Modeling of the Resistive Type Superconducting Fault ...

Modeling of the Resistive Type SuperconductingFault Current Limiter for Power System Analysis andOptimization

Antono MorandiMassimo Fabbri, Babak GholizadDEI Guglielmo MarconiDep. of Electrical, Electronic and InformationEngineering

Università di Bologna

May 12, 2014Bratislava, Slovakia

• Resistive fault current limiters and the state of the art

• Motivations and case study

• Numerical model of the resistive SFCLElectromagnetic model

Thermal model

• Coupling with power system

• Numerical resultsThe exact reference solution

Reduced equivalent circuit - a step by step approach

Effect of the mesh

Heat exchange condition

Temperature homogenization

Neglecting the thermal effects

• Conclusion

Outline

… faulthappens !

a poly-phase fault produces an overcurrent:

• Damage of components

• Outage or even black out

• voltage disturbance

Network operators are required to ensureappropriate power quality and to provideinformation about the type and thenumber of expected dips

short circuit power

norm

alco

nditi

onfa

ult

• poor persistentvoltage quality

• high persistentvoltage quality

• low vulnerability• high transient

voltage quality

• high vulnerability• poor transient

voltage quality

For obtaining high network’s performance both in normal condition and during thefault a condition-based increase of the impedance is required

Fault current limiter (FCL): a device with anegligible impedance in normal operation whichis able to switch to a high impedance state incase of extra current (fault)

Faultthreshold

impe

danc

e

current

loadscc

cc XV

S2

short circuit power

By direct exploitation of the SC/Normal transition resistive fault current limitersoffer an excellent solution to fault current limitation

Resistive Type Superconducting fault Current Limiters (R-SFCL)

conventional shunt reactor

non linear SC resistor• bifilar helical windings

(1GHTS/bulks)• alternate pancakes

(2G HTS)

Advantages• Immediate and and fail safe

operation• Compact size

Critical aspects• Recovery time• AC loss• Hot spots during light

overcurrent

mechanical switch

Distribution (MV) level resistive HTS-FCL is now a mature technology

Two more units of similarrating have been orderedrecently to be installed in UK

Nexans R-SFCL16.6 MVA (12 kV / 0.8 kA)BSCCO bulk material

RSE-A2A R-SFCL3.8 MVA (10 kV / 0.2 kA)1G HTS tape (Bi2223)

Upgrade to 15.6 MVA(9 kV/1kA) is programmed

ECCOFLOW R-SFCL40.0 MVA (24 kV / 1 kA)2G HTS tape (YBCO-CC)

The device has bee built andsuccessfully tested. Live gridinstallation is under discussion

Paris, October 13, 2011 – Nexans, Siemens and American Superconductor Corporation (NASDAQ: AMSC)today announced the successful qualification of a transmission voltage resistive fault current limiter (FCL) thatutilizes high temperature superconductor (HTS) wire. This marks the first time a resistive superconductor FCLhas been developed and successfully tested for power levels suitable for application in the transmission grid(138 kV insulation class and nominal current of 900 A).

138 kV / 0.9 kA2G HTS tape (YBCO-CC)

Feasibility of industry grade resistive HTS-FCL technology forTransmission (HV) level is also proved

superconductingcommunity

distribution networkoperators

Motivation

Technology details are not of the first interest of the operators, who first want toknow the benefits

A model for the reliable evaluation of the effects of the device on real word (nottoo simplified) grids is needed

!

#* FCLp%§ &ò@@ ##+ ]] !

