Flux-Based Modeling of Inductive Shield-Type High ... - SERL

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Flux-Based Modeling of Inductive Shield-Type High-Temperature Superconducting Fault Current Limiter for Power Networks Arsalan Hekmati, Mehdi Vakilian, and Mehdi Fardmanesh, Senior Member, IEEE

Abstract—Distributed power generation and the ever-growing load demand have caused fault current levels to exceed the nominal rating of the power system devices, and fault current limiters are more needed. Superconducting fault current limiter (SFCL) forms an important category of current limiters. In this paper, a novel flux-based model for the inductive shield-type hightemperature SFCL is developed based on the Bean model. This model is employed to simulate the SFCL performance in a sample circuit. Utilizing the model, the signal characterization of the limited current is determined. A prototype laboratory scale SFCL has been fabricated with superconducting rings. Yttrium barium copper oxide powders have been used for superconducting ring production. The critical current density of fabricated rings has been measured with an innovative method based on application of a magnet device. The fabricated SFCL has been tested in a circuit by applying different types of faults. The related experimental results are recorded and compared with the model results. The results obtained based on the modeling shows full compatibility with the experimental results. Index Terms—High temperature, inductive shield type, modeling, superconducting fault current limiter.

I. I NTRODUCTION

S

UPERCONDUCTING fault current limiters (SFCLs) can be used to limit short-circuit current levels in electrical transmission and distribution networks. It is one of the most promising fault-current-limiting devices to be used in transmission and distribution networks due to its low nominal losses, reliable operation, very short reaction times to fault currents and an automatic response feature without the requirement of external trigger mechanism [1], [2]. An inductive current limiter works like a transformer that has a shorted superconducting secondary winding. The impedance of this current limiter under normal operating conditions is nearly zero since the zero impedance of the secondary suManuscript received November 15, 2010; revised January 16, 2011; accepted March 15, 2011. Date of publication April 25, 2011; date of current version July 29, 2011. This paper was recommended by Associate Editor P. J. Masson. A. Hekmati is with the Superconductor Electronics Research Laboratory, Department of Electrical Engineering, Sharif University of Technology, Tehran 11365-11155, Iran. M. Vakilian is with the Department of Electrical Engineering, Sharif University of Technology, Tehran 11365-11155, Iran. M. Fardmanesh was with the Department of Electrical Engineering, Bilkent University, Ankara 06800, Turkey. He is now with the School of Electrical Engineering, Sharif University of Technology, Tehran 11365-9363, Iran (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2011.2138137

Fig. 1.

Cross-cut view of the inductive SFCL [14].

perconducting winding is reflected on the primary circuit. In the event of a fault, the secondary superconducting winding fails to be superconducting. Hence, the secondary resistance will increase, which will subsequently limit the fault current [3]–[6]. The secondary winding may be a high-temperature superconducting bulk cylinder; the function of which under normal condition is to shield the flux generated by the primary winding from entering the iron core of the current limiter, as shown in Fig. 1. The primary winding is usually made of copper directly connected to an electric circuit. In the normal operation of the SFCL, according to Meissner effect, no flux enters the core, and the SFCL acts as a very low inductance. While during fault condition, the ampere-turns balance fails to be satisfied in this transformer. Therefore, flux of the primary winding passes through the iron core and links the secondary. The inductance and impedance seen from the primary winding rapidly increases, and consequently, the fault current of the circuit is confined [2], [7]. Various designs have been proposed for this type of SFCL [1], [7]–[13]. The cross-cut view of an inductive shield-type SFCL using superconducting tubes, considered in this paper, is shown in Fig. 1. In this paper, an innovative modeling of an inductive shieldtype SFCL has been introduced, which fully simulates its operation in different states. No general analytical model describing all of the operation phases of the inductive shield-type SFCL has been developed using the flux-based model obtained from the Bean model, from which the relations governing the flux linkages and inductances in all operation modes of this type of SFCL are obtained. This model has been used in a sample circuit to simulate the SFCL operation. A prototype inductive shield-type SFCL has been also designed and fabricated using

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Fig. 3. Flux density distribution in the normal operating phase of the inductive SFCL.

