IEC TR 61869-102:2014

IEC TR 61869-102 ®
Edition 1.0 2014-01
TECHNICAL
REPORT
colour
inside
Instrument transformers –
Part 102: Ferroresonance oscillations in substations with inductive voltage
transformers
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IEC TR 61869-102 ®
Edition 1.0 2014-01
TECHNICAL
REPORT
colour
inside
Instrument transformers –
Part 102: Ferroresonance oscillations in substations with inductive voltage

transformers
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
XA
ICS 17.220.20 ISBN 978-2-8322-1308-7

– 2 – TR 61869-102 © IEC:2014(E)
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Introduction to ferroresonance oscillations . 8
3.1 Definition of ferroresonance . 8
3.2 Excitation of steady state and non-steady state ferroresonance
oscillations . 10
4 Single phase and three phase oscillations . 12
4.1 Single phase ferroresonance oscillations . 12
4.2 The simplified circuit for the single phase ferroresonance oscillations . 13
4.3 Capacitive voltage transformers . 15
4.4 Three-phase ferroresonance oscillations . 15
4.4.1 General . 15
4.4.2 Configuration . 15
4.4.3 Ferroresonance generation . 16
4.4.4 Resulting waveform of ferroresonance oscillation . 16
4.4.5 Typical oscillogram of three phase ferroresonance . 19
5 Examples of ferroresonance configurations . 20
5.1 Single-phase ferroresonance power line field in a 245 kV outdoor
substation . 20
5.2 Single phase ferroresonance oscillations due to line coupling . 22
5.3 Three-phase ferroresonance oscillations . 25
6 Inductive voltage transformer (key parts) . 26
7 The circuit of the single-phase ferroresonance configuration . 28
7.1 Schematic diagram . 28
7.2 Magnetisation characteristic . 29
7.3 Circuit losses . 30
8 Necessary information for ferroresonance investigation . 31
8.1 General . 31
8.2 Single phase ferroresonance. 31
8.3 Three phase ferroresonance . 32
9 Computer simulation of ferroresonance oscillations . 33
9.1 General . 33
9.2 Electrical circuit and circuit elements . 33
9.3 Circuit losses . 33
9.4 Examples of simulation results for single phase ferroresonance
oscillations . 33
9.4.1 General . 33
9.4.2 Case 1: Transient, decreasing ferroresonance oscillation . 34
9.4.3 Case 2: Steady-state ferroresonance oscillation at network
frequency . 34
9.4.4 Case 3: Steady-state subharmonic ferroresonance oscillation. 35
9.4.5 Case 4: Steady-state chaotic ferroresonance oscillation . 36
9.5 Simulation of three phase ferroresonance . 37

TR 61869-102 © IEC:2014(E) – 3 –
10 Experimental investigations, test methods and practical measurements. 38
10.1 General . 38
10.2 Single-phase ferroresonance oscillations . 38
10.3 Three-phase ferroresonance oscillations . 41
11 Avoidance and suppression of ferroresonance oscillations . 42
11.1 Flow diagram . 42
11.2 Existing substations . 44
11.3 New projects . 44
11.4 Avoidance of ferroresonance oscillations . 44
11.4.1 General . 44
11.4.2 Single phase ferroresonance oscillations . 44
11.4.3 Three phase ferroresonance oscillations . 45
11.5 Damping of ferroresonance oscillation . 45
11.5.1 General . 45
11.5.2 Single-phase ferroresonance oscillations . 45
11.5.3 Three-phase-ferroresonance oscillations . 47
Annex A (informative) Oscillations in non-linear circuits . 49
A.1 Overview . 49
A.2 The simplification of non-linear electrical circuits with the theorem of
Thévenin . 51
A.3 The differential equation for ferroresonance oscillations . 51
A.4 Oscillation frequencies in ferroresonance systems . 53
Bibliography . 54

