International Electrical Engineering Journal (IEEJ)
Vol. 2 (2011) No. 2, pp. 536-542
ISSN 2078-2365
Voltage Sag mitigation in Electric Arc Furnace
with D-STATCOM
Saji Chacko, Naveen Goel

Abstract— Arc furnace represents one of the most intensive
and disturbing loads in the electric power system. Utilities are
concerned about these effects and try to take precautions to
minimize them. Therefore, an accurate model of an arc furnace
is needed to test and verify proposed solutions to this end. This
paper, presents the results of a study, where furnace arc is
modeled using both chaotic and deterministic elements. Voltage
fluctuations (Sag), is captured using the well-studied circuit
whereas a dynamic model in the form of differential equation is
used for the electric arc. Simulation of developed model is done
in Sim-Power-System environment of the MATLAB 7.1
Version.
Index Terms— Electric Arc Furnace, Simulink, Voltage
Flicker
I. INTRODUCTION
Electric Arc Furnace (EAF) is a widely used device in
metallurgical and processing industries. It is a nonlinear time
varying load, which can cause many problems to the power
system quality such as unbalance, harmonic inter harmonic
and voltage flicker. Thus study of electric arc furnaces has
potential benefits for both customers and utilities. An accurate
modeling of an EAF will help in dealing with the problems
caused by its operation. Minimization of the undesirable
impact of EAFs can improve electric efficiency and reduce
power fluctuations in the system.
The description of an arc furnace load depends on the
following parameters: arc voltage, arc current and arc length
(which is determined by the position of the electrodes). Based
on the study of above essential parameters, many models are
set up for the purpose of harmonic and flicker analysis. In
general, they may be classified as follows, a) Time domain
analysis method (Characteristic Method, Time Domain
Equivalent Nonlinear Circuit Method), and b) Frequency
Saji Chacko, Shri Shankaracharya College of Engineering &
Technology, Department of Electrical & Electronics, Junwani, Bhilai (CG)
490020, INDIA. e-mail: chackosaji68@gmail.com, Ph: +919893174845
Naveen Goel, Shri Shankaracharya College of Engineering &
Technology, Department of Electrical & Electronics, Junwani, Bhilai (CG)
490020, INDIA. e-mail: ngoel_18@rediffmail.com. Ph: +917828699244
Domain analysis method (Harmonic Voltage Source Model,
Harmonic domain Solution of nonlinear differential
equation). Each method has its own advantages and
disadvantages. Comparison and commendation of different
arc furnace models were presented in [1]. Most of the existing
models make some kinds of approximation on the
characteristic of arc. There have been two general approaches
to the problem of arc furnace modeling: stochastic and
chaotic. In most of the previous studies, stochastic ideas are
used to capture the periodic, nonlinear, and time-varying
behavior of arc furnaces [2]–[4]. In [2], the arc furnace load is
modeled as a voltage source. The model is based on
representation of the V-I characteristics using sinusoidal
variations of arc resistance and band limited white noise. Here
empirical formulas related to the arcing process are used.
Recent study shows that, the electrical fluctuations in the
arc furnace voltage have proven to be chaotic in nature. Some
chaos-based models reported in specialized literature [5]–[6]
have been applied to simulate ac [7]-[8] and dc arc furnaces
[9]. In [7] the Lorenz chaotic model has been used to
represent the highly varying behavior of currents in an ac arc
furnace and a tuning procedure is applied to obtain the model
parameters.
In this work instead of using single valued piece-wise
linear V-I characteristics of the arc furnace load, a dynamic
and multi-valued V-I characteristics are obtained by using
corresponding differential equations [8]. The output of
dynamic model developed is modulated with low frequency
chaos signal to produce the arc furnace model. The model
developed is connected to sample power system to study the
voltage fluctuation.
II. ARC FURNACE OPERATION
Electric arc furnaces are available in both alternating current
(AC) and Direct current (DC) models. A transformer directly
energizes furnace electrodes in a high current circuit in arc
furnaces, whereas dc furnaces employ a controlled rectifier to
supply dc to the furnace electrodes. Arc furnace operation
may be classified into stages, depending on the status of the
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Saji et al. Voltage Sag mitigation in Electric Arc Furnace with D-STATCOM
melt and the time lapse from the initial energization of the
unit.