*% £$?]] pp^ç FCL

The case study

Nominal Voltage 20 kVrmsNominal current 480 Arms (12.5 MVA)Opening time of circuit breaker, toCB 120 msTime delay for opening command, tdCB

Is1 = 630 Arms I Is2 = 1400 Arms 800 ms tdCB 0 msIs2 = 1400 Arms I tdCB = 0 ms

Reclosing time of circuit breaker, trCB 400 ms

This is to take into accounttemporary overcurrentswhich routinely occurs inthe grid

12 km0.5 km

0.5 km1.5 km

4 km

Subt

ram

issi

on 1 km40 MVAXcc = 0.87

8 MVA4 MVA

6 MVA4 MVA

2 MVA

4 MVA10 MVA

A

15 kV

132 kV

F G

D

E

BC

FCL

sensitivecustomers

disturbingcustomers

overheadrural feeder

A typical distribution gridsupplying a mix of industrial,commercial, residential andrural loads

Typical settings of the protections

Design Criteria for YBCO-CC based resistive SFCL

• The device must provide appropriate limiting effect

• The device must provide appropriate protection from voltage disturbancesto costumers not directly affects by the fault

• The device must not affect existing protections

• No damage must occur to the device during the fault

• The temperature must not overcame 300 K at the end of the fault

• For typical CC tapes (AMSC and Superpower) and fault duration of120 ms the during fault RMS electric field must not overcome thetypical value of 20-30 V/m

The need to provide appropriateprotection from voltage disturbancesets the actual limit on the minimumpossible impedance of the device

Syst

em le

vel

Devi

ce le

vel

Parameters of the device• Critical current Ic

• Shunt reactance Xs

• Quenched resistance Rq of the SC coil

12 sc II

33

and3

2 VXsX

VXI

XX

V

cc

ss

scc

sq XR

Main characteristics of the Reference Coated ConductorSubstrate, Hastelloy 100 mYBCO 1 mStabilizer, Silver 2 mReinforcement, stainless steel 127 mCritical current, 77 K, self field 330 AQuenched resistance at 91 K 77.8 m

Parameters of the FCL for the case study

Main characteristics of the deviceNumber of tapes in parallel of the conductor 3Critical current 1000 ATotal resistance of the conductor per unit length 25.9 mTotal length of conductor 400 mTotal quenched resistance 10.4Shunt reactance 2.5

Design constrains

Ic > 890 A

2 < Xs < 3.5

Rq >Xs < 3.5




Thermal model




Effect of the mesh




• Conclusion

Outline

Mathematical formulation

The basic assumption is that the behavior is homogeneous along the full lengthof the HTS conductor

Commercial HTS tapes have goodlongitudinal uniformity of the criticalcurrent which assures homogenoustransition of the whole conductor length

Hobl et al., IEEE TASC,2013

A 2D approach is used form modeling the device

xx

x t

AE

The A- formulation is used forexpressing the electric field

Geometrical model of the FCL

Circuit model of the complete system

A 2D composite (multi-material) domain isconsidered

A Cartesian reference frame is introduced

FCL

Power system

x y

z

IFCL

vFCL dl+

dl

S

The FCL interacts with the powersystem by meas of two terminals

Electromagnetic model

The problem involving can be solvedautonomously in terms of appliedvoltage v per unit length of conductor

The domain is connected to a two terminals component (bipole) which represents thepower system. An electric scalar potential exists within the domain not due to chargeaccumulation but to satisfy the boundary condition

xFCL

FCL

FCL

x

dlx

x

v

xv

dlvdx

n e

e

ˆ

ˆ

0

02

22

0

''

1ln

''','2

,

zzyywith

dzdyzyJzyAS

The vector potential can be expressed in terms of local current density J as

Since in fault current limiters a noninducting configuration is used to allocatethe required conductor length no externalsources exists for the vector potential

The bounded E-J power law is assumedfor modeling the superconductor

1

cc

0SC

SCNS

SCNSeq

eq

,

,)(

,)(,

,

n

TJ

J

TJ

ETJ

TJT

TJTTJ

JTJE

Bran

dt, 1

999

Duro

n et

. al.,

200

4

A constitutive relation able to link the superconducting and the normal conducting state isrequired since high current (above Ic) operation is to be dealt with

A linear (though temperature dependent) relation is assumed for the normalconducting constituents of the tape (buffer layer, stabilizer, reinforcement)

Merely a phenomenological relation. No currentsharing between “a normal and a SC path” isassumed

creep

normalstate

JTE

Due to the non inducting layout no dependence of Jc on B is assumed

L

VdzdyzyJ

tJJT FCL

S

''','

