proposed design for a tunable inductive shield-type sfcl

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 24, NO. 4, AUGUST 2014 5601907

Proposed Design for a Tunable InductiveShield-Type SFCL

Arsalan Hekmati

Abstract—Superconducting fault current limiters (SFCLs) offera good solution for the increased level of short circuits in powersystems. Inductive shield-type SFCLs are one of the most promis-ing categories of the SFCLs. A design has been proposed for atunable fault current limiter, which has the capability to vary thelevel of current limitation via varying some control parameters.This increases the utilization flexibility of the SFCL and may resultin economic gains. Regarding the ever-growing short-circuit levelin the power systems that may demand upgrade or replacementof protection devices, if SFCLs are installed with the proposedstructure, several current limitation levels may be available andselected due to the short-circuit level of the system and the nominalrating of different power system devices. The proposed designis verified calculating theoretically the through current of theSFCL and studying the impact of different control parameters onit. Furthermore, a prototype SFCL has been fabricated and hasshown the desirable tunable current limitation characteristics.

Index Terms—Fault current limiter, shield-type, superconduct-ing, tunable.

I. INTRODUCTION

INDUCTIVE shield-type superconducting fault currentlimiters (SFCLs) form an important category of SFCLs.

They bring about many advantages, including high reliability,low losses, and isolation of superconductive material from theelectrical network [1]. Investigations have been done on its fab-rication, simulation, modeling, and characterization [2]–[11].Basically, it consists of a superconductor cylinder around anopen or closed iron core and a copper winding around thesuperconductor cylinder. The copper winding is directly con-nected to the electric circuit. In the normal operation of theSFCL, screening currents are induced in the superconductorcylinder, and therefore, no flux enters the core. In this case,the SFCL acts as a very low inductance. While during thefault condition, the ampere-turns balance fails to be satisfiedbetween the superconductor cylinder and the copper winding.Therefore, the magnetic flux passes through the iron core.Consequently, the impedance seen from the primary windingrapidly increases, and the fault current of the circuit is confined[2], [12]. A cross-sectional view of the shield-type SFCL isshown in Fig. 1.

Manuscript received June 30, 2013; revised October 28, 2013 andJanuary 19, 2014; accepted February 12, 2014. Date of publication March 12,2014; date of current version April 21, 2014. This paper was recommended byAssociate Editor M. Noe.

The author is with the Department of Electrical and Computer Engineering,Shahid Beheshti University, Tehran 19839 63113, Iran (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASC.2014.2311408

Fig. 1. Cross-sectional view of the shield-type SFCL [13].

In this paper, a design for the tunable shield-type SFCL hasbeen proposed via adding a second copper winding, as a controlwinding, around the closed iron core. The tunability means thecurrent at which the limitation starts and the value to which thecurrent is limited may be varied via changing some controllableparameters in the SFCL structure. The control winding isconnected in series with a resistance and an ac voltage source,which one or both of them may be variable. In this paper, ithas been shown that varying the series control resistance andthe amplitude and phase of the voltage source considerablychange the limitation characteristics of the SFCL. The throughcurrent of the SFCL has been calculated utilizing the Bean’scritical state model for the supercurrent and magnetic flux den-sity distribution inside the superconductor tube. Based on thecalculated through current, the influence of varying the controlparameters on the limited current of the SFCL is investigated. Aprototype has been fabricated, and the tunable operation of theproposed design has been experimentally tested. The results ofthe experimental measurements have been compared with thetheoretical results and have shown good consistency.

II. PROPOSED STRUCTURE

The proposed inductive shield-type SFCL consists of aprimary copper winding and a bulk superconductor cylinderaround a closed iron core. A second winding is utilized as acontrol winding, which is connected to an ac voltage sourcevia a series resistance, as shown in Fig. 2. Both the voltagesource and the resistance may be variable. Thus, three controlparameters are available, i.e., the control resistance, the controlvoltage amplitude, and the control voltage phase. Two operationregimes may be defined for the SFCL.

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5601907 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 24, NO. 4, AUGUST 2014

Fig. 2. Schematic of the proposed tunable inductive shield-type SFCL.

A. Normal Operating Condition

In this phase, no flux enters the core. Thus, from the well-known Ampere’s law in (1) for a closed path inside the core[14], (2) is concluded ∮

c

−→H.

−→d� =

∑i (1)

N1i1 +N2i2 = J(ro − r)h (2)

where N1, i1, N2, and i2 are the number of turns and thethrough current in the primary and control windings, respec-tively. Additionally, ro and h are the exterior radius and theheight of the superconductor ring, respectively. J is the super-current density inside the superconductor ring, and r is the ra-dius that the magnetic flux penetrates inside the superconductorring.

