Numerical Study on Transient State of Inductive Fault Current Limiter Based on Field-Circuit Coupling Method

materials

Article Numerical Study on Transient State of Inductive Fault Current Limiter Based on Field-Circuit Coupling Method

Wenrong Li 1 , Jie Sheng 1,*, Derong Qiu 1, Junbo Cheng 2, Haosheng Ye 1 and Zhiyong Hong 1

1 School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 2 Russian Representative Oﬃce of State Grid Corporation of China, Moscow 109807, Russian * Correspondence: [email protected]

Received: 13 July 2019; Accepted: 28 August 2019; Published: 31 August 2019

Abstract: As the capacity of the power grid continues to expand, high-level fault currents might be caused during a contingency, and the problem of short-circuit current over-limitation is imminent. The high-temperature superconducting (HTS) fault current limiter (FCL) is an effective method to solve this problem. In this paper, a transient numerical model for the process of limiting current in the inductive FCL is proposed. The model is based on the coupling of multiphysics finite element simulation and a circuit model. The voltage source is used as input, which can simulate the macroscopic characteristics in the process of limiting current, such as the voltage and current waveforms, and can also simulate microscopic characteristics, such as temperature, magnetic field, and electrodynamic force distribution. The short-circuit experimental data of an air core inductive superconducting fault current limiter (SFCL) prototype was compared with the simulation results to verify the reliability of the simulation.

Keywords: inductive fault current limiter; magnetic ﬂux shielding; multiphysics simulation; transient state; ﬁeld-circuit coupling method

1. Introduction With the increasing power load and increased short-circuit capacity, the short-circuit current of the grid will continue to rise and will gradually approach the limits of the breaking capacity, which will greatly affect the stability of the power system and equipment. Among the current-limiting equipment, the superconducting fault current limiter (SFCL) is considered as one of the most effective methods to solve the problem of exceeding short-circuit current. Thus, simulating and conducting experimental research on it is significant [1]. SFCLs can be divided into resistive, inductive, three-phase reactor, saturated iron core, and bridge types. The principle of resistive SFCL is the transition of the superconductor from superconducting to normal state. They are relatively simple in structure, but continuous losses during rated operation is unavoidable. The inductive SFCL omit the current leads, but in general use an iron core, which makes this SFCL relatively heavy and costly. Recently, the inductive SFCL has received more attention [2–5]. In 1996, the Swiss ABB technology company developed a 1.2 MVA/10.5 kV three-phase inductive high-temperature superconducting fault current limiter (HTS FCL), installed it in a hydropower station in Lausanne, and carried out a durability test for one year. It was the first superconducting electrical equipment tested under the actual operating conditions of a power station [6]. The secondary winding is a superconducting magnetic shielding ring made of BSCCO-2212, cooled by liquid nitrogen. In the test, the peak value of short-circuit current was limited to a range from 60 kA to 700 A. The Warsaw Institute

Materials 2019, 12, 2805; doi:10.3390/ma12172805 www.mdpi.com/journal/materials Materials 2019, 12, 2805 2 of 17 of Superconductivity in Poland and the Karlsruhe Institute of Technology in Germany developed an air-core inductive FCL. In 2016 and 2018, 15 kV/140 A [7] and 10 kV/600 A [8] single-phase inductive FCLs were developed. The inductive current limiter simulation is divided into a steady-state simulation for rated operation and a transient-state simulation for the current-limiting process. When the SFCL is in rated operation, the temperature variation of superconducting winding can be neglected, because the HTS tapes do not generated large heat quickly. The steady-state simulation can be based on the numerical model using the H formulation [9,10] or the T-A formulation [11,12]. These numerical models usually use the finite element method (FEM) or the finite difference method to solve Maxwell equations (including Gauss’s law for magnetism, Faraday’s law of induction, and Ampere’s law with Maxwell’s addition); the detailed derivation process is shown in the above references. The input of the simulation model is current, and the output is the current density distribution, magnetic field distribution, and AC loss in the SFCL. When the SFCL is in the current-limiting process, the temperature of the superconducting winding rises significantly, affected by the short-circuit current. Since impedance of the superconducting winding is affected by current, magnetic field, and temperature simultaneously, multiple factors are combined, so a transient simulation of the inductive FCL is more difficult. In [13], resistance connected in parallel with a switch was used to simulate the resistive component of the superconducting winding, and the secondary induced current was calculated by the finite element simulation based on an electromagnetic model. The advantage of the model is that it provided fast computation speed and could simulate the macroscopic working characteristics of the current limiter, including voltage and current curves. However, since the model, lumped parameter model, equated the resistive component of tape to the parallel connection of the resistor and the switch, only the equivalent parameter value can be obtained. It was impossible to simulate microscopic working characteristics, such as the distribution of current and temperature. In [14–16], the magnetic field shielding characteristics of a single inductive current limiter unit in air or iron core were measured at different currents, and then equivalent inductance of the entire current limiter was estimated from the angle of the alternating magnetic flux and the winding hinge. The calculation result was used in the circuit model calculation. Since the model combined the measured values, the calculation results were more accurate. However, the measured value of a single current-limiting unit cannot fully represent the electromagnetic environment of the current limiter. At the same time, since the current-limiter impedance was calculated by the overall equivalent method, it was impossible to simulate the microscopic properties of the tape. In this paper, a transient numerical model for the process of limiting current in the inductive FCL is proposed. This numerical model including three main models: Circuit model, electromagnetic model, and heat transfer model. Then, an optimization method to accelerate convergence velocity of iteration is proposed. Based on the model, several typical examples are discussed, including the following parameters: The current and voltage, magnetic field and electrodynamic force distribution, and temperature distribution. A SFCL prototype is fabricated, and a short-circuit test of the SFCL is compared with the simulation results to verify the reliability of the simulation.

2. Methodology of Numerical Model

2.1. Model Overview When a short-circuit fault occurs in the power grid, the short-circuit current will far exceed the critical current in the current limiter. Meanwhile, part of the current will flow through the metal layer, and a large amount of joule heat will cause a significant temperature rise in the winding. Therefore, to calculate the temperature change inside the winding, the temperature field in a simulation model is needed, which is combined with the electromagnetic model to calculate the current-limiter impedance. In addition, in actual situations, the voltage value of the transformer is known instead of the short-circuit current, so the circuit model is used to calculate the instantaneous short-circuit current Materials 2019, 12, 2805 3 of 17 MaterialsMaterials 20192019,, 1212,, xx FORFOR PEERPEER REVIEWREVIEW 33 ofof 1717 multiplemultiplebased onphysicalphysical the power fieldsfields voltage involvedinvolved and current-limiterinin thethe wholwholee modelmodel impedance. areare interdependentinterdependent Since the calculation (such(such resultsasas currentcurrent of multiple andand current-limitercurrent-limiterphysical fields impedance),impedance), involved in multilmultil the wholeayerayer iterativeiterative model are calculcalcul interdependentationsations areare neededneeded (such astoto currentconvergeconverge and thethe current-limiter modelmodel andand simulatesimulateimpedance), thethe operatingoperating multilayer characteristicscharacteristics iterative calculations ofof thethe actualactual are currentcurrent needed limiterlimiter to converge [17,18].[17,18]. the model and simulate the operatingTheThe sophisticatedsophisticated characteristics commercialcommercial of the actual FEMFEM current softwaresoftware limiter cancan [17 solvesolve,18]. thethe complexcomplex problemsproblems quicklyquickly andand accurately.accurately.The sophisticatedTheThe abilityability ofof commercial interactiveinteractive FEM post-processpost-process software caninging solve andand thevisualizationvisualization complex problems makemake thethe quickly analyzinganalyzing and accurately. ofof thethe resultsresultsThe ability easier.easier. of TheThe interactive FEMFEM softwaresoftware post-processing beingbeing usedused and inin visualizationthisthis paperpaper isis COMSOL makeCOMSOL the analyzing multiphysicsmultiphysics of the 3.0,3.0, results andand bothboth easier. electromagneticelectromagneticThe FEM software modelmodel being andand used heatheat in transfertransfer this paper modelmodel is COMSOL araree basedbased multiphysics onon thethe software.software. 3.0, and TheThe both circuitcircuit electromagnetic modelmodel isis calculatedcalculatedmodel and byby heatMATLAB.MATLAB. transfer model are based on the software. The circuit model is calculated by MATLAB. TheTheThe overalloverall overall calculationcalculation calculation structurestructure structure ofof ofthethe the modelmodel model isis shown isshown shown inin in FigureFigure Figure 1.1.1 .

