Performance Investigation and Optimization of a

energies Article

Performance Investigation and Optimization of a Novel Hybrid Saturated-Core Fault-Current Limiter Considering the Leakage Effect Liangliang Wei 1,2 , Baichao Chen 1 , Yushun Liu 3 and Tianan Zhu 5 1 2 3 4 5

*

ID

, Cuihua Tian 1 , Jiaxin Yuan 1, *

ID

, Yuxin Bu 4

School of Electrical Engineering, Wuhan University, No.299, Bayi Street, Wuchang District, Wuhan 430072, China; [email protected] (L.W.); [email protected] (B.C.); [email protected] (C.T.) Department of Electrical Engineering, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan Anhui Grid Co., Anhui Electric Power Research Institute, No.73, Jinzhai Road, Hefei 230022, China; [email protected] State Grid Taiyuan Power Supply Company, No.89, Binzhou North Road, Taiyuan 030012, China; [email protected] State Grid Yichang Power Supply Company, No.42, Chengdong road, Yichang 443000, China; [email protected] Correspondence: [email protected]; Tel.: +86-186-2775-5068

Received: 20 November 2017; Accepted: 20 December 2017; Published: 1 January 2018

Abstract: To reduce the requirement of DC-biasing capacity and improve the biasing ability of a permanent magnet (PM), a novel hybrid saturated-core fault-current limiter (HSCFCL) is proposed in this paper. Compared with traditional saturated-core fault-current limiter (SCFCL), the HSCFCL has the advantages of small size, low DC-biasing capacity, a high biasing ability of the PM and excellent limiting performance. Firstly, the principle and the magnetic circuit model of the HSCFCL are introduced. Then, the improvement of DC-biasing capacity with a PM is analyzed. In addition, the influence of the leakage-flux effect on the biasing ability of the PM is presented in detail, and a small-section optimal structure is proposed to improve the biasing ability of the PM. Finally, to validate the principle and performance of the HSCFCL, various electromagnetic simulations, optimization studies and experiments are carried out. The simulation and experimental results demonstrate the effectiveness of the proposed method. Keywords: saturated-core fault-current limiter; DC biasing ability; permanent magnet; leakage flux effect; small section

1. Introduction Since renewable energy, energy demand and the scale of power grids continue to grow, excessive short-circuit current has been a serious problem for power systems [1–4]. Traditional current-limiting measures such as an air-core reactor and network splitting have some disadvantages [5]. Fault-current limiter devices (FCL) are becoming a promising technology to limit fault current. There are several types of FCLs [6–8]. The saturated-core fault-current limiter (SCFCL) has attracted worldwide attention from researchers and companies and has the advantages of fault self-detection, fast action and a high withstanding voltage [9–11]. The SCFCL utilizes the non-linear permeability of ferromagnetic materials to provide a low impedance under normal conditions and a large limiting impedance under fault conditions in order to limit the fault current [12]. Under normal conditions, the DC magnetic-motive-force (MMF) produced by DC coils drives the cores into saturation, and the impedance of SCFCL is low. During a fault event, Energies 2018, 11, 61; doi:10.3390/en11010061

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the large fault current drops the cores out of saturation, resulting in a large increase of impedance for limiting the fault current. However, there are two major problems limiting the development of traditional SCFCLs. The first problem is the large DC-biasing capacity of DC coils under normal conditions. Superconducting coils and permanent magnets (PMs) can be used to solve the problem. However, the superconducting materials and cooling system are expensive and energy consuming [13–15]. In addition, the biasing capacity of PMs is inadequate [16]. To reduce the requirement of the DC-biasing capacity of traditional SCFCLs, a hybrid DC coil/PM design in an open-core SCFCL is discussed [17]. However, the reduction of the fault-clipping performance needs to be improved. Modelled on an open-core type, a hybrid 4-limb close-core SCFCL based on PMs is discussed [18]. But the structure is complex and large in size. Moreover, there is a lack of detail in comparative studies about the impact of PMs on DC-biasing capacity and the fault-clipping performance of PMs. Additionally, due to the PM and the deep saturation of cores, the leakage-flux effect is obvious, and has a significant influence on the performance of the SCFCL and the biasing ability of the PM. An analytical model of a PM fault-current limiter device (PMFCL) considering the leakage-flux effect is established in [19]. A small-section structure of the PMFCL is proposed to improve the biasing ability of the PM in [20]. However, there has been a lack of attention to the biasing ability of the PM that considers the leakage effect and the optimization of a small-section structure in a hybrid DC coil/PM structure. The second problem for existing SCFCLs is insufficient limiting performance. Due to the coupling effect between the AC and DC windings, even though the cores are driven out of saturation, the limiting impedance of the SCFCL is still not large, resulting in insufficient limiting performance [21]. A bridge-type SCFCL with limiting inductor is proposed to improve limiting performance [22]. This paper proposed a novel hybrid saturated-core fault-current limiter (HSCFCL), which has the advantages of small size, low DC-biasing capacity, a high biasing ability of the PM, and excellent limiting performance. The hybrid DC coil/PM structure is proposed to reduce the DC-biasing capacity. A small-section optimal structure is proposed to improve the biasing ability of the PM. A limiting inductor in series with the DC-biasing circuit is proposed to improve the limiting performance. Firstly, the fundamental principle and the magnetic circuit model of HSFCCL are introduced in Section 2. Then, Section 3 presents the biasing ability analysis of the PM considering the leakage effect in detail. Finally, various simulations, optimization studies and experiments are performed in Section 4. The simulation and experimental results verify the effectiveness of the proposed structure. In Section 5, conclusions are summarized. 2. Fundamental Principle and Magnetic Circuit Model of the HSCFCL To describe the principle conveniently, the main symbols and definitions in this paper are firstly given, as shown in Table 1. Table 1. Symbols and definitions. Symbol

Definition

Symbol

Definition

φm1 φm2 φm3 re1 re2 ru µu µsr Lu Ls N

Flux of cores I Flux in cores II Flux in cores III Reluctance of core I Reluctance of core II Reluctance of core III Unsaturated permeability of iron core Saturated permeability of iron core Unsaturated inductance of a winding Saturated inductance of a winding Number of winding turns

Xnom ZFCL L0 MMFd MMFPM ∆MMFPM Id Se le Sb lb

Normal impedance of HSCFCL Inserted impedance of HSCFCL Limiting inductance DC MMF produced by DC coils DC MMF produced by PMs Improvement of DC MMF DC current Cross-sectional area of core I Length of core I Cross-sectional area of small section Length of small section

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2018, 11, 61 2.1.Energies Basic of the the HSCFCL HSCFCL 2.1. Basic Configuration Configuration of

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Figure 1 shows shows aa basic of 2.1.Figure Basic Configuration of theconfiguration HSCFCL 1 basic configuration of the the HSCFCL, HSCFCL, which which has has three three cores, cores, AC AC coils, coils, DC DC coils, coils, PMs, a limiting inductor and a biasing DC source. The hybrid biasing structure of the DC coils and PMs, a Figure limiting inductor and a biasing DC source. The hybrid biasing structure of the DC coils and 1 shows a basic configuration of the HSCFCL, which has three cores, AC coils, DC coils, PMs is totodrop the into saturation, resulting in ainreduction of the capacity. The PMs is used used drop thecores cores saturation, resulting a reduction of DC-biasing the of DC-biasing capacity. PMs, a limiting inductor and ainto biasing DC source. The hybrid biasing structure the DC coils and MMF produced by the PMs and DC coils are in same direction. In order to limit both the positive and The MMF produced the PMsinto andsaturation, DC coils are in same to limit both the positive PMs is used to dropby the cores resulting in adirection. reductionIn oforder the DC-biasing capacity. The negative half half cycles of aoffault-current effectively, thethe DCDC MMFs ofofcores I Iand IIII are in opposite and negative cycles a fault-current effectively, MMFs cores and are in opposite MMF produced by the PMs and DC coils are in same direction. In order to limit both the positive and directions. The limiting inductor L is with the DC is used to enhance enhance directions. L00 which which is in in series series the biasing biasing DC source used negative The half limiting cycles ofinductor a fault-current effectively, thewith DC MMFs of cores Isource and IIisare in to opposite the limiting performance. The small-section parts in cores I and II are used to improve the biasing thedirections. limiting performance. The small-section parts in with coresthe I and II are used to improve biasing The limiting inductor L0 which is in series biasing DC source is used tothe enhance ability of the PMs. The cross-sectional area of the small-section part is reduced to S b (which is smaller the limiting performance. The small-section in cores I and II are used to to improve the is biasing ability of the PMs. The cross-sectional area of parts the small-section part is reduced Sb (which smaller than that of the main core S e); the length of the small-section part is lb. ability cross-sectional area of the small-sectionpart partisisl reduced to Sb (which is smaller than that of ofthe thePMs. mainThe core S ); the length of the small-section . e

b

than that of the main core Se); the length of the small-section part is lb. I ac Core PM I ac

Coil Coil 1 Small 1 section Small section 2 2

Core N SN N SN

S S

PM

3 I I

III III

Ed

4 4 S S

I ac I ac

NS NS

L0 L0

II 3 II

Ed

N N

Basic configuration configuration of the hybrid saturated-core fault-current limiter (HSCFCL). Figure 1. Basic Figure 1. Basic configuration of the hybrid saturated-core fault-current limiter (HSCFCL).