2),( 0

This equation can be discretized and solved numerically provided that

1. The temperature is known at any point of the domain A thermal model is needed

2. The total voltage across the FCL is known Coupling with the power system is needed

The following equation is finally obtained which links the distribution of current within thecross section to the total voltage across the FCL

total voltage across the FCL

total length of conductor

Thermal model

0),()( 2 JJTTdt

dTc q

00 )( TTTTh qn Non linear convection is assumed at the boundaryT0 is the equilibrium temperature of the coolant

Energy conservation

x y

z),(),,(

),(

zyqzyq

zyT

zy

TTk )(q Fourier’s Law relates the heat flux to the temperature

Temperature dependence of specific heat c, thermal conductivity k and heat exchange coefficient h isassumed

Finite dimensional model – electromagnetic

1. A subdivision of the composite domain in finite number NE ofrectangular elements is introduced

3. A solution is looked for in the weak form bye means of the weightedresiduals approach

2. A uniform current density is assumed within each element

h

hh S

IJ

E

E

S

FCLk

k Skh

hh Nk

NhdSV

dt

IddS

S

LI

S

L

Sh k

,...,1

,...,1'

2

1 0

discontinuity of J is naturally allowed at theinterface between different materials

• The whole conductor is subdivided in anumber NE of independent current elements(branches) in parallel which are mutuallycoupled.

• All branches are subject to the voltage acrossthe FCL.

• The total current through all branches is thecurrent of the FCL

E

S Skhhk NkdSdS

SS

LM

h k

,...,1'2

0

hhh S

LITR ,

Each of the discretized equation of the weak form corresponds to the voltage balance(Kirchhoff’s voltage law) of a circuit branch

IhMh,k Rh

VFCL

The electromagnetic finite element model isstated in the form of an equivalent circuit

IFCL

I1

I2

INE

VF

CL

FCLVdt

d1IITRIM ),(

Solvingsystem

Tape 1 Tape 2 Tape 3

Structured rectangular meshes are very well suited to cope with domain with highaspect ratio

A mix of elements with very different aspect ratio isintroduced to discretize the different layers of theHTS tape. This allows to deal with the geometricalcomplexity of the domain without introducing a toolarge number of elements.

h kS Skh

hk dSdSSS

LM '

20

Thanks to the logarithmic kernel no troubles arisewith the calculation of the coupling coefficientsprovided that a different order of integration isused for the inner and the outer integral in order toavoid overlapping of the field ant e source point

As a limit the second dimension of very thin elements can be neglected and theline integrals can be used instead of the surface ones

It can be shown that

• Two equivalent solving systems are assembledCircuit method formulates one voltage balance equation for each of the rectanglescomposing the mesh

Edge elements method formulates a set of collective voltage balance equationapplying to the clusters of rectangles enclosed in the fundamental loops

• The same solution in terms of current distribution is arrived at

• Both models use piecewise uniform approximation of thecurrent density within the elements on the y-z plane

• Both models introduce the same number of unknowns(the number of rectangles is equal to the number ofcotree branches)

Comparison between circuit and edge elements models

Finite dimensional model – Thermal

1. The same subdivision introduced for the electric problem is used

4. The heat flux through boundary faces Is expressed as

3. The line integral of the Fourier law along the (horizontal or vertical) pathconnecting each pair of neighbouring elements is taken. It is assumed theheat flux is oriented perpendicular to the shared face

hkkkhh

kkhhhk

khhkhk

TkTk

TkTkG

with

TTGQ

rrn

ˆ2

rh

rk

farhfarhh TTTThQ )(0

rh

2. A uniform temperature is assumed within each element

hh SifTT rr)(

3. A solution is looked for in the weak form bye means of the weighted residualsapproach

E

E

S h

hh

khkhh

h Nk

NhdS

S

IQT

dt

dc

Sh

,...,1,0

,...,10

12

Each of the discretized equation of the weak form formally corresponds to the currentbalance (Kirchhoff’s currents law) of a circuit node

