Validation of a Power Transformer Model for
Ferroresonance with System Tests on a 400 kV
Circuit
Charalambos Charalambous1, Z.D. Wang1, Jie Li1, Mark Osborne2 and Paul Jarman2
Abstract-- National Grid has performed in the past a number
of switching tests on a circuit configuration which was known to
exhibit ferroresonance. The aim of the tests was to establish the
likelihood of ferroresonance and quantify the effect on
switchgear due to the de-energisation of a power transformer
attached to a long over head line circuit. This paper, describes
and compares the modeling work carried out in ATP
(commercially available software) with the field ferroresonance
test recordings. The accomplishment of a suitable simulation
model will allow sensitivity studies to be carried out to determine
the degree of influence of different components and parameters
on the ferroresonance phenomenon.
Keywords: ATP, Ferroresonance,
Simulation Model, Field Tests.
Power
Transformer,
I. INTRODUCTION
Certain
Failing to detect or remove a ferroresonant condition can
result in overheating of parts of the transformer as it is being
repeatedly driven into magnetic saturation by the
ferroresonance. Both instrument transformers and power
transformers can be subject to ferroresonance.
In 1998 National Grid performed a number of switching
tests on a circuit configuration which was known to exhibit
ferroresonance.
This paper describes the modeling work carried out in ATP
[2] (commercially available software) to reproduce the field
ferroresonance
tests
performed.
Furthermore,
the
accomplishment of a suitable simulation model will allow the
authors to perform sensitivity studies to determine the degree
of influence of different components and parameters on the
ferroresonance phenomenon [3].
circuit configuration of the UK transmission
network provides an ideal environment for ferroresonance to
occur. The possibility of Ferroresonance can be eliminated by
the use of additional circuit brakers; however the economic
justification needs to be carefully considered. Ferroresonance
can be established when a transformer feeder circuit has been
isolated, but continues to be energized through capacitive
coupling to the energized parallel circuit [1].
A particular example is when one side of a double circuit
transmission line connected to a transformer is switched out
but remains capacitively energized, normally at a subharmonic frequency, because of coupling from the parallel
circuit. Recovering from this condition requires the operation
of a disconnector or earth switch on the resonating circuit,
potentially resulting in arcing and damage, or switching off
the parallel circuit resulting in an unplanned double circuit
outage.
II. THE 400KV DOUBLE CIRCUIT CONFIGURATION
A. Physical Circuit Description and Testing
The Brinsworth/ Thorpe Marsh circuit was identified as a
suitable circuit that could be induced to resonate, and that
could be reasonably accessed. The purpose of the tests was to
establish the likelihood of ferroresonance to occurring and the
impact on the switchgear during quenching of the condition.
[4].
Figure 1 illustrates a single line diagram of the Brinsworth/
Thorpe Marsh circuit arrangement. The length of the parallel
overhead line circuit is approximately 37km and the feeder
has a 1000 MVA 400/275/13 kV power transformer.
SGT1
X303 OPEN
X103 CLOSED
X113 CLOSED
T10 OPEN
Cable 170 m
X420 POW
switching
Mesh Corner 3
Thorpe Marsh 400 kV
1. Charalambos Charalambous Zhongdong Wang and Jie Li are with the
School of Electrical and Electronic Engineering, The University of
Manchester,
Manchester,
M60
1QD,
U.K
(charalambos.charalambous@manchester.ac.uk,
zhongdong.wang@manchester.ac.uk).
2. Mark Osborne and Paul Jarman are with National Grid, UK
(mark.osborne@uk.ngrid.com, paul.jarman@uk.ngrid.com).
Presented at the International Conference on Power Systems
Transients (IPST’07) in Lyon, France on June 4-7, 2007
Cable 170 m
SGT2
Brinsworth 275 kV
Fig. 1. Single line diagram of the Brinsworth / Thorpe Marsh circuit
arrangement
It should be noted this is not a normal running
arrangement, however to facilitate the testing this
configuration was used on the day. The circuit equipment
conditions prior to Ferroresonance testing are as follows: At
Thorpe Marsh 400 kV substation side the disconnector X303
was locked open and mesh corner 3 restored to service. At
Brinsworth 275kV substation the circuit breaker T10 is open.