Magnetic Circuit Modeling 2.2.2.2. Magnetic Circuit Modeling According totothe magneticflux fluxloops loopsofofcores coresand and PMs have been According theconfiguration configurationof ofthe the HSCFCL, HSCFCL, magnetic PMs have been as shown upup byby the DC coils dcφand theDC DC flux set up by established, asas shown in Figure 2a. TheDC DCflux fluxset setup the DC coils the DC flux dc and established, shownin inFigure Figure2a. 2a.The The DC flux set by the DC coils φφ dc and the flux set upset byup the PMs φ PM mainly flow through cores I and II, and the AC flux mainly flows through core III. Figure bythe thePMs PMsφPM φPM mainly flow through and and flux flows mainly flows core through core III. mainly flow through corescores I andIII, andII,the ACthe fluxAC mainly through III. Figure 2b 2b shows anan equivalent magnetic circuit model of HSCFCL. Tosimplify simplify theanalysis, analysis, assume that Figure 2b shows an equivalent magnetic the HSCFCL. To simplify the analysis, assume shows equivalent magnetic circuitcircuit modelmodel of the the of HSCFCL. To the assume that thethe magnetization curve ofofthe iron core is aa double-line model. The saturated permeability that the magnetization curve of iron core a double-line model. The saturated permeability of magnetization curve thethe iron core is is double-line model. The saturated permeability of of thethe iron core is is equal to permeability thethe iron core u.µ φu,m1 ,m2φ m2, and iron core equal thatof ofair airμµ μ0,00,and the unsaturated permeability ofofthe iron core is is μuμ .isφ m1 and equal totothat that of air , and andthe theunsaturated unsaturated permeability of iron core .φφ φm2 m1 represent thefluxes fluxes cores and III,III, respectively. rre1e1,,rre1 e2e2,and rururepresent the of of φm3φm3 represent the inincores I,I,IIIII,and III, respectively. and represent thereluctances reluctances and φm3 represent the fluxes in cores II and respectively. re2 and ru represent the reluctances core I,I, and II respectively. core I, II III,III, respectively. of core II and and III, respectively.

rrmm H Hccllmm HHclcmlm rmrm

mm11  ac1 dc dc ac1

ac2 ac2

NIa1 NI a1 PM NId PM NId r ree11

 

m3 m3 rru

u

m2m2

 NI NIa2a2  NId

NId re2 re2

rm Hclm Hclm rm (a) Magnetic flux loops

(a) Magnetic flux loops

rm r Hclm circuit Hclmmodel (b)mMagnetic (b) Magnetic circuit model

Figure 2. Equivalent magnetic circuit model of the HSCFCL. (a) Magnetic flux loops; (b) magnetic Figure 2. Equivalent magnetic circuit model of the HSCFCL. (a) Magnetic flux loops; (b) magnetic Figure 2.model. Equivalent magnetic circuit model of the HSCFCL. (a) Magnetic flux loops; (b) magnetic circuit circuit model.

circuit model.

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the AC is in the positive half cycle. Using the loop current method:

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 2 Hc lm  2rmm1  He 1le  NI ac  NI d  ru 3 (m1  m 2 )  0  AC is in the positive half cycle. Using the loop current method: Assume that the 2 Hc lm  2rmm 2  He 2 le  NI ac  NI d  ru 3 (m 2  m1 )  0    1 2rmmφ2m1 + He1 le − N Iac − N Id + ru3 (φm1 − φm2 ) = 0  −m2H 3 c lmm+ 

(1)

(1) −2Hc lm + 2rm φm2 − He2 le + N Iac − N Id + ru3 (φm2 − φm1 ) = 0  where He1 is the magnetic strength of core I; He2 is the magnetic field strength of core II; le is the  φ =field φm1 − φm2 m3 length of the magnetic path of core I or core II; N is the number of winding turns; Iac is the alternating current the HSCFCL; and Id is the DC biasing current. where Hthrough e1 is the magnetic field strength of core I; He2 is the magnetic field strength of core II; le is the Under normal conditions, cores I and deep saturation MMFs length of the magnetic path of core I or core II; II N are is thedropped number into of winding turns; Iac is by the DC alternating produced by the the DCHSCFCL; coils and and PM.IIac1is=the Iac2DC = Iacbiasing , re1 = re2current. = rs = le/Azμsr, He1 = He2 = He. Hence, the fluxes current through d in core I, II, and III can be calculated by solving (1): Under normal conditions, cores I and II are dropped into deep saturation by DC MMFs produced by the DC coils and PM. Iac1 = Iac2 /Az µsr , He1 = He2 = He . Hence, the fluxes in  = Iac ,2re1 H c=lmre2 =NIrsd= leNI  H e le ac core I, II, and III can be calculated by solving (1):     m1

2(r  r )

2r

m m u3  2H l + N I N I − H l c m ac d     φm1 =2 H c lm  NI d + NI ac  H eelee   2r 2 ( r + r )    m m u3   m 2 2(Iracm −  rHu 3e l)e  φm2 = 2Hc l2mrm+ N Id − N  2rm + rlu3 )   NI2(rm H   N Iacac − Heelee  m 3=φm1m1−φm2   φm3 m2 =  rru3 ) ((rrmm +  u3)

(2) (2)

It can can be be seen seenthat thatthe theDC DCMMF MMFproduced producedby bythe thePMs PMsand andDC DCcoils coilsmainly mainlyflow flowthrough throughcores coresI It I and Core mainly transports MMF, as shown in Figure Moreover, although the and II.II. Core IIIIII mainly transports thethe ACAC MMF, as shown in Figure 3a. 3a. Moreover, although the DC DC MMF is enhanced the PMs, the reluctance of DC the magnetic DC magnetic increases. Hence, MMF is enhanced withwith the PMs, the reluctance of the looploop also also increases. Hence, the the improvement of DC-biasing capacity by PMs needs tofurther be further studied. improvement of DC-biasing capacity by PMs needs to be studied. 0.2

B /T

0.15 0.1 0.05 0

PM PM

Core I PM PM Distance /m

Core II

Figure Leakageflux fluxdensity density distribution of the air region the HSCFCL without thesection. small Figure 3. Leakage distribution of the air region near near the HSCFCL without the small section.

Since φm1 , φm2 , He and Iac are functions of time t, the saturated inductance of a winding can be Since φm1, φm2, He and Iac are functions of time t, the saturated inductance of a winding can be expressed as: expressed as: dφ . d( Iac /2) 2N 2 Ls = N m1 = (3) u32) + rs ddtm1 （ d Idtac / 2) 2(rm +2rN Ls  of Na winding / can alsobe expressed as: (3) The unsaturated inductance

dt

dt

2(rm  ru 3 )  rs

2N 2 The unsaturated inductance of a winding Lu == can also be expressed as: 2(rm + ru3 ) + ru

2N 2 2(rm  ru 3 )  ru

Lu  is: Hence, the normal impedance of HSCFCL

= ω · Lsis: = nomHSCFCL Hence, the normal impedanceXof

2 · ω · N2 2(rm + ru3 ) + rs

(4)

(4) (5)

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Since the permeability of the cores in saturation and the PM are approximately equal to that of air, the normal impedance of the HSCFCL under normal conditions is very low. Under fault conditions, assume that the fault current is in the positive half cycle. Then, core I is saturated, and core II is unsaturated. The fault current flows through the windings of core I and the limiting inductor L0 . Hence, the inserted impedance of the HSCFCL under fault conditions ZFCL can be expressed as: 4N 2 ZFCL = ω ∗ (2Ls + L0 ) = ω ∗ ( + L0 ) (6) 2(rm + ru3 ) + rs 2.3. Improvement of DC-Biasing Capacity with PMs Compared with traditional SCFCLs with DC coils, the hybrid structure of the DC coils and PMs can reduce the DC current of the DC coil, resulting in a reduction of the DC-biasing capacity and losses. To drive cores into saturation under normal conditions, using the loop current method: N Id + 2Hc lm − 2rm φs − Hs le = N Icm

(7)

where Icm is the critical normal current. Assume the DC MMF produced by the DC coils MMFd = NId , the DC MMF produced by PMs MMFPM = 2Hc lm . Since Hc = Br /µm , rm = lm /(µm Sm ), the DC MMF produced by the DC coils can be expressed as: Bs Se MMFd = N Icp + Hs le + MMFPM (1 − ) (8) Br Sm Without PMs, the DC MMF of the traditional SCFCL which is needed to drive the cores into saturation is: MMFd0 = N Icp + Hs le (9) Thus, the improvement of the DC MMF with PMs can be calculated as: ∆MMFd = MMFd0 − MMFd = MMFPM (1 −

Bs Se ) Br Sm

(10)

