />
<strong>Arc</strong>furnace Conn 3<br />
538<br />
Conn 2<br />
Conn 1
Saji et al. <strong>Voltage</strong> <strong>Sag</strong> <strong>mitigation</strong> <strong>in</strong> <strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong> <strong>with</strong> D-STATCOM<br />
The dynamic voltage/current characteristic of the<br />
electric arc furnace fig. 2 us<strong>in</strong>g the above equations is<br />
implemented us<strong>in</strong>g Simul<strong>in</strong>k blockset as shown <strong>in</strong> fig. 4. This<br />
model is then comb<strong>in</strong>ed <strong>with</strong> the band limit white noise to<br />
create the chaotic nature of the arc furnace voltage and<br />
current parameters as shown <strong>in</strong> fig. 5.<br />
Unit<br />
Delay<br />
1<br />
z<br />
1/s<br />
Integrator<br />
1 Unit<br />
z Delay<br />
1/s<br />
Integrator<br />
-K-<br />
Ga<strong>in</strong><br />
-K-<br />
f(u) Fcn2<br />
7 Ga<strong>in</strong>1<br />
1/(u^2)<br />
Fcn1<br />
Fcn<br />
(u^2)<br />
-K-<br />
Ga<strong>in</strong>2<br />
Fig. 4.Control Structure of <strong>Arc</strong> <strong>Furnace</strong><br />
f(u) Fcn2<br />
7<br />
1/(u^2)<br />
Fcn1<br />
Fcn<br />
(u^2)<br />
-K-<br />
Band-Limited<br />
White Noise<br />
In1<br />
1<br />
1<br />
In1<br />
1<br />
Fig. 5 Control Structure of <strong>Arc</strong> <strong>Furnace</strong> <strong>with</strong> Chaotic nature<br />
1<br />
Out1<br />
s<br />
+<br />
-<br />
Controlled<br />
<strong>Voltage</strong> Source<br />
1<br />
Conn1<br />
The MATLAB implementation for a 3 phase EAF model that<br />
<strong>in</strong>cludes dynamic arc model and chaotic circuit is shown <strong>in</strong><br />
Fig. 2.<br />
V. SHUNT VOLTAGE CONTROLLER:<br />
DISTRIBUTION STATIC COMPENSATOR (DSTATCOM)<br />
A D-STATCOM, which is schematically depicted <strong>in</strong> Fig. 6<br />
consists of a voltage source converter (VSC) shunt connected<br />
to the distribution network through a coupl<strong>in</strong>g transformer.<br />
This configuration allows the device to absorb or generate<br />
controllable reactive power. The D-STATCOM has been<br />
utilized for voltage regulation, correction of power factor and<br />
elim<strong>in</strong>ation of current harmonics. In distribution voltage<br />
level, the switch<strong>in</strong>g element is usually the IGBT (Integrated<br />
Gate Bipolar Transistor) due to its lower switch<strong>in</strong>g losses and<br />
reduced size.<br />
Moreover, the power rat<strong>in</strong>g of custom power devices is<br />
relatively low. Consequently, the output voltage control may<br />
be executed through PWM (Pulse Width Modulation)<br />
switch<strong>in</strong>g method.<br />
It is also capable of flicker and harmonics <strong>mitigation</strong>. A<br />
D-STATCOM is connected <strong>in</strong> parallel <strong>with</strong> the distribution<br />
feeder. It generates a current <strong>in</strong>jection, which is summed to<br />
the non-s<strong>in</strong>usoidal load current. Thus the phase currents<br />
taken from the grid will be nearly s<strong>in</strong>e wave. If<br />
D-STATCOM does not conta<strong>in</strong> any active power storage it<br />
only <strong>in</strong>jects or draws reactive power. Limited voltage sag<br />
<strong>mitigation</strong> is possible <strong>with</strong> the <strong>in</strong>jection of reactive power<br />
only, but active power is needed if both magnitude and phase<br />
angle of the pre-event voltage need to be kept constant. The<br />
device rat<strong>in</strong>g determ<strong>in</strong>es the maximum total current which<br />
can be <strong>in</strong>jected. In case an energy storage is connected to the<br />
D-STATCOM its capacity also needs to be rated.<br />
D-STATCOM equipped <strong>with</strong> energy storage and additional<br />
