Research Journal of Applied Sciences, Engineering and Technology 4(20): 4085-4092, 2012
ISNN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: March 14, 2012
Accepted: April 07, 2012
Published: October 15, 2012
Application of Metal Oxide Surge Arrester on the Non-Conventional Chaotic
Ferroresonance Oscillation in Voltage Transformers
1,2
1
Hamid Radmanesh, 1Hamid Fathi and 1Hossein Hosseinian
Electrical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic),
Tehran, Iran
2
Electrical Engineering Department, Islamic Azad University, Takestan Branch, Takestan,
Ghazvin, Iran
Abstract: In this study the effect of MOSA on controlling of the non-conventional ferroresonance overvoltage
in the iron core voltage transformer is studied. It is expected that MOSA can generally damp ferroresonance
overvoltages. Time-domain study is used to analyze this effect. Study is done on a voltage transformer rated
100VA, 275 kV. The magnetization characteristic of the transformer coil is modeled by a single-parameter twoterm polynomial with q = 7 degree of nonlinearity. Core loss is modeled by linear resistance. Simulation results
show that connecting the MOSA in parallel to the voltage transformer, shows a great controlling effect of the
ferroresonance oscillations. Phase plane, time domain voltage waveforms, FFT analysis and bifurcation
diagrams are also given. Significant effect on settling down to the chaos, the range of parameter values that may
lead to ferroresonance overvoltages and controlling these phenomena are obtained and presented.
Keywords: MOSA, Chaos Control, Bifurcation Diagram, Ferroresonance oscillation, Voltage Transformers
INTRODUCTION
Ferroresonance is a complicated nonlinear electrical
phenomenon, which can cause to dangerous transformer
overvoltages multi times more than the normal equipment
nominal voltages. The first analytical work was done by
Rudenberg in the 1940’s (Rudenberg, 1950). More
detailed work was carried out later by Hayashi in the
1950’s (Hayashi, 1964). Transformer models for transient
studies based on field measurement are given in Dick and
Watson (1981). A systematical method for suppressing
ferroresonance at neutral-grounded substations is given in
Yunge et al. (2003). In this study, the scheme for
suppressing the ferroresonance is to insert resistance,
made from parallel-connected resistors into the VT’s wye
secondary circuit. Sensitivity studies on power
transformer ferroresonance of a 400 kV double circuit are
given in Charalambous et al. (2008). Novel analytical
solution to fundamental ferroresonance in Yunge et al.
(2006) investigated a major problem with the Traditional
Excitation Characteristic (TEC) of nonlinear inductors,
which the TEC contains harmonic voltages and/or
currents and has been used the way as if it were made up
of pure fundamental voltage and current. Stability domain
calculations of period-1 ferroresonance in a nonlinear
resonance circuit have been investigated in Jacobson et al.
(2002). Later research has been divided into two main
areas: improving the transformer models and studying
ferroresonance. Application of wavelet transform and
MLP neural network for ferroresonance identification was
done in Mokryani and Haghifam (2008). In this paper an
efficient method for detection of ferroresonance in
distribution transformer based on wavelet transform is
presented. Impacts of transformer core hysteresis
formation on stability domain of ferroresonance modes
were done in Rezaei-Zare et al. (2007).The susceptibility
of a ferroresonance circuit to a quasi-periodic and
frequency locked oscillations are presented in
Chkravarthy and Nayar (1997). The effect of initial
conditions on the chaotic ferroresonance is investigated in
Mozaffari et al. (1997). Effect of circuit breaker grading
capacitance on ferroresonance in VT is investigated in Al
Zahawi et al. (1998). Analysis of ferroresonance modes in
power transformers using preisach-type hysteretic
magnetizing inductance is described in Rezaei-Zare et al.
(2007). Frame in Frame et al. (1982) has developed
piecewise-linear methods of modeling the nonlinearities
in saturable inductances. Smith (Smith et al., 1975)
categorized the modes of ferroresonance in the
distribution transformer based on the magnitude and
appearance of the voltage waveforms. The implications of
applying MOSA arresters in the distribution environment
are described in Short et al. (1994) and Kershaw et al.