At Brinsworth 400kV substation all disconnectors and circuit
breaker X420 are in service. Point-on-wave (POW) switching
was carried out on the Brinsworth/ Thorpe Marsh circuit using
circuit breaker X420 to induce Ferroresonance. This type of
switching prevents switching overvoltage conditions and
provides a degree of controllability to the tests. The circuit
breaker was tripped via an external POW control device.
data available and is illustrated by Table I.
For cylindrical coil construction, it is assumed that the flux
in the winding closest to the core will mostly go through the
core, since there should be very little leakage. This winding is
usually the tertiary winding, and is therefore best to connect
the nonlinear inductance across the tertiary terminals.
Although attaching the non-linear effect externally is an
approximation, it is reasonably accurate for frequencies below
1 kHz [5].
TABLE I
TRANSFORMER MAGNETIZING CHARACTERISTICS
Current (A)
Flux Linkage
(Wb-turn)
7.18
48.77
7.85
52.02
8.35
55.27
19.37
58.52
35.40
61.77
78.48
65.02
222.09
65.92
5531.04
66.72
After each switching operation the POW switching control
was advanced by 1ms. At +3ms POW switching, a subharmonic mode ferroresonance was established, while at
+11ms POW a fundamental mode ferroresonance was
induced. The ferroresonance voltage and current waveforms
available from field tests are illustrated in Appendix I .The
waveforms presented correspond to the fundamental and
subharmonic case.
B. Simulation Model Description
An ATP model has been developed to simulate the testing
carried out on the circuit with the ultimate purpose to match
field recordings that were available. Figure 2 illustrates a
layout of the simulation model, which includes a description
of the components of the model.
The main components of the network are: a parallel
overhead line circuit (37 km) modeled considering the
transmission line characteristics (typical overhead line
spacings for a 400kV double circuit) [7], a transformer model
utilizing the BCTRAN transformer matrix mode. Saturation
effects have been considered by attaching the non- linear
characteristics externally in the form of a non-linear inductive
element branch.
ATP Draw Model
6.3 m
9.12 m
9.12 m
7.12 m
7.12 m
Series and Shunt
capacitances of
windings
40.5m
30.8m
TV BUS A
21.5m
TV BUSB
C. Transformer Characteristics and Data
The transformer characteristics available are tabulated in
Table II.
TABLE II
TRANSFORMER CHARACTERISTICS
Rating
Type
Core Construction
Vector
Bolt main:
Bolt Yoke:
% Ratio 4&5 \ Y \ M
Transformer nonlinear
characteristics
6.3 m
In low frequency transformer models is possible to
represent each winding as one element. This does not come at
the expense of accuracy. The model also comprises the
interwinding and shunt capacitance elements, which have
been calculated by employing mathematical methods taking
into consideration the transformer equivalent circuit and the
winding disc configurations types.
1000 MVA
400/275/13 kV (auto)
Five Limb Core
Yy0
No
No
60\60\100
12.8m
TV BUSC
TV-LV A TV-LV B TV-LV C
X103
U
X303
X113
LV BUSA LV BUSB LV BUSC
Circuit
Breaker
Committee type
disconnectors
T 10
BCTRAN
model
37km
Cable
170m
HV-LV A
HV BUSC
U
HV BUSB
HV BUSA
HV-LV B
COWL
Circuit
Breaker
X420 POW
The transformer has been modeled in the BCTRAN module
of ATP draw which utilizes an admittance matrix
representation of the form
(1)
[ I ] = [Y ].[V ]
HV-LV C
and in transient calculations can be represented as
SGT 2
Fig. 2. Layout of ATPDraw simulation Model, including a description of the
components characteristics utilized
Non-linear inductances can be modeled as a two slope
piecewise linear inductances, with sufficient accuracy [2]. The
slope in the saturated region above the knee reflects the air
core inductance which is almost linear and low compared with
the slope in the unsaturated region. The transformer
magnetisation curve has been derived from manufacturer’s
[
di
] = [ L] −1 [v] − [ L] −1 ⋅ [ R ][i ]
dt
(2)
The elements of the matrices are derived from open circuit
and short circuit tests that are made in the factory. The data
used in this simulation model include impedances and losses
averaged for the test results of 8 transformers rated at1000
MVA (400/275/13 kV). Saturation effects have been modeled
externally as previously described.