FigureFigureFigure 1.1. SchematicSchematic 1. Schematic diagramdiagram diagram ofof inductiveinductive of inductive superconductingsuperconducting superconducting faultfault fault currentcurrent current limiterlimiter limiter (SFCL)(SFCL) (SFCL) transient-statetransient-state transient-state simulationsimulationsimulation model.model. model.

2.2. Circuit Model 2.2.2.2. CircuitCircuit ModelModel The SFCL model can be equivalent to a transformer with a secondary short circuit. The circuit TheThe SFCLSFCL modelmodel cancan bebe equivalentequivalent toto aa transfortransformermer withwith aa secondarysecondary shortshort circuit.circuit. TheThe circuitcircuit model of the SFCL is shown in Figure2. modelmodel ofof thethe SFCLSFCL isis shownshown inin FigureFigure 2.2.

FigureFigureFigure 2.2. SchematicSchematic 2. Schematic diagramdiagram diagram ofof circuit ofcircuit circuit model.model. model.

Materials 2019, 12, 2805 4 of 17

In Figure2, U is the power voltage, r is the line resistance, i1 and i2 are the primary and secondary currents, respectively, R1(YBCO) and R1(Shunt) are the equivalent resistance of the HTS layer and metal layer in primary winding, respectively, R2(YBCO) and R2(Shunt) are the same as above in the secondary winding, L1 and L2 are self-inductance of the primary and secondary winding, respectively, and M is mutual inductance. In this model, the calculation of resistance is equivalent to the calculation of the resistance voltage drop. The resistance of the primary and secondary windings is in parallel with the resistance of the HTS layer and the metal layer. For the HTS layer, the resistive voltage drop is related to the temperature, amplitude, and direction of the magnetic field. Because of the nonuniform magnetic field and different positions of the primary and secondary windings, it is necessary to separately calculate the resistive voltage drop of each turn, and then accumulate the entire winding to obtain the total resistive voltage drop, as shown in Equation (1): !n X IYBCO U = Ec∆l (1) I (B, T) N c where N is the total number of turns, ∆l is the length of each turn, Ec is the critical electrical field, usually taking a constant value 1 10 6 V/m, n value is 29 for the tape used in this study. I is the × − YBCO current of the HTS layer, and Ic(B, T) is the critical current under magnetic field B and temperature T, as shown in Equation (2) [19]:

Ic(T) Ic(B, T) = " #α (2) q 2 2 1 + kB + B /Bc k ⊥

In the formula, B is the components of the magnetic field parallel to the superconducting surface, k B is the components of the magnetic field vertical to the superconducting surface, k, α, Bc are ⊥ physical parameter of superconducting tape, which represent the degradation of critical under different background magnetic field, and the value of k is between 0 and 1. In this paper, according to the test results of the critical current magnetic field angle-dependency of the YBa2Cu3O7-x (YBCO) tape, k = 0.3672, α = 0.6267, and Bc = 0.05249 T. For the metal layer, resistivity is only related to temperature, but since it is composed of various metals, the resistivity of each metal varies with temperature. The resistivity of superconducting tape as a function of temperature is measured when it is above the critical temperature. Below the critical temperature, a linear cubic spline fit is made at 92 K based on the measured data. In summary, the overall circuit model formula can be obtained, and discrete iterations are used in the actual calculation, as shown in Equation (3):

 n  P i1(YBCO)(m) i1(m) i1(m 1) i2(m) i2(m 1)  U( ) = i ( )r + Ec∆l + L1 − − M − −  m 1 m Ic(B,T) ∆t ∆t  N1 −  n (3)  P i2(YBCO)(m) i2(m) i2(m 1) i1(m) i1(m 1)  0 = Ec∆l + L2 − − M − −  Ic(B,T) ∆t ∆t N2 −

In the formula, i1(YBCO)(m) is taken as an example, the number 1 represents the primary side, (m) represents the mth step iteration, and (YBCO) represents the HTS layer, so i1(YBCO)(m) represents the current of the HTS layer in the primary winding at the mth iteration; i2(m 1) represents the total current − in the secondary winding at the (m 1)th iteration; N and N is the total number of primary winding − 1 2 and secondary winding, respectively, and ∆t is the size of the iterative step (1 10 5 s). × − Materials 2019, 12, x FOR PEER REVIEW 5 of 17

2.3. Electromagnetic Model

MaterialsThe electromagnetic2019, 12, 2805 model is based on the COMSOL AC/DC module, and it is based on Maxwell5 of 17 equations, as shown in Equation (4): 2.3. Electromagnetic Model   ∇⋅B =0 The electromagnetic model is based on the COMSOL AC/DC module, and it is based on Maxwell equations, as shown in Equation (4):  JH=∇× (4)  =  B ∂B0 ∇× ∇ =−·  JE= H (4)  ∇ ×∂t  E = ∂B ∇ × − ∂t wherewhere B isB theis themagnetic magnetic flux flux density, density, J is Jtheis thecurrent current density, density, H isH theis themagnetic magnetic field field strength, strength, E isE theis the electricelectric field field strength, strength, and and t representt represent time. time. FigureFigure 3 shows3 shows a schematic a schematic diagram diagram of the of theelectromagnetic electromagnetic model, model, which which is a is two-dimensional a two-dimensional axisymmetricaxisymmetric graph. graph. Figure Figure 3b is3b a isdiagram a diagram with with mesh mesh generation generation in simulation, in simulation, the thethickness thickness of the of the superconductingsuperconducting layer layer is magnified is magnified 10 times 10 times to acce to acceleratelerate the thesimulation. simulation. About About mesh mesh generation generation in in superconductingsuperconducting layer, layer, 20 grids 20 grids in z in direction z direction and and 1 grid 1 grid in r in direction r direction are aregenerated. generated.

Symmetry Axis Liquid Superconducting Nitrogen Layer Air Metal Layer

Superconducting layer

(a) (b)

FigureFigure 3. Schematic 3. Schematic diagram diagram of electromagnetic of electromagnetic model. model. (a) Structure; (a) Structure; (b) mesh. (b) mesh.

