Post on 02-Oct-2021
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
• 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
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
• 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
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
• 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
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
Total number of elements: 12
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
Total number of elements: 4
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
Neglecting the thermal effects
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