Fig. 2.

Two-dimensional schematic of the inductive SFCL.

yttrium barium copper oxide (YBCO) rings to test the model. The superconductive rings have been fabricated from YBCO powders using melt-texture process. The prototype SFCL has been tested in a 30-V circuit of 2-A nominal current. Two kinds of faults, i.e., the supply terminal fault and the load terminal fault, are introduced to the circuit, and the related fault currents are measured. These experimental results are employed to verify the modeling results. II. SFCL O PERATION M ODELING Based on the structure shown for this type of SFCL in Fig. 1, realizing its axial symmetry, a 2-D model of the inductive shield-type SFCL is developed, as shown in Fig. 2. As for a principle investigation, an open-core type is considered in this paper. In an inductive shield-type SFCL, the open core’s length does not have considerable impact on limitation characteristics [14], although this type of SFCL with larger cross section of open magnetic core has greater limiting impedance, i.e., the core cross section highly influences the inductive limiter’s limiting current [15]. The main design parameters of this type of SFCL, as shown in Fig. 2, are as follows: 1 length of the copper winding; 2 length of the bulk superconducting tube; N number of turns of the copper winding; r2i interior radius of the superconducting bulk; r2o exterior radius of the superconducting bulk; r1i interior radius of the copper winding; r1o exterior radius of the copper winding; rc radius of the iron core; Jc critical current density of the YBCO bulk; μr relative permeability of the iron core. To further clarify the operation principles of this type of the SFCL, three main attributes of the SFCL are calculated and investigated in the following. The attributes are as follows: L inductance of the SFCL; Istart current magnitude at which the inductance starts to increase;

Ilimit current magnitude to which the current is limited. Two assumptions are made in this modeling. 1) No pinning force is present in the superconducting bulk. 2) The radius of the core has been set equal to the interior radius of the superconducting bulk. Meanwhile, three operation phases can be distinguished in the SFCL operation, which are simulated in this modeling. A. Normal Operating Phase In this state, no flux enters the core, and hence, the core is invisible, and no limitation is enforced. The SFCL represents a very small inductance in this state. The flux density in the air gap space of r2o < r < r1i is approximately given by [16] B0 = μ0

N I 1

(1)

where I is the through current of the copper winding. To simulate the flux density inside the bulk, the Bean model is employed, which states the following [17]: dB = μ0 Jc dr

(2)

where B is the flux density inside the bulk, r is the radius from the center of the bulk, and Jc is the critical current density of the bulk. The overall flux density distribution over the cross section of the SFCL would be as shown in Fig. 3. Where r is the radius at which the flux density goes to zero inside the bulk. According to (2), from the Bean model, the current density in the bulk, would be the constant value of Jc in r < r < r2o and zero elsewhere. B. Fault-Current-Limiting Inception At this state, the flux density is at the threshold of entering the core, while no abrupt impedance rise has occurred. The flux density distribution would be as shown in Fig. 4. From the Bean model, the current density in the whole bulk, i.e., r2i < r < r2o , would be the constant value of Jc . Therefore, according to (1) and (2), the minimum current Istart required to have the flux penetrate into the core and initiate the current limiting process can be obtained from μ0 N Istart = μ0 Jc (r2o − r2i ). 1

(3)

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Fig. 4. Flux density distribution in the current-limiting phase initiation of the inductive SFCL operation.

This yields Istart

Jc L1 (r2o − r2i ) . = N

(4)

Through it, an important principle can be deduced as follows: The current that controls the SFCL operation is directly proportional to the critical current density Jc of the YBCO bulk and the thickness of the superconducting bulk (r2o − r2i ), whereas it is inversely proportional to the number of turns of copper winding per unit length, N/1 . This current is not dependent to the superconducting bulk length 2 and to the radius of the copper winding.