In order to simplify the model and speed up the calculation, B (Equation (2)) is the average In order to simplify the model and speed up the calculation, B (Equationk (2)) is the average of of parallel magnetic field in one turn, and B (Equation (2)) is the average of vertical magnetic ⊥ parallelfield magnetic in one turn. field Di inff oneerences turn, in and current B⊥ density (Equation at (2)) diff erentis the pointsaverage are of ignoredvertical formagnetic the same field turn. in oneThe turn. electromagnetic Differences model in current is used density to calculate at di thefferentIYBCO pointsand I shuntare ignoredwhen the for total the current same isturn. determined. The electromagneticThe specifications model is used of the to SFCLcalculate model the areIYBCO shown and Ishunt in Table when1. the total current is determined. The specifications of the SFCL model are shown in Table 1. Table 1. Specifications of SFCL model. Table 1. Specifications of SFCL model. Item Specifications Value Item SpecificationsTape width Value 4.8 mm Thickness without insulation 0.25 mm YBCO tape Tape width 4.8 mm ThicknessIc/n-value without (@77 K, self-field) insulation 0.25 40 mm A/29 YBCO tape Critical temperature 92 K Ic/n-value (@77 K, self-field) 40 A/29 CriticalNumber temperature of turns 92 K 40 Primary winding (insulation) Inner/outer diameter 114 mm/116.8 mm Number of turns 40 Turn-to-turn gap 0.35 mm Primary winding (insulation) Inner/outer diameter 114 mm/116.8 mm Number of turns 40 Turn-to-turn gap 0.35 mm Secondary winding (no-insulation) Inner/outer diameter 110 mm/112 mm NumberTurn-to-turn of turns gap 0.2540 mm Secondary winding (no-insulation) Inner/outer diameter 110 mm/112 mm Turn-to-turn gap 0.25 mm

Materials 2019, 12, 2805 6 of 17 Materials 2019, 12, x FOR PEER REVIEW 6 of 17

2.4.2.4. Heat Heat Transfer Transfer Model Model TheThe heat heat transfer transfer model model is is based based on on the the COMSOL COMSOL heat heat transfer transfer in in solids solids module. module. As As shown shown in in FigureFigure 4,4, a heat flux ﬂux is applied applied to to the the outer outer boundary boundary to to simulate simulate the the process process of boiling boiling liquid liquid nitrogen nitrogen heatheat transfer, transfer, so so that that the the simulated simulated liquid liquid nitrogen nitrogen region region can be directly deleted.

Symmetry Axis Metal Layer Superconducting Heat Flux Insulating Layer Temperature Layer Boundary Initial

FigureFigure 4. 4. SchematicSchematic diagram diagram of of heat heat transfer transfer model. model. The heat transfer model is divided into two parts. The first part is solid heat transfer, including The heat transfer model is divided into two parts. The first part is solid heat transfer, including heat transfer inside the superconducting tape, between tapes, and between tape and insulating material. heat transfer inside the superconducting tape, between tapes, and between tape and insulating The basic equation is as follows [20]: material. The basic equation is as follows [20]: ∂∂TT ρλρCp()(T) ==∇⋅(λ(T()) T ∇) + Q + (5) CTp t () T T Q (5) ∂∂t ∇ · ∇ where ρ is density, T is temperature, Cp(T) is specific heat capacity, λ(T) is thermal conductivity, where ρ is density, T is temperature, Cp(T) is specific heat capacity, λ(T) is thermal conductivity, t t represent time, and Q is the heat source in this model, which is the density loss E J of the winding. represent time, and Q is the heat source in this model, which is the density loss E·J ·of the winding. In the model, the simulation space is divided into three parts: Superconducting, metal, and In the model, the simulation space is divided into three parts: Superconducting, metal, and insulating layers. The metal layer is composed of multiple layers of different materials, and the specific insulating layers. The metal layer is composed of multiple layers of different materials, and the heat capacity Cp(T) and thermal conductivity λ(T) as functions of the temperature of each layer are specific heat capacity Cp(T) and thermal conductivity λ(T) as functions of the temperature of each different. To simplify the model, uniform thermal parameters are needed. Cp(T) and λ(T) of each layer layer are different. To simplify the model, uniform thermal parameters are needed. Cp(T) and λ(T) of are equivalently calculated, as shown in Equations (6) and (7): each layer are equivalently calculated, as shown in Equations (6) and (7): P CCTn(T())ρnρtn t = N nnn Ceq = N P (6) Ceq ρntn (6) N ρ  nnt P N λn(T)tn N λeq = Pλ ()Tt (7)  nntn N λ = N (7) eq t where, respectively, Ceq and λeq are equivalent specific heatn capacity and thermal conductivity and Cn N and λn are specific heat capacity and thermal conductivity of each metal layer, and ρn is the density where,and tn respectively,is the thickness Ceqof and each λeq metalare equivalent layer. N representsspecific heat the capa typescity of and mental thermal materials. conductivity and Cn and λThen are second specific part heat of capacity the heat and transfer thermal model conductivity is the heat of exchange each metal between layer, the and outer ρn is boundarythe density of andthe t windingn is the thickness and the of liquid each nitrogen, metal layer. which N represents is dominated the types by thermal of mental convection. materials. However, since the increasedThe second temperature part of the ofheat the transfer winding model causes is the liquidheat exchange nitrogen between to boil, thethe heatouter transfer boundary model of theis complicated. winding and Inthe order liquid to nitrogen, simplify which the calculation, is dominated a heat by fluxthermal is applied convection. to the However, outer boundary since the to increased temperature of the winding causes the liquid nitrogen to boil, the heat transfer model is complicated. In order to simplify the calculation, a heat flux is applied to the outer boundary to

Materials 2019, 12, 2805 7 of 17 simulate the process of boiling liquid nitrogen heat transfer, so that the simulated liquid nitrogen region can be directly deleted. The basic equation is as follows:

Q = h(Ts T ) A (Ts T ) (8) − 0 · · − 0 where Ts is the temperature of the heat flux boundary, A is the boundary cross-sectional area, T0 is the liquid nitrogen temperature (77 K), and h (Ts T0) is the effective nonlinear steady-state convection 2 − coefficient (W/(K m )). The value of h (Ts T ) is liquid nitrogen boiling heat flux curve in the · − 0 simulation, which is cited in [21].

2.5. Model Convergence and Optimization

2.5.1. Middle Voltage Loop Optimization As shown in Figure1, the iterative calculation is divided into three layers: Inner, middle, and outer. The middle voltage loop is used to iterate in the circuit model (calculating the primary and secondary currents) and the electromagnetic model (calculating the resistive voltage drop of the superconducting winding) under a specified supply voltage. The intermediate variable is the superconducting winding resistive voltage drop Usc_p, Usc_s, and the updating method is shown as Equation (9): ( Usc_p(k) = Usc_p(k 1) θ∆Usc_p(k) − − (9) Usc_s(k) = Usc_s(k 1) θ∆Usc_s(k) − − where Usc_p(k) represents the primary resistive voltage drop at the kth iteration and Usc_s(k) is the secondary voltage drop, where k refers to the number of iterations in the middle voltage loop; ∆Usc_p(k) is the difference between Usc_p(k) and Usc_p(k 1); and θ is the learning rate. In order to accelerate − convergence in the early stage, a method of exponential decay plus constant is used to calculate θ, such as Equation (10): k θ(k) = βe− τ + ξ (10) where β is the exponential decay coefficient, and the value is large (0.2), which ensures that the model can be quickly converged at the beginning; τ controls the decay rate; and ξ is the constant learning rate, which ensures that the learning rate of the model does not decay to a too small value after multiple iterations and cannot update. In the simulation, β = 0.2, τ = 30, and ξ = 0.01.