high-speed switchgear is able to <strong>in</strong>ject also active power and<br />
thus support the load even dur<strong>in</strong>g an <strong>in</strong>terruption on the grid<br />
side. The steady state model of analyz<strong>in</strong>g the rms voltages<br />
and currents, fundamental frequency power and energy<br />
flows, applies to D-STATCOM.<br />
Operat<strong>in</strong>g modes of D-STATCOM<br />
This is shunt connected device operates <strong>in</strong> two control<br />
modes<br />
Current Control: In this mode D-STATCOM acts as active<br />
filter, power factor controller, load balance etc. These<br />
functions are called load compensation.<br />
<strong>Voltage</strong> Control: In this mode a D-STATCOM can regulate<br />
voltage aga<strong>in</strong>st any distortion, <strong>Sag</strong>/ Swells, unbalance and<br />
even short duration <strong>in</strong>terruptions.<br />
<strong>Voltage</strong> <strong>Sag</strong> Correction by D-STATCOM<br />
The schematic diagram of a D-STATCOM is shown <strong>in</strong><br />
Fig. 3. In this diagram, the shunt <strong>in</strong>jected current corrects the<br />
voltage sag by adjust<strong>in</strong>g the voltage drop across the system<br />
impedance Z. The value of current can be controlled by<br />
adjust<strong>in</strong>g the output voltage of the converter. The shunt<br />
<strong>in</strong>jected current can be written as:<br />
Vth jX th<br />
Rth L V<br />
Is<br />
D-STATCOM<br />
volate source<br />
converter<br />
Energy storage<br />
Fig. 6 Schematic representation of the D-STATCOM<br />
Ish = (IL – IS ) = IL – (VTH / ZTH ) ……….(1)<br />
VL = VL<br />
Ish = Ish ∠η<br />
Ish<br />
PL jQL<br />
539 | P a g e
<strong>International</strong> <strong>Electric</strong>al Eng<strong>in</strong>eer<strong>in</strong>g Journal (IEEJ)<br />
Vol. 2 (2011) No. 2, pp. 536-542<br />
ISSN 2078-2365<br />
IL = IL ∠-φ<br />
VTH = VTH ∠δ<br />
ZTH = ZTH ∠β<br />
Put this value <strong>in</strong> equation (1)<br />
ISh∠η= IL∠- φ – (VTH ∠δ - VL ∠0) / ZTH ∠ β)<br />
ISh∠η= IL∠- φ – (VTH ∠(δ- β ) / ZTH ) + (VL ∠- β )/ ZTH<br />
………….………..(2)<br />
The complex power <strong>in</strong>jection of the D-STATCOM can be<br />
expressed as<br />
SSh = VL ISh * ……………….…….. (3)<br />
It may be mentioned here that the effectiveness of the<br />
D-STATCOM <strong>in</strong> correct<strong>in</strong>g voltage sag depends on the value<br />
of Z or fault level of the load bus. When the shunt <strong>in</strong>jected<br />
current I is kept <strong>in</strong> quadrature <strong>with</strong> the desired voltage<br />
correction can aga<strong>in</strong> be achieved <strong>with</strong>out <strong>in</strong>ject<strong>in</strong>g any active<br />
power <strong>in</strong>to the system. On the other hand when the value of is<br />
m<strong>in</strong>imized, the same voltage correction can be achieved <strong>with</strong><br />
m<strong>in</strong>imum apparent power <strong>in</strong>jection <strong>in</strong>to the system [18-19].<br />
<strong>Voltage</strong> (pu)<br />
1.4<br />
1.2<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
Time(sec)<br />
Fig. 7 S<strong>in</strong>gle Phase System <strong>Voltage</strong> (pu) <strong>with</strong>out Statcom<br />
Current (pu)<br />
<strong>Arc</strong> current (pu)<br />
500<br />
400<br />
300<br />
200<br />
100<br />
0<br />
-100<br />
-200<br />
-300<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
1.5<br />
0.5<br />
-0.5<br />
x 104<br />
2<br />
1<br />
0<br />
Time (sec)<br />
Fig. 8 S<strong>in</strong>gle phase System Current <strong>with</strong>out Statcom<br />
-1<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
Time (sec)<br />
Fig. 9 <strong>Arc</strong> <strong>Furnace</strong> Current <strong>with</strong>out Statcom<br />
540
