Insulation_coordination Of_arcing Horns_on_hvdc_electrode_lines_protection_perforance_evaluation_influence_factors_and_improvement_method.pdf

energies Article

Insulation Coordination of Arcing Horns on HVDC Electrode Lines: Protection Performance Evaluation, Influence Factors and Improvement Method Xiandong Li 1,2,3, * 1

2 3

*

ID

, Hua Li 1,2,3, *, Yi Liu 1,2,3 and Fuchang Lin 1,2,3

State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science & Technology, Wuhan 430074, China; [email protected] (Y.L.); [email protected] (F.L.) School of Electrical and Electronic Engineering, Huazhong University of Science & Technology, Wuhan 430074, China Key Laboratory of Pulsed Power Technology (Huazhong University of Science and Technology), Ministry of Education, Wuhan 430074, China Correspondence: [email protected] (X.L.); [email protected] (H.L.)

Received: 19 January 2018; Accepted: 11 February 2018; Published: 13 February 2018

Abstract: Arcing horns are widely used in high voltage overhead lines to protect insulator strings from being destroyed by the free burning arcs caused by lightening faults. In this paper, we focus on the insulation coordination of arcing horns on the electrode lines of a 5000 MW, ±800 kV high voltage direct current (HVDC) system. The protection performance of arcing horns are determined by the characteristics of not only the external system but also the fault arc. Therefore, the behaviors and characteristics of long free burning arcs are investigated by the experiments at first. In order to evaluate the protection performance of arcing horns, the static stability criterion U-I characteristic method is introduced. The influence factors on the protection performance of arcing horns are analyzed theoretically. Finally, the improvement methods for the protection performance of arcing horns are proposed, and the diversified configuration strategy of arcing horns is recommended for cost saving. Keywords: HVDC electrode line; arcing horn; insulation coordination; protection performance; long free burning arc; arc behavior and characteristic

1. Introduction 1.1. Insulation Coordination Problem of Arcing Horns on HVDC Electrode Lines Arcing horns are widely used on high voltage overhead transmission lines to protect insulator strings from being destroyed by the free burning arcs caused by lightening faults. However, it is hard to extinguish arcs in high voltage direct current (HVDC) system, since there is no natural current zero point. Besides, it is difficult to detect fault arcs, especially for HVDC electrode lines, so fault arcs may continue to burn once formed if the fault arc is not detected. As a result, both arcing horns and insulator strings will be destroyed in the end. With the fast growing power transfer and transmission distance of HVDC systems, the insulation coordination problem of HVDC electrode lines is becoming more serious. Therefore, research on the performance of the arcing horns on HVDC electrode lines is very necessary. Electrode lines are used for the current return pass and as the voltage reference point of HVDC system. When the system is operating in bi-polar mode, as shown in Figure 1a, the unbalanced current on the electrode lines can be ignored. Hence, there will be no problem with the extinction of fault arcs. However, when the system is operating in mono-polar mode, as shown in Figure 1b, the operation Energies 2018, 11, 430; doi:10.3390/en11020430

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current on thecurrent electrode lines is rather If alarge. lightning fault happens, the fault arc arc may not be operation on the electrode lineslarge. is rather If a lightning fault happens, the fault may extinguished, then boththen the arcing insulator stringsstrings will be burned and and destroyed. not be extinguished, both thehorns arcingand horns and insulator will be burned destroyed.

(a) HVDC system operated in bi-polar mode

(b) HVDC system operated in mono-polar mode Figure 1. Operation mode of HVDC system.

Figure 1. Operation mode of HVDC system.