2.5.2. Inner Voltage Loop Optimization The inner voltage loop is used to calculate the current distribution in the superconducting and metal layers under a speciﬁed total winding current. In the actual calculation, due to the characteristics of the HTS, its current will enter a large nonlinear region when it reaches the critical current, as shown in Equation (1). At this time, if only Usc_p and Usc_s are used as the convergence conditions, the model will oscillate easily and cannot converge. To solve this problem, when the total winding current is close to or greater than the critical current, Umetal_p and Umetal_s are used as convergence conditions. The superconducting layer has nonnegligible resistance at this time, a part of current ﬂow through the metal layer, which results in a nonnegligible voltage drop in the metal layer, and this voltage drop can be directly calculated. Because the resistance of the metal layer is constant at the same temperature, there is no oscillation. Figure5 shows the number of iterations per step in two cycles (40 ms) before and after optimization. The ordinate represents the iterations of the inner current loop when the outer voltage loop is iterated once; the abscissa is the iterations of the outer voltage loop. Figure5 shows that the number of iterations at some special points can be greatly reduced after optimization. MaterialsMaterials 20192019, 12, 12, x, 2805FOR PEER REVIEW 8 8of of 17 17 Materials 2019, 12, x FOR PEER REVIEW 8 of 17

before optimazation 600 before optimazation 600 after optimazation after optimazation 500 500

400 400

300 300

200 200

100 100 Inner layer iteration times for each step iterationfor layer times Inner

Inner layer iteration times for each step iterationfor layer times Inner 0 0 0 2000 4000 6000 8000 0 2000 4000 6000 8000 step step Figure 5. Number of iterations at each step before optimization and after optimization. FigureFigure 5.5. NumberNumber ofof iterationsiterations atat eacheach stepstep beforebefore optimizationoptimization andand after after optimization. optimization. 3. Results and Discussion 3.3. ResultsResults andand DiscussionDiscussion 3.1.3.1. Typical Typical Examples Examples 3.1. Typical Examples 3.1.1.3.1.1. Current Current and and Voltage Voltage 3.1.1. Current and Voltage TheThe primary primary and and secondary secondary current current curves curves at at different different supply supply voltages voltages were were obtained obtained and and used used The primary and secondary current curves at different supply voltages were obtained and used toto analyze analyze the the macroscopic macroscopic operating operating characteristic characteristicss of of the the SFCL SFCL in in the the simulation. simulation. The The operating operating to analyze the macroscopic operating characteristics of the SFCL in the simulation. The operating conditionsconditions under under two two typical typical voltages voltages (voltage (voltage amplit amplitudesudes of of 0.5 0.5 V, V, 30 30 V) V) are are listed, listed, including including primary primary conditions under two typical voltages (voltage amplitudes of 0.5 V, 30 V) are listed, including primary current,current, primary primary superconductingsuperconducting layerlayer current, current, secondary secondary current, current, secondary secondary superconducting superconducting layer current, primary superconducting layer current, secondary current, secondary superconducting layercurrent, current, and voltage.and voltage. layer current, and voltage. FigureFigure 6 shows the simulation resultsresults ofof thethe voltage voltage and and current current curves curves at at a a voltage voltage magnitude magnitude of Figure 6 shows the simulation results of the voltage and current curves at a voltage magnitude of0.5 0.5 V. V. The The current current flows flows from from the the superconducting superconducting layer layer before before the the primary primary current current reaches reaches 60 60 A forA of 0.5 V. The current flows from the superconducting layer before the primary current reaches 60 A forthe the first first time; time; after after the the current current exceeds exceeds 60 A,60 theA, th shuntinge shunting phenomenon phenomenon begins begi tons appear. to appear. It shows It shows that for the first time; after the current exceeds 60 A, the shunting phenomenon begins to appear. It shows thatthe superconductingthe superconducting layer layer begins begins to show to show obvious obvious resistance resistance because because its current its current exceeds exceeds the critical the that the superconducting layer begins to show obvious resistance because its current exceeds the criticalcurrent. current. However, However, compared compared with the with metal the layer metal resistance, layer resistance, this resistance this resistance is still small, is still so onlysmall, a fewso critical current. However, compared with the metal layer resistance, this resistance is still small, so onlyamperes a few of amperes current of flow current through flow the through metal layer.the metal layer. only a few amperes of current flow through the metal layer. 100 2.0 100 primary YBCO current secondary YBCO current 2.0 80 primaryprimary total YBCO current current secondarysecondary total YBCO current current 1.5 80 voltageprimary total current sumsecondary of primary total and current secondary current 1.5 60 voltage sum of primary and secondary current 60 1.0 40 1.0 40 0.5 20 0.5 20 Voltage (V) Current (A) 0 0.0 Voltage (V) Current (A) 0 0.0 -20 -0.5 -20 -0.5 -40 -40 -1.0 -60 -1.0 -600.00 0.02 0.04 0.06 0.08 0.10 0.00 0.02 0.04Time (s) 0.06 0.08 0.10 Time (s) FigureFigure 6. 6. SimulationSimulation results results of of voltage voltage and and current current curves curves at at voltage voltage magnitude magnitude of of 0.5 0.5 V. V. Figure 6. Simulation results of voltage and current curves at voltage magnitude of 0.5 V.

Materials 2019, 12, 2805 9 of 17 Materials 2019, 12, x FOR PEER REVIEW 9 of 17

WhenWhen the the waveform waveform is is stable, stable, the the primary primary current current amplitude amplitude is is 53.9 53.9 A, A, the the secondary secondary current current amplitudeamplitude is is 51.2 51.2 A, A, and and the the phase phase difference difference betw betweeneen the the two two is 174.6°. 174.6◦. In In order order to to explain explain the the shieldingshielding effect effect of of the the secondary secondary winding winding on on the the magnetic magnetic flux flux generated generated by by the the primary primary winding, winding, thethe sum sum of of the the primary primary and and secondar secondaryy currents currents is is defined defined as as “net “net current,” current,” which which generates generates magnetic magnetic fluxflux (the ratioratio ofof primary primary to to secondary secondary is 1:1). is 1:1). The purpleThe purple curve curve in Figure in 6Figure is net current;6 is net the current; amplitude the amplitudeis 5.1 A and is bias5.1 A is and 6.0 A,bias which is 6.0 is A, 9.5% which of the is primary9.5% of the current. primary The current. secondary The winding secondary shields winding most shieldsof the magneticmost of the flux magnetic generated flux by generated the primary by winding.the primary Only winding. 9.5% of Only the primary 9.5% of current the primary builds currentan alternating builds an magnetic alternating field, magnetic so the overall field, so leakage the overall inductance leakage is inductance close to zero. is close The primaryto zero. The and primarysecondary and currents secondary flow currents through flow the HTSthrough layer, the so HT theS overall layer, so impedance the overall of theimpedance SFCL is of close the toSFCL zero. isThe close phase to zero. diff erenceThe phase between difference the primary between current the primary and the current voltage and waveform the voltage is waveform 84.6◦. The is leakage 84.6°. Theinductance leakage ofinductance the primary of the and primary secondary and windings secondary makes windings the SFCL makes inductive. the SFCL inductive. FigureFigure 7 shows thethe simulationsimulation resultsresults of of the the voltage voltage and and current current curves curves at at a voltagea voltage magnitude magnitude of of30 30 V. V. The The first first peak peak of of the the primary primary current current is is 652.7 652.7 A, A, and and the the current current wave wave becomes becomes steady steady state state in inthe the fifth fifth cycle cycle with with the the peak peak value value of of 427.4 427.4 A.A. AfterAfter thethe currentcurrent of the secondary winding winding becomes becomes stable,stable, the the peak peak value value is is 127.1 127.1 A, A, and and the the amplitude amplitude of of net net current current generating generating the the alternating alternating magnetic magnetic fieldfield is is 399.5 399.5 A, A, which which is is 93.5% 93.5% of of the the primary primary current. current. It It indicates indicates that that most most of of the the primary primary current current is is usedused to to construct construct the the alternating alternating magnetic magnetic field, field, an andd the the secondary secondary current current can can only only shield shield a a fraction fraction ofof the the magnetic magnetic flux flux generated generated by by the the primary primary current. current. The The SFCL SFCL has has large large inductance; inductance; meanwhile, meanwhile, thethe resistive resistive component component of of the the winding winding is is also also in increasedcreased due due to to the the large large primary primary current. current. The The phase phase differencedifference between between the the primary primary current current and and the the voltage voltage is is 57.6° 57.6◦ inin steady steady state. state.