At the normal operating condition of the SFCL, the throughcurrent, i.e., i1, is dictated by the system and has a sinusoidalform of I1m cosωt. Because there is no flux in the core, itmay be concluded that the induced voltage, by the transformereffect, in the control winding would be zero. Thus, supposingthe voltage of the control source as Vm cos(ωt+ α), where α isthe phase difference between the control voltage and the SFCLthrough current, the current in the control winding would be as

i2 =Vm

Rcos(ωt+ α) (3)

where R is the control resistance. The ohmic resistance andleakage inductance of the control winding have been neglectedin (3).

According to the Bean’s critical state model [15], J in (2) iseither Jc or −Jc, where Jc is the critical current density of thesuperconductor ring. In addition, the current limitation startswhen the screening currents cover all over the cross section ofthe superconductor ring [16]. Therefore, according to (2), theminimum requirement for the SFCL to remain in the normaloperating phase would be as

N2Vm cosα

R≤ Jc(ro − ri)h−N1I1m (4)

where ri is the interior radius of the superconductor ring.It is concluded from (4) that varying the control resistance

and the amplitude and phase of the control voltage, the transi-tion current from the normal operating phase to the limitationphase, i.e., Istart, may change. Istart, is the current that thelimitation starts. However, the most important characteristic for

the SFCL application is the current to which the SFCL throughcurrent is limited, i.e., Ilimit, in the fault condition [16].

B. Fault Condition

The worst case of the fault has been considered, that is, theSFCL terminal fault. At the fault condition, the flux entersthe core, and the screening currents cover all over the crosssection of the superconductor ring and the Ampere’s law in (1)results in

N1i1 +N2i2 − J(ro − ri)h =B

μ�c (5)

where B is the magnetic flux density inside the core, and �cand μ are the average length and the permeability of the core,respectively.

According to Faraday’s law [17], (6) specifies the relationbetween the maximum input voltage to the SFCL terminals, i.e.,Vimax, and the maximum magnetic flux density inside the core,i.e., Bmax. The ohmic resistance and leakage reactance of theprimary winding have been neglected. Thus

Vi = Vimax cosωt = (ωN1BmaxA) cosωt (6)

where A is the cross section of the core, which is assumed to beuniform.

The magnetic flux density inside the core would be as

B = Bmax sinωt =Vimax

ωN1Asinωt. (7)

Similarly, the induced voltage in the control winding, i.e., V2,may be calculated as

V2 =V2max cosωt=(ωN2BmaxA) cosωt

=

(N2

N1Vimax

)cosωt. (8)

The current in the control winding would be as

i2 =(V2max cosωt− Vm cos(ωt+ ϕ))

R(9)

where ϕ is the phase difference between the SFCL input voltageand the control voltage source. After trigonometric simplifica-tions, (9) would turn to

i2 =

(V 22max + V 2

m − 2V2maxVm cosϕ) 1

2

Rsin(ωt+ β),

β = tg−1

(V2max − Vm cosϕ

Vm sinϕ

). (10)

The induced energy in a superconductor bulk, with respectto superconducting tapes and wires, distributes over a largevolume; and therefore, the damp of any excess energy is rel-atively fast. As a result, the quench does not occur. In addition,the superconductor ring is not directly exposed to the externalmagnetic fields (the magnetic flux passes the core). In addition,there is strong flux pinning in the superconductor bulk [18] dueto the special fabrication process [19]. Therefore, the magnitudeof the screening current density may be assumed constant at Jc.Furthermore, when the direction of the current in the primarywinding is changed, the direction of the screening currents in

HEKMATI: PROPOSED DESIGN FOR A TUNABLE INDUCTIVE SHIELD-TYPE SFCL 5601907

TABLE ISTRUCTURAL CHARACTERISTICS OF THE PROPOSED SFCL DESIGN

the superconductor bulk should accordingly change. That isbecause the generated flux is always in phase with the throughcurrent, and the generated fluxes by the primary winding andthe superconductor bulk should oppose each other. Thus, (5)would yield

N1i1 = −N2i2 +B

μ�+ (Jc(ro − ri)h) sgn(i1) (11)

where sgn is the well-known sign function, which is +1 forpositive arguments and −1 for negative ones.

