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Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Pedro Arsénio1, João Murta-Pina1, Anabela Pronto1, Alfredo Álvarez2
1 UNINOVA – CTS, Portugal2 Universidad de Extremadura, Spain
Bologna, June 16 2016
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Outline 2
1. Introduction2. Problem and Approaches3. Results and Discussion4. Conclusions
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
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Introduction
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Introduction
4
Inductive Type Limiters are commonly simulated in FEMsoftware. For a proper accuracy, both electromagnetic andthermal phenomena must be taken into account.
The properties of high temperature superconducting (HTS)materials, such as electrical resistivity, heat capacity,thermal conductivity, critical current density and n-index,are strongly dependent on temperature values.
Motivation
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Introduction
5
Develop a practical tool for a fast and accurate prediction ofthe behaviour of inductive type FCLs in electrical grids.
Reverse Engineering Simulations: Matlab/SimulinkFEM Simulations: Matlab/Simulink + Cedrat Flux2D
Objective
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
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Problem and Approaches
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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120
180
60
60
Primary winding
Material Copper
Number of turns 60
Conductor cross section 1.5 mm2
Inner radius 32.5 mm
Width 0.7 mm
Height 40 mm
Secondary winding
Material Superpower SCS4050
Number of turns 1
Conductor cross section 0.4 mm2
Critical current density at 77 K 250 A·mm-2
Inner radius 40 mm
Width 0.1 mm
Height 4 mm
Cryostat
Material Extruded polystyrene
Inner radius 31.5 mm
Outer radius 60.5 mm
Wall thickness 6 mm
Dimensions
(Dimensions in mm)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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120
180
60
60
Primary winding
Material Copper
Number of turns 60
Conductor cross section 1.5 mm2
Inner radius 32.5 mm
Width 0.7 mm
Height 40 mm
Secondary winding
Material Superpower SCS4050
Number of turns 1
Conductor cross section 0.4 mm2
Critical current density at 77 K 250 A·mm-2
Inner radius 40 mm
Width 0.1 mm
Height 4 mm
Cryostat
Material Extruded polystyrene
Inner radius 31.5 mm
Outer radius 60.5 mm
Wall thickness 6 mm
Dimensions
Secondary
Core
Primary
(Dimensions in mm)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
9
120
180
60
60
Test Circuit
Secondary
Core
Primary
N1 = 601
300 93 Vrms
HTS
(Dimensions in mm)
N1 = 601
300 93 Vrms
HTS
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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120
180
60
60
Test Circuit
Secondary
Core
Primary
Open : 0.00 s – 1.25 s
Close : 1.25 s – 2.75 s
Open : 2.75 s – 5.00 s
Normal current: 0.4 A
Prospective current: 131.5 A
1.5 s
(Dimensions in mm)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
11
120
180
60
60
Parameters
Secondary
Core
Primary
Temperature dependent properties:
Convective heat transfer.
Critical current density.
n-value.
Resistivity of copper, silver, Hastelloy, (Re)BCO.
Thermal conductivity.
Heat capacity.
(Dimensions in mm)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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10
100
1000
10000
100000
0.0 0.1 1.0 10.0 100.0 1000.0
Co
nve
ctiv
e h
eat t
rans
fer
coef
fici
ent
(W∙m
-2∙K
-1)
Temperature difference (K)
A B
C
ED
Convective boiling
Film boiling
ℎ =𝑄ℎ
Δ𝑇[W·m-2·K-1]
𝑄ℎ : Convective heat transfer (W·m-2)
Δ𝑇 : Temperature difference (K)
Reference:
Kaufmann B, Dreier S, Haberstroh Cand Grossmann S 2013 Integration ofLN2 Multiphase Heat Transfer IntoThermal Networks for High CurrentComponents IEEE Trans. Appl.Supercond. 23 5000104–5000104.
