Download International Electrical Engineering Journal (IEEJ) Vol. 5 (2014) No.10, pp. 1559-1566

International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
Improved Performance of Chaotic
Model of AC Electric Arc Furnace Using
Unified Power Quality Conditioner
A Sai Pavani, A.Rama Devi
[email protected]
Abstract—For improvement of power quality (PQ) problems in
a three-phase distribution system, two topologies are proposed.
Electric arc furnaces (EAFs) are a main cause of voltage flicker
due to the interaction of the high demand currents of the loads
with the supply system impedance. In order to adequately
understand and analyze the effects on the power system from
these loads, obtaining an accurate representation of the
characteristics of the loads is crucial. In this paper, a mixed
chaotic EAF model to represent the low frequency and high
frequency variations of the arc current respectively and a
chain-shaped chaotic EAF model to characterize the current
variation have been proposed by using UPQC model. The
concept of chaotic parameters, such as chaotic resistance,
inductance or admittance has been also proposed for the
characterization of arc furnace operation and the highly
nonlinear physical processes. Then, a dynamic model based on
static model created previous is built to simulate AC electric
arc furnace dynamic characteristics and for these concerns
utilize a back-back compensation scheme is preferred to
maintain power quality standards. The dynamic analysis of
this proposed system is evaluated with the help of
Matlab/Simulink environment and results are conferred.
Index Terms— AC electric arc furnace model, Dynamic
Voltage Restorer, Distributed compensator, power quality,
Unified Power Quality Conditioner
I. INTRODUCTION
Power quality determines the fitness of electrical
power to consumer devices. Synchronization of the voltage
frequency and phase allows electrical systems to function in
their intended manner without significant loss of
performance or life. The term is used to describe electric
power that drives an electrical load and the load's ability to
function properly. Without the proper power, an electrical
device (or load) may malfunction, fail prematurely or not
operate at all. There are many ways in which electric power
can be of poor quality and many more causes of such poor
quality power. The term power quality has become one of
the most prolific buzzwords in the power industry since the
late 1980s. 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 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. The proposed model can be connected to
the power system as a controlled voltage source directly,
which is useful for harmonics and voltage flicker studies
II. EAF EQUIVALENT SYSTEM
The main discussion in this paper relates to AC electric arc
furnaces, although a similar modeling approach is possible
1559
Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
for dc furnaces. Electric arc furnace operation may be
classified into several stages, depending on the melting
status and the time lapse from the initial energization of the
unit. During the melting period, sets of steel nearly create a
short circuit on the secondary side of the furnace
transformer, and it creates large fluctuations of current at
low power factors. These 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.
A typical and detailed arc furnace structure is shown in Fig.
1. It includes a system equivalent at substation bus S,
substation transformer Ts, cable run to furnace D1, power
factor correction equipment C, arc furnace transformer Ta,
flexible cables D2, bus conductors B, graphite electrodes G
and the melting vessel M.
III. THE STATIC ARC FURNACE MODEL
Typical V− I characteristic of arc furnace load am shown in
Fig.3. Where, V is the arc voltage, i is the arc current, Vig
and Vex are the ignition voltage and extinction voltage of the
arc in the first quadrant respectively, iig and iex are the
currents correspond to Vig and vex respectively, r1and r2are
the slopes of segments BA and AC(DB) respectively. The
piece-wise linear approximation of the V−I characteristic
curve is defined in terms of equation (1).
(1)
Where,
(2)
Fig. 1 Structure of a Typical Arc Furnace
In order to analyze the arc process and the interaction
between the arc furnace and power system, a mathematical
simplification of the given system is performed. The
simplification in Fig. 2 is reasonable because the mechanical
process is much slower than the electrical dynamics.
Fig.3. Actual and piece-wise linear approximation of v-i characteristic
curve of arc furnace load
(3)
In Fig.3, the active power P consumed by an arc furnace is
equal to the area under the piece wise linear v-I
characteristic curve, which is defined as equation (4).
Fig. 2 Circuit Representation of the Arc Furnace
In Fig. 2, R1and L1represent the resistance and the reactance
of power system at substation level, the substation
transformer winding and the cable run to the furnace
transformer, and R2and L2 represents the resistance and the
reactance of the flexible cables, the bus conductors and the
graphite electrodes. The dynamic variation of arc resistance
and inductance is represented by Rf and Lf, and both
nonlinear variables are time varying and bounded.