The impedances and load losses can only be measured for
winding pairs, but the designed load capability for the tertiary
winding of this 1000 MVA design is only 60 MVA compared
with the 1000 MVA throughput for the HV and LV terminals.
Thus the H-T and L-T losses and impedances would be
measured at 60 MVA. For this simulation model data a
common base load is chosen to be 1000 MVA.
In service, the tertiary load would never be above 60 MVA
if it was loaded, so the total losses for three-winding loading
would be not much greater than the H-L load loss at 1000
MVA. The impedances and losses averaged for the test results
of 8 transformers are tabulated in Table III.
TABLE III
point has been marked as a reference point to start POW
switching. Fundamental and subharmonic ferroresonance
waveforms have been produced by simulation at a specific
time. Table IV illustrates a comparison between the POW
switching time corresponding to the field tests and to the
simulation model. The ferroresonance voltage and current
waveforms produced by simulation are also illustrated in
Appendix I.
TABLE IV
P.O.W SWITCHING TIME COMPARISON
Field
Waveform
Simulation
Tests
Description
POW switching
Impedance (%)
Power (MVA)
Loss (kW)
HV-LV
15.8
1000
1764
HV-TV
117.2
1000 (60)
28677 (1720.62)
LV-TV
91.5
1000 (60)
29875 (1792.5)
Furthermore, the average no-load loss at rated voltage and
frequency (measured on the tertiary) was 74.4 kW, whilst the
average magnetizing current was 0.012% at 1000 MVA base.
Zero sequence data was not available and therefore zero
sequence data that had been employed in this simulation
model has been set equal to the positive sequence data. This is
a reasonable assumption to make for a 5-limb core transformer
with a tertiary winding. Provision of a tertiary winding on 5limb cores drastically alters the zero sequence impedance,
since zero sequence currents are able to circulate around the
delta tertiary winding and thus balance those flowing into the
primary winding [6].
Without a tertiary winding, the 5 limb core would have a
higher zero sequence impedance (than the case where a
tertiary winding is present) due to the 4th and 5th return limbs
shunting the high reluctance zero sequence path (air path).
The 4th and 5th return limbs of a 5 limb core are of much
reduced section compared with the three main limbs. A zero
sequence test at full load current would cause the 4th and 5th
limbs to saturate and the core would turn into a 3-limb
equivalent. In such a case the assumption of setting the zero
sequence equal to the positive sequence data would not be
valid.
+3 ms
+3.2 ms
Subharmonic Mode
+11 ms
+12.6 ms
Fundamental Mode
control (time)
POW switching
control (time)
The following set of figures illustrates a comparison of a
sector of the final steady state ferroresonance mode
waveforms produced by ATP and those available from field
recordings, for the fundamental and subharmonic case, for
each one of the 3 phases (R, Y, and B).
Figures 4-9 compare the simulation results with the field
results obtained for voltage and current corresponding to
Phase R, Y and B respectively, for the fundamental mode
ferroresonance.
300
250
200
150
Voltage Magnitude (kV)
TRANSFORMER SHORT CIRCUIT FACTORY DATA
100
50
0
-50
-100
-150
-200
-250
2
2.05
2.1
2.15
2.2
Time (s)
Simulation Results_Phase R
Field Test Results_Phase R
Fig. 4. Comparison of Fundamental Mode Ferroresonance- Section of
Voltage waveform – R phase
250
200
150
100
ATP MODEL VERIFICATION
Current (A)
50
III.
