Title:
A New Hysteretic Reactor Model for
Transformer Energization Applications
By:
Afshin Rezaei-Zare & Reza Iravani
University of Toronto
June 2011
Outline
1. Existing hysteresis models in EMT programs
2. Drawbacks of the existing models
3. New hysteretic reactor model
4. Impact on Remnant Flux (Lab. Measurement)
5. De-energization / Re-energization
6. 33kV-VT Ferroresonance Lab. test results
7. Conclusions
8. Applications
Existing Hysteresis Models in
EMT Programs
• EMTP Type-96
• EMTP Type-92
(Current Hysteresis model of the EMTP-RV)
• PSCAD/EMTDC Jiles-Atherton model
(Not a reactor but incorporated in the CT
model)
• Proposed New Hysteretic Reactor
Type 96 model




Piecewise linear model
Originally developed by Talukdar and Bailey in 1976
and modified in 1982 by Frame and Mohan
Simple and computationally efficient
Minor loops are obtained by linearly decreasing the
distance between the reversal point and the
penultimate reversal point
Drawbacks of Type 96 Model
 No stack is used to store the extrema of excitation which
leads to open cycles
 Similarity of minor loops to the major loop due to scaling
approach used by the model
(such a similarity is not valid in reality)
 The existence of a saturation point is not verified
experimentally
 The model implemented in EMTP-V3 is pseudo nonlinear
Drawbacks of Type 96 Model –
Cont’d
 Noisy behavior and erroneous results (in some transients such as
ferroresonance) due to switching the operating point between two adjacent
branches of the piece-wise linear characteristic (Artificial switching &
Numerical oscillations)
Piece-wise linear model
Smooth nonlinear model
Type 92 model

Developed in 1996 by Ontario Hydro

Based on hyperbolic functions


Instantaneous flux is separated in two components:
i) hysteresis (irreversible)
ii) saturation (reversible)
Current EMTP-RV model is based on this approach
Model Type 92
Hyperbolic functions in Type 92:
instantaneous flux is used to find unsaturated flux
which is then used to find instantaneous current
Saturated flux vs. Unsaturated flux (to
describe saturation)
slope
slope
Unsaturated flux vs. Current (to describe
hysteresis)
Drawbacks of Type 92 Model
Inaccuracy (1)
 Limited flexibility to fit to the hysteresis major loop
(only based on one hyperbolic term)
Raw data
Fitted data
Drawbacks of Type 92 Model
Inaccuracy (2)
 Only upper part of the trajectory is used and the
lower part is assumed to be symmetric to the upper
part (while in reality the shapes of the two parts are
independent)
600
400
Flux(Wb)
200
IC
0
-200
-400
-600
-30
-20
-10
0
Courant(A)
Current (A)
10
20
30
Jiles-Atherton Model
 Physically correct model
 decomposes the magnetization into “reversible
anhysteretic” and “irreversible” components based on a
weighted average:
 Reversible part is based on Langevin function:
 Irreversible part is based on the differential equation:
Drawbacks of the Jiles-Atherton Model
 Limited flexibility to fit to the measurements
due to the utilized Langevin function, and the
model very few parameters (5 parameters)
 In some cases, non-physical results as the
input current changes the direction
 Formations of minor loops and the major
loop are dependent (changing the parameters
changes both minor and major loop shapes)
In the PSCAD/EMTDC, it is not available as a
reactor to build a desired general system for
transient studies.
(Only incorporated in a CT model)
New Hysteretic Reactor Model
• A modified Preisach Model
- a time-domain implementation with true-nonlinear solution within
the EMTP-RV
- Independent formation of minor loops from the major loop (consistent
with the observed hysteresis loops of the magnetic materials)
• Physically correct hysteresis model
• Memory dependent model: past excitation extrema are stored
in memory to form the magnetization trajectories.
• Representing wiping-out property, (a well-known physical
property of the ferromagnetic materials)
New Hysteretic Reactor Model
F  x  , 
 