1.2. Current Reaserches on Insulation Coordination of Arcing Horns on HVDC Electrode Lines

1.2. Current Reaserches on Insulation Coordination of Arcing Horns on HVDC Electrode Lines

To solve this problem, the characteristics of fault arcs should be investigated firstly, and an optimized coordination scheme should beofstudied characteristics of fault arcs. To solve insulation this problem, the characteristics fault based arcs the should be investigated firstly, the wholeinsulation problem involves two aspects: the should characteristics of fault arcs and the insulation of and Thus, an optimized coordination scheme be studied based the characteristics faultcoordination arcs. Thus,scheme. the whole problem involves two aspects: the characteristics of fault arcs and the fault arcs in scheme. HVDC systems are long free burning arcs. The long free burning arc (>100 mm) insulationThe coordination has quite different properties compared with the short arc (<10 mm) and the arc in closed space The fault arcs in HVDC systems are long free burning arcs. The long free burning arc (>100 mm) because of its complex behavior. The existing studies about long arcs are mainly concerned with its has quite different properties compared with the short arc (<10 mm) and the arc in closed space movement [1–5] and electrical [4–11] characteristics. because of behavior. The existing studies mainly with its Asits forcomplex the insulation coordination scheme, some about studieslong havearcs beenare carried outconcerned [12–14]. Those movement [1–5] electrical [4–11] characteristics. works can be and classified by their methods into two kinds: the maximum arc extinction current method As the for U-I thecharacteristic insulation method. coordination scheme, some studies have been carried out [12–14]. and Those works can [12] be classified bystudies their methods into two the maximum current Canellas carried out on the extinction of kinds: direct current (DC) arcsarc on extinction long electrode lines based on the experimental results of the Itaipu group, and gave the relations between the method and the U-I characteristic method. maximum arc carried extinction the extinction gap lengthofofdirect arcingcurrent horns. (DC) However, thelong maximum arclines Canellas [12] outcurrent studiesand on the arcs on electrode extinction current is only few hundreds (≤400group, A) andand the gave maximum gap length is less the thanmaximum 500 mm, arc based on the experimental results of the Itaipu the relations between which current are not suitable the HVDC with large operation usedarc today. extinction and thefor gap length ofsystems arcing horns. However, thecurrents maximum extinction current is Jankov [13] discussed about the protection performance of arcing horns on the HVDC system only few hundreds (≤400 A) and the maximum gap length is less than 500 mm, which are not suitable with neutral conductor. The static stability criterion Voltage-Current characteristic method (or U-I for the HVDC systems with large operation currents used today. characteristic method as usually called) was adopted to find the maximum protection region of arc JankovIn[13] aboutthe theprotection protection performance of arcing on the HVDClines system horns. our discussed previous works. performance of arcing hornshorns in HVDC electrode withwas neutral conductor. The static stability criterion Voltage-Current characteristic method (or U-I investigated also based on the U-I characteristic method, and the influence factors were analyzed characteristic method as usuallythe called) was adopted to find maximum region of arc preliminarily [14]. Although, U-I characteristic method hasthe been proved toprotection be an effective way horns. previous works. theofprotection performance of arcing horns in HVDC electrode lines forIn theour insulation coordination arcing horns by [13,14], none of them provided a comprehensive study on the influence factors andU-I the characteristic protection performance strategy for arcing was investigated also based on the method,improvement and the influence factors werehorns. analyzed

preliminarily [14]. Although, the U-I characteristic method has been proved to be an effective way for the insulation coordination of arcing horns by [13,14], none of them provided a comprehensive study on the influence factors and the protection performance improvement strategy for arcing horns.

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Energies 11, x FOR REVIEW coordination of arcing horns on the electrode lines of a 35000 of 19 MW, In this2018, paper, thePEER insulation ±800 kV HVDC system is studied. The U-I characteristic method is used to evaluate the protection In this paper, the insulation coordination of arcing horns on the electrode lines of a 5000 MW, performance of arcing horns. Since the protection performance of arcing horns is decided by the ±800 kV HVDC system is studied. The U-I characteristic method is used to evaluate the protection characteristics of not only electrode line system but also the fault arc, experiments have been carried performance of arcing horns. Since the protection performance of arcing horns is decided by the out to investigate of thenot characteristics long freebut burning influencing thecarried protection characteristics only electrodeof line system also thearcs. faultThe arc, factors experiments have been performance of arcing are analyzed Finally, the improvement for the out to investigate thehorns characteristics of longtheoretically. free burning arcs. The factors influencing thestrategy protection protection performance of arcing horns is proposed based on the theoretical analysis. performance of arcing horns are analyzed theoretically. Finally, the improvement strategy for the

protection performance of arcing horns is proposed based on the theoretical analysis.

1.3. Static Stability Criterion of Fault Arc on HVDC System (U-I Characteristic Method) 1.3. Static Stability Criterion of Fault Arc on HVDC System (U-I Characteristic Method)

U-I characteristic method [13,14] can be used as the static stability criterion for the fault arc on U-I characteristic method [13,14]2,can used as the static stability for thestate fault U arc HVDC system. As shown in Figure thebeU-I characteristic of faultcriterion arc in static (I) has arcon HVDC system. As shown in Figure 2, the U-I characteristic of fault arc in static state U arc (I) has a a negative power function form [11], on the other hand, the U-I characteristic of external DC system negative power function form [11], on the other hand, the U-I characteristic of external DC system Uex (I) system has a linear function form. Usually, the U-I characteristic of external system is varied Uex (I) system has a linear function form. Usually, the U-I characteristic of external system is varied with the fault location. Therefore, the possible number of cross point would be zero, one (P) or two (P1 , with the fault location. Therefore, the possible number of cross point would be zero, one (P) or two P2 ) depending on the fault location. The cross points can be regarded as the solutions of state equation (P1, P2) depending on the fault location. The cross points can be regarded as the solutions of state Uarc (I) = U (I), forstands the possible burning state for the arc. arc. ex Uarc which equation (I) = Uexactually (I), whichstands actually for the possible burning state forfault the fault

Figure 2. U-I characteristic method for investigating static stability of fault arc.

Figure 2. U-I characteristic method for investigating static stability of fault arc.