Figure 1 – Example of a typical magnetisation characteristic of a ferromagnetic core . 9
Figure 2 – Schematic diagram of the simplest ferroresonance circuit . 9
Figure 3 – Examples of measured single-phase ferroresonance oscillation with
16 / Hz oscillation . 11
Figure 4 – Schematic diagram of a de-energised outgoing feeder bay with voltage
transformers as an example in which single-phase ferroresonance oscillations can
occur . 12
Figure 5 – Diagram of a network situation that tends toward single-phase
ferroresonance oscillations, in which they can be excited and maintained over the
capacitive coupling of parallel overhead power line systems . 13
Figure 6 – Electrical circuits for theoretical analysis of a single-phase ferroresonance
oscillation . 14
Figure 7 – Insulated network as an example of a schematic diagram of a situation in
which a three-phase ferroresonance oscillation can occur . 15
Figure 8 – Phasor diagram to explain the oscillation of the earth potential . 16
Figure 9 – Laboratory test set used by Bergmann . 17
Figure 10 – Domains in the capacitance C and line voltage U where different harmonic
and sub-harmonic ferroresonance oscillations are obtained for a given resistance R of
6,7 Ω in Bergmann’s test set . 18
Figure 11 – Domains in the capacitance C and line voltage U where second sub-
harmonic ferroresonance oscillations are obtained for a variation of the resistance R in
Bergmann’s test set . 18
Figure 12 – Domains in the capacitance C and line voltage U where different modes of
second sub-harmonic ferroresonance oscillations are obtained for a given resistance R
of 6,7 Ω in Bergmann’s test set . 19
Figure 13 – Fault recorder display of a three-phase ferroresonance oscillation . 20

– 4 – TR 61869-102 © IEC:2014(E)
Figure 14 – Switching fields in the 245 kV substation in which single-phase
ferroresonances occur . 21
Figure 15 – Examples of oscillations of single-phase ferroresonance when switching off
the circuit breaker in Figure 14 . 22
Figure 16 – Single-phase schematic of the network situation on the 60 kV voltage level
in the area of substations 1, 2, and 3 . 23
Figure 17 – Tower schematic of the common stretch of overhead lines between
substations 1 and 2 . 24
Figure 18 – Ferroresonance oscillations recorded in line no. 5 at Substation 2 . 24
Figure 19 – Single-line diagram of the 170-kV substation (left) and the 12-kV
substation (right); where during switching operation three phase ferroresonance
oscillations occurred . 25
Figure 20 – Oscillograms of the three-phase voltages at inductive voltage transformer
T04 (Figure 19) . 26
Figure 21 – Schematic circuit of voltage transformer and the simplification for
ferroresonace studies . 27
Figure 22 – Circuit for the analysis of single-phase ferroresonance oscillation . 29
Figure 23 – Example of a hysteresis curve of a voltage transformer core measured at
50 Hz . 30
Figure 24 – Schematic diagram for three phase ferroresonance oscillation . 32
Figure 25 – Transient decreasing ferroresonance oscillation with the fifth subharmonic
50/5 Hz (10 Hz) . 34
Figure 26 – Steady state ferroresonance oscillation with network frequency . 35
Figure 27 – Steady state ferroresonance oscillation with 10 Hz . 36
Figure 28 – Steady state chaotic ferroresonance oscillation . 37
Figure 29 – Example of the connection of a measuring resistor for capturing the current
signal through the voltage transformer’s primary winding at terminal N (see connection
diagram in Figure 30) . 39
Figure 30 – Current measurement through voltage transformer’s primary winding and
the voltage at the secondary winding . 40
Figure 31 – Measurement of a single-phase ferroresonance oscillation . 41
Figure 32 – Measurement of three-phase ferroresonance oscillations with an
oscilloscope . 42
Figure 33 – Flow diagram for analysis and avoidance of ferroresonance oscillations. 43
Figure 34 – Electrical circuit with damping device (red circles) connected to the
secondary winding of the voltage transformer . 45
Figure 35 – Example of successful damping of single-phase ferroresonance
oscillations of 16 / Hz . 46
Figure 36 – Damping of the ferroresonance oscillation in the open delta connection of
the voltage transformers in the feeder bay . 47
Figure 37 – Damping of ferroresonance oscillations with voltage transformer in the star
point of the power transformer . 48
Figure A.1 – A simplified electrical circuit for the analysis of ferroresonance oscillation . 49
Figure A.2 – Diagram for the derivation of non-linear differential equation of second
order . 52
Figure A.3 – A non-linear oscillation system. 53