(1989). In Walling et al. (1994), it has been pointed out
that the arresters have a mitigating effect on the chaotic
ferroresonance in pad mount transformers. The effect of
a connected MOSA arrester in parallel to the power
transformer is illustrated in Al-Anbarri et al. (2001).
Corresponding Author: Hamid Radmanesh, Electrical Engineering Department, Amirkabir University of Technology (Tehran
Polytechnic), Tehran, Iran Tel: (+98-21)64543335, Fax: (+98-21) 88212072
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
Reserve Busbar
Main Busbar
i
Cseries
i3
i1
D isconnector1
Grading Capacitor
Cshunt
e
D isconnector2
i2
Rcore
Ltrans
V
Fig. 2: Basic reduced equivalent ferroresonance circuit (Hamid,
2010)
Circuit Breaker
VT
D isconnector3
Fig. 1: Power system one line diagram arrangement resulting in
VT ferroresonance oscillation (Hamid, 2010)
Ferroresonance of power transformers considering nonlinear core losses and metal oxide surge arrester effects
has been studied in Hamid et al. (2012). Considering the
hysteresis loop to study a single-phase transformer
working under switching devices (mostly SCR) operations
shows steady state depended on load and firing angles
values (Strimbu et al., 2007). In Hamid (2010) and Hamid
(2010) controlling ferroresonance in voltage transformer
including linear and nonlinear core losses by considering
circuit breaker shunt resistance effect has been shown and
is clearly indicative of the effect of core losses
nonlinearity on the system behavior and margin of
occurring ferroresonance. Current paper studies
controlling effect of the MOSA on the ferroresonance
oscillation in the voltage transformer.
magnetizing characteristic of the 100VA voltage
transformer can be presented by 7 order polynomial
(Hamid, 2010). Figure 1 shows the single line diagram of
the most commonly encountered system arrangement be
basin voltage transformer ferroresonance. Ferroresonance
oscillation can occur upon opening of the disconnector 3
while circuit breaker open and either disconnector 1 or 2
are closed. Alternatively it can also occur upon closure of
both disconnectors 1 or 2 with circuit breaker and
disconnector 3 is open.
By using the thevenin theorem and applying it to the
power system in Fig. 1, it can be changed to an equivalent
circuit that is known as ferroresonance circuit as shown in
Fig. 2.
In Fig. 2, E is the RMS input phase voltage, Cseries is
the circuit breaker capacitance and Cshunt is the total
existing capacitance of the power system. The resistor R
represents voltage transformer core losses. In the peak
current range, flux-current characteristic becomes highly
nonlinear and 8-i characteristic of the voltage transformer
is modeled by the polynomial:
I = a8+b87
(1)
where, " = 3.14 and b = 0.41.
The polynomial of (1) and the coefficient (b) of it are
chosen for the best fit of the saturation region.
METHODOLOGY
system modeling without MOSA: Voltage Transformer
(VT) ferroresonance oscillation originates between the
nonlinear iron core inductance of the voltage transformer
and existing capacitances of the power system. In this
case, energy is coupled with the nonlinear core of the
voltage transformer via the open circuit breaker grading
capacitance or system capacitance to sustain the
resonance (Hamid, 2010). The result might be the
saturation in the VT core and depicts very high voltage
values up to 4p.u which can be theoretically gained in the