800 80 primary YBCO current secondary YBCO current primary total current secondary total current 600 60 voltage primary 400 current 40

200 20

0 0 Voltage (V) Current(A) sceondary -200 current -20 voltage -400 -40

-600 -60 0.00 0.02 0.04 0.06 0.08 0.10 Time (s) (a)

800 80 800 primary total current secondary total current sum of primary and secondary current 600 60 600 primary voltage current

400 40 400 primary YBCO 200 20 200 current

0 0 0 Voltage (V) Current (A) Current(A) -200 -20 -200 secondary YBCO sceondary current -400 -40 -400 current

-600 -60 -600 0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.01 0.02 0.03 0.04 Time (s) Time (s) (b) (c) FigureFigure 7. 7. SimulationSimulation results results of of voltage voltage and and current current curves curves at at voltage voltage magnitude magnitude of of 30 30 V: V: ( (aa)) Overall Overall curves,curves, ( (bb)) net net current current that that generates generates magnetic magnetic flux, ﬂux, ( (cc)) details details of of curves curves at at first ﬁrst two two cycles. cycles.

AtAt this this moment, moment, due due to to the the large large primary primary and and se secondarycondary current, current, a a consider considerableable amount amount of of joule joule heatheat is is generated, generated, and and the the influence inﬂuence of ofthe the increa increasedsed winding winding temperature temperature on onthe theHTS HTS strip strip cannot cannot be ignored.be ignored. As shown As shown in Figure in Figure 7a, th7ea, heat the heataccumulation accumulation results results in decreased in decreased saturation saturation currents currents in the primary and secondary superconducting layers, because the critical current decreases as the winding

Materials 2019, 12, 2805 10 of 17

Materials 2019, 12, x FOR PEER REVIEW 10 of 17 in the primary and secondary superconducting layers, because the critical current decreases as the windingtemperature temperature rises, and rises, the and equivalent the equivalent impedanc impedancee increases. increases. The The temperature temperature rise rise curve curve and temperature distribution of the windingwinding willwill bebe analyzedanalyzed inin detaildetail later.later.

3.1.2. Magnetic Field and Electrodynamic Force By analyzinganalyzing the the distribution distribution of theof the magnetic magnetic field, fiel thed, distribution the distribution of critical of critical current current can be derived, can be thenderived, the distributionthen the distribution of power densityof power can bedens inferred.ity can Inbe addition, inferred. the In maximum addition, electrodynamicthe maximum forceelectrodynamic acting on the force limiter acting depends on the onlimiter the firstdepends peak ofon primarythe first currentpeak of underprimary short-circuit current under conditions. short- Figurecircuit8 conditions. shows the magneticFigure 8 fieldshows distribution the magnetic at the fiel firstd currentdistribution peak at of the primaryfirst current winding peak under of the a voltageprimary magnitude winding under of 30 a V. voltage magnitude of 30 V.

(a) (b)

Figure 8.8.Magnetic Magnetic field field distribution distribution at first at currentfirst current peak ofpeak primary of primary winding underwinding voltage under magnitude voltage ofmagnitude 30 V: (a) Fluxof 30 densityV: (a) Flux norm density value norm distribution, value distribution, (b) magnetic (b field) magnetic direction field diagram. direction diagram.

In the area betweenbetween primaryprimary and secondarysecondary windings, the entire secondary winding, and the inside and ends of thethe primaryprimary winding,winding, thethe magneticmagnetic fieldfield isis largest.largest. Among them, the secondary winding and inside and ends of the primary winding are mainly influencedinfluenced by the magnetic fieldfield parallel toto thethe tape. tape. According According to to Equation Equation (2), (2), this this magnetic magnetic field field has little has elittleffect oneffect the criticalon the current,critical whichcurrent, results which in results a low power in a low loss power density; loss the density; ends of thethe primaryends of windingthe primary are mainly winding affected are mainly by the magneticaffected by field the verticalmagnetic to field the tape, vertical and to this the results tape, inand low this critical results current in low density critical andcurrent high density power and loss density.high power To improve loss density. the recovery To improve speed the after recovery cutting speed off the after short cutting fault, theoff the above short problem fault, the should above be takenproblem into should consideration be taken ininto the consideration design of a cooling in the structure.design of a If cooling necessary, structure. tapes with If necessary, higher critical tapes currentwith higher and bettercritical cooling current structure and better can becooling used instructure the ends can of thebe primaryused in winding.the ends of the primary winding.Figure 9 shows the electrodynamic force distribution at the first current peak of the primary windingFigure under 9 shows a voltage the magnitudeelectrodynamic of 30 V.force The distribu electrodynamiction at the force first aff ectingcurrent the peak secondary of the windingprimary iswinding small and under the directiona voltage is magnitude negative; in of the 30 primary V. The winding,electrodynamic the inner force side isaffecting influenced the bysecondary positive forcewinding and is the small outer and side, the and direction the winding is negative; is squeezed in the inprimary the r-axis winding, direction. the Forinner electrodynamic side is influenced force inby thepositive z-axis direction,force and the the secondary outer side, winding and the has awinding small influence is squeezed and the in directionthe r-axis is positive;direction. in For the primaryelectrodynamic winding, force the in end the is z-axis greatly direction, affected the by asecondary negative forcewinding and has the middlea small isinfluence influenced and by the a positivedirection force, is positive; and the in winding the primary is squeezed winding, in the en z-axisd is direction.greatly affected by a negative force and the middleAs is shown influenced in Figure by a9 c,positive di fferent force, parts and of the the winding winding is are squeezed influenced in the by z-axis electrodynamic direction. force in differentAs shown directions. in Figure Electrodynamic 9c, different force parts is of a the macro winding performance are influenced of the Lorentzby electrodynamic force; the magnetic force in fielddifferent of the directions. conductor Electrodynamic is generated by force its own is a current, macro soperformance the direction of ofthe electrodynamic Lorentz force; forcethe magnetic does not changefield of withthe conductor the direction is generated of the current. by its own current, so the direction of electrodynamic force does not change with the direction of the current.

Materials 2019, 12, 2805 11 of 17 Materials 2019, 12, x FOR PEER REVIEW 11 of 17

(a) (b) (c)

FigureFigure 9. 9. ElectrodynamicElectrodynamic force force distribution distribution at at the the first ﬁrst current current peak peak of of primary primary winding winding under under voltage voltage magnitudemagnitude of of 30 30 V: V: ( (aa)) R-axial R-axial component, component, ( (bb)) z-axial z-axial component, component, ( (cc)) electrodynamic electrodynamic force force direction. direction.

ToTo ensure ensure that that the the SFCL SFCL will will not not be bedestroyed destroyed in the in thestructure structure under under short-circuit short-circuit current, current, the electrodynamicthe electrodynamic force force affecting affecting different different parts parts of the of winding the winding should should be considered be considered in the in design. the design. The superconductingThe superconducting coils coilsin the in primary the primary and and secondary secondary windings windings of ofthe the upper upper half half of of the the SFCL SFCL are are numberednumbered and and calculated calculated by the electrodynamicelectrodynamic forceforce theythey a affect;ffect; the the numbers numbers are are shown shown in in Figure Figure9c 9cand and the the calculation calculation results results are are shown shown in in Table Table2. 2.