As i1 is symmetrical, assuming i1 > 0, the SFCL throughcurrent would be calculated as

i1 =1

N1

(N2

2 i22max +

B2max�

2

μ2− 2N2i2maxBmax� cosβ

μ

) 12

× cos(ωt+ γ) +Jc(ro − ri)h

N1,

γ = tg−1

(Bmax�

μ −N2i2max cosβ

N2i2max sinβ

). (12)

For i1 < 0, the same result would be obtained with a negativesign.

From (12), the maximum SFCL through current may bededuced as

i1max=

(N2

2i22max+

B2max�

2

μ2− 2N2i2maxBmax� cosβ

μ

) 12

/N1

+Jc(ro − ri)h

N1. (13)

In (13), i1max is the amplitude to which the fault currentwould be limited and is the main characteristic that an SFCLis designed based on it.

III. RESULTS

The structural characteristics of the proposed SFCL designhave been assumed to be as Table I throughout this paper.

The variation of i1max with the control resistance and theamplitude and phase of the control voltage source, accordingto (7), (8), (10), and (13), are plotted in Figs. 3–5. The systemvoltage and frequency are assumed to be Vimax = 30 V peak,and f = 60 Hz, respectively.

Fig. 3. Variation of the SFCL through current, i.e., i1, versus the controlvoltage amplitude, i.e., Vm. (a) For different values of the control resistance,i.e., R, ϕ = 0. (b) For different values of the control voltage phase, i.e., ϕ,R = 3 Ω.


Fig. 4. Variation of the SFCL through current, i.e., i1, versus the controlvoltage phase, i.e., ϕ. (a) For different values of the control resistance, i.e.,R, Vm = 8 V. (b) For different values of the control voltage amplitude, i.e.,Vm, R = 3 Ω.

As may be shown from Figs. 3–5, it is possible to achieve awide range of SFCL limitation currents via varying the controlparameters. Various combinations of the control parameters arepossible for a certain limitation current, and practically, moreavailable values may be chosen. Furthermore, everywhere inthe figures, which a value is assigned to the limitation currentfor a positive control voltage phase, the same is obtained forthe negative of that phase, thus not included in the figures. Thevariation range of the control voltage phase is −π < ϕ ≤ π.

The turns ratio of the control winding relative to the primarywinding also influences the limitation characteristics of theSFCL. Assuming n = N2/N1, the variation of the limitedcurrent versus the control parameters for different values of nwould be as Figs. 6–8.

Fig. 5. Variation of the SFCL through current, i.e., i1, versus the controlresistance, i.e., R. (a) For different values of the control voltage amplitude,i.e., Vm, ϕ = 0. (b) For different control voltage phases, i.e., ϕ, Vm = 7 V.

As shown from Figs. 6–8, for a specific turns ratio, theamplitude or the variations of the limitation current versus aspecific control parameter may be higher than other controlparameters. This means certainly, design optimization wouldbe required to yield the maximum tunability for the SFCLlimitation current.

A. Fabricated Prototype

A prototype has been fabricated (see Fig. 9) with the mainstructural characteristics as in Table I. The bulk superconduct-ing rings have been fabricated out of YBCO powder throughthe casting method presented in [19].


Fig. 6. Variation of the SFCL through current, i.e., i1, versus the controlvoltage amplitude, i.e., Vm, for different turns ratios of the control windingrelative to the primary winding, i.e., n, R = 3 Ω, ϕ = 0.

Fig. 7. Variation of the SFCL through current, i.e., i1, versus the controlvoltage phase, i.e., ϕ, for different turns ratios of the control winding relativeto the primary winding, i.e., n, R = 3 Ω, Vm = 8 V.

The parameters of the control circuit were varied, and themeasured limited through currents were compared with thetheoretical results. Three experiments were performed. Variablevoltage amplitude has been obtained via a 220-V 10-kW single

Fig. 8. Variation of the SFCL through current, i.e., i1, versus the controlresistance, i.e., R, for different turns ratios of the control winding relative tothe primary winding, i.e., n, ϕ = 0, Vm = 8 V.

Fig. 9. Fabricated prototype.

phase autotransformer. For measuring the phase differencebetween the input voltage to the SFCL and the control voltagesource, i.e., an M-type phasor measurement unit for measure-ment applications with high precision, has been utilized.

1) Experiment 1: The control resistance and the controlvoltage phase are set constant at R = 3 Ω, ϕ = 0. The controlvoltage amplitude is varied, and the SFCL limited currentamplitude is measured at each step. The results compared withthe theoretically obtained curve are shown in Fig. 10.