Parameters: Convective Heat Transfer Coefficient
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
13
𝑇0 : LN2 temperature (77.2 K)
𝑇C : Critical temperature (93.0 K)
𝛿 : Fitting parameter (-67.09)
𝛾 : Fitting parameter (0.4107)
𝜅: Fitting parameter (22.96)
References:
Lee W S, Nam S, Kim J, Lee J and Ko T K2015 A Numerical and ExperimentalAnalysis of the Temperature Dependenceof the n-Index for 2G HTS TapeSurrounding the 77 K Temperature RangeIEEE Trans. Appl. Supercond. 25 1–4.
Cedrat 2007 Flux 10 User’s Guide vol 2.
𝐽𝐶 𝑇 = 𝐽𝐶 𝑇0 ∙1 −
𝑇𝑇𝐶
𝛿
1 −𝑇0𝑇𝐶
𝛿
𝛾
[A·mm−2]
𝑛 𝑇 = 𝑛 𝑇0 ∙𝑇0𝑇
𝜅
Parameters: Critical Current Density and n-Value
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
14
𝐸𝐶 : Critical electrical field (1 µ ∙ cm-1)
𝐽 : Current density (K)
𝐽𝐶 : Critical current density (A∙m-2)
𝑛 : n-value
𝑇 : Temperature (K)
0
5000
10000
15000
20000
25000
30000
75 80 85 90 95 100 105 110 115 120 125
Ele
ctr
ica
l re
sist
ivit
y (n
Ω·m
)
Temperature (K)
𝜌𝑌𝐵𝐶𝑂,𝑆 𝐽, 𝑇 =
𝐸𝑐
𝐽∙
𝐽
𝐽𝑐 𝑇
𝑛 𝑇
𝜌𝑌𝐵𝐶𝑂,𝑁 𝑇 = 1.25 × 10−7 ∙ 𝑇 + 1.15 × 10−5
[Ω·m]
𝜌𝑌𝐵𝐶𝑂,𝑆
𝑇𝐶
Parameters: Resistivity of Superconducting Layer
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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References:
Moore J P, McElroy D L and Graves R S1967 Thermal Conductivity andElectrical Resistivity of High-PurityCopper from 78 to 400 K Can. J. Phys.45 3849–65.
Matula R A 1979 Electrical resistivityof copper, gold, palladium, and silverJ. Phys. Chem. Ref. Data 8 1147.
Lu J, Choi E S and Zhou H D 2008Physical properties of Hastelloy® C-276TM at cryogenic temperatures J.Appl. Phys. 103 064908.
𝜌𝐶𝑜𝑝𝑝𝑒𝑟 𝑇 = 6.85 × 10−11 ∙ 𝑇 − 3.30 × 10−9
𝜌𝑆𝑖𝑙𝑣𝑒𝑟 𝑇 = 6.11 × 10−11 ∙ 𝑇 − 1.97 × 10−9
𝜌𝐻𝑎𝑠𝑡𝑒𝑙𝑙𝑜𝑦 𝑇 = 1.17 × 10−10 ∙ 𝑇 + 1.25 × 10−6
[Ω·m]
Parameters: Resistivity of Copper, Silver and HastelloyLayers
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
16
References:
Moore J P, McElroy D L and Graves R S1967 Thermal Conductivity andElectrical Resistivity of High-PurityCopper from 78 to 400 K Can. J. Phys.45 3849–65.
Lu J, Choi E S and Zhou H D 2008Physical properties of Hastelloy® C276at cryogenic temperatures J. Appl.Phys. 103 064908.
Ho C Y, Powell R W and Liley P E 1974Journal of Physical and ChemicalReference Data, Volume 3.