It can be seen that, if Bs Se /(Br Sm ) < 1, the improvement is positive. Hence, the HSCFCL can reduce the DC-biasing capacity when appropriate parameters of cores and PM materials are designed. The materials of the core and PM in this paper are Grade Silicon steel 30Q140 (Hs = 10 kA/m, Bs = 2.0 T and NdFeB N50 (Hc = 836 kA/m, Br = 1.45 T), respectively. Thus, the cross-sectional area of the PM and cores should be satisfied as: Sm Bs > = 1.379 (11) Se Br In addition, to ensure excellent limiting performance under fault conditions, the limiting inductance L0 should be less than kLu , k is 0.01~0.1. Hence: X FCL − 2Xnom kN 2 ≤ kLu = ω 2rm + 2ru

(12)

Since ru is much less than rm , ru can be ignored. Hence, to ensure the limiting performance, MMFPM has a maximum value: MMFPM ≤

ωkN 2 Br Sm = MMFPmax 20( X FCL − Xnom )

(13)

MMFPM 

 kN BrSm

20( XFCL  Xnom )

 MMFP max

(13)

By increasing the MMFPM, the improvement of the DC MMF will increase. When MMFPM = MMFEnergies Pmax, the improvement of the DC MMF is maximum, and the length of PM can be calculated 2018, 11, 61 6 of 17 as:

 kN 2 BrSm

By increasing the MMFPM ,lm  the improvement of the DC MMF will increase.(14) 2 Hc ( XofFCLthe  XDC ) nom MMF is maximum, and the length When MMFPM = MMFPmax , the improvement of PM can be calculated as: ωkN 2 Br Sm lm = (14) 3. Biasing Ability Analysis of the PM Considering Effect 2Hc ( X FCLthe − XLeakage nom )

Under normal conditions, cores I and II are driven into deep saturation. The leakage flux will make the flux density distribution of the cores uneven. Moreover, due to the PMs, the leakage effect Under normal cores I and IIbeare driven intoFigure deep saturation. Theleakage-flux leakage flux will of the HSCFCL is moreconditions, obvious and should considered. 3 shows the density make the flux density distribution of the cores uneven. Moreover, due to the PMs, the leakage effect distribution of the air region near the HSCFCL without small sections. of the HSCFCL is more obvious and should be considered. Figure 3 shows the leakage-flux density It can be seen that the leakage effect of the HSCFCL is significant. The leakage-flux density near distribution of the air region near the HSCFCL without small sections. the PM is largest with about 0.15 T. In addition, the leakage-flux density near cores I and II is smaller, It can be seen that the leakage effect of the HSCFCL is significant. The leakage-flux density near but the density distribution is uneven, resulting indensity uneven flux density the leakage-flux PM is largest with about 0.15 T. In addition, the leakage-flux near cores I and IIdistribution is smaller, of the cores. flux density in the central part of theresulting cores isinsmaller that indistribution the terminal part of but theThe leakage-flux density distribution is uneven, uneven than flux density of the the cores close to the PMs. cores. The flux density in the central part of the cores is smaller than that in the terminal part of the The significant leakage effect will severely weaken the biasing ability of the PMs and the cores close to the PMs. The significant leakage effect will severelythe weaken theflux biasing ability of the PMs theI and improvement of DC-biasing capacity. Moreover, uneven density distribution ofand cores improvement of DC-biasing capacity. Moreover, the uneven flux density distribution of cores I the II will reduce the saturation degree of the cores, leading to a reduction in the biasing ability of and II will reduce the saturation degree of the cores, leading to a reduction in the biasing ability of the PMs and an improvement of DC-biasing capacity. Hence, the influence on the biasing ability of the and an improvement of DC-biasing Hence, influence on the biasing ability of the PMs PMs considering the leakage effect should capacity. be analyzed andthe improved. PMs considering the leakage effect should be analyzed and improved. To simplify the analysis, the HSCFCL is equivalent to a 2D model, ignoring the edge effect. To simplify the analysis, the HSCFCL is equivalent to a 2D model, ignoring the edge effect. According to the principle of magnetic field division, the air region above the HSCFCL is divided in According to the principle of magnetic field division, the air region above the HSCFCL is divided in six types of cylindrical flux tubes with areas,which which referred as arch the arch six types of cylindrical flux tubes withdifferent differentcross-sectional cross-sectional areas, areare referred to astothe type type A1, similar circular type A2A, 2semi-lunar A33,, semi-circular semi-circulartype type 4, semi-lunar type A5, and A1 , similar circular type , semi-lunartype type A A4A , semi-lunar type A5 , and semi-circular typetype A6,Aas shown in Figure 4. semi-circular , as shown in Figure 4. 6 3. Biasing Ability Analysis of the PM Considering the Leakage Effect

A6

A3 A2 A1 H  O1 I r2 K  r1 O2 PM1

J

A5

2

1

A4

A4

N

L Core

(b)

A3 A2 A1

A3 A2

A1

J H O1 I K P Q M R O3 S O2 Core PM1 Core PM2 ' ' O3 ' O1 ' ' '

J

R

K

S

PM1 O4 r5

J

'

O1'

r4

5

PM2 4

A7 A8 A9

O3'

S'

(c) (a) Figure 4. Magnetic field division theair airregion region of of the HSCFCL. field division of whole Figure 4. Magnetic field division ofofthe HSCFCL.(a) (a)Magnetic Magnetic field division of whole air region; (b)Magnetic field divisionofofair airregion region near near PM1; field division of air air region; (b)Magnetic field division PM1;and and(c)(c)Magnetic Magnetic field division of air region below PMs. region below PMs.

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3.1. Arch-Type Flux Tube A1 The arch-type flux tube represents the leakage flux emitted from line HO1 of the PM to line IO1 . According to the principle of magnetic-field division, the permeance of the arch-type flux tube A1 can be calculated as: µ0 Wd θ1 G A1 = (15) 12 where Wd is the width of PM; and θ 1 is the angle of arc HI. 3.2. Similar Circular-Type Flux Tube A2 The similar circular type flux tube A2 represents the leakage flux emitted from line JH of the PM to line IK. According to the infinitesimal method, the permeance of the similar circular type flux tube A2 can be calculated as: G A2 =

Zr2

r1

µ0 Wd dr rπ

(16)

where r1 and r2 are the radius of arcs HI and JK, respectively. 3.3. Semi-Lunar Type Flux Tube A3 The semi-lunar type flux tube A3 represents the leakage flux emitted from point J to point K. The permeance of the semi-lunar type flux tube A3 can be calculated as: G A3 =

µ0 Wd (π − θ2 ) 12

(17)

where θ 2 is the angle of arc JK. 3.4. Semi-Circular Type Flux Tube A4 The semi-circular type flux tube A4 represents the leakage flux emitted from side LJ of the iron core to side KM. Point M is the center of core III. The permeance of the semi-circular type flux tube A4 can be calculated as: µ0 Wd LM G A4 = ln (18) π JP where LM and JP are the length of lines LM and JP. 3.5. Semi-Lunar Type Flux Tube A5 The semi-lunar type flux tube A5 represents the leakage flux emitted from point L of PM1 to point P of PM2. The permeance of the semi-lunar type flux tube A5 can be calculated as: G A5 =

µ0 Wd (π − θ3 ) 12

(19)

where θ 3 is the angle of arc LP. 3.6. Semi-Circular Type Flux Tube A6 The semi-circular type flux tube A6 represents the leakage flux emitted from surface side NL of the iron core to surface side PQ. The permeance of the semi-circular type flux tube A6 can be calculated as: G A6 =

µ0 Wd NQ ln π LP

where NQ and LP are the length of lines NQ and LP.

(20)

GA 6 

0Wd NQ ln  LP

(20)

Energies 2018,and 11, 61LP where NQ

8 of 17 are the length of lines NQ and LP. In addition, the air region below the PMs can be divided into three magnetic tubes: A7, A8 and A9, as shown in Figure 4c. The permeance of the three magnetic tubes can be expressed as: In addition, the air region below the PMs can be divided into three magnetic tubes: A7 , A8 and A9 , as shown in Figure 4c. The permeance of the three tubes can be expressed as:  Wmagnetic  (21) GA7  0 d 4 12d θ4 µ0 W G A7 = (21) 12 r5

GA 8  Zr5

G A8 =

r4

0Wd dr µr0 Wd rπ

(22)

dr

(22)

 4W (   ) GA 9  µ00Wdd(π − θ55) 12 r

(23) (23)

G A9 =

12 where θ 4 and θ5 are the angles of arcs O01’O30’ and J0’O’0, respectively; and r4 and r5 are the radius of arcs where θ 4 and θ 5 are the angles of arcs O1 O3 and J O , respectively; and r4 and r5 are the radius of arcs O1’0O 3’ 0and J’O 0 ’, 0respectively. O 1 O3 and J O , respectively. It can 1, A2, A3 and A4 are parallel, the permeances of tube It can be be seen seen that thatthe thepermeances permeancesofoftube tubeAA 1 , A2 , A3 and A4 are parallel, the permeances of A 5 and A6 are parallel, and the permeances of tube A7, A8 and A9 are parallel. Assuming G1 = GA1 + tube A5 and A6 are parallel, and the permeances of tube A7 , A8 and A9 are parallel. Assuming GA2=+ G GA3 ++GGA4, G+2 =GGA5++G GA6,, G 3 = GA7 + GA8 + GA9, Gm is the permeance of PM. Hence, the equivalent G 1 A1 A2 A3 A4 G2 = GA5 + GA6 , G3 = GA7 + GA8 + GA9 , Gm is the permeance of PM. permeance model of the PMs considering leakage effect is shown in Figure Hence, the equivalent permeance model of the the PMs considering the leakage effect5.is shown in Figure 5.