2) Experiment 2: The control resistance and the controlvoltage amplitude are set constant at R = 3 Ω, Vm = 8 V. Thecontrol voltage phase is varied, and the SFCL limited currentamplitude is measured at each step. The results compared withthe theoretically obtained curve are shown in Fig. 11.

3) Experiment 3: The control voltage amplitude and phaseare set constant to ϕ = 0, Vm = 5 V. The control resistance isvaried, and the SFCL limited current amplitude is measured ateach step. The results compared with the theoretically obtainedcurve are shown in Fig. 12.


Fig. 10. Measured SFCL limited current amplitude versus the control voltageamplitude compared with the theoretical result, i.e., R = 3 Ω, ϕ = 0.

Fig. 11. Measured SFCL limited current amplitude versus the control voltagephase compared with the theoretical result, i.e., R = 3 Ω, Vm = 8 V.

From the measurement results, it is concluded that the pro-posed design shows satisfactory results for the tunable SFCLexperimentally. Furthermore, the measurement results are ingood consistency with the theoretical curves, being a verifica-tion for the performed modeling. The small deviations from thepredicted values may be due to the simplifications assumed inthe modeling process as neglecting the intrinsic impedance ofthe voltage sources and the ohmic resistance and the leakagereactance of the windings. These parameters should be takeninto account for more precise modeling, particularly in the caseof higher rating SFCLs.

The proposed device is similar to a classic transformer fromthe winding and core point of view. Therefore, at higher ratings,every consideration for such a transformer should be appliedin the SFCL design with regard to the fault condition ratings.

Fig. 12. Measured SFCL limited current amplitude versus the control resis-tance compared with the theoretical result, i.e., ϕ = 0, Vm = 5 V.

These considerations may include special winding arrange-ments for carrying higher magnitude currents (e.g., parallelwires) and the insulation strength requirements. It should benoted that the fault currents with the SFCL in the circuit incred-ibly decrease relative to the fault currents without the SFCLin the circuit. The limitation factor may be around 20 times[16]. The SFCL windings design for the current-carrying ca-pability should be based on the limited current. Furthermore,the insulation system of the windings should withstand themaximum possible voltages at the worst case faults for specifictimes (several cycles) until the breakers operate.

In this paper, the modeling of the SFCL operation is per-formed, assuming the core operates in the linear region. It isquite a matter of design to have a core not saturated even inthe worst fault cases (terminal fault). Furthermore, this directlydepends on the saturation level of the core material, quite likea classic transformer, which is always designed not to work inthe saturation region.

The superconductor bulks are present with different di-mensions. The special fabrication process utilized for thesuperconductor bulks production in this paper is extendablefor higher dimensions, as stated in [19]. These superconductorbulks do not quench as the induced energy distributes over alarge volume, and therefore, the damp of any excess energyis relatively fast. In other words, for higher rating SFCLs,the energy is higher; but, at the same time, the volume ofthe superconductor bulk is high, which moderates the energydensity in the bulk.

IV. SUMMARY AND CONCLUSION

A tunable shield-type SFCL design has been proposed withthe control parameters as a resistance and the amplitude andphase of an ac voltage source. The SFCL through current wascalculated, and the influence of the control parameters was stud-ied and compared with the experimental results obtained from


the fabricated prototype. The experimental results show thesatisfactory tunable operation of the SFCL with the proposeddesign.

Future works may include the optimized design for maxi-mum tunability of this type of SFCL and study on the higherrating tunable SFCL design.

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Arsalan Hekmati was born in Iran in 1982. He received the B.S., M.S., andPh.D. degrees from Sharif University of Technology, Tehran, Iran, in 2005,2007, and 2011, respectively, all in electrical power engineering.

Since 2007, he has been a Member of the Superconductive ElectronicsResearch Laboratory, Sharif University of Technology. From 2011 to 2012,he was a Postdoctoral Research Fellow with Sharif University of Technol-ogy, where he conducted projects in applied superconductivity, such as thefabrication and characterization of superconductor YBCO cylinders and thefabrication and test of inductive superconducting fault current limiters forthe first time in Iran. From 2006 to 2011, he was the Head of the ResearchDevelopment Department, Iran Transformer Research Institute, Tehran; and aProject Leader with Iran Transfo Company, Tehran; with Ofogh ConsultingEngineers Company, Tehran; and with the Great Tehran Electrical DistributionCompany. Since 2012, he has been with the Department of Electrical and Com-puter Engineering, Shahid Beheshti University, Tehran. His research interestsinclude superconducting power devices, insulation and high-voltage systems,and electric machinery, particularly transformers.

proposed design for a tunable inductive shield-type sfcl

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