Table 1 – Types of excitation and possible developments of ferroresonance oscillations. 10
Table 2 – Parameters . 31

TR 61869-102 © IEC:2014(E) – 5 –

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
INSTRUMENT TRANSFORMERS –
PART 102: FERRORESONANCE OSCILLATIONS IN SUBSTATIONS
WITH INDUCTIVE VOLTAGE TRANSFORMERS

FOREWORD
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example "state of the art".
IEC 61869-102, which is a technical report, has been prepared by IEC technical
committee 38: Instrument transformers.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
38/440A/DTR 38/445/RVC
– 6 – TR 61869-102 © IEC:2014(E)

Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all the parts in the IEC 61869 series, published under the general title Instrument
transformers, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
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IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
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TR 61869-102 © IEC:2014(E) – 7 –
INTRODUCTION
During the last twenty years ferroresonance oscillations in substations with inductive voltage
transformers according to IEC 61869-3 or with combined transformers according to
IEC 61869-4 were discussed in the international Cigré working groups and in IEEE
committees in the US.
The results were published in Cigré [1] technical report or IEEE [2] publications.
The reasons for these publications were the more frequent occurrence of ferroresonance
oscillations in substations. As a consequence of the price pressure on the operating
authorities and the component manufacturers such as instrument transformers, power
transformers and grading capacitors for high-performance circuit breakers have led to an
increasingly higher exploitation of the system and components.
This trend results in:
a) the shift from normal rated voltage U in the direction of the maximum permitted highest
pr
voltage for equipment U (IEC 60071-1 [3]);
m

ˆ
b) increasing the flux density B by reducing the cross-section of the core of the inductive
voltage transformer;
c) the reduction of the substation capacitance by using new components (e.g. MV and HV
instrument transformers) leads to an increase of the excitation-voltage for the non-linear
circuits;
d) reduction of the actual burden in the substation by using digital meters and relays with
burden of approximately 1 VA, while still specifying the high nominal burden (50 VA to
400 VA) for the inductive voltage transformer. However, even these higher burdens are
often not sufficient to prevent ferroresonance oscillations.

– 8 – TR 61869-102 © IEC:2014(E)
PART 102: INSTRUMENT TRANSFORMERS –
FERRORESONANCE OSCILLATIONS IN SUBSTATIONS
WITH INDUCTIVE VOLTAGE TRANSFORMERS

1 Scope
This part of IEC 61869 provides technical information for understanding the undesirable
phenomenon of ferroresonance oscillations in medium voltage and high voltage networks in
connection with inductive voltage transformers. Ferroresonance can cause considerable
damage to voltage transformers and other equipment. Ferroresonance oscillations may also
occur with other non-linear inductive components.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 61869-3, Instrument Transformers – Part 3: Specific requirements for inductive voltage
transformers
IEC 61869-5, Instrument Transformers – Part 5: Specific requirements for capacitive voltage
transformers
3 Introduction to ferroresonance oscillations
3.1 Definition of ferroresonance
Ferroresonance refers to non-linear oscillations that can occur in switching facilities where
inductive components with a ferromagnetic core, together with capacitances and an AC
voltage source comprise a system capable of oscillation. Numerous reports and publications
on occurrences of ferroresonance have already been documented in the first half of the last
century. A classic example of these occurrences comes from R. Rüdenberg [4]. His research
was only done for fundamental frequencies; others carried out research on harmonics and
subharmonics. A modern, didactically prepared introduction to ferroresonance problems can
be found in K. Heuck and K.-D. Dettmann [5]. Much-cited basic examinations of the wide
variety of ferroresonance oscillations were described by Bergmann [6, 7]. A review article on
the problem was presented at the Cigré Conference in 1974 [1].
All ferromagnetic materials only allow themselves to be magnetised to a certain saturation flux

density B . If inductive voltage transformers are magnetised over their saturation flux density,
S