TableTable 2. 2. StressStress of of pancake pancake winding winding under under firs ﬁrstt peak peak current current of of primary primary winding. winding.

PrimaryPrimary Winding Winding Secondary Secondary Winding Winding No.No. Electrodynamic Electrodynamic force force r-axial r-axial component component (N/m) (N/m) 11 438.3 438.3 −116.6116.6 − 22 493.4 493.4 −138.6138.6 − 3 517.7 144.9 3 517.7 −144.9− 4 528.4 147.1 4 528.4 −147.1− No.No. Electrodynamic Electrodynamic force force z-axial z-axial component component (N/m) (N/m) 1 1023.4 75.9 1 −1023.4− 75.9 2 535.8 45.8 2 −535.8− 45.8 3 283.8 24.7 − 4 3 −283.889.9 24.7 7.9 4 −89.9− 7.9

TheThe force force acting on thethe secondarysecondary windingwinding is is not not large, large, and and the the external external shedding shedding force force in thein the z-axis z- axisshould should be considered be considered in the in design; the design; the force the actingforce onacting the primaryon the primary winding winding is large, is more large, attention more attentionshould be should paid be to paid the outward to the outward force, andforce, it and is necessary it is necessary to enhance to enhance the structurethe structure because because of theof thelarge large force. force. 3.1.3. Temperature 3.1.3. Temperature When the short-circuit current is large, a large amount of joule heat generated by winding will When the short-circuit current is large, a large amount of joule heat generated by winding will result in a significant temperature rise, affecting the electromagnetic properties of the tape. Taking the result in a significant temperature rise, affecting the electromagnetic properties of the tape. Taking simulation result voltage magnitude of 30 V as an example, the rising temperature curve of primary the simulation result voltage magnitude of 30 V as an example, the rising temperature curve of and secondary windings is shown in Figure 10. Since the rising temperatures of different turns are primary and secondary windings is shown in Figure 10. Since the rising temperatures of different different in the same winding, the averages of temperature rise of the primary and secondary sides turns are different in the same winding, the averages of temperature rise of the primary and are used. As shown in Figure 10, the average temperature of the primary winding increases from the secondary sides are used. As shown in Figure 10, the average temperature of the primary winding initial 77 K to 85.8 K, and that of the secondary winding increases from 77 K to 81.1 K. Figure6 shows increases from the initial 77 K to 85.8 K, and that of the secondary winding increases from 77 K to that the primary current is greater than the secondary current, so the primary temperature rise should 81.1 K. Figure 6 shows that the primary current is greater than the secondary current, so the primary temperature rise should be greater than the secondary, but because the primary side resistivity is less than the secondary side, the combined action causes a minor difference in temperature rise.

Materials 2019, 12, x FOR PEER REVIEW 12 of 17

Materials 2019, 12, 2805 12 of 17 be greater than the secondary, but because the primary side resistivity is less than the secondary side, theMaterials combined 2019, 12, action x FOR PEER causes REVIEW a minor diﬀerence in temperature rise. 12 of 17

Figure 10. Rising temperature of primary and secondary windings under voltage magnitude of 30 V.

In order to further analyze the internal operation of the SFCL, Figure 11 shows the temperature distribution of the primary and secondary windings at 0.02 s, 0.04 s, 0.06 s, and 0.08 s (only the upper half of the winding is drawn because it is symmetric). As shown in Figure 11, the portion with the greatest temperature rise is at the end of the primary innermost winding. Since it is affected by the largest magnetic field (especially the magnetic field perpendicular to the tape), the critical current there is minimized. A large amount of joule heat causes the greatest temperature rise. In the space between the primary and secondary windings, due to the opposite direction of the current, the generated magnetic fields are superimposed and enlarged, but the magnetic field direction is parallel to the strip, so the field has little effect on the critical current. It canFigure be seen 10. thatRisingRising the temperature temperature of primary rises more and insisecondary de the windings primary under winding voltage than magnitude outside. Similarly, of 30 V. in the secondary winding, the temperature rises the most at the end. Since the structure of all-metal and no-insulationIn order tolayers further makes analyze it possible the internal to operationexchangeoperation ofheat the with SFCL, liquid Figure nitrogen 11 shows directly, the temperature the heat distributionconduction speed of the is primary fast. So and overall, secondary the temperatur windingse atatrises 0.02 significantly s, 0.04 s, 0.06 less s, andin the 0.08 secondary s (only the winding upper halfthan of in the the winding primary iswinding. drawn because itit isis symmetric).symmetric). As shown in Figure 11, the portion with the greatest temperature rise is at the end of the primary innermost winding. Since it is affected by the largest magnetic field (especially the magnetic field perpendicular to the tape), the critical current there is minimized. A large amount of joule heat causes the greatest temperature rise. In the space between the primary and secondary windings, due to the opposite direction of the current, the generated magnetic fields are superimposed and enlarged, but the magnetic field direction is parallel to the strip, so the field has little effect on the critical current. It can be seen that the temperature rises more inside the primary winding than outside. Similarly, in the secondary winding, the temperature rises the most at the end. Since the structure of all-metal and no-insulation layers makes it possible to exchange heat with liquid nitrogen directly, the heat conduction speed is fast. So overall, the temperature rises significantly less in the secondary winding than in the primary winding.

Figure 11.11. TemperatureTemperature distribution distribution of of primary primary and and secondary secondary windings windings at (a at) 0.02 (a) s,0.02 (b) s, 0.04 (b) s, 0.04 (c) 0.06 s, (c s,) and0.06 (s,d )and 0.08 (d s.) 0.08 s.

As shown in Figure 11, the portion with the greatest temperature rise is at the end of the primary innermost winding. Since it is affected by the largest magnetic field (especially the magnetic field perpendicular to the tape), the critical current there is minimized. A large amount of joule heat causes the greatest temperature rise. In the space between the primary and secondary windings, due to the opposite direction of the current, the generated magnetic fields are superimposed and enlarged, but the magnetic field direction is parallel to the strip, so the field has little effect on the critical current. It can be seen that the temperature rises more inside the primary winding than outside. Similarly,

Figure 11. Temperature distribution of primary and secondary windings at (a) 0.02 s, (b) 0.04 s, (c) 0.06 s, and (d) 0.08 s.

