Abstract: This paper presents the analysis and simulation of occurrence and development of ferroresonance in real electrical networks. The necessary and sufficient conditions for ferroresonance occurrence have been examined. It has been shown that in electrical networks this phenomenon is non-linear, so some special methods should be applied. A computer simulation has been performed to calculate the ferroresonance mode. During the analysis the application of the Jiles-Atherton model has allowed taking into account the hysteresis effect and improving the reliability of simulation. The ways of preventing ferroresonance phenomena in electrical networks at open-phase operating conditions are presented

Iryna Tugai

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COMPUTATIONAL PROBLEMS OF ELECTRICAL ENGINEERING 
Vol. 5, No. 1, 2015 
INVESTIGATION OF FERRORESONANCE IN ELECTRICAL 
NETWORKS AT OPEN-PHASE OPERATING CONDITIONS 
Iryna Tugai 
Institute of Electrodynamics of NAS of Ukraine, Kyiv, Ukraine  
iryna_tugai@i.ua 
© Tugai I., 2015 
Abstract: This paper presents the analysis and 
simulation of occurrence and development of ferro-
resonance in real electrical networks. The necessary and 
sufficient conditions for ferroresonance occurrence have 
been examined. It has been shown that in electrical 
networks this phenomenon is non-linear, so some special 
methods should be applied. A computer simulation has 
been performed to calculate the ferroresonance mode. 
During the analysis the application of the Jiles-Atherton 
model has allowed taking into account the hysteresis 
effect and improving the reliability of simulation. The 
ways of preventing ferroresonance phenomena in 
electrical networks at open-phase operating conditions 
are presented. 
Key words: ferroresonance, open-phase mode, 
electrical networks. 
1. Introduction 
Ferroresonance is complex nonlinear oscillations 
that can occur in electrical circuits with serial or parallel 
connection of nonlinear inductance and capacitance. 
Methods for ferroresonance study have been already 
developed for many decades. 
According to practical experience and theoretical 
studies this phenomenon leads to the occurrence of high 
overvoltages and overcurrents with high levels of harmo-
nic distortion and it cannot be eliminated by traditional 
means of overvoltages and overcurrents suppression.  
In electrical networks, ferroresonance can cause serious 
damage of the equipment and long-term failure of power 
supply. Therefore, it must be avoided by all means. Since 
the number of failures caused by the ferroresonance has not 
been reduced in the course of networks operation, the given 
problem is relevant in the present. 
In electrical power systems, ferroresonance may 
occur either at fundamental frequency or at one of the 
subharmonic or higher order harmonic frequencies. The 
nonlinear transformer introduces those current and 
voltage harmonics. Ferroresonance emerges when a 
capacitance and an inductance tune in with one of these 
harmonics. Ferroresonance is found to occur at the 
fundamental frequency mainly while subharmonic 
ferroresonance may also happen sometimes. In the latter 
case the ferroresonant overvoltages are less severe and 
more difficult to mitigate. Such type of ferroresonance 
occurs sometimes in an extra high voltage transmission 
network where a voltage transformer is connected to a 
de-energized transmission line that runs alongside an 
energized line [1].  
Ferroresonance is also considered as a jump 
phenomenon. The system suddenly jumps from one 
stable state (the normal mode) to another stable state (the 
ferroresonant mode) upon a system disturbance, such as 
a small change in system voltage, circuit capacitance, or 
transients. This sudden jump is sometimes referred to as 
bifurcation. Researchers investigated it analytically or by 
using time domain methods, such as numerical 
integration techniques. Nowadays they are trying to 
investigate this phenomenon more deeply by applying 
the theory of nonlinear dynamics and chaos [2]. 
2. The ferroresonance conditions 
For the occurrence of ferroresonance phenomena in 
electric networks the necessary and sufficient conditions 
must be fulfilled. The ferroresonance presence can be 
expected if the following characteristic features are 
observed: phase-to-phase and/or phase-to-ground over-
voltages; overcurrents; voltage and current distortions; 
neutral shift; transformer heating (in no-load mode); too 
loud continuous noise from transformers and reactors; 
failure of electrical equipment (such as voltage trans-
formers). In such cases, the necessary and sufficient con-
ditions of ferroresonance processes should be checked.  
The necessary conditions include: the presence of 
relatively large capacitance in electrical networks (long 
aerial transmission lines; shorter, but relatively more 
capacitive underground cable lines; capacitive voltage 
dividers in circuit breakers; capacitive voltage 
transformers etc.) and the presence of an inductive 
element with a ferromagnetic core (power transformers, 
electromagnetic voltage transformers, etc.). 
The sufficient condition is the appearance of the 
relevant disturbance that precedes and induces ferro-
resonance (atmospheric overvoltage, connection or 
disconnection of transformers or loads, short circuit 
occurrence or clearance and others). 
Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua
Iryna Tugai 
 