ˆ
the relationship between the magnetic field strength H and the magnetic flux density B are
eff
given by a strong non-linear characteristic (Figure 1). This means that the main inductance of
an inductive voltage transformer in excess of the saturation flux density will collapse to a
small fraction. This occurrence of core saturation plays an important role in the phenomena of
ferroresonance.
Ferroresonance oscillations will only occur in configurations in high and medium voltage
substations or in sections of networks. Single phase oscillations will occur in systems in which
the high voltage winding of the inductive voltage transformer is connected in series with a

TR 61869-102 © IEC:2014(E) – 9 –
capacitance to the AC voltage source (Figure 2). Three phase oscillations occur in systems in
which the low voltage side of the power transformer is isolated from earth.
The above gives a basic picture about ferroresonance. In practice, ferroresonance can occur
in many complicated network situations.
^ 2
B [T = Vs/m ]
1.5
0.5
0 200 400 600 800 1000 1200 1400
H  [A/m]
eff
IEC  3021/13
Key
∧

Peak value of flux density in the iron core
B

Effective value of magnetic field strength in the iron core
H
eff
The curve is valid for cold-rolled Si-iron (standard material).
Reproduced from [8], with the permission of ewz/CH.
Figure 1 – Example of a typical magnetisation characteristic of a ferromagnetic core
CC
ss
LL (|(|BB||))
HH
uu((tt))
uu ((tt))
ss
||BB((ii))||
uu ((tt))
LL
HH
ii((tt))
Key
IEC  3022/13
u(t) AC voltage source
u (t) Voltage at series capacitance
S
u (t) Voltage at the main inductance of the voltage transformer (VT)
LH
i(t) Circuit current
C Series capacitance
S

Flux density as function of the current i(t)
B(i(t))

L ( ) Non-linear main inductance of voltage transformer
B
H
Reproduced from [8], with the permission of ewz/CH
Figure 2 – Schematic diagram of the simplest ferroresonance circuit

– 10 – TR 61869-102 © IEC:2014(E)
In practice, parts of networks endangered by ferroresonance are usually comprised by other
high voltage equipment, which also play a role in determining the conditions for the
occurrence of ferroresonance oscillations.
Due to the small inductance of the saturated voltage transformer at maximum saturation of the
core, the very large excitation current leads to a quick reverse of the polarity of the charge of
the series capacitances.
Oscillations resulting from excitation of a resonance circuit in substation sections can also
occur without saturation of voltage transformers. Such linear oscillations usually occur at
operating frequency and have a sinusoidal wave form.
From the theory of non-linear oscillations and modern stability theory [9] for non-linear
systems follows that the occurrence of steady state oscillations requires a system comprised
of an equivalent capacitor, a non-linear inductance, and an AC voltage source for covering
system losses. The non-linear element for such a system is the main inductance of the
inductive voltage transformer. When the voltage increases non-linear oscillations are gene-
rated on account of the saturation characteristics of the magnetic flux density according to the
 