Fig. 5. Flux density distribution in the current-limiting phase of the inductive SFCL operation.

result would be as shown in the following:   S  Φ = N B.d 2π r1i  Φ =N 0 r2o

μ0 N I 1

2π r2o +N

C. Current-Limiting Phase

0

When a fault occurs, the current passing SFCL and, consequently, its primary winding flux density increases, causing the flux lines to penetrate the core which accordingly results in a considerable impedance increase. At the interface of the core and the superconducting bulk, according to the Ampere’s law, the tangential flux intensities should satisfy the following [18]: H1t − H2t = Jsn

 rdrdϕ

μ0 N I μ0 Jc (r − r2o ) + 1

 rdrdϕ.

(8)

Therefore, the flux linkage in the operating phase can be presented by   3  2 πμ0 N 2 r1i N πμ0 Jc NI 3 Φoperating = r2o − r2o − I− . 1 3 1 Jc (9) Then, the inductance in the operating phase would be as

(5)

where Jsn is the surface current density at the interface and is zero because the current in the bulk has volume density. Thus, the flux density inside the core, using (2) and (5), would be as Bc = μr (B0 − μ0 Jc (r2o − r2i )) .

r

(7)

(6)

Following the aforementioned, the flux density distribution would be as shown in Fig. 5. As shown in Fig. 5, the flux density penetrates into the core by a factor of μr , and consequently, the inductance substantially increases. According to the Bean model, the current density in the bulk would be the constant value of Jc over the whole bulk, with the same value as in the fault-current-limiting inception phase.

Loperating = =

d Φoperating dI 2 πμ0 N 2 r1i N 2 πμ0 − 1 1

r2o −

NI 1 Jc

2 .

(10)

The flux linkage and the inductance in the current limiting phase would be consequently similarly calculated based in Fig. 5, as given in 2π r1i  Φ =N 0 r2o

μ0 N I 1

 rdrdϕ

2π r2o μ0 Jc (r − r2o ) +

+N 0 r2i

III. SFCL I NDUCTANCE C ALCULATION In the normal operating phase of SFCL operation, the flux linkage would be calculated through (7). Based in Fig. 3, the



2π r2i +N 0

0

μ0 N I 1

 μN I − μJc d rdrdϕ 1

 rdrdϕ

(11)

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TABLE I SUPERCONDUCTING RING PARAMETERS

Φlimiting =

2 2 + π(μ − μ0 )N 2 r2i πμ0 N 2 r1i I + N πJc 1     −1 2 3 2 3 μ0 r2o −(μ−μ0 )r2o ri + μ− μ0 r2i × 3 3

(12) Llimiting =

2 2 + π(μ − μ0 )N 2 r2i πμ0 N 2 r1i . 1

Fig. 6. Trapped flux density versus the applied field for the fabricated superconducting ring.

(13)

As it is apparent in (10) and (13), the inductances in the normal operating phase and the current limiting phase change with the through current of the SFCL. In other words, the SFCL acts as a nonlinear current-dependent inductance, i.e., L = f (I). Under circumstances where assumptions 1 and 2 on the SFCL operation modeling cannot be employed, if the radius of the core is less than the interior radius of the superconducting bulk, then there will be a change in Fig. 5 by adding a plateau at r2i , changing the resulting derived equations. For the case of having strong pinning, there will be the well-known considerable hysteresis in the field variation, which should be taken into account in flux density curves. IV. Jc M EASUREMENT OF THE S UPERCONDUCTING R ING A superconducting ring, according to the dimensions presented in Table I, is made using YBCO powder in the laboratory for use in the fabricated prototype SFCL structure. In order to simulate the SFCL operation, first of all, the critical current density Jc of the superconducting ring should be calculated. To calculate Jc , a novel method has been used. The superconducting bulk is immersed in liquid nitrogen in a styrofoam chamber. The chamber should be placed in a uniform magnetic field. For the production of a uniform magnetic field, a tunable magnet device has been used with alloyed-type core plates with saturation field of about 1.8 T, the core cross section of 14 cm × 14 cm, and an adjustable gap of 0–8 cm. Two copper coils wound on both sides of the gap are charged by a tunable direct-current power supply of 550 V, with 30 A allowing about up to 2-T field in small gaps and for short time duration. The nominal field of the magnet is 1.7 T. The magnetic flux density is increased from a low value (some millitesla) in several steps. At each step, the chamber is taken off the magnetic field, and the magnetic flux density trapped at the ring center is measured using a digital Hall sensor magnetometer. The measurement result is presented in Fig. 6. As it is apparent in Fig. 6, by increasing the imposed magnetic field, the trapped flux density distribution in the superconducting ring remains approximately constant in 20 mT. This phenomenon is explained using the Bean model.