Major  x  * Minor ( x )
 B tanh(
n
Major ( x ) 
i
 i x )  c i sech (  i x ) 
2
Forms major loop
i 1
1.5
1.5
1
1
Flux Linkage [V.s]
Flux Linkage [V.s]
Minor ( x )  C  D tanh( p ( x  x _ shift ))
0.5
0
-0.5
Major loop
Magnetization
Trajectory
-1
-1.5
-1.5
-1
-0.5
0
0.5
Magnetizing Current [A]
1
Forms minor loop
0.5
0
-0.5
-1
1.5
-1.5
-1.5
-1
-0.5
0
0.5
Magnetizing Current [A]
Same major loops – Different minor loops
1
1.5
New Hysteretic Reactor Model
Hys_Power
scope
m2
VM+
R1
+
ic
60
60Hz
?v
m1
+A
?i
DEV1
+
Voltage
scope Voltage
L
scope
L
Flux
scope
Fulx
Current
scope Current
P
+
20kVRMS /_0
P p1
AC1
New Hysteretic Reactor Model
Hysteresis Shapes
PLOT
PLOT
100
100
80
80
60
60
40
40
20
20
0
y
y
0
-20
-20
-40
-40
-60
-60
-80
-80
-100
-5
-4
-3
-2
-1
0
1
Current@control@1
2
3
4
5
-100
-5
-4
-3
-2
-1
0
1
Current@control@1
2
3
4
5
PLOT
PLOT
100
80
80
60
60
40
40
20
y
y
20
0
0
-20
-20
-40
-40
-60
-60
-80
-80
-5
-4
-3
-2
-1
0
1
Current@control@1
2
3
4
5
-0.6
-0.4
-0.2
0
Current@control@1
0.2
0.4
0.6
Remnant Flux
PLOT
PLOT
100
100
Fulx@control@1
Fulx@control@1
50
80%
y
y
50
40%
0
0
-50
-0.1
0
0.1
0.2
0.3
Current@control@1
0.4
0.5
-50
-0.1
0
0.1
PLOT
0.2
Current@control@1
0.3
0.4
0.5
PLOT
80
50
60
40
-50%
20
y
y
0
0
-20
-50
0%
-40
-60
-100
-0.4
-0.3
-0.2
-0.1
Current@control@1
0
0.1
-80
-0.2
-0.15
-0.1
-0.05
0
Current@control@1
0.05
0.1
0.15
0.2
Harmonic Initialization
m2
VM+
?v
L1
R2
+
30
60kVRMS /_30
m1
+A
?i
+
80mH
+
+
Voltage
L
Flux
Current
P
R1
+
AC2
DEV1
+
30
25kVRMS /_0
C2
+
300nF
scope Voltage
scope L
scope Flux
scope Current
60 Hz
AC1
180 Hz
R3
+
100
AC3
80
R4
+
60
30
y
40kVRMS /_30
+
300 Hz
30
+
40kVRMS /_135
PLOT
120
420 Hz
20
R5
+
0
2k
0 Hz
1
40
AC4
DC1
-20
-40
-0.005
0
0.005
0.01
0.015
Current@control@1
0.02
0.025
0.03
0.035
Impact on Remnant Flux (Lab. Measurement)
Iron Core
im
secondary voltage [V]
VS
2
1.5
1
Magntizing Current*10 [A]
Core Magnetizing Current [A]
im
0.5
Close-up Window
0
0
10
20
30
40
50
60
Time [ms]
70
80
90
100
6
5
4
3
VS
2
1
0
im
-1
40
50
60
70
Time [ms]
80
90
100
Impact on Remnant Flux (Lab. Measurement) –
Cont’d
Major loop
Measured trajectory
0.09
0.08
0.07
Major loop
Measurement
EMTP Type-96
New Reactor
0.02
0.05
0.015
0.04
0.03
0.01
0.02
Flux [V.s]
Flux [V.s]
0.06
0.01
0
-0.01
0
0.5
0.005
0
1.0
Magnetizing Current [A]
-0.005
-0.01
-150
1.5
2.0
-100
-50
Magnetizing Current [mA]
0
50
De-energization / Re-energization
Auto-reclosure operations on a 12kA Fault Current
40
Fault Current [kA]
30
20
10
0.6 sec
1.0 sec
0
-10
-20
-30
0
0.2
0.4
0.6
