numerical simulations of an inductive type fault current ... · numerical simulations of an...

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


Outline 2

1. Introduction2. Problem and Approaches3. Results and Discussion4. Conclusions


3

Introduction


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


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


6

Problem and Approaches



7

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


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


Outer radius 60.5 mm

Wall thickness 6 mm

Dimensions

(Dimensions in mm)



8

120

180

60

60

Primary winding

Material Copper

Number of turns 60



Width 0.7 mm

Height 40 mm

Secondary winding

Material Superpower SCS4050

Number of turns 1


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


Outer radius 60.5 mm

Wall thickness 6 mm

Dimensions

Secondary

Core

Primary

(Dimensions in mm)



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



10

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)



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)



12

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



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



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



15

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



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



17

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



18

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



19

Approach 1: Coupled Electromagnetic-Thermal Simulation

Co-Simulation:Matlab/Simulink + Cedrat Flux2D



20




21


Secondary

Core

Primary



22


Primary winding

Secondary winding

Line

LoadVoltage

source

Switch



23




24


Cu

rrent

sou

rce

Co

pper

Sil

ver

Hast

ell

oy

YB

CO



25

Approach 2: Reverse Engineering Methodology

Matlab/Simulink



26


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.



27


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



28


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



29


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.



30

Experimental Test Bench



31

Rogowski

coilRTD

Pt100

Rogowski

coilRTD

Pt100

SFCL



32

Rogowski

coilRTD

Pt100

Rogowski

coilRTD

Pt100

SFCL


NI-6008

Keithley-2001



33

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)



35

Line Current



36

Linked Flux and Hysteresis Loop

Maximum flux: 0.239 Wb (Experimental) 0.252 Wb (FEM Coupling) 0.242 Wb (Reverse Engineering)



37

Linked Flux and Hysteresis Loop



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)



39

Current in Superconducting Secondary



40

Temperature in Superconducting Secondary

Maximum temperature: 80.2 K (Experimental) 80.1 K (FEM Coupling) 80.2 K (Reverse Engineering)


41


Temperature in Superconducting Secondary


42

Conclusions


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

numerical simulations of an inductive type fault current ... · numerical simulations of an...

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