Fig. 7. Flux density distribution in the superconducting ring for the three applied magnetic fields. ri is the internal radius of the ring, ro is the external radius of the ring, and Jc is the critical current density.

According to the Bean model, the flux density distributions in the bulk ring, for the three applied magnetic fields, are shown in Fig. 7. As it is apparent in Fig. 7, increasing the applied magnetic field beyond level “2,” according to the Bean model, the current density remains constant over the whole bulk ring width; therefore, the trapped flux density in the ring tends to a constant value. From Fig. 7 and (2), it may be deduced that at the center of a superconducting bulk of internal radius r2i and the external radius r2o , while carrying a current density of Jc , the magnetic flux density can be determined using B = μ0 Jc (r2o − r2i ).

(14)

With r2o = 17 mm and r2i = 15 mm, for B = 20 mT, and Jc is found to be 800 A/cm2 . V. FABRICATED P ROTOTYPE SFCL A prototype has been made employing the design parameters of the SFCL, as presented in Tables I and II. A view of the fabricated SFCL is shown in Fig. 8. The copper winding has been split into two parts, and the superconducting ring is set between these two coil parts. This structure makes the cooling of the superconducting ring more efficient. With the design parameters, as given in Tables I and II, the flux linkage and the inductance of the SFCL are obtained as a function of the through current using (9), (12) and (10), (13) and are shown in Fig. 9. Having the critical current for bulk YBCO material as Jc = 0.80 × 107 A/m2 , Istart would be approximately 2.67 A from (4).

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TABLE II COPPER WINDING AND CORE PARAMETERS

Fig. 10.

Test system and the fault cases.

Fig. 11.

Simulation result for the fault in the SFCL terminals.

Fig. 8. View of the fabricated SFCL.

Fig. 9. Flux linkage and the inductance of the SFCL as a function of the through current.

It is apparent in Fig. 9 that before Istart , the value of inductance is too low. However, as the current exceeds Istart , a sharp impedance increase occurs. VI. T EST OF THE P ROTOTYPE SFCL The developed prototype is used in a test system, and the related results are compared with those obtained by the model. For the cooling of the device, 77-K liquid nitrogen has been used by immersing the device in it. A typical single-phase system of 30-V peak, with the internal source inductance of 2 mH and the line resistance and inductance of 0.2 Ω and 2 mH, respectively, is employed for the test system, as shown in Fig. 10. The impedance of the fabricated prototype SFCL is much larger than the impedance of the source used in the test circuit in the activated mode of the SFCL. In realistic cases, the impedance of this type of SFCL with respect to that of its network should be definitely taken

into consideration. As an advantage of this typical SFCL, its impedance is well adjustable based on its structure as a design matter with consideration of the network impedance. Two fault cases are investigated. In the first case, a shortcircuit fault at the SFCL terminal is studied, which is named “Fault case 1,” whereas, in the second test, a fault at the load terminal is studied, which is named “Fault case 2.” A. Results and Analysis The differential equations governing cases 1 and 2 are given in dI dΦ + Ls = Vm cos(ωt + ϕ) dt dt dΦ dI + (Ls + L) + RI = Vm cos(ωt + ϕ). dt dt