Consider the case of the processing of scrap steel in an ac
EAF. During the melting period, pieces of steel create
momentary short circuits on the secondary side of the furnace
transformer. These load changes affect the arc characteristics,
causing fluctuations of current. The current fluctuations cause
variations in reactive power, which cause a momentary
voltage drop or flicker, both at the supply bus and at nearby
buses in the interconnected system. The arc currents are more
uniform during the refining period and result in less impact on
the power quality of the system. Arc furnaces also create
harmonic load currents and asynchronous spectral
components. Harmonics represent an important power quality
issue, because they may cause undesirable operating
conditions such as excess losses in transformers maloperation
of drive controllers etc.[12]. Figure.1 shows typical
installation of EAF.
Transmission system
xsc
Substation transformer
HV/MV
EAF transformer
MV/LV
Xe
Re
Generating source
Electric arc furnace
Fig. 1 Typical installation of EAF
III. CHAOTIC DYNAMICS IN ELECTRIC ARC FURNACES
Chaos, also known as the strange attractor, does not
generally have an accepted precise mathematical definition.
Usually from a practical view point, it can be defined as the
bounded steady-state behavior that does not fall into the
categories of the other three steady-state behaviors i.e. the
equilibrium points, periodic solutions, and quasi periodic
solutions [6]. The equilibrium points are zero dimensional
and periodic solutions are one dimensional ,where as strange
attractors are more complex and their dimension is a fraction.
A chaotic system is a deterministic system that exhibits
random movement and it is a nonlinear system that exhibits
extreme sensitivity in the state trajectory with respect to the
initial conditions. It has been observed that the electric
fluctuations in an arc furnace are chaotic in nature.
The chaotic component of the arc furnace voltage is
obtained from the chaotic circuit of Chua [8]. To exhibit
chaos, the circuit consisting of resistors capacitors and
inductors has to contain the following:
(i) At least one locally active reactor
(ii) At least one nonlinear element.
(iii) At least three energy storage elements
Chuas circuit satisfies the above requirements.
The arc furnace model is composed of two main parts.
The first point is about the use of dynamic multi valued
voltage current characteristic of the electric arc. The second
point makes use of the chaotic current.
The dynamic V-I characteristics of arc furnace load is
obtained by using a general dynamic arc model in the form of
a differential equation derived as
k1r n  k2 r
dr
k
 m3 2 i 2
dt r
where r stands for the arc radius and is chosen as the state
variable. The arc voltage is given by
i
v
g
where g is defined as arc conductance and is given by the
following equation
g
r m 2
k3
IV. ARC FURNACE MODEL
The development of general dynamic arc model in the form
of a differential equation is based on the principle of
conservation of energy. The approach is fundamentally
different from those methods where some empirical relation is
used to represents the electrical arc. In the dynamic model
such relations which are implicit for steady state conditions
are not pre defined and gives result for different conditions
depending on both frequency and current magnitude. Here the
arc furnace is modeled in two stages. First dynamic electric
arc modeling is done and the obtained arc voltage is then
modulated with chaotic signal to produce final arc furnace
model.
The power balance equation for the arc is
p1  p2  p3
(1)
Where, p1 represents the power transmitted in the form of
heat to the external environment, p2 represents the power,
which increases the internal energy in the arc, and which
therefore affects its radius, and p3 represents the total power
developed in the arc and converted into heat. The above
equation can be represented in the form of differential
equation [10] of the arc:
k1r n  k2 r
dr
k
 m3 2 i 2
dt r
(2)
Here ―r‖ stands for the arc radius which is chosen as a state
variable instead of taking arc resistance or conductance. The
arc voltage is then given by
i
(3)
v
g
Where g is defined as arc conductance and given by the
m 2
equation g  r
(4)
k3
It is possible to represent the different stages of the arcing
process by simply modifying the parameters of m and n in (2).
The complete set of combination of these parameters for
different stages of electric arc can be found in [7].