G2 G1

G1 Hclm

Gm

Hclm

Gm

G3

Figure 5. 5. Equivalent model of of permanent permanent magnets magnets (PMs) (PMs) considering considering the the leakage leakage effect. effect. Figure Equivalent permeance permeance model

According to Thevenin equivalent principle, Thevenin equivalent MMF and reluctance of PM According to Thevenin equivalent principle, Thevenin equivalent MMF and reluctance of PM can can be expressed as: be expressed as: G Gmm Fm0' = Hc lm · (24) F  H l  (24) m c m Gm + G1 + 2G2 + 2G3 R0m =

Gm  G1  2G2  2G3

1 Gm + G1 +12G2 + 2G3

(25)

R  (25) Hence, due the leakage effect, themequivalent decrease, resulting in a reduction Gm  GMMF  2Gof2 PM 2Gwill 1 3 of the biasing ability of the PM. The length of the PM that is needed should be longer than that of Hence, the considering leakage effect, equivalenteffect. MMF of PM will decrease, resulting in a reduction Equation (14)due when thethe leakage-flux of the biasing ability of the PM. The length of the is needed should bePMs, longer than section that of Hence, to improve the biasing ability of the PMPM andthat reduce the length of the a small Equation (14) when the leakage-flux effect. part is proposed. Dueconsidering to the cross-sectional area being smaller than that of main core, this can make the Hence, distribution to improve the biasing of theThe PMcross-sectional and reduce thearea length the PMs, small section flux-density of the coresability more even. andof length of thea small-section part should is proposed. Due to the cross-sectional area being smaller than that of main core, this can make part be studied. the flux-density distribution of the cores more even. The cross-sectional area and length of the small4. Results section part should be studied. '

To validate the performance and improvement of the DC-biasing capacity of a HSCFCL in a power grid, a single-phase 10 kV/1 kA HSCFCL finite element analysis (FEA) model was established. Various FEA simulations using the non-linear field-circuit coupling method and optimization studies of the HSCFCL were performed. In the simulation setup, the material characteristics of the cores were the actual non-linear model. An ideal voltage source was used as the power source, and an ideal

To validate the performance and improvement of the DC-biasing capacity of a HSCFCL in a power grid, a single-phase 10 kV/1 kA HSCFCL finite element analysis (FEA) model was established. Various FEA simulations using the non-linear field-circuit coupling method and optimization studies of the HSCFCL were performed. In the simulation setup, the material characteristics of the cores were Energies 2018, 11, 61 9 of 17 the actual non-linear model. An ideal voltage source was used as the power source, and an ideal switch was used as the circuit breaker. The parameters of the HSCFCL model are presented in Table 2. To validate theas influence of the PMs,The the SCFCL without PMs whosemodel other parameters areinthe same switch was used the circuit breaker. parameters of the HSCFCL are presented Table 2. was performed for comparison. The of the PM and other the small-section part To validate the influence of the PMs, theparameters SCFCL without PMs whose parameters are thehave samebeen was optimized.for comparison. The parameters of the PM and the small-section part have been optimized. performed Table 2. 2. Parameters Parameters of of the the HSCFCL HSCFCL model. model. Table Parameter Parameter Cross-sectional area of cores I and II/m2 2 Cross-sectional area of cores I and II/m Cross-sectional area of cores III/m2 2 Cross-sectional area of cores III/m Cross-sectional area of small section/m2 2 Cross-sectionalLength area of of small section/m cores le/m Length of cores le /m Length of small section lb/m Length of small section lb /m 2 Cross-sectional area of PM/m Cross-sectional area of PM/m2 Length of PM/m Length of PM/m Number of winding Number of winding turnsturns N N Inductance of limiting inductor L0/mH Inductance of limiting inductor L0 /mH SteelSteel corescores Permanent magnets Permanent magnets

Value Value 0.2025 0.2025 0.261 0.261 0.189 0.189 2.2 2.2 1.8 1.8 0.405 0.405 0.15 0.15 3737 1.93 1.93 HH s = 10 kA/m, Bs B =s2.0 T T = 10 kA/m, = 2.0 s 836kA/m, kA/m, = 1.45 HH c = 836 Br B =r1.45 T T c=

4.1. FEA FEA Simulation Simulation and and Optimization Optimization 4.1. Figure 66 shows shows the the DC DC current current and and normal normal voltage voltage of of the the HSCFCL HSCFCL and and SCFCL SCFCL without without PMs PMs Figure under normal conditions. It can be seen that, compared with SCFCL without PMs, the DC current under normal conditions. It can be seen that, compared with SCFCL without PMs, the DC current can canreduced be reduced kA. Hence, the HSCFCL has areduction 52.3% reduction in DC-biasing be from from 2.1 kA2.1 to kA 1.0 to kA.1.0 Hence, the HSCFCL has a 52.3% in DC-biasing capacity. capacity. Additionally, of the of reluctance PMs, voltage the normal voltage can alsofrom be reduced Additionally, because of because the reluctance the PMs, of thethe normal can also be reduced 179.0 V from 179.0 V to 156.0 V with a 12.8% reduction. to 156.0 V with a 12.8% reduction.

500

2 1.5

400 DC of SCFCL DC of HSCFCL

Voltage of SCFCL Voltage of HSCFCL

300

1

200

0.5

100

0

0

-0.5

-100

-1 0

0.01

0.02

0.03 Time /s

0.04

0.05

Normal voltage U/V

DC biasing current Idc/kA

2.5

-200 0.06

6. DC Figure 6. DC current current and and normal normal voltage voltage of of the the HSCFCL HSCFCL and SCFCL without PMs under normal conditions. conditions.

The current current of of the the HSCFCL HSCFCL is is shown shown in in Figure Figure 7. 7. It It shows shows that that the the fault fault current current is is limited limited from from The 30 kA AA HSCFCL with L0 =L0 = mH represents the traditional hybrid FCL. 30 kA to to 11.0 11.0kA kAwith withthe theHSCFCL. HSCFCL. HSCFCL with 0 mH represents the traditional hybrid 0 It can be seen that, compared with traditional hybrid FCLs, the proposed HSCFCL has better limiting FCL. It can be seen that, compared with traditional hybrid FCLs, the proposed HSCFCL has better performance. In addition, compared with the without PMs,PMs, the the limiting performance is limiting performance. In addition, compared withSCFCL the SCFCL without limiting performance is weakened by 10%. However, the HSCFCL also has good limiting performance, meeting the limiting requirement of the power grid.

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weakened by 10%. However, the HSCFCL also has good limiting performance, meeting the limiting Energies 2018,by 11,10%. 61 10 of 17 weakened However, the HSCFCL also has good limiting performance, meeting the limiting requirement of the power grid. requirement of the power grid.

currentIfI/kA Faultcurrent Fault f/kA

40 40 30 30 20 20 10 10 0 0 -10 -10 -20 -20 -30 -30 -40 -400 0

Without FCL Without FCL SCFCL with L0=1.93mH SCFCL with L0=1.93mH HSCFCL with L0=0mH HSCFCL with L0=0mH HSCFCL with L0=1.93mH HSCFCL with L0=1.93mH

0.02 0.02

0.04 0.04

0.06 0.08 0.1 0.06 Time 0.08/s 0.1 Time /s

0.12 0.12

0.14 0.14

0.16 0.16

Figure current. Figure 7. 7. Comparative Comparative results results of Figure 7. Comparative results of current.

Figure 8 shows the currents of the coil on core II under different limiting inductances. It can be Figure 8 shows the currents of the coil on core II under different limiting inductances. It can be seen that the limiting performance of the HSCFCL can be improved when the limiting inductance seen that the limiting performance performance of the HSCFCL can be improved when the limiting inductance increases. However, due to the reluctance of the PMs, the unsaturated inductance of the winding is increases. However, However,due dueto tothe thereluctance reluctanceofofthe the PMs, unsaturated inductance of the winding is PMs, thethe unsaturated inductance of the winding is not not so large compared with the limiting inductance. Hence, with an increase in the limiting not so large compared with the limiting inductance. Hence, with aninincrease in the limiting so large compared with the limiting inductance. Hence, with an increase the limiting inductance, inductance, the current of the coil on the unsaturated core will also increase, resulting in a weakening inductance, thethe current theunsaturated coil on the unsaturated core will also increase, in a weakening the current of coil onofthe core will also increase, resulting inresulting a weakening of limiting of limiting performance. Compared with the SCFCL with the same limiting inductance L0 = 1.93 mH, of limiting performance. with with the SCFCL with the same limiting Linductance L0 the = 1.93 mH, performance. Compared Compared with the SCFCL the same limiting inductance current 0 = 1.93 mH, the current of the HSCFCL coil is larger. Hence, Figures 7 and 8 demonstrate that the reluctance of the current of the HSCFCL is larger. Hence, Figures 7 and 8 demonstrate that the of of the HSCFCL coil is larger.coil Hence, Figures 7 and 8 demonstrate that the reluctance of reluctance the PMs will the PMs will have some impact on the limiting performance of the HSCFCL. the PMs will have some impact on the limiting performance of the HSCFCL. have some impact on the limiting performance of the HSCFCL.