Materials 2019, 12, 2805 13 of 17

Materialsin the secondary 2019, 12, x FOR winding, PEER REVI theEW temperature rises the most at the end. Since the structure of all-metal13 of 17 and no-insulation layers makes it possible to exchange heat with liquid nitrogen directly, the heat conductionAs shown speed in F isigure fast. 1 So1, overall,compared the with temperature the secondary rises significantly winding, the less temperature in the secondary of the windingprimary windingthan in the rises primary more winding.greatly in the current-limiting state of the HTS FCL. In order to speed up the recoveryAs shown time after in Figure the fault 11, current compared is cut with off, the the secondary heat dissipation winding, problem the temperature should be ofconsidered the primary in thewinding actual rises design more and greatly manufact in theure current-limiting of the primary state winding of the HTSstructure. FCL. WhileIn order ensuring to speed support up the strength,recovery time the contact after the area fault between current is the cut winding off, the heat and dissipation the liquid problem nitrogen should is increased be considered as much in the as possible.actual design and manufacture of the primary winding structure. While ensuring support strength, the contact area between the winding and the liquid nitrogen is increased as much as possible. 3.2. Short-Circuit Test 3.2. Short-Circuit Test In order to simulate the fault conditions in an actual grid, a SFCL prototype with the same simulationIn order structure to simulate is fabricated the fault and conditions connected in an to actual the short grid,-circuit a SFCL test prototype platform. with The the primary same windingsimulation is structurean insulation is fabricated superconducting and connected winding to the with short-circuit insulating test material platform. of The KAPTON, primary windingand the secondaryis an insulation winding superconducting is a no-insulation winding sup witherconducting insulating winding. material In of KAPTON, this paper, and superconducting the secondary winding is is a woundno-insulation with superconductingsecond-generation winding. high temperature In this paper, superconducting superconducting windingmaterial is— woundYBCO tapeswith second-generationwith stainless-steel high packag temperaturee, which are superconducting produced by Shanghai material—YBCO Superconductor. tapes with stainless-steel package,HTS whichcoated are conductor produced (CC by) tapes Shanghai were Superconductor. used in this paper is 4.8 mm wide and critical current is 40 A HTS(77 K, coated self-field conductor). Superconducting (CC) tapes were tapes used are inwith this a paper1.5 μm is thick 4.8 mm YBCO wide layer, and criticala 50 μm current thick Hastelloyis 40 A (77 substrate, K, self-field). a 2 μ Superconductingm thick silver cap tapes layer are, and with a 10 a 1.5μmµ m+ 10 thick μm YBCOthick copper layer, a stabilization 50 µm thick layer.Hastelloy The substrate,structure adiagram 2 µm thick of YBCO silver captape layer, is shown and ain 10 Fiµgurem + 1012.µ Then,m thick the copper outermost stabilization is packaged layer. inThe 75 structure m thick stainless diagram s ofteel YBCO. tape is shown in Figure 12. Then, the outermost is packaged in 75 m thick stainless steel.

Figure 12. Structure diagram of YBCO tape.

The primary winding andFigure secondary 12. Structure winding diagram consist of ofYBCO four tape double-pancake. coils, respectively. A pancake coil is a coil with a flat spiral form, and a double-pancake coil is two pancake coils made by The primary winding and secondary winding consist of four double-pancake coils, respectively. a superconducting tape. Double-pancake coils are connected in series by soldering, and resistance is A pancake coil is a coil with a flat spiral form, and a double-pancake coil is two pancake coils made 1.5 µΩ. Specifications of the SFCL prototype is shown in Table1, same with the SFCL model, and the by a superconducting tape. Double-pancake coils are connected in series by soldering, and resistance inductive SFCL prototype is shown in Figure 13. is 1.5 μΩ. Specifications of the SFCL prototype is shown in Table 1, same with the SFCL model, and Critical current of primary winding and secondary winding is 28 A and 30 A (77 K), respectively. the inductive SFCL prototype is shown in Figure 13. Self-inductance of primary winding and secondary winding is 0.237 mH and 0.206 mH. The mutual Critical current of primary winding and secondary winding is 28 A and 30 A (77 K), respectively. inductance between the primary and the secondary is 0.196 mH, and the coupling coefficient is 0.887. Self-inductance of primary winding and secondary winding is 0.237 mH and 0.206 mH. The mutual The short-circuit test platform is shown in Figure 14; voltage source consists of voltage regulator inductance between the primary and the secondary is 0.196 mH, and the coupling coefficient is 0.887. (input: 400 V, output: 0~400 V) and step-down transformer (ratio is 20:1 or 10:1). Different voltage can The short-circuit test platform is shown in Figure 14; voltage source consists of voltage regulator be obtained by changing output voltage of voltage regulator. A load resistor connected in parallel (input: 400 V, output: 0~400 V) and step-down transformer (ratio is 20:1 or 10:1). Different voltage with IGBT fast switching is in series with the SFCL prototype, and the IGBT controlled by the host can be obtained by changing output voltage of voltage regulator. A load resistor connected in parallel computer is used to generate a short-circuit voltage for a specified duration. with IGBT fast switching is in series with the SFCL prototype, and the IGBT controlled by the host computer is used to generate a short-circuit voltage for a specified duration.

Materials 2019, 12, x FOR PEER REVIEW 14 of 17 Materials 2019, 12, 2805 14 of 17 Materials 2019, 12, x FOR PEER REVIEW 14 of 17

odp = 116.8 mm

odp = 116.8 mm idp = 114 mm

idp = 114 mm

Primary winding Primary winding 40 mm 40 mm h = h = Secondary winding h = h = Secondary winding

ids = 110 mm id = 110 mm gap = 1 mm s ods= 112 mm

gap = 1 mm od(a)s= 112 mm (a)

Voltage lead Voltage lead Primary winding Primary winding

Current lead Current lead

(b) (c) (b) (c) Figure 13. Superconducting inductive SFCL prototype: (a) Schematic diagram, (b) secondary winding,Figure 13.13. (c Superconducting) SuperconductingSFCL prototype. inductive inductiv SFCLe SFCL prototype: prototype: (a) Schematic (a) Schematic diagram, diagram, (b) secondary (b) secondary winding, (winding,c) SFCL prototype.(c) SFCL prototype.

Figure 14. Short-circuit test platform. Figure 14. Short-circuit test platform. The step-down transformerFigure is used 14. as Short-circuit a voltage test source platform. and the turn-off time is controlled to provideThe a step-down short-circuit transformer current with is aused fixed as time a voltage for the SFCL.source In and this the experiment, turn-off time the short-circuit is controlled time to provideis 5 cyclesThe astep-down ofshort-circuit 100 ms. transformer current with is useda fixed as timea voltage for the so urceSFCL. and In thethis turn-offexperiment, time theis controlled short-circuit to timeprovide Consideringis 5 acycles short-circuit of the100 di ms. fficurrentculty of with measuring a fixed and time simulating for the SFCL. the internal In this impedance experiment, of voltagethe short-circuit regulator, timethe experimental Consideringis 5 cycles of voltage100the ms.difficulty value isof directlymeasuring input and into simulating the transient the model internal for impedance calculation. of Figure voltage 15 regulator,showsConsidering the the comparison experimental the difficulty of the voltage experimental of measuringvalue is waveformdirect andly simulating input (left) into and the the transientinternal simulated impedancemodel waveform for calculation.of (right) voltage at Figureregulator,different 15 voltages showsthe experimental the (waveforms comparison voltage in twoof thevalue cycles experiment is after direct thelyal short-circuit inputwaveform into the (left) current transient and becomes the model simulated steady for calculation. state).waveform (right)Figure at15 differentshows the voltages comparison (waveforms of the experimentin two cyclesal waveformafter the short-circuit (left) and the current simulated becomes waveform steady state).(right) at different voltages (waveforms in two cycles after the short-circuit current becomes steady state).

Materials 2019, 12, 2805 15 of 17

(a) (b)

(e) (f)

Figure 15. Comparison of experimental (left) and simulation (right) results of voltage and current curves. (a) Comparison of primary current curve between experimental and simulation under voltage magnitude of 2.6 V, (b) overall simulation current under voltage magnitude of 2.6 V, (c) comparison of primary current curve between experimental and simulation under voltage magnitude of 4.5 V, (d) overall simulation current under voltage magnitude of 4.5 V,(e) comparison of primary current curve between experimental and simulation under voltage magnitude of 19.5 V, and (f) overall simulation current under voltage magnitude of 19.5 V.