(4)
(5)
The static arc furnace model may be obtained from a
combination of equation (1) and (5).
1560
Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
IV. THE DYNAMIC ARC FURNACE MODEL
We use the chaotic signal to modulate the static arc voltage
to describe the dynamic behavior of arc furnace; the chaotic
signal is generated via asymmetric nonlinear Chua’s circuit.
Chua’s circuit is a simple and typical third-order
autonomous circuit for generating bifurcations and chaos.
The double-scroll strange attractor is observed in Chua’s
circuit, which has been proved mathematically by
Shil’nikov theorem. Varying the value of linear resistor R in
the circuit, rich variety dynamical behaviors may be
observed, such as DC equilibrium point, Hopf bifurcation,
period-doubling bifurcation, single-scroll strange attractor,
periodic windows, and double-scroll strange attractor. Note
that the circuit is able to generate chaotic signal at any
frequency by scaling the values of the energy-storage
elements. Therefore using the chaotic phenomenon in
Chua’s circuit to simulate the actual chaotic system is a
practical feasible modeling method. For accurately
describing the asymmetric double-scroll strange attractor, an
asymmetric nonlinear Chua’s circuit is proposed.
Choosing VC1, VC2and iL as state variables, with Kichh off
voltage law and current law, the state equations of the
proposed Chua’s circuit are obtained.
(6)
Where, G=1/R
(7)
In contrast with the general Chua’s circuit, note that Gb≠Gc
in asymmetric nonlinear Chua’s circuit.
B. The Dynamic Model of Arc Furnace
Here, we use the chaotic signal to modulate the static arc
voltage to describe the dynamic behavior of arc furnace.
(8)
Where Vd is the dynamic arc voltage, Vs is the static arc
voltage, Vchaotic is the chaotic signal.
V. SEVERAL COMPENSATION SCHEMES
Fig.4. Asymmetric nonlinear Chua’s circuit: (a) the diagram of asymmetric
nonlinear Chua’s circuit and (b) the i v− characteristic of Nr.
A. Asymmetric Nonlinear Chua’s Circuit
An asymmetric nonlinear Chua’s circuit is shown in Fig.4
(a). It consists of a linear inductor L, two linear capacitors
C1 and C2, a linear resistor R, and a voltage–controlled
asymmetric nonlinear resistive element Nr. vC1, vC2are the
voltages across capacitors C1and C2respectively, iL is the
current through inductor L, and iris the current through
asymmetric nonlinear resistive element Nr. The v−i
characteristic of Nr is shown in Fig.4 (b).
Power quality is an issue that is becoming increasingly
important to electricity consumers at all levels of usage.
Sensitive power electronic equipment and non-linear loads
are widely used in industrial, commercial and domestic
applications leading to distortion in voltage and current
waveforms. Both electric utilities and end users of electric
power are becoming increasingly concerned about the
quality of electric power.
A. Dynamic Voltage Restorer
Switching off a large inductive load or Energizing a large
capacitor bank is a typical system event that causes swells.
Then, a simple control based on dqo method is used to
compensate
voltage
sags/swell.
At
the
end,
MATLAB/SIMULINK model based simulated results were
presented to validate the effectiveness of the proposed DVR.
Voltage sag is the most sever power quality problem faced
by industrial customers. Voltage sag is common reasons for
malfunctioning in production plants. Voltage sag is a short
term reduction in voltage magnitude. According to IEEE
standard 1159 voltage sag is “a decrease in RMS voltage
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Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
between 10 to 90 % at a power frequency for durations from
0.5 cycles to 1 minute”.
Fig.5. Basic Components of a DVR
During voltage sag, the DVR injects a voltage to restore the
load supply voltages. The DVR needs a source for this
energy. Two types of system are considered; one using
stored energy to supply the delivered power as shown in
Fig.5, and the other having no internal energy storage. There
are a number of voltage sag/swell mitigating methods
available but the use of custom power service is considered
to the most efficient method. This paper introduce basic
concept of DVR (Dynamic Voltage Restore). DVR inject an
appropriate voltage magnitude with an appropriate phase
angle dynamically. Dynamic compensating signals are
determine based on the difference between desired and
actual values. Main components of DVR are voltage source
converter, injecting transformer, passive filter, and energy
storage device. The performance of DVR depends on the
efficiency control technique of switching of voltage source
inverter (VSI).