I/kA currentI/kA Coilcurrent Coil

44 22 00 -2 -2 -4 -4 -6 -6

-8 -8 -10 -100 0

2.7 2.7 2.4 2.4 2.1 2.1 1.8 1.8

SCFCL: L0=1.930mH SCFCL: L0=1.930mH HSCFCL: L0=0.965mH HSCFCL: L0=0.965mH HSCFCL: L0=1.930mH HSCFCL: L0=1.930mH HSCFCL: L0=2.896mH HSCFCL: L0=2.896mH

0.02 0.02

0.04 0.04

0.06 0.06

0.08 0.08 /s 0.1 0.1 Time Time /s

0.12 0.12

0.14 0.14

0.16 0.16

Figure 8. Currents of the coil on core II under different limiting inductances. Figure Figure 8. 8. Currents Currents of of the the coil coil on on core core II under different limiting inductances.

Figure 9 shows the flux density distribution of the HSCFCL under different conditions. Under Figure 9 shows the flux density distribution of the HSCFCL under different conditions. Under Figure 9 showscores the flux density distribution of the under different Under normal conditions, I and II are both saturated, the HSCFCL flux density of cores I andconditions. II is about 2.05 T, normal conditions, cores I and II are both saturated, the flux density of cores I and II is about 2.05 T, normal conditions, cores I and II are both saturated, the flux density of cores I and II is about 2.05 T, and the flux density of the PM is 1.12 T. Under fault conditions, cores I and II are alternately driven and the flux density of the PM is 1.12 T. Under fault conditions, cores I and II are alternately driven andof thesaturation, flux density of the PM is 1.12 T. Under fault conditions, cores I and II are alternately driven out out respectively. out of saturation, respectively. of saturation, respectively. To validate the influence of a small-section structure on the saturation degree of the cores and To validate the influence of a small-section structure on the saturation degree of the cores and To ability validate of a small-section structure on the saturation degreeof ofsmall the cores and biasing ofthe theinfluence PMs, various comparative studies with different parameters sections biasing ability of the PMs, various comparative studies with different parameters of small sections biasing abilityThe of the various studies with different parameters of small sections are are analyzed. DCPMs, current is 1.0comparative kA. are analyzed. The DC current is 1.0 kA. analyzed. The DC current is 1.0 kA. Figure 10 shows the flux-density distribution of core I in different cross-sectional areas of the Figure 10 shows the flux-density distribution of core I in different cross-sectional areas of the 10Itshows flux-density distribution of core Idue in different cross-sectional areas of the smallFigure section. can bethe seen that, without the small section, to the leakage effect the flux-density small section. It can be seen that, without the small section, due to the leakage effect the flux-density small section. It can be seen that, without the small section, due to the leakage effect the flux-density distribution of core I is uneven, the minimum B is 1.984 T in the center, and core I is not saturated. distribution of core I is uneven, the minimum B is 1.984 T in the center, and core I is not saturated. distribution ofPM coreorI the is uneven, the minimum B is 1.984 T in the center, I is notsaturation. saturated. The use of the DC-biasing capacity should be increased to dropand thecore cores into The use of the PM or the DC-biasing capacity should be increased to drop the cores into saturation. The length use of the PMPM or the DC-biasing capacity should be driving increased drop into the cores into saturation. The of the should be increased to 0.22 m for thetocores saturation. With the The length of the PM should be increased to 0.22 m for driving the cores into saturation. With the The length of the PM should be increased to 0.22 m for driving the cores into saturation. With the small

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section, saturation is deep and the biasing ability of theof PMs is enhanced. When Sb = 0.1935 m2 and22 small small section, section,2saturation saturation is is deep deep and and the the biasing biasing ability ability of the the PMs PMs is is enhanced. enhanced. When When S Sbb == 0.1935 0.1935 m m 2minimum Sb = 0.1912 m , the B can be enhanced to 1.9969toT 1.9969 and 1.9984 T, but coreT, I isbut stillcore unsaturated. and S b = 0.1912 m , the minimum B can be enhanced T and 1.9984 I is still 2 and Sb = 0.1912 m2 , the minimum B can be enhanced to 1.9969 T and 1.9984 T, but core I is still 2 B isminimum When Sb = 0.189 m , the minimum 2.0003 T, andiscore I is saturated. However, when Sb is reduced to unsaturated. When unsaturated. When S Sbb == 0.189 0.189 m m2,, the the minimum B B is 2.0003 2.0003 T, T, and and core core II is is saturated. saturated. However, However, when when 2 2, the 0.1867 m , thetoflux density of the core center increases, but the flux density of the core end decreases to S b is reduced 0.1867 m flux density of the core center increases, but the flux density of the core Sb is reduced to 0.1867 m2, the flux density of the core center increases, but the flux density of the core 1.9923 T, resulting in a weakening of the saturation degree. Hence, with the reduction of cross-sectional end end decreases decreases to to 1.9923 1.9923 T, T, resulting resulting in in aa weakening weakening of of the the saturation saturation degree. degree. Hence, Hence, with with the the area of theof small section, the saturation degree of the cores does not always increase, and is relatively reduction cross-sectional area of the small section, the saturation degree of the cores does not reduction of cross-sectional area of the small section, the saturation degree of the cores does not 2 optimalincrease, in Sb = 0.189 m2relatively . always and optimal always increase, and is is relatively optimal in in S Sbb == 0.189 0.189 m m2.. B/tesla B/tesla 2.0723 2.0723 1.9464 1.9464 1.8205 1.8205 1.6946 1.6946 1.5886 1.5886 1.4427 1.4427 1.3168 1.3168 1.1909 1.1909 1.0650 1.0650 0.9391 0.9391 0.8132 0.8132 0.6873 0.6873 0.5614 0.5614 0.4355 0.4355 0.3096 0.3096 0.1836 0.1836 0.0577 0.0577

Positive Negative Positive cycle cycle Negative cycle cycle (a) Under normal conditions (b) Under fault (a) Under normal conditions (b) Under fault conditions conditions Figure Figure 9. 9. Flux Flux density density distribution distribution of of the the HSCFCL HSCFCL under under different different conditions. conditions. Figure 9. Flux density distribution of the HSCFCL

2.08 2.08 Without section Without small small 2 section 2,lb=1.8m SSb=0.1867m =0.1867m ,l =1.8m b 2 b 2,lb=1.8m SSb=0.1890m =0.1890m ,l b 2 b=1.8m 2,lb=1.8m SSb=0.1912m =0.1912m b 2,lb=1.8m SSb=0.1935m =0.1935m2,l ,lb=1.8m =1.8m

BB/T/T

2.06 2.06 2.04 2.04 2.02 2.02 22

b

b

Saturation line Saturation line

1.98 1.98 1.96 1.960 0

0.2 0.2

0.4 0.4

0.6 0.6 0.8 0.8 11 1.2 1.2 1.4 1.4 1.6 1.6 Distance from core bottom Distance from core bottom /m /m

1.8 1.8

22

2.2 2.2

Figure 10. Flux-density distribution of core II in different cross-sectional areas of the small section. Figure Figure 10. 10. Flux-density Flux-density distribution distribution of of core core I in in different different cross-sectional areas of the small section.

