a b s t r a c t The main goal of this paper is the determination of the effect of the metal oxide varistor (MOV) on various ferroresonance modes including fundamental resonance, subharmonic and chaos mode which are generated in electrical power systems. Chaos theory is used for analyzing this effect. Also, the bifurcation, phase plan diagram and time domain simulation are used for this purpose. The proposed power system contains a no-load or lightly loaded power transformer. The magnetization curve of the transformer core is modeled by a single-value two-term polynomial. The core loss is modeled based on the flux of the transformer. The MOV modeled as a nonlinear voltage dependent resistance. The suppression effect of MOV on chaotic ferroresonance in power transformer is studied in this paper. The simulation results confirm that connecting the MOV to the transformer has a considerable suppression effect on ferroresonance phenomena

G B Gharehpetian

Hamid Radmanesh

CiteSeerX

Ferroresonance suppression in power transformers using chaos theory
Hamid Radmanesh a,b,⇑, G.B. Gharehpetian b
a Department of Electrical Engineering, Islamic Azad University, Takestan Branch, Takestan, Iran
b Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran
a r t i c l e i n f o
Article history:
Received 8 October 2010
Received in revised form 16 August 2012
Accepted 19 August 2012
Available online 5 October 2012
Keywords:
Metal oxide varistor
Control of chaos
Bifurcation
Ferroresonance
Power transformers
a b s t r a c t
The main goal of this paper is the determination of the effect of the metal oxide varistor (MOV) on various
ferroresonance modes including fundamental resonance, subharmonic and chaos mode which are gener-
ated in electrical power systems. Chaos theory is used for analyzing this effect. Also, the bifurcation,
phase plan diagram and time domain simulation are used for this purpose. The proposed power system
contains a no-load or lightly loaded power transformer. The magnetization curve of the transformer core
is modeled by a single-value two-term polynomial. The core loss is modeled based on the flux of the
transformer. The MOV modeled as a nonlinear voltage dependent resistance. The suppression effect of
MOV on chaotic ferroresonance in power transformer is studied in this paper. The simulation results con-
firm that connecting the MOV to the transformer has a considerable suppression effect on ferroresonance
phenomena.
 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The ferroresonance is a nonlinear resonance, which has result in
multiple periodic and non-periodic modes in the system behavior.
Considering system parameters and the initial condition of the fer-
roresonant circuit, it may settle to one of the following behaviors
such as fundamental, subharmonic, quasi-periodic or chaotic
resonances. Usually, the ferroresonance contains a nonlinear induc-
tance and capacitances. The nonlinear inductance typically is a sat-
urate magnetizing inductance of a transformer and the capacitance
is a capacitive distribution cable or transmission line connected to
the transformer. Ferroresonance phenomenon has been recognized
and investigated in many papers as early as 1907 [1–4]. Isolated fer-
roresonant solutions in transmission lines have been investigated
in [5], which presents the detailed analysis of the subharmonic
mode of the ferroresonance and its sensitivity with respect to the
length of the deenergised line. The study of the periodic ferroreso-
nance in electrical power networks by bifurcation diagrams has
been carried out in [6]. The analysis of the lightning-caused ferrore-
sonance in capacitor voltage transformer (CVT) has been given in
[7]. In the paper, a dynamic response to lightening and switching
has been studied. So, the study investigates the effect of the
lightning strike on a tower with a 132 kV CVT. The s-domain model
of three winding transformer for modal analysis has been given in
[8]. The influence of non-differential components to the power sys-
tem small signal stability region has been studied in [9]. Consider-
ing the importance of the initial condition in the nonlinear systems,
in [10], the impact of initial conditions on the initiation of the fer-
roresonance in the model of a 275 kV magnetic voltage transformer
has been investigated. The transient response of a practical ferro-
resonant circuit has been studied in detail in [11]. The iterative
approximation technique has been used for the determination of
the transient response due to sudden application of a sinusoidal
voltage. The analysis of subharmonic oscillations in a ferroresonant
circuit with the focused on subharmonic (period-3) ferroresonant
oscillations has been given in [12]. A novel analytical solution to
the fundamental ferroresonance including power frequency excita-
tion characteristic has been investigated in detail in [13]. A method
of protecting the voltage transformer against ferroresonance over-
voltages with a compact active load has been developed by [14].
The static VAR compensator (SVC) and the thyristor-controlled ser-
ies capacitor (TCSC) analytical model, a systematical method for
suppressing ferroresonance at neutral-grounded substations and
the frequency response of the unfiled power flow controller (UPFC)
has been simultaneously studied in [15]. A sensitivity study on
power transformer ferroresonance in a 400 kV power system is pre-
sented in [16]. In that paper, the model of 1000 MV-400/275/13 kV
power transformer has been described and the simulations have
been compaired with field test results. The influence of supply,
circuit and magnetic material parameters on the occurrence of
the fundamental ferroresonance mode in a series inductance–