0.8
1
Time [sec]
1.2
1.4
1.6
1.8
2
Remnant flux
1.5
1.5
1
Flux Linkage [V.s]
Remnant Flux subsequent
to the second current
interruption
0
-0.5
-1
0.5
-1.5
-1.5
-1
-0.5
0
0.5
Magnetizing Current [A]
1
1.5
-1
-0.5
0
0.5
Magnetizing Current [A]
1
1.5
0
1.5
-0.5
1
Major loop
Magnetization
Trajectory
-1
-1.5
-1.5
-1
-0.5
0
0.5
Magnetizing Current [A]
1
Different Minor loop shapes
 Different Remnant Flux
(for the same switching scenario)
Flux Linkage [V.s]
Flux Linkage [V.s]
1
0.5
1.5
0.5
0
-0.5
-1
-1.5
-1.5
Impacts on CT Saturation and protection
Secondary Current [A]
100
(Following the final reclosure on the permanent fault)
50
0
-50
1.79
1.8
1.81
1.82
1.83
Time [sec]
1.84
1.85
1.86
1.8
1.81
1.82
1.83
Time [sec]
1.84
1.85
1.86
1.8
1.81
1.82
1.83
Time [sec]
1.84
1.85
1.86
Secondary Current [A]
100
50
0
-50
1.79
Secondary Current [A]
100
50
0
-50
1.79
33kV-VT Ferroresonance
Laboratory test results
63.5 kV (2.36pu)
60
52.4 kV (1.94pu)
38.4 kV (1.43pu)
Voltage [kV]
40
30.7 kV
(1.14pu)
11.8 kV (0.44pu)
20
0
-20
-40
-60
0
10
20
30
50
40
Time [sec]
60
Source peak voltage
Measured VT voltage
70
80
33kV-VT Ferroresonance Lab Test
63.5 kV (2.36pu)
Voltage
52.4 kV (1.94pu)
60
Voltage [kV]
40
20
0
-20
-40
-60
10
30
250
Pm [W]
200
50
70
90
110
130
Time [ms]
150
170
190
218 W
Power Loss
150
103 W
100
50
0
29 W
210
230
33kV-VT Ferroresonance Lab Test
Model Type-92
Hysteresis Loop
180
160
140
Core Flux [V.s]
120
100
80
60
EMTP-RV
Fitted Hysteresis Loop
Test data
40
20
0
-20
-10
0
10
20
30
40
Magnetizing Current [mA]
50
60
33kV-VT Ferroresonance Lab Test
New Reactor
Hysteresis Loops
100
160
80
140
60
120
40
100
20
 [Vs]
Core Flux [V.s]
180
80
60
40
-20
Measurement
New Reactor
20
0
-40
0
-60
-20
-80
-40
-10
0
10
20
30
40
Magnetizing Current [mA]
Major loop
50
60
-100
-5
New Reactor
Measurement
0
i [mA]
m
Hysteresis loop
at rated voltage
5
33kV-VT Ferroresonance Lab Test
Bifurcation Points
70
65
60
EMTP
Type-96
Hysteretic
Model
Single-valued
Saturation
Model
EMTP-RV
Hysteretic
Model
New Reactor
Model
Measurement
VT Peak Voltage [kV]
55
50
45
40
35
30
25
20
24
25
26
27
28
29
Source Peak Voltage [kV]
30
31
32
33kV-VT Ferroresonance Lab Test
Core Power Loss
220
220
Measurement
EMTP Type-96
200
180
180
160
Power Loss [W]
160
140
120
100
140
120
100
80
80
60
60
40
40
20
20
220
Measurement
New Reactor
200
180
Power Loss
Comparison
Power Loss [W]
Power Loss [W]
Measurement
EMTP-RV
200
160
140
120
100
80
60
40
20
0
50
100
Time [ms]
150
200
33kV-VT Ferroresonance Lab Test – Cont’d
100
100
80