537 | P a g e
International Electrical Engineering Journal (IEEJ)
Vol. 2 (2011) No. 2, pp. 536-542
ISSN 2078-2365
Fig. 2 Dynamic characteri
Ia
-CVs
Conn 2
Sequence Analyzer 2
abc
A
B
B
B
B
DSTATCOM1
A
a
N
C
Source
C
C
C
b
B
c
C
c2
A Vabc
Iabc
B
a
b
C
c
a3
Measurement 2
a2
b2
b3
Measurement 1
RL
Iarc
Vabc
N
A
B
C
a
b
c
Breaker
c3
Transformer 1
Arcfurnace
Discrete ,
Ts = 5e-005 s.
Transformer
A
A
a
a
A
a
A
B
B
b
b
B
b
B
C
c
c
C
c
C
C
RLC Load
Breaker1
Measurement
Fig. 3 Control Scheme and test system using MATLAB/ Simulink
stics of electric Arc Furnace
538
Conn 1
A
Mag
Phase
Conn 2
A
In 1
Conn 3
Conn 3
A
Conn 1
Saji et al. Voltage Sag mitigation in Electric Arc Furnace with D-STATCOM
The dynamic voltage/current characteristic of the
electric arc furnace fig. 2 using the above equations is
implemented using Simulink blockset as shown in fig. 4. This
model is then combined with the band limit white noise to
create the chaotic nature of the arc furnace voltage and
current parameters as shown in fig. 5.
Unit
Delay
1/s
1/(u^2)
Integrator
Fcn1
1
Out1
Gain2
f(u) Fcn2
Gain -K-
1
-K-
z
7
Gain1
Fcn
In1
1
(u^2)
Fig. 4.Control Structure of Arc Furnace
1/s
1/(u^2)
Integrator
1
z
Unit
Delay
-K-
-
1
f(u) Fcn2
-K-
Operating modes of D-STATCOM
s
Fcn1
+
Controlled
Voltage Source
1
Conn1
Band-Limited
White Noise
7
Fcn
(u^2)
taken from the grid will be nearly sine wave. If
D-STATCOM does not contain any active power storage it
only injects or draws reactive power. Limited voltage sag
mitigation is possible with the injection of reactive power
only, but active power is needed if both magnitude and phase
angle of the pre-event voltage need to be kept constant. The
device rating determines the maximum total current which
can be injected. In case an energy storage is connected to the
D-STATCOM its capacity also needs to be rated.
D-STATCOM equipped with energy storage and additional
high-speed switchgear is able to inject also active power and
thus support the load even during an interruption on the grid
side. The steady state model of analyzing the rms voltages
and currents, fundamental frequency power and energy
flows, applies to D-STATCOM.
In1
1
Fig. 5 Control Structure of Arc Furnace with Chaotic nature
The MATLAB implementation for a 3 phase EAF model that
includes dynamic arc model and chaotic circuit is shown in
Fig. 2.
V. SHUNT VOLTAGE CONTROLLER:
DISTRIBUTION STATIC COMPENSATOR (DSTATCOM)
A D-STATCOM, which is schematically depicted in Fig. 6
consists of a voltage source converter (VSC) shunt connected
to the distribution network through a coupling transformer.
This configuration allows the device to absorb or generate
controllable reactive power. The D-STATCOM has been
utilized for voltage regulation, correction of power factor and
elimination of current harmonics. In distribution voltage
level, the switching element is usually the IGBT (Integrated
Gate Bipolar Transistor) due to its lower switching losses and
reduced size.
Moreover, the power rating of custom power devices is
relatively low. Consequently, the output voltage control may
be executed through PWM (Pulse Width Modulation)
switching method.
It is also capable of flicker and harmonics mitigation. A
D-STATCOM is connected in parallel with the distribution
feeder. It generates a current injection, which is summed to
the non-sinusoidal load current. Thus the phase currents
This is shunt connected device operates in two control
modes
Current Control: In this mode D-STATCOM acts as active
filter, power factor controller, load balance etc. These
functions are called load compensation.
Voltage Control: In this mode a D-STATCOM can regulate
voltage against any distortion, Sag/ Swells, unbalance and
even short duration interruptions.