Ferroresonance occurs in power distribution systems 
with open-phase supply of a power transformer on no-
load or low-load, when the transformer coil is fed 
through the capacitive coupling from other phases or 
from parallel lines. In such a case, the linear phase-to-
phase and phase-to-ground capacitances of the trans-
mission line and the nonlinear inductance of the 
transformer could compose a series resonant circuit.  
Some typical system disturbances that may cause 
ferroresonance in power distribution system at open-
phase operating condition are: 
• Sudden de-energization of one phase while the 
other two phases remain energized. For instance, when a 
phase conductor is accidentally damaged, or upon loss of 
a phase due to a blown fuse as a result of a phase-to-
ground fault. 
• Open-phase switching-on: for instance, two 
phases are connected simultaneously when the third 
phase remains open for a few cycles. This could happen 
in distribution systems where single phase switching is 
performed. Single phase fuses are still commonly used in 
rural power grids due to their relatively low cost and also 
because their utilization enables limited power 
transmission to be sustained after clearance of 
frequently-occurring single phase-to-ground faults by 
powering out the damaged phase.  
• Open-phase switching-out may lead to similar 
ferroresonant overvoltages as open-phase swithing-on. 
As it has been mentioned above, such 
asymmetrical switching operations can lead to 
essential overvoltage when a transformer at no-load or 
low load is connected to a transmission line that 
operates with ungrounded neutral. But the situation 
gets more difficult when ferroresonance circuit is 
supplied not only through line capacitance, but also 
through electromagnetic coupling. 
This situation occurs in subtransmission substations 
with circuits where the step-down transformer is 
connected to the line by means of a shorting device and 
disconnector, rather than by a high-voltage circuit 
breaker. Usually, the step-down transformer has high-
voltage wye-connected windings with grounded neutral 
and low-voltage delta-connected windings. There is a 
possibility of such dangerous incidents as switching-out 
or switching-on of a line connected to a transformer on 
no-load or low-load by operating one of the line breakers 
and with its other breaker being open (Fig. 1).  
The application of three-winding transformers 
creates favorable conditions for the initiation of ferro-
resonance, because the tertiary winding has considerably 
lower power than other windings. Therefore, the leakage 
inductance of the lowest-voltage winding referred to the 
primary one is very high.  
 
Fig. 1. The ferroresonance occurrence  
in Ukrainian electrical network. 
It should be noted that corona discharge 
substantially restricts overvoltages due to additional 
energy losses. However, in a ferroresonance circuit, 
strong electromagnetic coupling diminishes this effect, 
so overvoltages can be still significant [3]. 
Ferroresonance phenomena are featured by long-
lasting transients, therefore the use of traditional 
methods and techniques utilized in studying 
electromagnetic transients are often ineffective in their 
case. The most suitable method to be used here is a 
computer simulation. It has been used for investigation 
of an accident in Ukrainian electrical network (Fig. 1). 
The substation (Fig. 1) is connected to 220 kV line. 
The line was scheduled for repair. One of the high-
voltage circuit breakers worked properly, but another 
one failed (open-phase swithing-out – only two phases 
cut out). The personnel of the substation noted a specific 
loud noise in the voltage transformer VT lasting for 
about fifteen minutes. Then the noise stopped. After 
thirty minutes since the start of the commutation, the 
high-voltage circuit breaker was manually switched out. 
The voltage transformer VT exploded, when the line was 
switched on after repairs. A subsequent analysis test 
indicated decomposition of oil and solid insulation. 
Close examination of the transformer details also 
revealed a smell of burnt insulation. 
The simulation of the process caused by open-phase 
operation has been performed for this network and it has 
been shown that ferroresonance occurred in both trans-
formers connected in parallel (power transformer and 
voltage transformer). The voltage transformer was da-
maged first, because it was weaker than the power one.  
3. Modeling nonlinear core characteristics of 
transformers  
As mentioned earlier, the appearance of ferro-
resonance processes in electrical networks requires the 
existence of an inductive element with a ferromagnetic 
core. This condition can be fulfilled by the presence of a 
power transformer on no-load or low-load and a voltage 
transformer. The accuracy of the mathematical models of 
62
Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua
Investigation of Ferroresonance in Electrical Networks at Open-Phase Operating Conditions 
the transformers influences considerably the reliability of 
the results of ferroresonance calculations. 
The nonlinear characteristic of the transformers is 
described as the dependency of magnetic flux density B  
on magnetic field intensity H  (magnetization curve): 
 0 ( ),B H M= +µ  (1) 
where 70 4 10
−= ⋅µ π  H/m is the permeability of va-
cuum; M  is magnetization. 
For modeling of the power and voltage transformers 
analytical methods (eg, harmonic balance method) can 
be used. However, to develop more accurate and ade-
quate mathematical models of the transformers the effect 
of hysteresis must be taken into account. To simulate the 
behavior of transformers in electrical networks, the 
application of Jiles-Atherton model is the most appro-
priate way [4, 5]. That model was developed with the 
focus on computer simulation and has a stable algorithm. 
This model can be described by differential equations; it 
uses only five parameters and needs only one hysteresis 
loop, obtained experimentally, for its identification. It 
should be noted that the original Jiles-Atherton model is 
valid only for isotropic materials. 
According to Jiles-Atherton model, the total magne-
tization M  can be written as the sum of irreversible 
magnetization irrM  and reversible magnetization revM .  
The irreversible magnetization can be determined 
from the equation: 
 