Saji et al. <strong>Voltage</strong> <strong>Sag</strong> <strong>mitigation</strong> <strong>in</strong> <strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong> <strong>with</strong> D-STATCOM<br />
Current (pu)<br />
<strong>Voltage</strong> (pu)<br />
<strong>Arc</strong> Current (pu)<br />
1.4<br />
1.2<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
500<br />
400<br />
300<br />
200<br />
100<br />
0<br />
-100<br />
-200<br />
Time (sec)<br />
Fig.10 System <strong>Voltage</strong> of s<strong>in</strong>gle phase <strong>with</strong> Statcom<br />
-300<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
x 106<br />
1.5<br />
1<br />
0.5<br />
0<br />
-0.5<br />
-1<br />
Time (sec)<br />
Fig. 11 System Current of S<strong>in</strong>gle phase <strong>with</strong> Statcom<br />
-1.5<br />
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8<br />
Time (sec)<br />
Fig. 12 <strong>Arc</strong> <strong>Furnace</strong> Current <strong>with</strong> Statcom<br />
VI. CONCLUSION<br />
The ma<strong>in</strong> aim of this Paper is to try to f<strong>in</strong>d out the types of<br />
power disturbances that are occurr<strong>in</strong>g <strong>in</strong> power distribution<br />
system, ma<strong>in</strong>ly due to nonl<strong>in</strong>ear loads <strong>with</strong> special emphasis<br />
on the <strong>Arc</strong> furnace loads. These loads not only <strong>in</strong>troduce<br />
harmonic <strong>in</strong> the power l<strong>in</strong>es but also cause heavy voltage sag<br />
and affect the work<strong>in</strong>g of Critical drive equipments<br />
connected to the Po<strong>in</strong>t of Common Coupl<strong>in</strong>g (PCC). The<br />
paper presents the modell<strong>in</strong>g of arc furnace loads and its<br />
implement<strong>in</strong>g us<strong>in</strong>g MATLAB/Simul<strong>in</strong>k, its effect on the<br />
Power system and how the use of voltage compensation<br />
devices like D-STATCOM improves the voltage stability.<br />
APPENDIX<br />
Parameters of EAF model and sample power system are as<br />
follows,<br />
Source: Ideal s<strong>in</strong>usoidal ac voltage source <strong>with</strong><br />
amplitude=50.6 kV and zero phase shift.<br />
Z Theven<strong>in</strong>: Resistance=0.346 and <strong>in</strong>ductance, L=9.8mH.<br />
Transformer: Three w<strong>in</strong>d<strong>in</strong>gs l<strong>in</strong>ear s<strong>in</strong>gle-phase<br />
transformer.<br />
Nom<strong>in</strong>al power: Pn=60 MVA.<br />
W<strong>in</strong>d<strong>in</strong>g 1 parameters: V1 (Vrms)=46 kV,<br />
R1 (pu)=0.002, L1 (pu)=0.55,<br />
W<strong>in</strong>d<strong>in</strong>g 2 parameters: V2 (Vrms)=770 V,<br />
R2 (pu)=0.002, L2 (pu)=0.55,<br />
Magnetization resistance and reactance: Rm(pu)=500<br />
Lm(pu)=500<br />
<strong>Arc</strong> <strong>Furnace</strong>: (Parameters for correspond<strong>in</strong>g differential<br />
equation) k1=3000.0,k2=1.0,k3=12.5 m=0,n=2.<br />
(Chua’s circuit) C1=200nF,C2=0.2 F,L=3.6m H <strong>with</strong> a<br />
series resistor Ro=12.5,G=5.442E-4 mho.<br />
541 | P a g e
<strong>International</strong> <strong>Electric</strong>al Eng<strong>in</strong>eer<strong>in</strong>g Journal (IEEJ)<br />
Vol. 2 (2011) No. 2, pp. 536-542<br />
ISSN 2078-2365<br />
REFERENCES<br />
[1] T. Zheng, E. B. Makram, and A. A. Girgis, ―Effect of different arc<br />
furnace models on voltage distortion,‖ <strong>in</strong> Proceed<strong>in</strong>gs of the Eighth<br />
<strong>International</strong> Conference on Harmonics and Quality of Power<br />
(ICHPQ), Oct.1998, Pp. 1079–1085<br />
[2] R. C.Bellido and T. Gomez, ―Identification and model<strong>in</strong>g of a three<br />
phase arc furnace for voltage disturbance systems,‖ IEEE Trans.<br />
PWRD. Vol. 12, Pp. 1812–1817, Oct. 1997.<br />
[3] G. C. Montanari, M. Logg<strong>in</strong>i, A. Cavall<strong>in</strong>i, L. Pitti, and D. Zanielli,<br />