0
-50
The circuit conditions described in section A of II, in terms
of the disconnectors and circuit breakers status, were
considered in the simulation model. Circuit breaker X420, was
utilized to carry out POW switching to initiate ferroresonance.
-100
-150
-200
-250
2
2.05
2.1
2.15
2.2
Time (s)
Simulation Results
It should be noted that the circuit breaker X420 was tripped
at a point in time (simultaneously for the three phases) that
would ensure minimum voltages and energy transfer. This
Field Test Results
Fig. 5. Comparison of Fundamental Mode Ferroresonance- Section of Current
waveform – R phase
Figures 10-15 compare the simulation results with the field
results obtained for voltage and current corresponding to
phase R, Y and B respectively, for the subharmonic mode
ferroresonance.
400
300
Voltage Magnitude (kV)
200
100
120
0
100
-100
80
60
Voltage R-Phase (kV)
-200
-300
-400
2
2.05
2.1
2.15
2.2
Time (s)
Simulation Results_Phase Y
40
20
0
-20
Field Test Results_Phase Y
-40
Fig. 6. Comparison of Fundamental Mode Ferroresonance- Section of
Voltage waveform – Y phase
300
-60
-80
-100
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
Field Test Results
200
Fig. 10. Comparison of subharmonic Mode Ferroresonance- Section of
Voltage waveform – R phase
100
Current (A)
Simulation Results
50
0
40
-100
30
20
Current R phase (A)
-200
-300
2
2.05
2.1
2.15
2.2
Time (s)
Simulation Results
10
0
-10
Field Test Results
-20
Fig. 7. Comparison of Fundamental Mode Ferroresonance- Section of Current
waveform – Y phase
-30
-40
-50
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
250
Field Test Results
Simulation Results
200
Fig. 11. Comparison of subharmonic Mode Ferroresonance- Section of
Current waveform – R phase
150
150
50
100
0
-50
50
Voltage Y phase (kV)
Voltage Magnitude (kV)
100
-100
-150
-200
0
-50
-250
2
2.05
2.1
2.15
2.2
-100
Time (s)
Simulation Results
Field Test Results
-150
Fig. 8. Comparison of Fundamental Mode Ferroresonance- Section of
Voltage waveform – B phase
250
1.6
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
Field Test Results
Simulation Results
Fig. 12. Comparison of subharmonic Mode Ferroresonance- Section of
Voltage waveform – Y phase
200
150
80
100
60
50
40
0
Current Y Phase (A)
Current (A)
1.65
-50
-100
20
0
-20
-150
-40
-200
-60
-250
2
2.05
2.1
2.15
2.2
-80
Time (s)
Simulation Results
Field Test Results
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
Fig. 9. Comparison of Fundamental Mode Ferroresonance- Section of Current
waveform – B phase
Field Test Results
Simulation Results
Fig. 13. Comparison of subharmonic Mode Ferroresonance- Section of
Current waveform – Y phase
100
TABLE VI
COMPARISON OF FIELD AND SIMULATION RESULTS (SUBHARMONIC)
80
60
Field Test Results
Voltage B phase (kV)
40
0
-20
Simulation Results
Peak Voltage (kV)
RMS Volt. (kV)
Peak Voltage (kV)
RMS Volt. (kV)
R Phase
90
48.29
75
50.64
Y Phase
100
60
95
69.41
50
37.06
45
41.05
20
-40
B Phase
-60
Field Test Results
-80
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
Field Tests
RMS Cur. (A)
Peak Current (A)
RMS Cur. (A)
R Phase
45
9.28
35
5.6
Y Phase
42
8.997
50
9.3
B Phase
38
8.72
35
5.5
Simulation Results
Fig. 14. Comparison of subharmonic Mode Ferroresonance- Section of
Voltage waveform – B phase
Simulation Results
Peak Current (A)
-100
50
40
The minor differences on the voltage and current
waveforms that appear on the illustrated Figures can also be
seen on the frequency analysis waveforms illustrated by
Figures 16 and 17, for the fundamental and subharmonic case
respectively. Figures 16 and 17 compare the frequency
content of voltage waveforms of the field recording results
and the produced simulation results for one phase.