time depending function B(t)= f (H(t)). This is a non-linear, time-invariant relationship (hys-
teresis curve of the magnetic material used), indicated by the limitation characteristic [10].
The difficulty in determining whether any steady state non-linear oscillations are occurring is
due to the fact that only estimated values are available for the earth capacity C and for the
e
configuration of the capacitors and especially for the losses occurring in the substation on
account of the leakage current from the high-voltage insulators (porcelain or composite) in air
insulated substations.
The economic aspects of ferroresonance have also been discussed, and it shall be
summarized that already in the planning stage of substations using inductive voltage
transformers, there should be an investigation about the possibility of non-linear oscillations.
This requires cooperation between switchgear manufacturers and instrument transformer
manufacturers, as well as system operators [9]. This process describes the most economical
solution. Ferroresonance investigations have also proven their worth in model substations. It
is more costly to eliminate ferroresonance at existing substations if cases of non-linear
oscillations (ferroresonance) arise as a result of component replacement such as grading
capacitors of circuit breakers, coupling capacitors or inductive voltage transformers.
3.2 Excitation of steady state and non-steady state ferroresonance oscillations
A ferroresonance oscillation can be gradually ramped up by a small disturbance (“soft
excitation”). Upon soft excitation the oscillations will begin at low initial amplitude.
However, ferroresonance is in most cases caused or “triggered” as a result of a switching
transient through which the core becomes saturated (“hard excitation”).
Table 1 (reproduced from [8]) gives an overview of the two kinds of excitation and the
possible developments of ferroresonance oscillations.
Table 1 – Types of excitation and possible developments of ferroresonance oscillations
Soft excitation
Slow increasing oscillation when 1a: Steady state ferroresonsnce oscillations
ferroresonance conditions are met 1b: Non-steady state increasing ferroresonance oscillations
Hard excitation
e.g. through sudden saturation of a transformer 2a: Steady state ferroresonance oscillations
core on account of a switching operation or 2b: Non-steady state increasing ferroresonance oscillations
through an intermittent earth fault, etc. 2c: Non-steady stae decreasing ferroresonance oscillations

TR 61869-102 © IEC:2014(E) – 11 –
Ferroresonance oscillations can become steady state or non-steady state (as shown in
Figure 3) with increasing or decreasing amplitude. Increasing ferroresonance oscillations can
lead to thermal dielectric destruction of the inductive voltage transformer or to a flashover in
the substation.
HHaardrd SSteteaaddyy s statatete ffererrororresesoonnaanncece
oossccillaillattioionn
exexcicittaattiioonn
uu(t) [k(t) [kVV]] 8888
--4444
--4444
VVololttageage a accrrososss t thhee
--8888
--8888
volvolttageage t trrananssfforormmeerr
--11--3232132132
--176176
--117676
ii(t) [(t) [mAmA]]
CCururrreentnt t thrhroougugh th thehe
volvolttageage t trrananssfforormmeerr
--2020
--2020
330000 440000
0000 110000 220000 350350 400400
5050 100100 150150 200200 250250 300300
t/t/msms IEC  3023/13
titimeme [ [mmss]]
a) Single-phase steady state ferroresonance oscillations, type 2a according to Table 1
CCapapacaciittveve
DDececrreaeassiinngg
HHaardrd
cocouupplleded
ffererrororresesoonnaanncece
exexcicittaattiioonn AACC vol volttageage
oossccillaillattioionn
uu(t) [k(t) [kVV]]
tt
-44-44
--4444
VVololttageage a accrrososss t thhee
-88-88
--8888
VVololttageage t trrananssfforormmeerr-132-132
--113232
-176-176
--117676
ii(t) [(t) [mAmA]]
tt
CCururrreentnt t thrhroougugh th thehe
-10-10
--2020
volvolttageage t trrananssfforormmeerr
00 100100 200200 300300 400400 500500 600600 700700
00 110000
t1t1 t3t3 220000 330000 440000t3t3 550000 660000
tt//msms
IEC  3024/13
titimeme [ [mmss]]
b) Single-phase decreasing ferroresonance oscillations, type 2c according to Table 1

Reproduced from [8], with the permission of Amprion (formerly RWE).
Figure 3 – Examples of measured single-phase ferroresonance oscillation
with 16 / Hz oscillation
i/mi/mAA
u/u/kkVV
ii//mAmA
uu//kVkV
– 12 – TR 61869-102 © IEC:2014(E)