Figure 11 shows the flux-density distribution of core II in different lengths of the small section. Figure 11 shows the flux-density distribution of core in different lengths of the small section. Figure 11 shows the flux-density distribution of core I in different lengths of the small section. When l b = 1.9 m and lb = 2.0 m, the flux density can be improved to 1.9982 T and 1.996 T, but core I is When llb ==1.9 m and lbl ==2.0 m,m,the flux density can bebe improved toto 1.9982 T and 1.996 T, T, butbut core I isI When 1.9 m and 2.0 the flux density can improved 1.9982 T and 1.996 core b b lb = 1.8 m, core I is saturated with 2.0003 T. However, when the length still unsaturated. When is still unsaturated. When l b = 1.8 m, core I is saturated with 2.0003 T. However, when the length is is still unsaturated. When lb = 1.8near m, core I is saturated with 2.0003 T.and However, when the to length is reduced to 1.7 m, the flux density the junction of the small section core I is reduced 1.9868 reduced to 1.7 m, the flux density near the junction of the small section and core I is reduced to 1.9868 reduced towith 1.7 m, thereduction flux density near the junction of section, the smallthe section and core I is reduced todoes 1.9868 T. T. Hence, the in of the degree of cores not T. Hence, with the reduction in length length ofsmall the small small section, the saturation saturation degree ofdoes coresnot does not Hence, with the reduction in length of the section, the saturation degree of cores always always increase, and optimal at llbb == 1.8 always increase, and is is relatively relatively optimal at m. 1.8 m. m. increase, and is relatively optimal at l = 1.8 b This demonstrates that the small-section optimal structure can improve the saturation degree of This demonstrates that optimal structure can the saturation degree of This demonstrates that the the small-section small-section optimal structure can improve improve theMoreover, saturationthe degree of cores, resulting in a reduction in the use of PMs and DC-biasing capacity. crosscores, resulting in a reduction in the use of PMs and DC-biasing capacity. Moreover, the crosscores, resulting in a reduction in the use of PMs and DC-biasing capacity. Moreover, the cross-sectional sectional area and length of small section have influence on The sectional area and length of the the smallhave section have aa significant significant influence on the the improvement. improvement. The area and length of the small section a significant influence on the improvement. The optimal 2 optimal parameter of the small section is S b = 0.189 m2, lb = 1.8 m. The length of the PM for traditional optimal parameter of the smallissection is Sbm = 20.189 , m. lb =The 1.8 m. The of length of the PM for traditional parameter of the without small section Sb =section 0.189 , lb = m 1.8 length themPM for traditional hybrid hybrid SCFCLs the small should be increased to 0.22 to drive the cores hybrid SCFCLs without the small section should be increased to 0.22 m to drive the cores into into SCFCLs without the small section should be increased to 0.22 m to drive the cores into saturation. saturation. Hence, compared with traditional hybrid SCFCLs without a small section, the length of saturation. Hence,with compared withhybrid traditional hybrid SCFCLs without a small section, thePM length of Hence, compared traditional SCFCLs without a small section, the length of the can be the the PM PM can can be be reduced reduced from from 220 220 mm mm to to 150 150 mm. mm. The The biasing biasing ability ability of of the the PM PM can can be be improved improved by by 31.8% 31.8% with with the the optimal optimal small-section small-section structure. structure.

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reduced from 220 mm to 150 mm. The biasing ability of the PM can be improved by 31.8% with the structure. 12 of 18

optimal small-section Energies 2018, 11, 61

2.08 Without small section Sb=0.1890m2,lb=1.7m Sb=0.1890m2,lb=1.8m Sb=0.1890m2,lb=1.9m Sb=0.1890m2,lb=2.0m

2.06 B /T

2.04 2.02 2 Saturation line

1.98 1.96 0

0.2

0.4

0.6 0.8 1 1.2 1.4 1.6 Distance from core bottom /m

1.8

2

2.2

Figure Figure 11. 11. Flux-density Flux-density distribution distribution of of core core II in in different different lengths of the small section.

In addition, the energy consumption of the DC-biasing circuit under normal conditions has an In addition, the energy consumption of the DC-biasing circuit under normal conditions has an important influence on the performance and cost of the HSCFCL. Reducing the energy consumption important influence on the performance and cost of the HSCFCL. Reducing the energy consumption of the DC-biasing circuit under normal conditions can also improve the efficiency of the HSCFCL. As of the DC-biasing circuit under normal conditions can also improve the efficiency of the HSCFCL. discussed previously, the DC-biasing current of SCFCLs without PMs is 2.0 kA, and the DC-biasing As discussed previously, the DC-biasing current of SCFCLs without PMs is 2.0 kA, and the DC-biasing current of the HSCFCL can be reduced to 1.0 kA. Moreover, when the length of the PM is 150 mm, current of the HSCFCL can be reduced to 1.0 kA. Moreover, when the length of the PM is 150 mm, the DC-biasing current of traditional hybrid SCFCLs will increase to 1.2 kA. Hence, assuming the the DC-biasing current of traditional hybrid SCFCLs will increase to 1.2 kA. Hence, assuming the lifetime of a FCL is 30 years (263,000 h), and each coil has a resistance of 0.05  , the energy lifetime of a FCL is 30 years (263,000 h), and each coil has a resistance of 0.05 Ω, the energy consumption consumption can be calculated as: can be calculated as:

0.02  263  84.16 GWh SCFCLs without PMs: Wloss1 = 4  20002  SCFCLs without PMs: Wloss1 = 4 × 20002 × 0.02 × 263 = 84.16 GWh Hybrid SCFCLs without small section: Wloss2 = 4 12002 2 0.02  263  30.30 GWh Hybrid SCFCLs without small section: Wloss2 = 4 × 1200 × 0.02 × 263 = 30.30 GWh HSCFCL with small section: Wloss3 = 4 10002 2 0.02  263  21.04 GWh HSCFCL with small section: Wloss3 = 4 × 1000 × 0.02 × 263 = 21.04 GWh Hence, compared with SCFCLs without PMs, the proposed HSCFCL has a 75% reduction of Hence, compared withnormal SCFCLs without PMs, the proposed HSCFCL has aSCFCLs 75% reduction energy consumption under conditions. Compared with traditional hybrid withoutof a energysection, consumption under normal conditions. Compared traditional hybrid SCFCLs withoutina small the proposed HSCFCL has a 30.5% reductionwith of the energy consumption, resulting small section, the in proposed HSCFCL hasHSCFCL a 30.5% reduction of theconditions. energy consumption, resulting in an an improvement the efficiency of the under normal improvement in the efficiency of the HSCFCL under normal conditions. The parameters of the PMs have an important impact on the improvement of the DC-biasing The Moreover, parameterssince of the have an improvement of the DC-biasing capacity. thePMs reluctance ofimportant the PM willimpact reduceon thethe unsaturated inductance of the core, capacity. Moreover, since the reluctance of the PM will reduce the unsaturated inductance the core, the parameters of PMs also have a significant impact on the limiting performance of theofHSCFCL. the parameters of the PMsinfluence also have significant impact on the limiting performance of the HSCFCL. Hence, to validate ofathe PM on the performance of the HSCFCL, various comparative Hence, to validate the parameters influence ofofthe PMare onperformed. the performance of current the HSCFCL, various comparative studies with different PMs The DC is 1.0 kA, the parameter of 2 studies with different parameters of PMs are performed. The DC current is 1.0 kA, the parameter of the small section is Sb = 0.189 m , and lb = 1.8 m. 2 the small section is Sb = 0.189 m , and lbdistribution = 1.8 m. Figure 12 shows the flux-density of core I in different lengths of PMs. When the Figure 12 shows the flux-density distribution of core I influx different lengths of PMs. When the length of the PM is 0.13 m, 0.15 m and 0.17 m, the minimum density is 1.9977 T, 2.0003 T and length of the PM is 0.13 m, 0.15 m and 0.17 m, the minimum flux density is 1.9977 T, 2.0003 T and 2.0036 T, respectively. Thus, as the length of the PM increases, the saturation degree also increases. 2.0036 T, respectively. Thus, as the performance length of the PM increases, the saturation degreethe also increases. Figure 13 shows the limiting in different lengths of PM. When lengths of the Figure 13 shows the limiting performance in different lengths of PM. When the lengths of the PM PM are 0.13 m, 0.15 m and 0.17 m, the peak fault current can be limited to 10.77 kA, 11.00 kA and are 0.13 m,respectively. 0.15 m and 0.17 m,length the peak current can beunsaturated limited to 10.77 kA, 11.00 kAdecrease, and 11.34and kA, 11.34 kA, If the of fault the PM increases, inductance will respectively. thePM length the PM increases, unsaturated inductance will decrease, and the lengththe of the length of Ifthe has of a significant influence on the limiting performance. Hence, increasing the PM has a significant influence on the limiting performance. Hence, increasing the length of the PM length of the PM can improve the saturation degree and reduce the DC-biasing capacity but will can improve the and saturation degree and reduce the DC-biasing capacity but will increase the cost and increase the cost weaken the limiting performance. weaken the limiting performance.

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2.08 2.08 Without Without small small section section 2 SSmm=0.405m =0.405m2,l ,lmm=0.17m =0.17m 2 SSmm=0.405m =0.405m2,l ,lmm=0.15m =0.15m 22 SSmm=0.405m =0.405m ,l ,lmm=0.13m =0.13m

/T BB/T

2.06 Energies 2018, 11, 61 2.06 2.04 2.042.08 2.06 2.02 2.02 2.04

B /T

2.00 2.00

2.02

1.98 1.98 0 0

2.00

Saturation Saturation line line 0.2 0.2

0.4 0.4

0.6 0.6

13 of 18

Without small section Sm=0.405m2,lm=0.17m Sm=0.405m2,lm=0.15m Sm=0.405m2,lm=0.13m

0.8 0.8 11 1.2 1.2 1.4 1.4 1.6 1.6 1.8 1.8 Distance Distance from from core core bottom/m bottom/m

22

2.2 2.2

Saturation line Figure 12. different lengths of PMs. Figure Flux density density distribution distribution of of core II in 1.98 Figure 12.0Flux Flux density lengths PMs. 0.2 0.4 distribution 0.6 0.8 1of core 1.2 in 1.4different 1.6 1.8 2 of2.2 Distance from core bottom/m

Fault current If/kA

currentIIf/kA Faultcurrent Fault f/kA

12 12 12 Figure 12. 10 12 Flux density distribution of core I in different lengths of PMs. 10 88 11 11 66 12 10 12 10 44 10 0.064 0.064 0.065 0.065 0.066 0.066 8 11 22 00 6 10 4 0.064 0.065 0.066 -2 -2 2 Without Without small small section section -4 -4 0 22 SSmm=0.405m ,l =0.17m m =0.405m ,l =0.17m -6 m -6 -2 2 Without small section SSmm=0.405m -8 =0.405m2,l ,l2mm=0.15m =0.15m -8 -4 S =0.405m m 22 ,lm=0.17m -10 -6 SSmm=0.405m -10 =0.405m ,l ,l2mm=0.13m =0.13m ,lm=0.15m -12 -120-8 0.02Sm=0.405m 0.04 0.06 0.1 0.12 0-10 0.02Sm=0.405m 0.04 2,lm=0.13m 0.06 0.08 0.08 0.1 0.12 0.14 0.14 0.16 0.16 Time /s -12 Time /s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Time /sdifferent lengths of the PM. Figure Figure 13. 13. Limiting Limiting performance in different lengths of the PM. Limiting performance performance in Figure 13. Limiting performance in different lengths of the PM.