( )
irr an
an
dM M M
dH k M M
−
=
− −δ α
 (2) 
where anM  is anhysteretic magnetization; k , A/m is the 
value of the hysteresis loop coercive force that deter-
mines the width of the hysteresis loop; δ  is a direction 
parameter, which takes on the values of either 1 (for 
dH/dt > 0) or −1 (for dH/dt < 0); α  is a parameter that 
quantifies the interdomain coupling in the material. 
The anhysteretic magnetization can be written as the 
modified Langevin function: 
 - ,ean s
e
H aM M coth
a H
  =   
  
 (3) 
where MS is saturation magnetization; eH H M= +α  is 
effective field acting on magnetic moments within 
domains [6]; a , A/m is a form factor for the anhysteretic 
curve which is determined as the value of magnetic field 
intensity at which / 2an sM M= . 
The reversible magnetization can be described by 
the differential equation: 
 - ,rev an
dM dM dMc
dH dH dH
 =  
 
 (4) 
where c  is the reversibility coefficient which ranges 
from 0 (completely irreversible magnetization) to 1 
(completely reversible magnetization). 
Then, the total magnetization can be written as: 
 
( - )1 .
(1 ) - ( - ) 1
an an
an
M M dMdM c
dH c k M M c dH
= +
+ +δ α
 (5) 
Using the mathematical model (5) we can simulate 
all hysteresis characteristics, such as initial magne-
tization, saturation, hysteresis losses, etc.  
4. The results of ferroresonance simulation 
The developed nonlinear inductance model makes it 
possible to assess directly the impact of losses in the 
steel on the character of ferroresonance processes in 
electrical networks. Simulation results of ferroresonance 
phenomenon at open-phase operating mode have shown 
that after the ferroresonance initiation the current sharply 
increased up to several amperes in the high-voltage 
winding of the voltage transformer. As the result of 
overheating in the high-voltage winding, short-circuits 
occurred. Those short-circuits changed the inductance of 
the voltage transformer, thus the ferroresonance loop 
was changed and process was terminated, but the 
winding damage caused subsequently an explosion. 
The results of simulation have shown impossibility 
of suppression with the aid of valve-type arresters. When 
the voltage of the neutral point reaches a magnitude 
sufficient for operation of a valve-type arrester, break-
down of its spark gaps occurs and a current surge 
appears. Voltage decreases promptly to its minimum 
value, further it rises and then rather slowly decreases 
once more. At the second and third operation of the 
valve-type arrester the voltage is less than at first one. 
Therefore, at consequent operations of the valve-type 
arrester the amplitude of its high-frequency current 
component rises and so the necessity for cutting off the 
current in the valve-type arrester occurs. In turn, it 
prompts recurrence of the voltage ferroresonance. The 
calculation has shown that after actuating the valve-type 
arrester and arc decay of the accompanying current, the 
overvoltage recurs and is repeatedly reduced in the 
course of new operation of the valve-type arrester and 
consequent current decay etc. If the ferroresonant 
overvoltages were not reduced within specifid time 
period, sooner or later the arrester would be destroyed 
due to thermal runaway.  
According to simulation results, the above-mentioned 
ferroresonance can be prevented by ground connection of 
the neutral of the transformer on no-load through the 
63
Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua
Iryna Tugai 
 