worst conditions (Hamid, 2010). Voltage transformers
have a relatively low thermal capacity, thus, overheating
can cause insulation failure sooner than expected. The
System dynamic and equation: Mathematical analysis
of the equivalent circuit by applying KVL and KCL is
done and equations of system can be presented as below:
4086
λ peak =
2
v RMS
ω
(2)
vL =
dλ
dt
(3)
e=
2 E sin ωt
(4)
Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
(aλ + bλ ) ⇒ ( C C + C ) (
7
ser
ser
+
d 2λ
dt 2
)
ω dt 2
(
)
2 E cosωt =
sh
Table 1: Parameter value for simulation without MOSA parameters
Parameter
Actual value
Per unit value
E
275kV
1 p.u
W
377 rad/sec
1 p.u
Cseries
0.5nf
39.959 p.u
Cshunt
1.25nf
98.962 p.u
Rcore
225 M
0.89 p.u
1 dλ
+
R dt
+
1 d 2λ
1
1
dλ
+
aλ + bκ 7
Rω ( Cser + Csh ) dt ω ( Cser + Csh )
(5)
Voltage of transformer (perunit)
2 Cser Eω cos ωt = ( Cser + Csh )
where, T is the input supply frequency, E is the RMS
input supply phase voltage, Cseries is the circuit breaker
capacitance and Cshunt is the total phase-to-ground
capacitance of the power system and in (1) a = 3.4 and
b = 0.41 are the seven order polynomial sufficient. The
state-space formulation (8 and d8/dt as state variables) is
as followed:
2
1
0
-1
-2
-3
-1.5
⎧ x1 (t ) = λ
⎪ x (t ) = x& (t )
⎪ 2
1
⎨
⎪ v = dλ / dt
⎪⎩ x2 (t ) = v
x&2 (t ) = −
3
(6)
λ2 + pλ + q = 0
)
1
ax1 (t ) + bx1 (t ) 7 +
cseries + cshunt
(7)
⎡ x&1 (t ) ⎤
⎢ x& (t ) ⎥ =
⎣ 2 ⎦
1
⎤
−1
⎥
R(cseries + cshunt ) ⎥⎦
(8)
0
⎡
⎤
⎡ u1 ⎤ ⎢
⎥
⎛
⎞
=
c
⎢u ⎥ ⎢
series
⎟ ωE 2 cos(ωt )⎥⎥
⎣ 2 ⎦ ⎢⎜
⎣ ⎝ cseries + cshunt ⎠
⎦
(9)
y(t) = CX(t)
(10)
y(t) = v(t) [0
1][x1(t)
x2(t)]
det[8I - A] = 0
λ
⎡
6
det ⎢ a + b( x1 (t ))
⎢
⎣⎢ cseries + cshunt
1
(11)
− p±
,q =
1.5
p 2 − 4q
2
(14)
a
cserie s + cshunt
(15)
R(cseries + cshunt )
p=
1
a
,q =
R(cseries + cshunt )
cseries + cshunt
(16)
Table 1 shows value of the power system parameters
are used to driving the simulation results while parameters
are not included.
By considering these values, Eigenvalue for normal
operation is:
81 = -0.002 + j0.73
82 = -0.002 ! j0.73
(12)
−1
⎤
⎥=0
1
λ+
⎥
( cseries + cshunt ) ⎥⎦
λ1,2
p=
⎛
⎞
cseries
⎜
⎟ ωE 2 cos(ωt )
c
+
c
⎝ shunt series ⎠
0
⎡
−a
b
⎢
−
x1( t ) 6
⎢c
+
c
c
series + cshunt
⎣ series shunt
⎡ x1 (t ) ⎤ ⎡ 0⎤
⎢ x ( t ) ⎥ + ⎢1 ⎥ u
⎣ 2 ⎦ ⎣ ⎦
0
-0.5
0.5
1.0
Current of MOV (perunit)
Fig. 3: V-I characteristic of MOSA
1
x2 (t ) −
R(cseries + cshunt )
(
-1.0
(17)
Metal oxide surge arrester model: MOSA is a highly
nonlinear resistor used to protect power system
equipments against ferroresonance and other over
voltages. The nonlinear V-I characteristic of the MOSA
surge arrester is modeled by exponential functions of the
form:
⎛ I ⎞
V
⎟⎟
= Ki ⎜⎜
Vref
⎝ I ref ⎠
(13)
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1/α i
(18)
Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
Cseries
Voltage of transformer
iL
iCser
iCshunt
Cshunt
e
2.5
2.0
KCL
KVL
iR
0
-0.5
V
Ltrans
R
MOV
-1.0
-1.5
-2.0
-2.5
Fig. 4: equivalent ferroresonance circuit with MOSA
0
Table 2: Parameter value for simulation with MOSA parameters
Parameter
Actual value
Per unit value
E
275kV
1 p.u
W
377 rad/sec
1 p.u
Cseries
0.5nf
39.959 p.u
Cshunt
1.25nf
98.962 p.u
Rcore
225 M
0.89 p.u
a
26
K
2.5101
=
(C
1 dλ 1 ⎛ dλ ⎞
− ⎜
⎟
Rcore dt C ⎝ kdt ⎠
+ Cshunt ) ⎛ d 2 λ ⎞
⎜ 2⎟
Cseries
⎝ dt ⎠
−
1
(aλ + bλ7 )
Cserie s
200
100
150
Current (perunit)
250
300
(19)
series
where, T represents the power system frequency, E is the
peak value of the input voltage source as shown in Fig. 2.