30
Current B phase (A)
20
10
0
-10
-20
-30
-40
-50
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
Time (s)
Field Test Results
Simulation Results
Fig. 15. Comparison of subharmonic Mode Ferroresonance- Section of
Current waveform – B phase
The figures presented clearly illustrate that the ATP model
can replicate the field recordings with a significant degree of
accuracy, both in the fundamental and subharmonic case.
For the subharmonic case the ferroresonance condition had
a frequency content of 16 2/3 Hz. Table VI tabulates the peak
and rms voltage and current values corresponding to field
recordings and to simulation results.
Fig. 16.
Comparison of Frequency content of voltage waveforms
(Fundamental –Y phase )
TABLE V
COMPARISON OF FIELD AND SIMULATION RESULTS (FUNDAMENTAL)
Field Test Results
Simulation Results (B)
Peak Voltage (kV)
RMS Volt. (kV)
Peak Voltage (kV)
RMS Volt. (kV)
R Phase
210
191
190
151
Y Phase
330
315
325
303
180
173
190
167
B Phase
Field Test Results
Simulation Results
Peak Current (A)
RMS Cur. (A)
Peak Current (A)
RMS Cur. (A)
200
62.56
145
46.45
Y Phase
220
70
220
70.52
B Phase
190
58.93
140
45.79
R Phase
Fig. 17.
Comparison of Frequency content of voltage waveforms
(subharmonic – Y phase)
IV. CONCLUSIONS
For the fundamental case the ferroresonance condition had
a frequency content of 50 Hz. Table V tabulates the peak and
rms voltage and current values corresponding to field
recordings and to simulation results.
Ferroresonance is a low frequency phenomenon that can
occur when a transmission line connected to a transformer is
switched out with the parallel circuit still energised. The
complex UK network is such that a few power transformers
are exposed to ferroresonance on mesh corner and circuit tee
connections, mainly because of historical design precedents.
Fundamental mode ferroresonance R phase Current (A)
Fundamental mode ferroresonance Y phase Current (A)
Fundamental mode ferroresonance B phase Current (A)
300
200
Current (A)
100
0
-100
-200
-300
1500
1550
1600
1650
1700
1750
1800
1850
1900
1950
2000
Time (ms)
Fig. 19. Fundamental Mode Ferroresonance – Current (Field Recordings)
Sub-harmonic mode ferroresonance R phase Voltage (kV)
Sub-harmonic mode ferroresonance Y phase Voltage (kV)
Sub-harmonic mode ferroresonance B phase Voltage (kV)
200
150
Voltage (kV)
100
50
0
-50
-100
-150
-200
1200
1300
1400
1500
1600
1700
1800
1900
Time (ms)
Fig. 20. Subharmonic Mode Ferroresonance – Voltage (Field Recordings)
Sub-harmonic mode ferroresonance R phase Current (A)
Sub-harmonic mode ferroresonance Y phase Current (A)
Sub-harmonic mode ferroresonance B phase Current (A)
100
80
60
40
20
0
-20
-40
Current (A)
A reliable ATP based simulation model can be achieved
when the parameters of the system and transformer are known
or can be derived with reasonable accuracy. The graphical
results presented in this paper clearly demonstrate the
capability of the simulation model to reproduce the field
recordings with a significant degree of accuracy, both in the
fundamental and subharmonic case. The development and
validation of this simulation model with the field recordings
available allowed the authors to perform a number of
sensitivity studies that deal with the effect on ferroresonance
of point on wave (P.O.W) switching, transmission line and
core losses and the interaction between these variables. The
sensitivity studies investigate the effect the above described
interactions have on energy transfer in the transformer, on the
magnitude of ferroresonant voltages and currents and the
duration of overvoltages, etc. The findings are the topic of a
scientific paper submitted [3]. Lastly this simulation model
will form the benchmark and will produce the input data of a
detailed (topologically and geometrically accurate)
transformer model that would enable the understanding of
magnetic field analysis (heating and fluxing) within a
transformer under ferroresonance and its degrading
mechanisms.