B. DSTATCOM
The STATCOM used in distribution systems is called
DSTATCOM
(Distribution-STATCOM)
and
its
configuration is the same, but with small modifications. It
can exchange both active and reactive power with the
distribution system by varying the amplitude and phase
angle of the converter voltage with respect to the line
terminal voltage. The D-STATCOM employs an inverter to
convert the DC link voltage Vdc on the capacitor to a
voltage source of adjustable magnitude and phase. Therefore
the D-STATCOM can be treated as a voltage-controlled
source. The D-STATCOM can also be seen as a
current-controlled source.
The DSTATCOM is based on the instantaneous real-power
theory; it provides good compensation characteristics in
steady state as well as transient states [3]. The instantaneous
real-power theory generates the reference currents required
to compensate the distorted line current harmonics and
reactive power. It also tries to maintain the dc-bus voltage
across the capacitor constant. Another important
characteristic of this real-power theory is the simplicity of
the calculations, which involves only algebraic calculation.
A D-STATCOM (Distribution Static Compensator), which
is schematically depicted in Fig-6, consists of a two-level
Voltage Source Converter (VSC), a dc energy storage
device, a coupling transformer connected in shunt to the
distribution network through a coupling transformer. The
VSC converts the dc voltage across the storage device into a
set of three-phase ac output voltages. These voltages are in
phase and coupled with the ac system through the reactance
of the coupling transformer. Suitable adjustment of the
phase and magnitude of the D-STATCOM output voltages
allows effective control of active and reactive power
exchanges between the DSTATCOM and the ac system.
Such configuration allows the device to absorb or generate
controllable active and reactive power.
Fig.6 Schematic Diagram of a DSTATCOM
The VSC connected in shunt with the ac system provides
a multifunctional topology which can be used for up to three
quite distinct purposes: 1. Voltage regulation and
compensation of reactive power;
2. Correction of power factor
3. Elimination of current harmonics.
C .UPQC
Improvement of Power Semiconductor Technology
since 1970, made it possible using these devices in electric
utility applications. One of the recent developed of these
applications is unified power quality conditioner (UPQC).
According to the basic idea of UPQC, it consists of
back-to-back connection of two three-phase active filters
(AFs) with a common dc link. The point of common
coupling (PCC) could be highly distorted, also the switching
ON/OFF of high rated load connected to PCC may result
into voltage sags or swells on the PCC has been discussed.
1562
Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
Fig.8 Matlab/Simulink Model of Proposed Chaotic Model of Arc Furnace
using Matlab/Simulink tool.
Fig.7 Power circuit configuration of UPQC
Fig.7 shows the general power circuit configuration of
UPQC. This system consists of a PAF and a SAF. The
control circuit of UPQC generates the reference
compensating currents and voltages of PAF and SAF in
instantaneous and simultaneous manner, respectively.
The series active filter connected in series through an
injection transformer is commonly termed as series filters
(SAF). It acts as a controlled voltage generator. It has
capability of voltage imbalance compensation, voltage
regulation
and
harmonic
compensation
at
the
utility-consumer point of common coupling (PCC). In
addition to this, it provides harmonic isolation between a
sub-transmission system and a distribution system. The
second unit connected in parallel with load, is termed as
Shunt Active Filter (PAF). It acts as a controlled current
generator. The shunt active filter absorbs current harmonics,
compensate for reactive power and negative sequence
current injected by the load. In addition, it controls dc link
current to a desired value. In power line conditioner one
more element is a dc link inductor, which acts as energy
storage device. A small amount of dc power supply is
required to operate active power filter for harmonic
compensation. The dc link inductor functions as dc power
supply sources and hence does not demand any external
power source. However, in order to maintain constant dc
current in the energy storage element, a small fundamental
current is drawn to compensate active filter losses.