Decreasing ferroresonance oscillations will not cause damages to voltage transformers.
Steady state oscillations will increase the current in the primary transformer windings and
ultimately damage transformers through overheating. The damage caused by increasing non-
steady state oscillations is obvious.
Current and voltage waveforms of the primary winding are shown in Figure 3a) for steady
state ferroresonance resulting from a hard excitation caused by a switching operation, and in
Figure 3b) for non-steady state, decreasing ferroresonance.
The occurrence of decreasing ferroresonance oscillations as shown in Figure 3b) is defined
by statistic events: for example by the instance of switching.
4 Single phase and three phase oscillations
4.1 Single phase ferroresonance oscillations
Individual phases of a de-energised, non-earthed equipment section containing one or more
inductive voltage transformers will be excited to oscillations independent of one another by
the network voltage over a coupling capacity C . Single-phase ferroresonances can occur in
C
all systems independently of the star point earthing.
An example of a switching configuration in which a single-phase ferroresonance can occur is
shown in Figure 4. It illustrates one phase of a disconnected outgoing feeder bay at an air
insulated substation. The coupling to the voltage network in this case happens over the
grading capacitors of the open circuit breaker.
S
CB S
1 L
CT VT
IEC  3025/13
Key
S Substation disconnector, closed
CB Circuit breaker, open
CT Current transformer
VT Voltage transformer
S Outgoing line disconnector opened
L Outgoing power lines, earthed

Reproduced from [8], with the permission of ewz/CH.
Figure 4 – Schematic diagram of a de-energised outgoing feeder bay
with voltage transformers as an example in which single-phase
ferroresonance oscillations can occur