-60
-80
-100
1200
1300
1400
1500
1600
1700
1800
1900
Time (ms)
Fig. 21. Subharmonic Mode Ferroresonance – Current (Field Recordings)
B_Phase Voltage
Y_Phase Voltage
R_Phase Voltage
600
The authors gratefully acknowledge the EPSRC – RAIS
funding scheme and National Grid for the financial support.
The authors also acknowledge the technical support provided
by National Grid.
Voltage (kV)
400
V. ACKNOWLEDGEMENT
-600
2.5
[3]
[4]
[5]
[6]
[7]
2.65
2.7
2.75
2.8
2.85
2.9
2.95
3
Fig. 22. Fundamental Mode Ferroresonance – Voltage (Simulation Results)
R_Phase Current
Y_Phase Current
B_Phase Current
Current (A)
200
100
0
-100
-200
-300
2.5
2.55
2.6
2.65
2.7
R_Phase Voltage
2.9
2.95
3
Y_Phase Voltage
B_Phase Voltage
150
100
50
0
-50
-100
-150
-200
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
Time (s)
Fig. 24. Subharmonic Mode Ferroresonance – Voltage (Simulation Results)
Current (A)
0
-100
-200
-300
2.85
200
Fundamental mode ferroresonance R phase Voltage (kV)
Fundamental mode ferroresonance Y phase Voltage (kV)
Fundamental mode ferroresonance B phase Voltage (kV)
300
200
100
2.8
Fig. 23. Fundamental Mode Ferroresonance – Current (Simulation Results)
R_Phase Current
500
400
2.75
Time (s)
VII. APPENDIX
Voltage (kV)
2.6
300
National Grid Seven Year statement ‘Control of Ferroresonance’
Technical Guidance Note, December 2004, National Grid, UK,
www.nationalgrid.com/sys
ATP Rule Book and Theory Book, Can/Am EMTP User Group,
Portland, OR, USA, 1997.
C. Charalambous, ZD Wang, Mark Osborne, Paul Jarman, ‘’ Sensitivity
studies on a power transformer model for ferroresonance on a 400 kV
Circuit. IET Proceedings in Generation, Transmission and Distribution
(Under Review)
‘Ferroresonance Tests on Brinsworth-Thorpe Marsh 400 kV circuit’,
Technical Report TR (E) 389, Issue 1, July 2001, National Grid, UK..
Juan A. Martine-Velasco, Bruce A. Mork, ‘’Transformer Modeling for
Low Frequency Transients – The state of the Art, IPST 2003 New
Orleans, USA.
A.C Franklin, D.P Franklin, The J&P Transformer Book, 12th Revised
edition , Elsevier Science & Technology
British Electricity International, Modern Power Station Practice, EHV
Transmission, Volume K, Pergamon Press
-400
-500
1500
2.55
Time (s)
Voltage (kV)
[2]
0
-200
-400
VI. REFERENCES
[1]
200
Y_Phase Current
B_Phase Current
100
80
60
40
20
0
-20
-40
-60
-80
-100
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
Time (s)
1550
1600
1650
1700
1750
1800
1850
1900
1950
2000
Time (ms)
Fig. 18. Fundamental Mode Ferroresonance – Voltage (Field Recordings)
Fig. 25. Subharmonic Mode Ferroresonance – Current (Simulation Results)