Table 2 shows the parameters value of the power system
including MOSA. In this state, system for both cases, with
and without MOSA is simulated for E = 1 and 4 p.u. The
studied system has a periodic behavior for E = 1 p.u and
fundamental or subharmonic resonance behavior for E =
4 p.u while by applying MOSA, system behavior remains
periodic and fundamental oscillation for E = 1 p.u and E
= 4 p.u.
Fig. 5 and 6 show time domain simulation for these
two cases that represented the sinusoidal voltage wave
form with a frequency equal to the power system
Voltage of transformer
3
System modelling with MOSA: Figure 4 shows system
modeling which MOSA is connected in parallel to the
transformer. The differential equation for the circuit in
Fig. 4 can be modified as follows:
ωE cosωt −
50
Fig. 5: Time domain simulation for fundamental
resonance motion without MOSA effect
where, V represents resistive voltage drop, I shows
arrester current, K and " are nonlinearity constant and its
value is dependent to the each column of the arrester. This
V-I characteristic is simulated and represented in Fig. 3.
Connecting MOSA to the power system including
voltage transformer in Fig. 2, circuit can be modified as is
shown in Fig. 4.
α
1.5
0.5
2
1
0
-1
-2
-3
0
50
200
100
150
Current (perunit)
250
300
Fig. 6: Time domain simulation for fundamental resonance
motion with MOSA efect
frequency, these results show the fundamental resonances
in the system.
SIMULATION RESULTS
The nonlinear dynamic questions do not have simple
analytical solution. So the equations were solved
numerically using an embedded Runge-Kutta- Fehlberg
algorithm. Values of E and T were assumed by 1 p.u.,
corresponding to AC input supply phase voltage and
frequency. Cseries is the circuit breaker grading capacitance
and its value directly depends on the type of circuit
breaker which is used. In this analysis Cseries is fixed 0.5nF
and Cshunt varies between 0.1nF to 3nf. Initial conditions
are V (t ) = 2 , λ (t ) = 0 at t = 0, showing circuit breaker
operation at maximum voltage.
Fig. 6 and 7 show the simulation results for E = 4 p.u
including MOSA. By referring to Fig. 6 and comparing it
with Fig. 8, it is shown that the MOSA clamps the
overvoltages and its behavior reaches to the normal
condition.
MOSA surge arrester successfully controlled these
oscillations and limits its amplitude to 3p.u as shown in
Fig. 7.
By applying MOSA to the system, fundamental
oscillations become smoother as are shown in Fig. 9.
Without MOSA, Phase plan of the chaotic case is shown
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
Voltage of transformer
4
3
2
1
0
-1
-2
-3
-4
0
50
200
100
150
Current (perunit)
250
300
Fig. 7: Time domain simulation for fundamental resonance
motion with MOSA effect
Voltage of transformer
10
5
0
-5
-10
0
50
200
100
150
Current (perunit)
250
300
Fig. 8: Time domain simulation for chaotic motion without
MOSA
in Fig. 10. In this case, overvoltage’s reaches up to 8 p.u.
By applying MOSA in parallel, overvoltage is decreased
to maximum 3p.u according to the Fig. 9. It is clear that
MOSA clamps the ferroresonance overvoltage and keep
it in E = 3p.u. Due to the nonlinear behavior of the MOSA
surge arrester, it doesn’t allow to the overvoltages
crossing 2.2 p.u which is operating threshold of this
device MOSA has operated and has damped extra
oscillation to the ground.