capacitance–resistance (LCR) circuit with a nonlinear inductor has
been discussed in [17,18]. The effect of the circuit breaker shunt
resistance on the chaotic ferroresonance in voltage transformers
0142-0615/$ - see front matter  2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ijepes.2012.08.028
⇑ Corresponding author at: Department of Electrical Engineering, Islamic Azad
University, Takestan Branch, Takestan, Iran. Tel.: +98 2164543335; fax: +98
2188212072.
E-mail addresses: Hamid.Radmanesh@aut.ac.ir (H. Radmanesh), grptian@aut.ac.ir
(G.B. Gharehpetian).
Electrical Power and Energy Systems 45 (2013) 1–9
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier .com/locate / i jepes
has been studied in [19]. The suppression technique of the ferrore-
sonance phenomenon in the coupling capacitor of the voltage
transformer has been given in [20]. The impact of hysteresis and
magnetic couplings on the stability domain of ferroresonance in
asymmetric three-phase three-leg transformers has been discussed
in [21]. Mitigating the ferroresonance of 161 kV electromagnetic
potential transformers by damping reactors in gas-insulated
switchgear has been presented in [22]. The frequency domain anal-
ysis of a power transformer ferroresonance has been studied in
[23]. The aim of the current paper is to show the controlling effect
of MOV on clamping the ferroresonance overvoltages and the appli-
cation of MOV as a practical solution for protecting power trans-
formers against ferroresonance overvoltages.
2. Power system modeling
The ferroresonance phenomenon, in most situations, consists of
a capacitance and an inductance and there is no definite resonant
frequency, so more than one response is possible for the same set
of parameters including fundamental, subharmonic and chaotic
resonances [24]. In this section, the ferroresonance equivalent
circuit is a power transformer connected to the power system.
But, one of the three poles of the circuit breaker is open and only
transformer two phases are energized. This switching action
produces induced voltage in the opened phase. This voltage causes
ferroresonance overvoltages, if the distribution line is capacitive.
This case here consists of a source with one conductor being inter-
rupted as shown in Fig. 1 [25]. Fig. 2 shows the circuit that feeds
the disconnected coil trough the capacitive coupling of the power
system [25].
The circuit shown in Fig. 2 has been analyzed using the venin’s
theorem. By shorting the two remaining voltage sources of phases
1 and 2 the capacitance of the remaining part of the power system
can be derived. So, Cg and transformer windings are short circuited
and phases 1 and 2 having the same voltage and can be omitted. So,
the remaining circuit will consist of two Cm and one Cg. Thus, the
equivalent capacitances can be given as Eq. (1) where Cg is ground
capacitance and Cm is mutual capacitance of the power system.
C ¼ Cg þ 2Cm ð1Þ
And the equivalent source voltage is given by equation:
E ¼ Cm
Cg þ 2Cm
Vl ð2Þ
In unloaded or very lightly loaded transformer, the current
causes the flux flow through the iron core. This phenomenon
increases the transformer core loss and therefore it should not be
neglected. Fig. 3 shows the reduced equivalent circuit including
R2, where it modeles the core loss including eddy current and hys-
teresis loss. C models the total remaining capacitance and Lcore rep-
resents the power transformer disconnected coil.
The magnetization curve is modeled by a nonlinear inductance
in parallel with a nonlinear resistor representing the saturation
and hysteresis and eddy current characteristics, respectively. Any
damping can be added to the circuit, which may cause the ferrore-
sonance voltage and current elimination. This damping effect can
be a resistive source impedance, transformer loss and corona loss.
But, the load applied to the secondary of the transformer is much
important. A lightly-loaded or unloaded transformer fed through
capacitive source impedance is a major candidate for ferroreso-
nance as shown in Fig. 1. Due to high currents and core fluxes,
the ferroresonance can overheat the transformer. The high temper-
ature may weaken the winding insulation and cause a transformer
failure. In extra high voltage systems, ferroresonance voltages oc-
cur during the first cycles and cause insulation coordination prob-
lems. Because of non-linearity nature of these circuits, the
analytical solution must be determined using time domain meth-
ods. So, a computer-based numerical integration method is applied
using time domain simulation programs such as the MATLAB.
In this paper, the iron core saturation characteristic is modeled
by equation:
iLm ¼ auþ buq ð3Þ
where q depends on degree of saturation. The adequate value of sat-
uration parameters of a power transformer have been derived by
Watson and listed in Table 1 [26].
For deriving the differential equation of the ferroresonance cir-
cuit we have:
i1  i2  i3 ¼ 0 ð4Þ
Vl ¼
du
dt
¼ _u ¼ R2ði1  i2Þ ð5Þ
where Vl is voltage of transformer, u is flux linkage, R2 is trans-
former core loss, i1 and i2 has been shown in Fig. 1. The nonlinear
v2 v3v1
Cg
Cm
1
2
3
Fig. 1. Model of ferroresonance circuit including line capacitances.
v1
v2
Cm
CmCm
Cg
Cg
1
2
Cg
L
3
Fig. 2. Circuit that feeds disconnected coil.
e(t)
i1
+Vc -R1
R2
Vl
C
Fig. 3. Equivalent ferroresonance circuit.
2 H. Radmanesh, G.B. Gharehpetian / Electrical Power and Energy Systems 45 (2013) 1–9



Ferroresonance Suppression in Power Transformers using Chaos Theory

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=2E9DCA9C1EF0A355BAF2FD64F62D6A77?doi=10.1.1.1056.6517&rep=rep1&type=pdf

Ferroresonance Suppression in Power Transformers using Chaos Theory

Abstract

Similar works

Full text

Available Versions

CiteSeerX