Voltage Sag Correction by D-STATCOM
The schematic diagram of a D-STATCOM is shown in
Fig. 3. In this diagram, the shunt injected current corrects the
voltage sag by adjusting the voltage drop across the system
impedance Z. The value of current can be controlled by
adjusting the output voltage of the converter. The shunt
injected current can be written as:
Vth
jX th
Rth
VL
I sh
Is
volate source
converter
PL  jQL
D-STATCOM
Energy storage
Fig. 6 Schematic representation of the D-STATCOM
Ish = (IL – IS ) = IL – (VTH / ZTH ) ……….(1)
VL = V L
Ish = Ish ∠η
539 | P a g e
International Electrical Engineering Journal (IEEJ)
Vol. 2 (2011) No. 2, pp. 536-542
ISSN 2078-2365
500
VTH = VTH ∠δ
400
ZTH = ZTH ∠β
300
Put this value in equation (1)
ISh∠η= IL∠- φ – (VTH ∠δ - VL ∠0) / ZTH ∠ β)
ISh∠η= IL∠- φ – (VTH ∠(δ- β ) / ZTH ) + (VL ∠- β )/ ZTH
………….………..(2)
The complex power injection of the D-STATCOM can be
expressed as
Current (pu)
IL = IL ∠-φ
200
100
0
-100
-200
-300
SSh = VL ISh * ……………….…….. (3)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (sec)
1.4
1.2
Fig. 8 Single phase System Current without Statcom
4
2
x 10
1.5
Arc current (pu)
It may be mentioned here that the effectiveness of the
D-STATCOM in correcting voltage sag depends on the value
of Z or fault level of the load bus. When the shunt injected
current I is kept in quadrature with the desired voltage
correction can again be achieved without injecting any active
power into the system. On the other hand when the value of is
minimized, the same voltage correction can be achieved with
minimum apparent power injection into the system [18-19].
1
0.5
0
Voltage (pu)
1
-0.5
0.8
-1
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (sec)
0.4
Fig. 9 Arc Furnace Current without Statcom
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time(sec)
Fig. 7 Single Phase System Voltage (pu) without Statcom
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Saji et al. Voltage Sag mitigation in Electric Arc Furnace with D-STATCOM
VI. CONCLUSION
1.4
1.2
The main aim of this Paper is to try to find out the types of
power disturbances that are occurring in power distribution
system, mainly due to nonlinear loads with special emphasis
on the Arc furnace loads. These loads not only introduce
harmonic in the power lines but also cause heavy voltage sag
and affect the working of Critical drive equipments
connected to the Point of Common Coupling (PCC). The
paper presents the modelling of arc furnace loads and its
implementing using MATLAB/Simulink, its effect on the
Power system and how the use of voltage compensation
devices like D-STATCOM improves the voltage stability.
Voltage (pu)
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (sec)
Fig.10 System Voltage of single phase with Statcom
APPENDIX
500
Parameters of EAF model and sample power system are as
follows,
Source: Ideal sinusoidal ac voltage source with
amplitude=50.6 kV and zero phase shift.
Z Thevenin: Resistance=0.346 and inductance, L=9.8mH.
Transformer: Three windings linear single-phase
transformer.
Nominal power: Pn=60 MVA.
Winding 1 parameters: V1 (Vrms)=46 kV,
R1 (pu)=0.002, L1 (pu)=0.55,
Winding 2 parameters: V2 (Vrms)=770 V,
R2 (pu)=0.002, L2 (pu)=0.55,
Magnetization resistance and reactance: Rm(pu)=500
Lm(pu)=500
Arc Furnace: (Parameters for corresponding differential
equation) k1=3000.0,k2=1.0,k3=12.5 m=0,n=2.
(Chua’s circuit) C1=200nF,C2=0.2 F,L=3.6m H with a
series resistor Ro=12.5,G=5.442E-4 mho.
400
Current (pu)
300
200
100
0
-100
-200
-300
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (sec)
Fig. 11 System Current of Single phase with Statcom
6
1.5
x 10
Arc Current (pu)
1
0.5
0
-0.5
-1
-1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (sec)
Fig. 12 Arc Furnace Current with Statcom
541 | P a g e
International Electrical Engineering Journal (IEEJ)
Vol. 2 (2011) No. 2, pp. 536-542
ISSN 2078-2365
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