(15) (16)

Equations (15) and (16) are solved using numerical methods. The results of fault current simulation together with the experimental test results are shown in Fig. 11 for case 1, whereas the related results of case 2 are shown in Fig. 12, where they are also compared with the fault current, without using the SFCL. The measured test results show full compatibility with the results of the modeling, as shown in Figs. 11 and 12. Since the superconductor is deeply immersed in liquid nitrogen bath in the considered design, the heating and the resulting decrease in Jc is considered negligible, and the fault current

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The constant time-independent term in (17) is equal to Istart after some simplifications that would result in Ilimit = Istart +

Fig. 12. Simulation result for the fault in the load terminals.

is almost a constant value during the fault. Due to this, while a conducting shunt would be helpful to prevent hotspots, it is not considered in this paper in addition to the fact that the prototype design does not include that. In addition, in the studied prototype design, no additional induced current is expected to be considered during the fault since there is no shunt path with the superconductor. Even in large-scale SFCLs of this type, the magnetic flux density outside the core is less than the flux density inside the core by a factor of the relative permeability of the core material. Hence, changes in the critical current density of the superconductor bulk due to the magnetic field would be negligible. In addition, in the activated mode, the superconductor shield is broken, and the inductance of the SFCL would increase, which forms the major part of the impedance, limiting the fault current. Due to these reasons, the possible enormous active power dissipation on the SFCL can be avoided. Therefore, from the insulation point of view for high voltages, one should take the major part of the insulation consideration in the primary of the SFCL as for conventional transformers. Moreover, since the model is independent of the design dimensions and insulating issues, these considerations do not hinder the use of the model in large-scale applications. B. Calculation of Ilimit The worst case of the SFCL operation is when a fault of zero resistance occurs exactly next to the SFCL, i.e., case 1. In this case, i.e., the terminal fault case, assuming nearly zero internal source inductance, (15) would be solved by a closedform approach. Thus, the maximum SFCL current would be found from Ilimit = +

Vm 1 2 +πω(μ−μ )N 2 r 2 πωμ0 N 2 r1i 0 2i

N πJc 1

1

Vm 1 2 . πωμ0 N 2 (μr − 1)r2i

(18)

Employing the design parameters of this paper, Ilimit is calculated to be 2.82 A, which is, to a good approximation, equal to the measured value shown in Figs. 11 and 12, being 3 A. The important result obtained is that whatever the fault is, and of what amplitude, the SFCL would limit the fault current to a determined value of Ilimit , as is apparent in Figs. 11 and 12. Therefore, based on the aforementioned analysis, it can be assured that by using an SFCL, the system current would not exceed Ilimit . The important factors that affect the value of Ilimit are the following parameters: 1) Istart ; 2) system voltage; 3) copper winding length; 4) turns number of the copper winding; 5) permeability of the core; 6) internal radius of the superconducting ring. Thus, the SFCL has the advantage of reliably limiting the fault current to a predetermined value. The magnitude of Ilimit sharply decreases with the internal radius of the bulk superconductor and the number of turns in the copper winding, and it increases when the ring thickness and the length of the copper winding increase. VII. S UMMARY AND C ONCLUSION In this paper, a specific type of SFCLs has been introduced and fabricated, and its performance has been modeled and discussed by a novel method. Utilizing this model, the SFCL operation has been simulated under fault conditions in a very simple system, and its results have been compared with the test results of the fabricated prototype. The model shows full compatibility with the performance of the developed sample. It was deduced that for fault currents of different types and magnitudes, the current is limited to a predetermined value of Ilimit . In other words, it was shown that according to modeling and the experiment, this type of SFCL passes a predetermined current during short-circuit fault conditions in a power system, regardless of the type of fault. Ilimit is calculated using the introduced model. The factors that affect the value of Ilimit have been also discussed. Using the analytical results of the SFCL operation from the developed model, one can proceed toward optimization of this type of SFCL. Furthermore, its performance in a power distribution system can be thoroughly evaluated. R EFERENCES

sin(ωt+ϕ) 