2

0 otherwise0

boundaryonn thefaceahashelemetsif

otherwise0

faceasharekandhelemetsif2

h

hhh

h

hkkh

kh

hk

hh

S

Ip

hG

kk

kk

G

cC

rr

T0

Th

Tk

Tl

TmCh

Gh0

T0

T0

Ghm

Ghl

Ghk

ph

• The whole conductor is subdivided in anumber NE of nodes connected throughthermal conductances

• All nods are connected to a reference oneby means of a capacitance. A NE -orderdynamic circuit is obtained

• A current is forced in each node to take intoaccount of the power dissipation

The thermal finite element model is stated in the form of an equivalent circuit

ITIRITTG1TTC ),()()( t0 T

dt

d

T2

T1 Tn

Tn+1

The coupled electromagnetic- thermal behaviourof the FCL is modelled by means of two coupledcircuits

ITIRITTG1TTC

1IITRIM

),()()(

),(

t0T

dt

d

Vdt

dFCL

I1

I2

INE

T2

T1 Tn

Tn+1

VFCL

IFCL

Power system

FCL

The state variables areI1, I2, … , INFE

T1, T2, … , TNFE

+ state variables of the power system




Thermal model




Effect of the mesh




• Conclusion

Outline

A

B C

D E

load

load

load

feeder

feeder

feeder

feeder feeder

feeder feeder

feeder feeder

switch

switch

switch

load

load

load

swit

ch

swit

ch

F G

shunt

FCL

transformer

Coupling with the power system

The equivalent circuit of eachof the components of thepower system is introduced

A global equivalent circuitis obtained

A tree-cotree decomposition of theglobal equivalent circuit is introduced

The shunt is placed within the tree.Cotree currents include the statevariable of the FCL

Tree currents are expressed as afunction of the cotree ones

0

V

I

I

TIR0

0R

I

I

M0

0M

1

V g

FCL dt

d

VcPScPSPS

),(

Voltage of all branches is expressed as function of the tree currents and the derivatives

This equation incorporates the electromagnetic model of the FCL

0

VL

I

I

TIR0

0RL

I

I

M0

0ML g

dt

d cPScPS

),(

The state equation is obtained by means of the Kirchhoff’s current law

L : matrix of thefundamental loops

The solving system of the thermal network must be added due to the temperaturedependence of the resistive terms of the FCL

The state variables areI1, I2, … , INFE

T1, T2, … , TNFE

+ cotree currents of the power system

ITIRITTG1TTC

0

VL

I

I

TIR0

0RL

I

I

M0

0ML

),()()(

),(

t0

cPScPS

Tdt

d

dt

d g

The voltage impressed by the generator is the forcing term of the system

Complete electromagneticand thermal model of theFCL and the power system

Solving procedures

• A zero order coupling exists between the electric and the thermal model• Time constants of the thermal problem are much longer than those of the electric one

A week coupling can be assumed for solving the electric amd the thermla state equation

0

VL

I

I

TR0

0RL

I

I

M0

0ML g

dt

d cPScPS

)(

Temperature is assumed constantduring the electric step

t0 t0+tt

Ic0, I0, T0 Ic, I, T

The average power during the electricstep is assumed as input of the thermalproblem

ITIRIITIRIP ),(),(2

10

t000

t0av

av0 PTG1TC Tdt

d

An implicit Euler scheme is used for solving the two differential systems

0

VL

I

I

TIR0

0RL

II

II

M0

0ML

g

t

cPS

0

c0cPS

),(

1

av0

1PTGTTC

t

Ih

Mh,k

Ih

t

M kh

,

+ hj

jjh I

t

M ,

+

jj

jh It

M0,

,

Th

Tk

Th

Tk

Inductors and capacitors are transformed in static componentsA non dynamic circuit is solved during thee time step

t

C

C

)( 00 gh TTt

C

Parameters of the model

• S. S. Kalsi, Applications of HighTemperature Supercond. to ElectricPower Equipment, 2011, Wiley-IEEE