𝜆𝑌𝐵𝐶𝑂 𝑇 = 5
𝜆𝐶𝑜𝑝𝑝𝑒𝑟 𝑇 = 416.3 − 5.904 × 10−2 ∙ 𝑇 +7.087 × 107
𝑇3
𝜆𝑆𝑖𝑙𝑣𝑒𝑟 𝑇 = 431.4 − 1.817 × 10−2 ∙ 𝑇 +1.708 × 107
𝑇3
𝜆𝐻𝑎𝑠𝑡𝑒𝑙𝑙𝑜𝑦 𝑇 = 0.0238 ∙ 𝑇 + 5.896
[W·m-1·K-1]
Parameters: Thermal Conductivity
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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References:
Lu J, Choi E S and Zhou H D 2008Physical properties of Hastelloy® C-276TM at cryogenic temperatures J.Appl. Phys. 103 064908.
Jensen J E, Tuttle W A, Stewart R B,Brechna H and Prodell A G 1980Specific heat of some solidsBrookhaven National LaboratorySelected Cryogenic Data Notebook,Volume 1.
Smith D R and Fickett F R 1995 Low-Temperature Properties of Silver J.Res. Natl. Inst. Stand. Technol. 100119.
𝐶𝑌𝐵𝐶𝑂 𝑇 = 4.05 × 106 − 1.73 × 108 ∙ 𝑇−0.9747
𝐶𝐶𝑜𝑝𝑝𝑒𝑟 𝑇 = −9.463 × 107 ∙ 𝑇−0.8292 + 4.279 × 106
𝐶𝑆𝑖𝑙𝑣𝑒𝑟 𝑇 = −1.983 × 108 ∙ 𝑇−1.23 + 2.643 × 106
𝐶𝐻𝑎𝑠𝑡𝑒𝑙𝑙𝑜𝑦 𝑇 = 4.14 × 106 +5.92 × 105 − 4.14 × 106
1 +𝑇
120.42
2.39
[J·K-1]
Parameters: Volumetric Heat Capacity
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1:CoupledElectromagnetic-ThermalSimulation
FEM Computation
Transient Thermal
JcYBCO, nYBCO
Update parametersTCu, TAg,
THastelloy, TYBCO
Losses
End
Final time step?
Yes
Compute next
time step
tk = tk-1+Δt
No
Initial conditions
definitionStart
Update parameters
Test circuit
parameters
FEM Computation
Transient Magnetic
tk-1 tk
ICC
UPrimary, IPrimary
ΨPrimary
tk
CCu, CAg, CHastelloy,CYBCo
kCu, kAg, kHastelloy,kYBCo
ρCu, ρAg, ρHastelloy,ρYBCo
hLN2
tk
tk-1
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1: Coupled Electromagnetic-Thermal Simulation
Co-Simulation:Matlab/Simulink + Cedrat Flux2D
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1: Coupled Electromagnetic-Thermal Simulation
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1: Coupled Electromagnetic-Thermal Simulation
Secondary
Core
Primary
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
22
Approach 1: Coupled Electromagnetic-Thermal Simulation
Primary winding
Secondary winding
Line
LoadVoltage
source
Switch
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1: Coupled Electromagnetic-Thermal Simulation
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 1: Coupled Electromagnetic-Thermal Simulation
Cu
rrent
sou
rce
Co
pper
Sil
ver
Hast
ell
oy
YB
CO
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
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Approach 2: Reverse Engineering Methodology
Matlab/Simulink
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
26
Approach 2: Reverse Engineering Methodology
Reference:
Pina J M, Suárez P, Neves M V, ÁlvarezA and Rodrigues A L 2010 Reverseengineering of inductive fault currentlimiters J. Phys. Conf. Ser. 234 032047.