In this study, the effect of variation in the voltage of
the system on the ferroresonance overvoltage in the VT
was investigated and finally the effect of applying MOSA
on this overvoltage by the bifurcation diagrams was
shown. By using the bifurcation diagrams, Fig.11
evidently shows the ferroresonance overvoltage in voltage
transformer when voltage of system increases up to 2.5
p.u.
In Fig. 11 when E = 0.25 p.u, voltage of VT has a
period-1 behavior, in E = 1 p.u, period-3 appears and in E
= 3 p.u, its behavior is similar to the one of Period-5
oscillation. Fig 12, show the controlling effect of MOSA
on the nonlinear oscillation of the same voltage of
transformer.
By applying MOSA, system behaviors coming out
from chaotic region and MOSA clamps the nonlinear
overvoltage, it is also shown subharmonic resonance of
the previous case is damped and in the worst case of over
voltages period-5 oscillation is appeared.
In Fig. 13 while E = 0.25 p.u, voltage of VT has
period-1 behavior but when E gets 0.95 p.u value, one
jump in the trajectory of the system happens.The behavior
becomes period-3 and after this sudden voltage, crisis
takes place and system behavior goes to the chaotic
region, after that, when the input voltage reaches to
2.3 p.u, system comes out from chaotic region, but with
too much subharmonic resonances in the system.
Finally,with E between 2.3- 2.7 p.u, system remains in
period-5 oscillations. After 1.5 p.u, system goes to chaotic
region again.It is shown that system behavior follow
period doubling bifurcation schema and there are many
fundamental and subharmonic resonances in the system.
Keeping system parameters, but applying MOSA leads
interesting results shown in Fig. 14.
Fig. 9: Phase plan diagram for fundamental resonance motion with MOSA effect
4089
Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
Fig. 10: Phase plan diagram for chaotic motion without MOSA effect
Fig. 11: Bifurcation diagram for voltage of transformer versus voltage of system, without MOSA effect
Fig. 12: Bifurcation diagram for voltage of transformer versus voltage of system with applying MOSA effect
4090
Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
Fig. 13: Bifurcation diagram for voltage of transformer versus voltage of system, without MOSA effect
Fig. 14: Bifurcation diagram for voltage of transformer versus voltage of system applying MOSA effect
Table 3: Parameter value for simulation
Parameter
Actual value
E
275kV
w
377 rad/sec
Cseries
0.5 nf
Cshunt
0.19nf
R
222M
period-1 and after 1.8 p.u, goes to chaotic region, again in
3.5 p.u it goes back to the linear region.
Per unit value
1 p.u
1 p.u
39.959 p.u
15.042 p.u
0.89p.u
CONCLUSION
Corresponding bifurcation diagram with the same
parameter in the case of applying MOSA in parallel is
clearly shown in Fig. 14.
According to the parameters of Table3, it is shown
that by changing the Cseries from 0.1 nf to 0.19 nf,
amplitude and behavior of ferroresonance overvoltage
greatly changes. This plot is completely different by Fig.
11. By applying MOSA in this case, it is shown that
MOSA has great effect on overvoltage and can
successfully cause ferroresonance drop out. In Fig. 14 by
applying MOSA to the system, overvoltage on VT has
been limited to 2.5 p.u, By varying voltage of system up
to 4 p.u it is shown that trajectory of system remains
Studying nonlinear phenomena in voltage
transformers is exhibiting fundamental frequency and
chaotic ferroresonance oscillation similar to power
transformers. Simulation results are indicative of a change
in the value of the equivalent line to ground capacitance,
circuit breaker grading capacitance and system parameters
may originate different types of non-conventional
ferroresonance oscillations. It is shown that if nonconventional oscillations occur, MOSA surge arrester can
successfully control the amplitude of these nonlinear
ferroresonance over voltages. Considering MOSA surge
arrester in parallel, system shows less sensitivity to the
change in initial conditions and variation in the system
parameters. Variation of the system and circuit breaker
grading capacitance shows that quasiperiodic oscillations
4091
Res. J. Appl. Sci. Eng. Technol., 4(20): 4085-4092, 2012
occurred rather than period doubling bifurcation in the
trajectory of the system.
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