• N. Bagrets et al, Thermal properties of2G coated conductor cable materials,Cryogenics 61 (2014) 8–1

Temperature dependence of physical parameters is implemented

• Sosnowski J., Analysis of theelectromagnetic losses generation in thehigh temperature superconductors, IC-SPETO’99, (1999),129-132

Parameter Material ValueNormal state resistivity YBCO 100 cm at 92 KThermal conductivity YBCO 7 W/m/KThermal conductivity Hastelloy 7 W/m/KThermal conductivity Silver 429 W/m/KSpecific Heat YBCO 1.62 MJ/m3/K

Constant values are assumedif data are not available

• F. Roy et al., Magneto-ThermalModeling of 2GHTS for Resistive FCLDesign Purposes, 2008, IEEE TASC

Temperature dependence of the heatexchange between the conductor andthe liquid nitrogen bath is alsoconsidered

Realistic values of the resistance and the inductance perunit length are used for modelling the MV feeders Zfeeders = 0.27 + j 0.35 /km




Thermal model




Effect of the mesh




• Conclusion

Outline

Performance of the system with no FCL

The thermal stress on the transformer due to the actualfault current, including the asymmetric component, isassessed by means of the total thermal let-through duringthe fault

ff

f

tt

t

rtransforme dtiQ 2

A fault occurs at bus F at the mostonerous instant

The mechanical stress on the transformer is assessed bymeans of the peak current

The voltage disturbance on all customers of the network inassessed by means of the RMS voltage at all buses

t

Tt

RMS

cycle

dtvT

tV 21)(

Standards EN61000-4-1 and EN61000-4-34specify the residual voltage VR on equipmentduring a disturbance

Tolerant (VR 40 % )

Sensitive (VR 70 % )

The residual voltage during the fault at allbus of the network is below the threshold ofeven tolerant equipment

A peak fault current of 21.4 kA is obtainedon the transformer

The total thermal let-through during thefault is 12.7*106 A2s. This is close to the limitof 18.8*106 A2s which can be soonapproached if the fault occur closer to bus A

Reference MeshTape 1 Tape 2 Tape 3Substrate 26*3 Substrate 26*3 Substrate 26*3YBCO 26*3 YBCO 26*3 YBCO 26*3Stabilizer 26*3 Stabilizer 26*3 Stabilizer 26*3Reinforcement 26*3 Reinforcement. 26*3 Reinforcement. 26*3

Total number of elements: 936

Two large equivalent circuits with 936unknowns each are obtained for modelingthe coupled electric and the thermalbehavior of the FCL

Further unknowns are added to theproblem for modeling the power system

In the following the solution obtained withthis mesh will considered as the reference“exact” solution

The residual voltage during the fault at allbus of the network is well above thethreshold of sensitive equipment.

Voltage disturbance is prevented.

Both the peak current and the thermal let-through are greatly reduced

unlimited limitedPeak current 21.4 kA 8.8 kA 61 %Thermallet-through 12.7*106 A2s 2.2*106 A2s 83 %

system level

During the fault thetemperature gap within thewhole conductor do notexceed 3 K

The conductor is isothermal.

A maximum temperature of129 K is reached after 120 ms

In the quenched state the current mainlyflows through the stabilizer. An appreciableshare also flows through the reinforcement.

device level

T map att = 20 ms

Effect of the Mesh

Tape 1 Tape 2 Tape 3Substrate 1*1 Substrate 1*1 Substrate 1*1YBCO 1*1 YBCO 1*1 YBCO 1*1Stabilizer 1*1 Stabilizer 1*1 Stabilizer 1*1Reinforcement 1*1 Reinforcement 1*1 Reinforcement 1*1

No subdivision along the tape width is assumed.Each component of each of the three tapes ismodeled by one single rectangle


A very coarse mesh with 12 elements in total is introduced

Two reduce equivalent circuits with 12 state variableseach are obtained for modeling the coupled electricand the thermal behavior of the FCL