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
27
Approach 2: Reverse Engineering Methodology
𝑖2 = −𝑁1 ∙ 𝑖1 −𝑖𝑐 𝑇 ≤ 𝑁1 ∙ 𝑖1 ≤ 𝑖𝑐 𝑇
𝑖2 =1 − 𝑘2𝑘1 − 1
∙ 𝑁1 ∙ 𝑖1 +𝑘1 − 𝑘2𝑘1 − 1
∙ 𝑖𝑐 𝑇 𝑁1 ∙ 𝑖1 < −𝑖𝑐 𝑇
𝑖2 =1 − 𝑘2𝑘1 − 1
∙ 𝑁1 ∙ 𝑖1 +𝑘2 − 𝑘1𝑘1 − 1
∙ 𝑖𝑐 𝑇 𝑁1 ∙ 𝑖1> 𝑖𝑐 𝑇
𝑖𝐶 𝑇 = 𝐽𝐶 𝑇 ∙ S𝑇𝑎𝑝𝑒
𝑘1 = 90𝑘2 = 3
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
28
Approach 2: Reverse Engineering Methodology
RC
opp
er
RS
ilve
r
RY
BC
O
RH
aste
lloy
I CC
I Cop
per
I Sil
ver
I Has
tell
oy
I YB
CO
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
29
Approach 2: Reverse Engineering Methodology
RC
opp
er
RS
ilve
r
RY
BC
O
RH
aste
lloy
I CC
I Cop
per
I Sil
ver
I Has
tell
oy
I YB
CO
RConvection
RCopper/2 RCopper/2
CCopperPCopper
RSilver/2 RSilver/2
CSilver
RHastelloy/2 RHastelloy/2
CHastelloy
RYBCO/2 RYBCO/2
CYBCO RConvectionPSilver PHastelloy PYBCO
77.2 V
TCopper TSilver THastelloy TYBCO
Reference:
de Sousa W, Polasek A, Dias R, Matt C and de Andrade R 2014 Thermal-electrical analogy for simulations of superconducting fault current limiters Cryogenics62 97–109.
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
30
Experimental Test Bench
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Problem and Approaches
31
Rogowski
coilRTD
Pt100
Rogowski
coilRTD
Pt100
SFCL
Experimental Test Bench
Problem and Approaches
32
Rogowski
coilRTD
Pt100
Rogowski
coilRTD
Pt100
SFCL
Experimental Test Bench
NI-6008
Keithley-2001
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
33
Results and Discussion
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
34
Line Current
Prospective current: 131.5 APeak current: 43.3 A (Experimental) 67.4 A (FEM Coupling) 59.0 A (Reverse Engineering)Limited current (excluding 1st peak): 36.8 A (Experimental) 37.2 A (FEM Coupling) 34.9 A (Reverse Engineering)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
35
Line Current
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
36
Linked Flux and Hysteresis Loop
Maximum flux: 0.239 Wb (Experimental) 0.252 Wb (FEM Coupling) 0.242 Wb (Reverse Engineering)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
37
Linked Flux and Hysteresis Loop
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
38
Current in Superconducting Secondary
Maximum current (1st peak): 342.6 A (Experimental) 142.7 A (FEM Coupling) 152.0 A (Reverse Engineering)Maximum current (steady-state): 74.2 A (Experimental) 95.1 A (FEM Coupling) 82.9 A (Reverse Engineering)
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
39
Current in Superconducting Secondary
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Results and Discussion
40
Temperature in Superconducting Secondary
Maximum temperature: 80.2 K (Experimental) 80.1 K (FEM Coupling) 80.2 K (Reverse Engineering)
Results and Discussion
41
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Temperature in Superconducting Secondary
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
42
Conclusions
Numerical Simulations of an Inductive Type Fault Current Limiter Based on Electromagnetic and Temperature Dependent Parameters
Conclusions
43
Good agreement between experimental and simulations wereachieved.
The reverse engineering methodology provides results in few secondswhile the electromagnetic-thermal coupled simulation based on FEMtakes several days (5~7 days depending on mesh quality).Furthermore, complex grids can be easily simulated by means of thereverse engineering methodology.
Experimental temperature measurements shows drift due to thermalinertia of the RTD sensor. Ripple during fault occurrence is alsoobserved.
Conclusions
Thank You!Pedro Arsénio, PhD Student
Bologna, June 16 2016