AA NN
aa nn
TR 61869-102 © IEC:2014(E) – 13 –
An alternative configuration that tends toward ferroresonance oscillations is that of a de-
energised overhead power line system L if it is on the same supporting tower as an
MV
activated system of a higher voltage level L . This situation is shown in Figure 5. The
HV
phases of the de-energised system remain unearthed and they are connected to voltage
transformers on one or both ends. In some circumstances this can lead to an excitation
causing ferroresonance oscillations via the coupling capacity C between the conductor wires
C
of the energised and de-energised overhead power lines. In this case the individual phases
will oscillate independently from one another.
LL
HVHV
L1L1
L2L2
L3L3
CC
CC CC
CCLL11 CCLL22
CCLL33
CCBB CCBB
11 22
CCTT
VTVT SS SS VTVT CCTT
11 11 22 22 22
P1P1 P2P2 P1P1 P2P2
LL
MVMV
S1S1 S2S2 CC S1S1 S2S2
EE
IEC  3026/13
Key
L Affected phase of the overhead power lines
MV
L Overhead power line system of a higher voltage level
HV
C , C , C Coupling capacitances between the phase under observation and the phases of the parallel
CL1 CL2 CL3
system of a higher voltage level
C Earth capacity
e
CT , CT Current transformers
1 2
VT , VT Voltage transformers
1 2
CB , CB Circuit breaker, open
1 2
S , S Disconnector switch, closed
1 2
Reproduced from [8], with the permission of ewz/CH.
Figure 5 – Diagram of a network situation that tends toward single-phase
ferroresonance oscillations, in which they can be excited and maintained over
the capacitive coupling of parallel overhead power line systems
4.2 The simplified circuit for the single phase ferroresonance oscillations
The previously treated considerations and schematics will not be sufficient for a theoretical
analysis of ferroresonance oscillations. In order to predict the occurrence of ferroresonance
oscillations a more detailed definition and description of the electrical components and their
characteristics is necessary. Figure 6 illustrates the general schematic circuits for the analysis
of single-phase ferroresonance oscillation. Figures 6a) and 6b) show two different ways of
excitations. A detailed treatment of the analysis and simulation methods with examples is
found in Clause 9.
AA
NN
nn aa
– 14 – TR 61869-102 © IEC:2014(E)
CC
gg
ZZ
ZZ CBCBCBCB
HSHS
NN
ZZ
ZZ
NSNS11
NSNS22
uu ((tt))
CC RR
ee ee
CC
HSHS
RR LL
FFee
HH
ZZ
ZZ
B1B1
B2B2
wwiindinding 1ng 1 wwiindinding 2ng 2
VTVT p primrimaaryry
VVTT s sececoondndararyy
IEC  3027/13
a) Excitation of ferroresonance oscillation through a grading capacitor
CC
CC
CBCB
ZZ ZZ
HSHS
NN
ZZ ZZ
NSNS11 NSNS22
uu ((tt)) uu ((tt))
CC RR
22 ee ee
CC
HSHS
LL
RR
HH
FFee
ZZ
ZZ
B1B1 B2B2
wwiindinding 1ng 1
wwiindinding 2ng 2
VTVT p primrimaaryry
VVTT s sececoondndararyy
IEC  3028/13
b) Ferroresonance oscillation caused by a parallel system
Key
C Total earth capacitance
e
C Capacitance of the HV-winding of voltage transformer
HS
C Coupling capacitance to a parallel system of a higher voltage level
C
C Capacitance of the grading capacitor of circuit breaker CB
g
R External resistance phase-earth e.g. through currents in dirty surfaces, corona
e
currents, and currents of metal oxide arrestors
R Non-linear resistance representing the iron losses of the inductive VT
Fe
L Non-linear main inductance of the HV-winding of the inductive VT
H
u (t) Phase to earth voltage before the circuit breaker in the system
u (t) Voltage of a neighbouring system of a higher voltage level with which there is a
capacitive coupling
VT Voltage transformer
Z Impedance of the burden of secondary winding 1 (load impedance and inductance)
B1
Z Impedance of the burden of secondary winding 2 (load impedance and inductance)
B2
Z Impedance of the HV winding (resistance and stray inductance)
HS
Z Network impedance
N
Z Impedance secondary winding 1 (resistance and stray inductance)
NS1
Z Impedance secondary winding 2 (resistance and stray inductance)
NS2
Reproduced from [8], with the permission of ewz/CH.
Figure 6 – Electrical circuits for theoretical analysis of a single-phase
ferroresonance oscillation
TR 61869-102 © IEC:2014(E) – 15 –
4.3 Capacitive voltage transformers
Conventional capacitive voltage transformers have an inductive intermediate transformer and
a compensation coil. Together with the primary and secondary capacitor they contain all the
components required to form a ferroresonance circuit. Therefore capacitive voltage
transformers can generate ferroresonance oscillations without additional series capacity.
Their design shall be arranged to exclude the possibility of a steady state ferroresonance
oscillation under all possible operational conditions (IEC 61869-5).
The most commonly used methods for damping the ferroresonance oscillations in capacitive
voltage transformers are LC-resonant circuits with low losses at 50/60 Hz, rated for
2 1 4
16 / /20 Hz, 10/12 Hz and 7 / /8 / Hz.
3 7 7
4.4 Three-phase ferroresonance oscillations
4.4.1 General
Three phase ferroresonance oscillations will occur in substations or network sections with
single-phase voltage transformers where the star point of the secondary side of the power
transformer is not solidly earthed. All three phases are involved in the ferroresonance
oscillation.
4.4.2 Configuration
Figure 7 illustrates a configuration vulnerable to ferroresonance as it occurs in networks with
a non-solidly earthed star point, if the voltage transformers are connected line to earth.
CCBB
CC
ee
LL
HH
CCooncnceentntrraatteedd e eaarrtthh
VoVoltagltagee t tranransfosformrmeersrs
capcapaacitacitancesnces
IEC  3029/13
Reproduced from [8], with the permission of ewz/CH.
Figure 7 – Insulated network as an example of a schematic diagram of a situation in
which a three-phase ferroresonance oscillation can occur
If voltage transformers are connected to the low voltage side of a power transformer, which is
energised on the high voltage side, saturation of one voltage transformer can lead to over
voltages on the other phases, if the star point of the secondary side of the power transformer

– 16 – TR 61869-102 © IEC:2014(E)
is not solidly earthed. The star point will thus shift and ultimately produce oscillations, driving
all three voltage transformers to alternately become saturated.
This move
...