Figures 14 and 15 show the flux-density cores and limiting Figures show the the flux-density flux-density distribution distribution of of and the the limiting limiting performance performance in in Figures 14 14 and and 15 15 show distribution of cores cores and the performance in Figures 14 and 15 show the flux-density distribution of cores and the limiting performance in different cross-sectional areas of the PM. It can be seen that as the cross-sectional area of PM increases, different cross-sectional areas of the PM. It can be seen that as the cross-sectional area of PM increases, different cross-sectional areas of the PM. It can be seen that as the cross-sectional area of PM increases, different cross-sectional areas of the effectively. PM. It can be When seen that as cross-sectional the cross-sectional areaof of the PM increases, the saturation degree also increases the area PM the saturation degreealso alsoincreases increases effectively. When the cross-sectional area of the increases PM increases increases the saturation degree effectively. When thethe cross-sectional area ofofthe PM from the saturation degree also increases effectively. When cross-sectional area the PM increases 2 2 2 2 from 0.382 m to 0.427 m , the minimum flux density also increases from 1.9959 T to 2.0029 T. from 0.382 m to 0.427 m , the minimum flux density also increases from 1.9959 T to 2.0029 T. 2 2 0.382from m to 0.427 the minimum flux density also increases from 1.9959 T to 2.0029 T. Moreover, 0.382 m2mto, 0.427 m2, the minimum flux density also increases from 1.9959 T to 2.0029 T. Moreover, the cross-sectional area of the PM has little impact on the limiting performance. Moreover, the cross-sectional area of the PM has little impact on the limiting performance. the cross-sectional area of the PM has impact on the limiting Moreover, the cross-sectional area oflittle the PM has little impact on theperformance. limiting performance.

2.08 2.082.08 Without small section Without small Without smallsection section 22 2,l,l =0.15m SSSmmm=0.427m =0.15m =0.427m =0.427m ,lmmm=0.15m S =0.405m222,l,l SSmmm=0.405m =0.15m =0.405m ,lmmm=0.15m =0.15m 22 S =0.382m ,l =0.15m 2 SSmmm=0.382m =0.382m ,l ,lmmm=0.15m =0.15m

2.04 2.042.04 B /T

/T BB /T

2.06 2.062.06

2.02 2.02 2.02 2.00

2.00 2.00

1.98

Saturation line

Saturation Saturation line line

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 1.98 1.980 0.2 0.4 0.6Distance 11 core 1.2 1.4 0 0.2 0.4 0.6 0.8 0.8 from 1.2bottom/m 1.4 1.6 1.6 1.8 1.8 22 2.2 2.2 Distance from core bottom/m Distance from core bottom/m Figure 14. Flux-density distribution of cores in the different cross-sectional areas of the PM.

Figure 14. Flux-density distribution of cores in the different cross-sectional areas of the PM. Figure Figure 14. 14. Flux-density Flux-density distribution distribution of of cores cores in in the the different different cross-sectional cross-sectional areas areas of of the the PM. PM.

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14 of 18

Fault current If/kA

Fault current If/kA

12 10 11.2 Energies 2018, 11, 61 8 11 6 12 4 10 10.8 0.064 11.2 0.065 0.066 2 8 11 0 6 -2 4 10.8 0.064 0.065 0.066 -4 2 Sm=0.427m2,lm=0.15m -6 0 Sm=0.405m2,lm=0.15m -8 -2 2 2 Sm=0.382m ,lm,l=0.15m Sm=0.427m m=0.15m -10 -4 -6 2 S =0.405m ,l m m=0.15m -12 -8 0 0.02 0.042 0.06

0.08

0.1

0.12

0.14

0.16

Sm=0.382m ,lm=0.15m -10 Time /s -12 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Figure different Figure 15. 15. Limiting Limiting performance performance in in the theTime different cross-sectional areas of the PM. /s cross-sectional

15. Limiting performance the different areas the Additionally, compared withCase Case1:1:SSmm=in =0.405 0.405 m22,,llmmcross-sectional 0.15 m, m, Case Case m= =PM. 0.405 m m22,, llm m = Additionally, Figure compared with m == 0.15 2:2:ofSSm 0.405 = 0.17 0.17 m m 3, and weaken 3 can reduce the DC capacity of 0.1 kA, but will increase the usage of the PM of 0.0081 m can reduce the DC capacity of 0.1 kA, but will increase 2the usage of the PM of 0.0081 m , and weaken Additionally, compared with Case 1: Sm = 0.405 m , lm = 0.15 m, Case 2: Sm = 0.405 m2, lm = 0.17 m the performance of 0.34 0.34 kA. kA. However, However, Case Case3:3: SSmm = = 0.427 0.427 m m22,, llmm ==0.15 m also reduce the limiting limiting performance of mcan can alsoweaken reduce the the 3, and can reduce the DC capacity of 0.1 kA, but will increase the usage of the PM2 of0.15 0.0081 m 2 DC capacity of 0.1 kA, but will just increase usage of the PM of 0.0031 m , and has little impact on the DC capacity of 0.1 kA, but will just kA. increase usage of the of 0.0031 m , and has little impact on the the limiting performance of 0.34 However, Case 3: SPM m = 0.427 m2, lm = 0.15 m can also reduce the limiting performance. Hence, compared with an increase in length of increase in limiting performance. Hence, compared with an increase in the length of the the PM, an increase in the the DC capacity of 0.1 kA, but will just increase usage of the PM ofthe 0.0031 m2, and hasPM, littlean impact on the cross-sectional area of the PM has better performance and economy. cross-sectional area of theHence, PM has better performance andineconomy. limiting performance. compared with an increase the length of the PM, an increase in the

cross-sectional area of the PM has better performance and economy.

4.2. 4.2. Experimental Experimental Study Study 4.2. Experimental Study

To proposed byby this paper, a To validate validate the the performance performanceand andoptimization optimizationstudies studiesofofthe theHSCFCL HSCFCL proposed this paper, To validate the performance and optimization studies of the HSCFCL proposed by this paper, a 220 V/10 A single-phase HSCFCL laboratory prototype was was tested, as shown in Figure 16a. The a 220 V/10 A single-phase HSCFCL laboratory prototype tested, as shown in Figure 16a. 220 V/10 HSCFCL laboratory prototype was tested, as shown circuit in Figure 16a. The A parameters of A thesingle-phase prototype are shown in Table The electrical ofcircuit the 220/10 The parameters ofexperimental the experimental prototype are shown in3.Table 3. The electrical of the parameters of the experimental prototype are shown in Table 3. The electrical circuit of the 220/10 A prototype platform shown inisFigure The power was provided by provided a transformer. 220/10 A test prototype testisplatform shown16b. in Figure 16b. supply The power supply was by a prototype test platform is shown in Figure 16b. The power supply was provided by a transformer. The prospective without FCLwithout was 500 A.was The500 DC-biasing current was adjusted transformer. The peak-fault prospectivecurrent peak-fault current FCL A. The DC-biasing current was The prospective peak-fault current without FCL was 500 A. The DC-biasing current was adjusted using a 100 A bridge rectifier. The exciting source was connected to the rectifier through an exciting adjusted using a 100 A bridge rectifier. The exciting source was connected to the rectifier through using a 100 A bridge rectifier. The exciting source was connected to the rectifier through an exciting an transformer to ensure insulation. AA400 wasused used simulate a fault across the exciting transformer to electrical ensure electrical insulation. A 400 A breaker was used to simulate a fault across transformer to ensure electrical insulation. 400 A A breaker breaker was toto simulate a fault across the load. The The currents were measured using 400 AAAC/DC closed-loop Hall effect current sensors. the load. were measured using A AC/DC closed-loop Hall effect current sensors. load. The currents currents were measured using 400400 AC/DC closed-loop Hall effect current sensors. Power PowerSupply Supply Exciting Transformer Exciting Transformer

Bridge Rectifier

Bridge Rectifier

HSCFCL Prototype

HSCFCL Prototype (a)

Figure(a) 16. Cont.