VI. MATLAB/SIMULINK MODELING & RESULTS
Here simulation is carried out in several cases, in
that 1). Proposed Chaotic Model of Arc Furnace controlled
by DSTATCOM 2). Proposed Chaotic Model of Arc
Furnace controlled by DVR 3). Proposed Chaotic Model of
Arc Furnace controlled by UPQC
Fig.9 Electric Arc Furnace of Voltage waveform in static model
Fig.10 Electric Arc Furnace of Current waveform in static model
Fig.9 Electric Arc Furnace of Voltage waveform in Dynamic model
Case 1: Proposed Chaotic Model of Arc Furnace controlled
by DSTATCOM
1563
Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
(a) Without Compensation
Fig.10 Electric Arc Furnace of Current waveform in Dynamic model
(b) With Compensation
Fig.14 PCC Currents of Proposed Chaotic Model of Arc Furnace without &
with DSTATCOM
Fig.11 FFT Analysis of Electric Arc Furnace of Current waveform in static
model
Fig.11 shows the FFT Analysis of Electric Arc Furnace of
Current waveform in static model, attain 21.16%.
Fig.15 FFT Analysis of Electric Arc Furnace of Current waveform in static
model with DSTATCOM
Fig.15 shows the FFT Analysis of Electric Arc Furnace of
Current waveform in static model with DSTATCOM, attain
2.23%.
Fig.12 FFT Analysis of Electric Arc Furnace of Current waveform in
dynamic model
Case 2: Proposed Chaotic Model of Arc Furnace controlled
by DVR
Fig.12 shows the FFT Analysis of Electric Arc Furnace of
Current waveform in dynamic model, attain 37.30%.
Fig.13 Matlab/Simulink Model of Proposed Chaotic Model of Arc Furnace
with DSTATCOM using Matlab/Simulink tool.
Fig.16 Matlab/Simulink Model of Proposed Chaotic Model of Arc Furnace
with DVR using Matlab/Simulink tool.
1564
Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
400
voltage(V)
200
0
-200
-400
0
0.02
0.04
0.06
0.08
0.1
time(sec)
0.12
0.14
0.16
0.18
0.2
0
0.05
0.1
0.15
0.2
0.25
time(sec)
0.3
0.35
0.4
0.45
0.5
current(Amperes)
400
(a) Without DVR
0
-200
-400
DVR output Voltage
500
200
Fig.20 Load Voltage & Current of Proposed Chaotic Model of Arc Furnace
with UPQC
400
300
Voltage (volts)
200
100
0
-100
-200
Fig.21 Shunt Compensation Voltage & Current of Proposed Chaotic Model
of Arc Furnace with UPQC
-300
-400
-500
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (secs)
0.07
0.08
0.09
0.1
(b) With DVR
Fig.17 PCC Voltages of Proposed Chaotic Model of Arc Furnace without &
with DVR
Case 3: Proposed Chaotic Model of Arc Furnace controlled
by UPQC
Fig.22 Series Compensation Voltage & Current of Proposed Chaotic Model
of Arc Furnace with UPQC
VII. CONCLUSION
Fig.18 Matlab/Simulink Model of Proposed Chaotic Model of Arc Furnace
with UPQC using Matlab/Simulink tool.
1
x 10
5
voltage(V)
0.5
0
-0.5
-1
0
0.02
0.04
0.06
0.08
0.1
time(sec)
0.12
0.14
0.16
0.18
0.2
0
0.02
0.04
0.06
0.08
0.1
time(sec)
0.12
0.14
0.16
0.18
0.2
100
current(amperes)
UPQC topology has been proposed in this paper which has
the capability to compensate voltage sags, voltage swells
and current harmonics at the load. A chaotic arc furnace
model for power quality studies is presented by using
back-back connection of DVR & DSTATCOM to regulate
the power quality concerns, which is not only useful for
harmonic study, but also useful for flicker study. Where the
dynamic arc furnace model is obtained using the chaotic
signal to modulate the static arc voltage, the chaotic signal is
generated via the asymmetric nonlinear Chua’s circuit.
50
0
-50
-100
Fig.19 Source Voltage & Current of Proposed Chaotic Model of Arc
Furnace with UPQC
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Pavani and Devi
Improved Performance of Chaotic Model of AC Electric Arc Furnace Using Unified Power Quality Conditioner
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.10, pp. 1559-1566
ISSN 2078-2365
http://www.ieejournal.com/
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