resistor during open-phase operation of the power line. 
The value of the resistance in the neutral is determined 
according to following requirements: to ensure preventing 
the ferroresonance, not to interfere with the operation of 
relay protection, to ensure lightning protection of the 
neutral, and to comply with production conditions. Those 
requirements are satisfied when the resistance value is of  
2 k Ω . Apart from the resistor protection of the 
transformer from the ferroresonance, it is suggested that 
the current through the resistor should be continuously 
monitored, otherwise the resistor may be damaged. By the 
way, if the delta winding of the power transformer can be 
open, the conditions of ferroresonance would be 
eliminated.  
For ferroresonance suppression a standard shorting 
device can be used. In this case there are two variants of 
its operation: the short-circuiter is used on live phase, so 
that its actuation causes opening this phase by means of 
a high-voltage circuit breaker; the short-circuiter is used 
on open phase and the current which appears in the 
circuit is approximately equal to the current of the 
transformer on no-load and the voltage on other open 
phase equals 0.5 phase voltage. Therefore, utilization of 
a standard shorting device insures switching-out the line 
(if eliminator is blocked) or interruption of the dangerous 
state [7]. 
5. Conclusion 
The analysis of ferroresonance occurrence in the real 
Ukrainian electrical network at open-phase operating 
conditions has been conducted. Jiles-Atherton model 
allows taking into account the hysteresis effect and 
increasing the reliability of computation results. Thus, 
the result obtained is the nearest equivalent to the real 
situation. The proposed methods of the prevention of 
ferroresonance phenomena help to avoid damage of the 
main equipment of electrical networks. 
References 
[1] A. C. Soudack and J. R. Marti, “Ferroresonance  
in power systems: Fundamental solutions”, IEEE 
Generation, Transmission and Distribution,  
vol. 138, no. 4, pp. 321–329, 1991. 
[2] A. E. Araujo and A. C. Soudack, “Ferroresonance in 
power systems: Chaotic behaviour”, IEEE 
Generation, Transmission and Distribution,  
vol. 140, no. 3, pp. 237–240, 1993. 
[3] L. F. Dmokhovskaya, Engineering calculations of 
internal overvoltages in electrotransmission. 
Moscow, Russia: Energy, 1972. (Russian) 
[4] D. C. Jiles and D. L. Atherton, “Theory of 
Ferromagnetic Hysteresis”, Journal of Magnetism 
and Magnetic Materials, vol. 61, pp. 48–60, 1986. 
[5] D. C. Jiles and J. B. Thoelke, “Theory of 
ferromagnetic hysteresis: determination of model 
parameters from experimental hysteresis loops”, 
IEEE Transactions on Magnetics, vol. 25, pp. 3928–
3930, 1989. 
[6] D. C. Jiles, J. B. Thoelke, and M. K. Devine, 
“Numerical Determination of Hysteresis Parameters 
for Modeling of Magnetic Properties using  
The Theory of Ferromagnetic Hysteresis”, IEEE 
Transactions on Magnetics, vol. 28, no. 1,  
pp. 27–34, 1992. 
[7] Y. I. Tugai and I. Y. Tugai, “A combined method for 
study of ferroresonance processes in voltage 
transformer”, in Proc. IEEE International 
Conference on Intelligent Energy and Power 
Systems, pp. 71–73, Kyiv, Ukraine, 2014. 
ДОСІДЖЕННЯ ФЕРОРЕЗОНАНСІВ В 
ЕЛЕКТРИЧНИХ МЕРЕЖАХ ПРИ 
НЕПОВНОФАЗНИХ РЕЖИМАХ РОБОТИ 
Ірина Тугай 
У цій статті наведено аналіз виникнення і розвитку 
ферорезонансу в реальних електричних мережах. 
Розглянуто необхідні та достатні умови для появи 
ферорезонансного процесу. Показано, що це явище в 
електричних мережах є нелінійним, тому повинні 
застосовуватися спеціальні методи. При проведенні 
розрахунку було використане комп'ютерне моделювання 
та модель Джілса–Атертона, що дозволило взяти до уваги 
ефект гістерезису і підвищити надійність моделювання. 
Запропоновано шляхи запобігання ферорезонансним 
явищам в електричних мережах при неповнофазних 
режимах роботи. 
 
 
Iryna Tugay graduated from 
National Technical University of 
Ukraine “Kyiv Polytechnic Institute” 
(major in “Electrical Networks and 
Systems”). She defended her PhD 
dissertation at the Institute of 
Electrodynamics of NAS of 
Ukraine, in Electrical Power Plants, 
Networks and Systems. She has 
been working as Senior Research  
Fellow at the Department of Power-Supply Systems 
Optimization of Institute of Electrodynamics. Her areas of 
interest include electrical networks and supply systems, 
computer simulation of power systems. 
 
 
 
64
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INVESTIGATION OF FERRORESONANCE IN ELECTRICAL NETWORKS AT OPEN-PHASE OPERATING CONDITIONS

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INVESTIGATION OF FERRORESONANCE IN ELECTRICAL NETWORKS AT OPEN-PHASE OPERATING CONDITIONS

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