80
60
60
40
40
Core Flux [V.s]
Core Flux [V.s]
Hysteresis Loops Comparison
20
0
-20
-40
-80
-20
-40
-60
-80
Reactor
-100
-6
-4
-2
0
2
Magnetizing Current [mA]
4
6
Measurement
-100
8
-8
100
100
80
80
60
60
40
40
Core Flux [V.s]
Core Flux [V.s]
0
New
-60
-8
20
20
0
-20
-40
-4
-2
0
2
Magnetizing Current [mA]
4
6
8
20
0
-20
-40
EMTP
-60
-80
-6
-4
-2
0
2
Magnetizing Current [mA]
4
6
EMTP-RV
-60
-80
Type-96
-100
-8
-6
(Type 92)
-100
8
-8
-6
-4
-2
0
2
4
Magnetizing Current [mA]
6
8
10
33kV-VT Ferroresonance Lab Test
Dynamic Inductance
( Slope of magnetization trajectories )
250
New Reactor
Measurement
Single-Valued
saturation model
EMTP Type-96
EMTP-RV model
180
160
200
140
[kH]
150
Dyn
L
L
Dyn
[kH]
120
100
100
80
60
40
50
20
0
-100
-50
0
Core Flux [V.s]
50
100
0
-150
-100
-50
0
Core Flux [V.s]
50
Before Ferroresonance
Under Ferroresonance
(Normal conditions)
conditions
100
150
Capability of the models to represent the core
dynamic behaviors
Core Inductance change
As the core is driven into ferroresonance with respect to
normal operation
Model
Change direction
Measurement
New Reactor
EMTP Type-96
EMTP-RV (Type-92)
No change
Single-valued
saturation curve
No change
Another Example –
Comparison between two hysteresis models with the
same major loop but different minor loop formations
Bifurcation diagrams
50
I
III
C
III
S
45
40
35
VT Voltage [kV]
VT Voltage [kV]
100
50
0
30
25
20
15
N
10
-50
5
0
5
10
C [nF]
S
Model 1
15
0
0
2
4
6
C [nF]
S
Model 2
8
10
Ferroresonance demo
SIL2S
b
a
c
SILVS
SILVH
+ VM
+
a
b
c
+ VM
C_SIL2H
a
b
c
CT
+
A3R02
ASROS
ASHERN
C_ASROS
R_ASROS
+
S_A3R_1
+
+
ASROS
S_ASROS
+ VM
c
b
a
S_SCITS
A3R_1
ROSAS
ZnO1
S_ROSDU
+
516kV
R_ROSDU
+
0.01
e_ZnO1a
Zno_energy_a
scope
e_ZnO1b
Zno_energy_b
scope
e_ZnO1c
Zno_energy_c
scope
+
+
C_ROSAS
R_ROSAS
+
8/6.937Ohm
RL1
GRAPD
SILVB
Trip line at T=80 ms and Rf at T=100ms
+
S_SILCT
+
C_SILVH
GRAPD
S_ROSIL
+
TRANSFO1
C_SILVS
95
C_SILCT
SILCT
Current
Transformer
1214/285.6Ohm
Disconnect Silver Charge at T=50 ms
+
+
S_SILRO
+
+
+
S_SILVL
CHARGE_SILVER
+
R_SILCT
+
3-Phases
SA
TransformerHA
SBBCTRANHB
SC
& HC
Hysteresis
C_ROSIL
+
ROSSER_SILVER
+
S_SIL2H
SILVER_230_66
R_SILVL
+
1E12
SILVB
+
TRANSFO2
C_SIL2S
Disconnect S ilver Charge
at t=50 ms
SILVL
a
b
c
C_SIL2H
+ ?vip>e ZnO +
+ VM
+
SILVS
3-Phases
Transformer
BCTRAN
&
Hysteresis
R_SIL2H
+
+
SILVH
SIL2H
SILVER_230_66
A3R_1_SILVB
c
b
a
+
S_ROSAS
ROSSR
+ VM
+ VM
+
+ VM
ROSAS
A3R02
GRG1
DYg_1
S_GRG1
?i
2
1
13.8/230
+
S_GRG2
?i
G1A_G2A
GRG2
234.35
+
S_ASG1A
+
ASRMAA
+
S_ASG2A