2 3 2 3 μ0 r2o +(μ−μ0 )r2o r2i − μ− 3 μ0 2 +π(μ−μ )N 2 r 2 πμ0 N 2 r1i 0 2i



3 r2i

. (17)

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Arsalan Hekmati was born in Sarab, Iran, in 1982. He received the B.Sc. degree in electrical engineering and the M.Sc. degree in electric power engineering in 2005 and 2007, respectively, from Sharif University of Technology, Tehran, Iran, where he is currently working toward the Ph.D. degree in electric power engineering. He is a member of the Superconductive Electronics Research Laboratory, Department of Electrical Engineering, Sharif University of Technology. His research interests include design and modeling of high-voltage equipment; optimum insulation design; and design, fabrication, and modeling of hightemperature superconducting devices.

Mehdi Vakilian received the B.Sc. degree in electrical engineering and the M.Sc. degree in electric power engineering from Sharif University of Technology, Tehran, Iran, in 1978 and 1986, respectively, and the Ph.D. degree in electric power engineering from Rensselaer Polytechnic Institute, Troy, NY, in 1993. From 1981 to 1983, he was with Iran Generation and Transmission Company, and then with the Iranian Ministry of Energy from 1984 to 1985. Since 1986, he has been with the Faculty of the Department of Electrical Engineering, Sharif University of Technology. From 2001 to 2003, he was an Associate Professor and also the Chairman of the department. From 2003 to 2004, and from August to December 2007, he was on leave to study at the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia. He is currently the Director of a committee in charge of restructuring the electrical engineering undergraduate education at Sharif University of Technology, where he is also the Director of the Electric Power Group, Department of Electrical Engineering. Since 2007, he has been a Professor in the department. His research interests include transient modeling of power system equipment, optimum design of high-voltage equipment insulation, insulation monitoring, and power system transients.

Mehdi Fardmanesh (SM’02) was born in Tehran, Iran, in 1961. He received the B.S. degree in electrical engineering from Tehran Polytechnic University, Tehran, in 1987, and the M.S. and Ph.D. degrees in electrical engineering from Drexel University, Philadelphia, PA, in 1991, and 1993, respectively. In 1989, he joined Drexel University, and until 1993, he conducted research in development of the thin- and thick-film high-temperature (High-Tc) superconducting materials, devices, and development of ultralow noise cryogenic characterization systems, where he was awarded a research fellowship by the Ben Franklin Superconductivity Center in 1989. From 1994 to 1996, he was the Principal Manager for Research and Development and the Director of a private sector research electrophysics laboratory while also teaching in the Departments of Electrical Engineering and Physics, Sharif University of Technology, Tehran. In 1996, he joined the Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey, where he teaches in the areas of solid state and electronics while also supervising his established Superconductivity Research Laboratory. In 1998 and 1999, he was invited to the Institut für Schicht- und Ionentechnik, Forschungszentrum Juelich, Juelich, Germany, where he pursued the development of low-noise High-Tc radio-frequency superconducting quantum interference device (SQUID)-based magnetic sensors. In 2000, he established an international collaboration between Bilkent University and the Juelich Research Center in the field of superconductivity, and from 2000 to 2004, he was the Director of the joint project for the development of high-resolution High-Tc SQUID-based magnetic imaging system.” In 2000, he also reestablished his activities in the Department of Electrical Engineering, Sharif University, where he is currently the Head of the said department. He established the “Superconductor Electronics Research Laboratory,” at Sharif University of Technology in 2003, which he has directed since then. His research interests have mainly focused on the design, fabrication, and modeling of High-Tc superconducting devices and circuits such as bolometers, microwave filters and resonators, Josephson junctions, and SQUID-based systems in the areas of which he is the holder of several international patents.