―<strong>Arc</strong> furnace model for the study of flicker compensation <strong>in</strong><br />
electrical networks‖ IEEE Trans. Power Delivery, Vol. 8, Pp.<br />
2026–2036, Oct. 1994.<br />
[4] S. Varadan, E. B. Makram, and A. A. Girgis, ―A new time doma<strong>in</strong><br />
voltage source model for an arc furnace us<strong>in</strong>g EMTP,‖ IEEE Trans.<br />
Power Delivery, Vol. 11, Pp. 1685–1690, July 1996.<br />
[5] M. P. Kennedy, ―Three steps to chaos, Part 1:Evolution,‖ IEEE<br />
Trans. Circuit Syst. I, vol. 40, no. 10, Pp. 640–656, October 1993.<br />
[6] M. P. Kennedy ―Three steps to chaos, Part 2:A Chua’s circuit<br />
primer,‖ IEEE Trans. Circuits Syst. I, Vol. 40, pp. 657–674, Oct.<br />
1993.<br />
[7] E. O’Neill-Carrillo, G. Heydt, E. J. Kostelich, S. S. Venkata, and<br />
A.Sundaram, ―Nonl<strong>in</strong>ear determ<strong>in</strong>istic model<strong>in</strong>g of highly vary<strong>in</strong>g<br />
loads,‖ IEEE Trans. Power Delivery, Vol. 14, pp. 537–542, Apr.<br />
1999.<br />
[8] O. Ozgun and A. Abur, ―Development of an arc furnace model for<br />
power quality studies,‖ Proc. IEEE-PES Summer Meet<strong>in</strong>g 1999,<br />
Vol. 1, Pp. 507–511, 1999.<br />
[9] G. Carp<strong>in</strong>elli, F. Iacovone, A. Russo, P. Verde, and D. Zan<strong>in</strong>elli,<br />
―DC arc furnaces: Comparison of arc models to evaluate waveform<br />
distortion and voltage fluctuations,‖ <strong>in</strong> Proc. IEEE Power<br />
Eng<strong>in</strong>eer<strong>in</strong>g Society 33rd Annual North America Power Symp., Pp.<br />
574–580<br />
[10] E. Acha, A. Semlyen, and N. Rajakovic, ―A harmonic doma<strong>in</strong><br />
computational Package for nonl<strong>in</strong>ear problems and its application<br />
to electric arcs,‖ IEEE Trans. Power Delivery, Vol. 5, Pp.<br />
1390–1397, July 1990.<br />
[11] M.M. Morcos, J.C. Gomez “Flicker Sources and Mitigation” IEEE<br />
Power Eng<strong>in</strong>eer<strong>in</strong>g Review, November 2002 P 5-10<br />
[12] M. H. J. Bollen, ―Understand<strong>in</strong>g Power Quality<br />
Problems—<strong>Voltage</strong> <strong>Sag</strong>s and Interruptions‖ Piscataway, New<br />
York: IEEE Press 2000.<br />
[13] O. Ozgun, A Abur ―Flicker study us<strong>in</strong>g a Novel <strong>Arc</strong> <strong>Furnace</strong><br />
Model‖ IEEE Trans. on PWRD, Vol. 17, No. 4, Oct-2002 pp.<br />
1158-1163<br />
[14] Adly A. Girgis, Jhon Stephens and Elam B. Makram<br />
―Measurement and prediction of voltage flicker magnitude and<br />
frequency,‖ IEEE Trans. on Power Delivery, July 1995.<br />
[15] S<strong>in</strong>gh G.K., ―Power System Harmonics Research: A Survey‖,<br />
European Transaction on <strong>Electric</strong>al Power, 2009, 19:151-172.<br />
[16] K. Anuradha, Muni B.P., Rajkumar A.D., ―<strong>Electric</strong> <strong>Arc</strong> <strong>Furnace</strong><br />
Model<strong>in</strong>g and <strong>Voltage</strong> Flicker Mitigation by D Statcom‖, IEEE<br />
Region 10 Collogium and the third ICIIS, Kharagpur, India,<br />
December 8-10, 2008<br />
[17] Chiang H., Liu C., Varaiya P.P., wu F., Lauby M.G. ― Chaos <strong>in</strong> a<br />
Simple Power System‖, IEEE Transaction on Power System, Vol.<br />
8, No. 4, Pp. 1407-1471,Nov.1993<br />
[18] Sung-M<strong>in</strong> Woo, Dae-Wook Kang and Woo-Chol Lee, ―The<br />
Distribution STATCOM for reduc<strong>in</strong>g the Effect of <strong>Voltage</strong> <strong>Sag</strong> and<br />
Swell‖ IECON’01: The 27 th Annual Conference of the IEEE<br />
Industrial Electronic Society, Pages 17-22, 2001<br />
[19] Ar<strong>in</strong>dam Ghosh, and Gerard Ledwich ―Compensation of<br />
Distribution System <strong>Voltage</strong> Us<strong>in</strong>g DVR‖, IEEE Transactions on<br />
Power Delivery, Vol. 17, No. 4, October 2002.<br />
542