S_ASROS_ASRMA
Damping
Reactor
a
b
c
A4D
c
b
a
a
b
c
c
b
a
+
DOR13
+
a
b
c
c
b
a
+
+
CHARGE_GRAPD
D13R_D16R
19.46
G31V
VERM
ASDOR
a
b
c
+
ROSSER
204.937080kV /_76.3223
D5R
19.46
DOR16
+
BUS2
b
a
c
+
transmission_lines
Trip line AR3
at t=80 ms
+
S_ASDOR_ASRMA
S_GRVER
b
a
c
DOR5R
+
ASG2A
+
+
+
+ VM
S_ASVER
129.71
+
184.629622kV /_79.0299
D36c
D36b
D36a
a
b
c
+ VM
+
+
+
S_DORRI
S_ASDOR
DORRI
c
b
a
+
+
C_ASDOR
C_DORAS
ASDOR
CHARGE_ASHERN
Data Case given to us by David Jacobson. See also:
Jacobson D. A. N., Marti, L., Menzies, R.W.,
"Modeling Ferroresonance in a 230 kV
Transformer-Terminated Double-Circuit Transmission Line"
Proceedings of the 1999 International Conf. on Power systems Transients
pp. 451-456, June 20-24, Budapest
D36R_R23R
ROSSR
DORB2A
+ VM
A6V
VERMILLION
BUS4
ASHERN
part
c
b
a
203.690636kV /_73.5250
RIDGEWAY
+
16.41
D36c
D36b
D36a
+
c
b
a
a
b
c
+
c
b
a
+
S_DORAS
+
DORASA
A4D07
+ VM
DORB2
+
DORSEY
193.198699kV /_84.5124
a
b
c
A4D07
+
13.8kV
460MVA
a
b
c
a
b
c
+
a
b
c
+
SM
a
b
c
a
b
c
+
?m
+ VM
AR3
a
b
c
ASG1A
+
GRAND_RAPIDS
Ferroresonance demo
Conclusions
New Model Features
• The model is based on widely-verified and accepted Preisach
model of hysteresis
• Independent formation of major and minor loops
• True nonlinear solution within the EMTP-RV
• Can accurately represent the physical properties of the
magnetic core materials
• Can accurately represent the dynamic core behavior under
electromagnetic transients
Applications
For accurate EMTP studies on :

De-energizing/re-energizing of transformers

Ferroresonance phenomena in power and instrument transformers

Determination of the core remnant flux

Precise modeling of VTs, CTs, and CVTs for protection studies

Accurate modeling of electrical machines

Efficient design of control systems for power-electronic based drives by
taking into account the machine nonlinearity and actual power loss
Important points
• It is evident that a more detailed model needs more parameters.
although, a model with simple implementation and with less required
parameters is generally preferable, the accuracy of such models are
limited.
• For a sophisticated hysteresis model, “not needing minor loop data”, is
a drawback not an advantage. Due to different behavior of minor loops
(extensively verified by experiments), neglecting the minor loop
parameters can result in completely different and unexpected results.
• For the new reactor, if the minor loop data are not available, a set of
pre-specified default values can be considered.