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

I1

I2

I3

I4

I5

I6

I7

I8

I9

I10

I11

I12

system level

“exact” solution coarse mesh 3*4*(1*1)

No difference arises at the system level with the two mesh

device level

Very small differences arise at the device level with the two meshThe detail of current and temperature diffusion within the tape do not affect the results

A slightly lowermaximumtemperatureof 127 K (1.5%) isreached at the end ofthe fault with thecoarse mesh

“exact” solution coarse mesh 3*4*(1*1)

T12

Adiabatic assumption

No heat exchange is assumed between the conductorand the liquid nitrogen bath

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11

I1

I2

I3

I4

I5

I6

I7

I8

I9

I10

I11

I12

Thermal conductances between he nodes and thethermal rework are not considered

syst

em le

vel

Very small differences arise both at the device and at the system level withnon-adiabatic and adiabatic conditions

devi

ce le

vel No significant

temperatureincrease isobtained at theend of the faultin adiabaticcondition

“exact” solutioncoarse mesh 3*4*(1*1)adiabatic

T Tfar

S

dSJtP 2)(

Total instantaneous power

))(()( farTtTftQ

Total instantaneous heatexchange with the bath

Total power

Total heatexchange

Even in realistic condition at any instant the heat exchanged with the bath is negligible withrespect to the power injected in to conductor due to joule loss. Heat exchange conditioncan be neglected.

T4

Merging the three tapes in one

An unique equivalent domainof equal total cross section isintroduced for each of thecomponent of the three tapes

T1 T2 T3

I1

I2

I3

I4

Tape 1 Tape 2 Tape 3 Equivalent Tape


Two reduce equivalent circuits with 4 state variables each are obtained for modeling thecoupled electric and the thermal behavior of the FCL

A coarse mesh with nosubdivision is used for each ofthe components

Not in scale Not in scale

syst

em le

vel

• No difference are obtained at the system level• Negligible difference appear at the device level

devi

ce le

vel A higher maximum

temperatureof 130.5 K ( +1 %)is reached at theend of the fault

“exact” solutioncoarse mesh + adiabatic+ merged tapes

Homogenization of the temperature within the conductor

No temperature difference is assumed between onecomponent of the tape and the adjacent one

Thermal resistances between the nodes of the thermalrework are substituted by short circuits ( k )

A thermal network with one active node is obtained. Onestate variables is needed

Both each capacities and losses of all components aresummed up to give a unique parameter

T4T1 T2 T3

I1

I2

I3

I4

No changes occur on the electric network

T1

T1

Ctot Ptot

syst

em le

vel

devi

ce le

vel A higher maximum

temperatureof 135.0 K (+4.6%)is reached at theend of the fault

“exact” solutioncoarse mesh + adiabatic +merged tapes + temp. homogen.

• No difference are obtained at the system level• A small difference appears at the device level


No thermal model is associated to the electromagneticone

Also during the fault the conductor is supposed tooperate at a constant and uniform temperature

T = Tfar

The limiting effect is due to the transition to the nor,malstat due to the current above Ic only

I1

I2

I3

I4

No changes occur on the electric network

T1

Ctot Ptot

syst

em le

vel

• Due to higher current predicted of the conductor unreliable results canarise especially in case e of light fault

devi

ce le

vel A much higher

current ispredicted for theFCL

“exact” solutioncoarse mesh + merged tapes +neglecting thermal effects

A higher peakcurrent ispredicted for thetransformer

• An equivalent circuit of the device was obtained on a rigorousbase without introducing any a priory assumption

• The equivalent circuit was coupled with the model of real worddistribution network and the effects of the device on thenetwork where evaluated

• A reduced equivalent circuit was arrived at by means of a stepby step approach. Simplifying assumption were introduced andtheir effect on the results at the system was analyzed

Conclusion

A simple equivalent circuit with adiabaticassumption and no details of the current andtemperature diffusion is enough forevaluating the effect of on the power systemand for estimating the over-temperature ofthe device

I1

I2

I3

I4

T1

Ctot Ptot

Modeling of the Resistive Type Superconducting Fault ...

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