As shown in Figure 15, the simulated current waveform is basically consistent with the experimental waveform, which proves that the simulation can well simulate the operating characteristics of the air core current limiter under short-circuit current, which lays a foundation for future SFCL design. 1

Materials 2019, 12, 2805 16 of 17

The error between the experiment and the simulation may be caused by the measurement error of the strip electrical and thermal parameters, or by nonuniform electrical and thermal parameters of the strip in the longitudinal direction. The primary current waveform is related to the secondary current waveform, especially when the secondary current begins to shunt in the HTS and metal layers, the secondary side impedance increases, and the instantaneous current value begins to decrease compared with the standard sine wave. At the same time, the primary current is distorted, and the overall distortion is less than the secondary winding.

4. Conclusions In this paper, a numerical study of transient states for the process of limiting current in inductive FCLs is proposed. The model is based on the coupling of multiphysics finite element simulation and a circuit model. By optimization, the number of iterations is reduced, and operational speed is greatly increased. The overall model calculation process, submodel setting, and analysis of the macroscopic characteristics (voltage, current) and microscopic characteristics (distribution of magnetic field, electrodynamic force, and temperature) of the SFCL under the current-limiting state are introduced. In SFCL design, more attention should be paid to the large outward force acting on the primary winding, and it is necessary to enhance the structure; the heat dissipation problem should be considered, while ensuring that the support strength and the contact area between the winding and the liquid nitrogen are increased as much as possible. The short-circuit experimental data of an air core inductive superconducting current limiter (SFCL) prototype was compared with the simulation results to verify the reliability of the simulation and provides a theoretical basis for the future design and manufacture of SFCL. Further, inductive SFCL applied in a short test of a large capability transformer under the grid operating condition can be designed. In this paper, some parameters in electromagnetic model and heat transfer model can be further refined and the simulation accuracy is improved. Similarly, better optimization method can be used to accelerate convergence.

Author Contributions: Conceptualization, J.S.; methodology, J.S. and W.L.; validation, D.Q.; data curation, J.C., H.Y.; writing—original draft, W.L.; writing—review and editing, W.L., D.Q., J.C., H.Y.; supervision, Z.H. Funding: This research was funded by the National Natural Science Foundation of China, grant number 51807118. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Ruiz, H.S.; Zhang, X.; Coombs, T.A. Resistive-type superconducting fault current limiters: Concepts, materials, and numerical modeling. IEEE Trans. Appl. Supercond. 2015, 25, 5601405. [CrossRef] 2. Naeckel, O.; Noe, M. Design and Test of an Air Coil Superconducting Fault Current Limiter Demonstrator. IEEE Trans. Appl. Supercond. 2014, 24, 5601605. [CrossRef] 3. Meerovich, V.; Sokolovsky, V.; Bock, J.; Gauss, S.; Goren, S.; Jung, G. Performance of an inductive fault current limiter employing BSCCO superconducting cylinders. IEEE Trans. Appl. Supercond. 1999, 9, 4666–4676. [CrossRef] 4. Usoskin, A.; Mumford, F.; Dietrich, R.; Handaze, A.; Prause, B.; Rutt, A.; Schlenga, K. Inductive Fault Current Limiters: Kinetics of Quenching and Recovery. IEEE Trans. Appl. Supercond. 2009, 19, 1859–1862. [CrossRef] 5. Kozak, J.; Majka, M.; Kozak, S.; Janowski, T. Design and tests of coreless inductive superconducting fault current limiter. IEEE Trans. Appl. Supercond. 2012, 22, 5601804. [CrossRef] 6. Paul, W.; Lakner, M.; Rhyner, J.; Unternährer, P.; Baumann, T.; Chen, M.; Guerig, A. Test of 1.2 MVA high-superconducting fault current limiter. Supercond. Sci. Technol. 1997, 10, 914–918. [CrossRef] 7. Kozak, J.; Majka, M.; Kozak, S. Experimental Results of a 15 kV, 140 A Superconducting Fault Current Limiter. IEEE Trans. Appl. Supercond. 2017, 27, 5600504. [CrossRef] 8. Cvoric, D.; De Haan, S.W.H.; Ferreira, J.A.; Van Riet, M.; Bozelie, J. Design and Testing of Full-Scale 10 kV Prototype of Inductive Fault Current Limiter with a Common Core and Triﬁlar Windings. In Proceedings of the 2010 International Conference on Electrical Machines and Systems, Incheon, South Korea, 10–13 October 2010. Materials 2019, 12, 2805 17 of 17

9. Hong, Z.; Campbell, A.M.; Coombs, T.A. Numerical solution of critical state in superconductivity by finite element software. Supercond. Sci. Technol. 2006, 19, 1246–1252. [CrossRef] 10. Hong, Z.; Coombs, T.A. Numerical Modelling of AC Loss in Coated Conductors by Finite Element Software Using H Formulation. J. Supercond. Nov. Magn. 2010, 23, 1551–1562. [CrossRef] 11. Zhang, H.; Zhang, M.; Yuan, W. An efficient 3D finite element method model based on the T–A formulation for superconducting coated conductors. Supercond. Sci. Technol. 2017, 30, 024005. [CrossRef] 12. Wang, Y.; Zhang, M.; Grilli, F.; Zhu, Z.; Yuan, W. Study of the magnetization loss of CORC cables using 3D TA formulation. Supercond. Sci. Technol. 2019, 32, 025003. [CrossRef] 13. Kozak, S.; Janowski, T.; Wojtasiewicz, G.; Kozak, J.; Kondratowicz-Kucewicz, B.; Majka, M. The 15 kV Class Inductive SFCL. IEEE Trans. Appl. Supercond. 2010, 20, 1203–1206. [CrossRef] 14. Naeckel, O.; Noe, M. Conceptual Design Study of an Air Coil Fault Current Limiter. IEEE Trans. Appl. Supercond. 2013, 23, 5602404. [CrossRef] 15. Hekmati, A.; Vakilian, M.; Fardmanesh, M. Flux-Based Modeling of Inductive Shield-Type High-Temperature Superconducting Fault Current Limiter for Power Networks. IEEE Trans. Appl. Supercond. 2011, 21, 3458–3464. [CrossRef] 16. Kado, H.; Ichikawa, M.; Ueda, H.; Ishiyama, A. Trial Design of 6.6kV Magnetic Shielding Type of Superconducting Fault Current Limiter and Performance Analysis Based on Finite Element Method. Electr. Eng. Jpn. 2010, 145, 50–57. [CrossRef] 17. Sheng, J.; Wen, J.; Wei, Y.; Zeng, W.; Jin, Z.; Hong, Z. Voltage-Source Finite-Element Model of High Temperature Superconducting Tapes. IEEE Trans. Appl. Supercond. 2015, 25, 7200305. [CrossRef] 18. Sheng, J.; Hu, D.; Ryu, K.; Yang, H.S.; Li, Z.Y.; Hong, Z. Numerical Study on Overcurrent Process of High-Temperature Superconducting Coated Conductors. J. Supercond. Nov. Magn. 2017, 30, 3263–3270. [CrossRef] 19. Grilli, F.; Sirois, F.; Zermeno, V.M.R.; Vojenciak, M. Selfconsistent modeling of the Ic of HTS devices: How accurate do models really need to be? IEEE Trans. Appl. Supercond. 2014, 24, 8000508. [CrossRef]

20. Wang, Y.; Chan, W.K.; Schwartz, J. Self-protection mechanisms in no-insulation (RE)Ba2Cu3Ox, high temperature superconductor pancake coils. Supercond. Sci. Technol. 2016, 29, 045007. [CrossRef] 21. Sakurai, A.; Shiotsu, M.; Hata, K. Boiling heat transfer characteristics for heat inputs with various increasing rates in liquid nitrogen. Cryogenics 1992, 32, 421–429. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).