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15 of 17 15 of 18

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Rectifier HSCFCL

Power supply Power supply

Rectifier

Exiting source Exiting source

HSCFCL

Load Load

Breaker Breaker

L0

Exiting Transformer Exiting Transformer

L0

(b)

(b)

Figure 16. 220 V/10 A prototype test platform. (a) 220 V/10 A HSCFCL prototype; (b) circuit scheme Figure 16.16. 220 (a) 220 220 V/10 V/10AAHSCFCL HSCFCL prototype; circuit scheme Figure 220V/10 V/10AAprototype prototype test test platform. platform. (a) prototype; (b)(b) circuit scheme of the 220 V/10 A prototype test. of of thethe 220 V/10 220 V/10AAprototype prototype test. test. Table Parametersof ofthe the220 220V/10 V/10AAAHSCFCL HSCFCL laboratory prototype. Table HSCFCL laboratory prototype. Table3.3. 3.Parameters Parameters of the 220 V/10 laboratory prototype. Parameter Value Parameter Value Value 2 2 Cross-sectional areaof ofcores coresI Iand andII/m II/m 0.0025 Cross-sectional area 0.0025 2 0.0025 Cross-sectional area of cores and II/m 2 2 Cross-sectional areaIof ofcores cores III/m 0.00325 Cross-sectional area III/m 0.00325 0.00325 Cross-sectional areaarea of cores III/m2section/m Cross-sectional ofsmall small 0.00244 Cross-sectional area of section/m2 2 0.00244 0.00244 Cross-sectional area of small section/m2 Length of cores e/m 0.27 Length of cores l el/m 0.27 Length of cores le /m 0.27 Length of 0.19 Length of small smallsection section b/m 0.19 Length of small section lb /m lbl/m 0.19 2 2 2 PM/m Cross-sectional ofofPM/m 0.005 0.005 Cross-sectional area ofarea PM/m Cross-sectional area 0.005 Length of PM/m 0.01 Length of 0.01 Length ofPM/m PM/m 0.01 DC-biasing current/A 10 DC-biasing current/A 10 DC-biasing current/A 10 Inductance of limiting inductor L0 /mHL0/mH Inductance of limiting inductor 88 8 Inductance of limiting inductor L 0/mH Steel cores Hs = 10 kA/m, Bs = 2.0 T Steel cores Hs = 10 kA/m, Bs =Bs2.0 T T cores = 10 kA/m, 2.0 PermanentSteel magnets HcH=s 836 kA/m, Br ==1.45 T Permanent magnets H c = 836 kA/m,Br = 1.45 T Permanent magnets Hc = 836 kA/m,Br = 1.45 T Parameter

Figure 17 17 shows the experimental limiting performance of the of HSCFCL. Under normal Figure shows the experimental limiting performance the HSCFCL. Under conditions, normal Figure 17 shows the experimental limiting performance of the HSCFCL. Under normal theconditions, current isthe 10 current A. When a fault occurs, the HSCFCL can limitcan thelimit fault effectively. Due to is 10 A. When a fault occurs, the HSCFCL thecurrent fault current effectively. conditions, the current is 10 A. When a fault occurs, the HSCFCL can limit the fault current effectively. theDue influence of the aperiodic component of the fault current, the fault current has a transient decay to the influence of the aperiodic component of the fault current, the fault current has a transient Due to the influence of the aperiodic component of the fault current, the fault current has a transient process. The firstThe peak fault current with thewith HSCFCL can be can limited to about 120 A.120 The decay process. first peak fault current the HSCFCL be limited to about A.fault The current fault decay process. The first peak fault current with the HSCFCL can be limited to about 120 A. The fault is limited tolimited approximately 70 A when it when reaches a steadya state. the DC-biasing current current is to approximately 70 A it reaches steadyAdditionally, state. Additionally, the DC-biasing current isoflimited to approximately 70 conditions A when it reaches steady state. Additionally, the DC-biasing the under HSCFCL underconditions normal 10 A. a However, the DC-biasing 20 A of current the HSCFCL normal is 10 A. is However, the DC-biasing currentcurrent is 20 Aiswithout current of the HSCFCL under normal conditions is 10 A. However, the DC-biasing current is 20 A without PMs. Hence, the DC-biasing capacity can be reduced by 50%. PMs. Hence, the DC-biasing capacity can be reduced by 50%. without PMs. Hence, the DC-biasing capacity can be reduced by 50%. 120 120 90

current If /AIf /A current FaultFault

90

60 60 30

30 0 0 -30 -30 -60 -60 -90

-120 -90

-120 Figure 17. Experimental fault clipping performance of the HSCFCL. Figure 17. Experimental fault clipping performance of the HSCFCL. Figure 17. Experimental fault clipping performance of the HSCFCL.

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Figure 18 18 shows shows the the fault fault current current and and DC-biasing DC-biasing current current when when the the fault fault current current reaches reaches the the Figure steady state. It can be seen that the frequency of the DC-biasing current is 100 HZ. Due to the reluctance steady state. It can be seen that the frequency of the DC-biasing current is 100 HZ. Due to the of the PM, of thethe fault will not only DC-biasing circuit, butcircuit, also the reluctance PM,current the fault current willflow not through only flowthe through the DC-biasing butwindings also the in the unsaturated core. Thecore. DC-biasing current is a littleissmaller thethan faultthe current. Hence, windings in the unsaturated The DC-biasing current a little than smaller fault current. the experimental results validate the effectiveness of the proposed structure. Hence, the experimental results validate the effectiveness of the proposed structure.

240 180

Current I /A

120 60 0 -60

-120 -180

Fault current DC biasing current

-240 Figure Figure 18. 18. Fault Faultcurrent currentand and DC-biasing DC-biasing current current when when the the fault fault current current reaches reaches aa steady steady state. state.

5. 5. Conclusions Conclusions This saturated-core fault-current limiter (HSCFCL), which has has the This paper paperpresents presentsaanovel novelhybrid hybrid saturated-core fault-current limiter (HSCFCL), which advantages of small size, low DC-biasing capacity, high biasing ability of the PM, and excellent the advantages of small size, low DC-biasing capacity, high biasing ability of the PM, and excellent limiting Compared with withtraditional traditionalSCFCLs, SCFCLs,the theDC-biasing DC-biasing capacity can reduced limiting performance. performance. Compared capacity can bebe reduced by by 50% and the biasing ability of the PM can be improved by 31.8% with optimal small-section 50% and the biasing ability of the PM can be improved by 31.8% with optimal small-section structure. structure. The hybrid DC coil/PM structure is proposed for reducing the DC-biasing capacity. As the hybrid DC coil/PM structure is proposed for reducing the DC-biasing capacity. As the MMFThe PM increases, the improvement of the DC MMF will increase. Considering the limiting MMF PM increases, the improvement of the DC MMF will increase. Considering the limiting performance, the improvement of the DC MMF has a maximum value. In addition, according to performance, the improvement of the DC MMF the hasleakage a maximum In addition, to the the biasing ability of the PM when considering effect,value. the leakage effect according will weaken the biasing ability of the PM when considering the leakage effect, the leakage effect will weaken biasing ability of the PM, and the flux-density distribution of the cores is also uneven, resulting inthe an biasing the PM, and the flux-density distribution increaseability in the of usage of the PM and DC-biasing capacity. of the cores is also uneven, resulting in an increase the usage ofoptimal the PMstructure and DC-biasing capacity. Thein small-section can improve the biasing ability of the PM. The cross-sectional The small-section optimal structure can improve theinfluence biasing ability the ofPM. The crossarea and length of the small section have a significant on the of level improvement. sectional area and length of the small section have a significant influence on the level of improvement. Additionally, the cross-sectional area and length of the PM also have an important influence on Additionally, the cross-sectional and and length of the performance. PM also have Compared an important influence on the the improvement of DC-biasing area capacity limiting with an increase in improvement of DC-biasing capacity and limiting performance. Compared with an increase in the the length of the PM, an increase in the cross-sectional area of the PM can yield better performance length of the PM, an increase in the cross-sectional area of the PM can yield better performance and and economy. economy. Acknowledgments: This work was supported in part by the National Natural Science Foundation of China under Grant No. 50807041. This work was supported in part by the National Natural Science Foundation of China Acknowledgments: under No. 50807041. AuthorGrant Contributions: This article has seven authors: Liangliang Wei, Baichao Chen and Jiaxin Yuan conceived and designed the research method; Liangliang Wei, Cuihua Tian, Jiaxin Yuan and Yushun Liu performed the Author Contributions: This article has seven authors: Liangliang Wei, Baichao Chen and Jiaxin Yuan conceived experiments; Liangliang Wei, Yuxin Bu and Tianan Zhu analyzed the data; and Liangliang Wei wrote the paper. and designed the research method; Liangliang Wei, Cuihua Tian, Jiaxin Yuan and Yushun Liu performed the Conflicts of Interest: TheWei, authors declare noTianan conflict of interest. experiments; Liangliang Yuxin Bu and Zhu analyzed the data; and Liangliang Wei wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

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