If there is no cross point, which means the arc would go into the extinction state. In this situation, the U-I characteristic of the fault arcmeans is higher U-I characteristic of the external system, sosituation, the If there is no cross point, which thethan arc the would go into the extinction state. In this external system cannot sufficient energy to keep the fault arc burning. The areasystem, which isso the the U-I characteristic of theprovide fault arc is higher than the U-I characteristic of the external lower than the U-I characteristic of fault energy arc is called the protected zone. external system cannot provide sufficient to keep the fault arc burning. The area which is lower If there is any cross point, it means the arc would keep burning in some state. In this situation, than the U-I characteristic of fault arc is called the protected zone. the U-I characteristic of fault arc is lower than the U-I characteristic of the external system, so the If there is any cross point, it means the arc would keep burning in some state. In this situation, external system can provide sufficient energy to keep the fault arc burning. The area which is higher the U-I of faultofarc lower thanthe the U-I characteristic of the external system, so the thancharacteristic the U-I characteristic faultisarc is called unprotected zone external system can provide sufficient energy to keep the fault arc burning. TheParea which is higher It should be mentioned that only P1 is a stable burning point (state), while, 2 is an unstable than burning the U-I characteristic faultany arcdisturbance is called thewill unprotected zone from P2 and a transit to P1 point (state) in of which lead to a deviation eventually. Thementioned critical burning occurs P2 and P1 are overlapped at P. In fact, the It should be thatstate only P1 iswhen a stable burning point (state), while, P2 maximum is an unstable protection is in determined by disturbance the U-I characteristic of the external P is to P1 burning point zone (state) which any will leadcurve to a deviation fromsystem P2 andwhere a transit located. Hence the maximum protection region is the fault location where the critical burning state eventually. The critical burning state occurs when P2 and P1 are overlapped at P. In fact, the maximum happens, andiscan be used toby evaluate protection performance of external arcing horns. protection zone determined the U-Ithe characteristic curve of the system where P is located.

Hence the maximum protection region is the fault location where the critical burning state happens, 2. Experimental Settings and can be used to evaluate the protection performance of arcing horns.

Figure 3 shows the diagram of our experimental system. A cascade circuit pulse-wave generator (total equivalent capacitance Ceq = 18 mF) is chosen as the power source whose maximum pulse width 2. Experimental Settings is 70 ms and peak current is 2500 A. Two steel arcing horns are used as electrodes of which the Figure 3 shows the diagram of our system. cascade pulse-wave discharge gap length Lgap is from 400experimental mm to 1500 mm, and Athe arcing circuit horns are installed generator both (totalvertically equivalent Ceq 18 mF) is chosen asarc theispower whose and capacitance horizontally in the=experiments. The fault ignited source by a ϕ 0.05 mmmaximum cooper wirepulse

width is 70 ms and peak current is 2500 A. Two steel arcing horns are used as electrodes of which the discharge gap length Lgap is from 400 mm to 1500 mm, and the arcing horns are installed both

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vertically and2018, horizontally the experiments. The fault arc is ignited by a ϕ 0.05 mm cooper wire Energies 11, x FOR PEERin REVIEW 4 of 19 connected to the edge of arcing horns. A 500 MHz oscilloscope (TDS3052C, Tektronix, Beaverton, OR, connected to the edge of arcing horns. A 500 MHz oscilloscope (TDS3052C, Tektronix, Beaverton, USA) and a high-speed camera (FASTCAM SA5, Motion Engineering Company, Chicago, IL,OR, USA) are Energies 2018, 11,ax high-speed FOR PEER REVIEW 4 of 19 USA) and camera (FASTCAM SA5, Motion Engineering Company, Chicago, IL, USA) applied to record the voltage, current and development process of fault arc, respectively.

14mH

1.5Ω 5.4mF 7.2mF

3.5mH

3.5mH 3.5mH 3.5mH 3.5mH

7.2mF

14mH 3.5mH

are applied to record the voltage, current and development process of fault arc, respectively. connected to the edge of arcing horns. A 500 MHz oscilloscope (TDS3052C, Tektronix, Beaverton, OR, USA) and a high-speed camera (FASTCAM SA5, Motion Engineering Company, Chicago, IL, USA) are applied to record the voltage, current and development process of fault arc, respectively. Voltage 1.5Ω Switch Probe

Arcing Horns (vertical)

Voltage Probe

Switch Fuse Arcing Horns wire (vertical)

3.6mF 5.4mF

High-speed Camera

Fuse wire

1.8mF 3.6mF

High-speed Camera Current Probe

Pulse-wave Generator 1.8mF

Support

Figure 3. Diagram of experimental system.

Figure 3. Diagram of experimental system. Current

Support

Pulse-wave Generator In the experiment, the capacitors are charged firstly to the voltage U0 = 6000 V, and the total Probe energy stored in capacitors is 0.324 MJ. Then, the switch is the energies capacitors In the experiment, the capacitors charged firstly closed tosystem. theand voltage U0 = in 6000 V, andare the total Figure 3. are Diagram of experimental released to ignite the cooper wire. The arc will be formed and burns in open air freely until the energy energy stored in capacitors is 0.324 MJ. Then, the switch is closed and the energies in capacitors are runs out. In ignite the experiment, thewire. capacitors arewill charged firstly to theburns voltage 0 = 6000 V, and the total released to the cooper The arc be formed and in U open air freely until the energy energy stored in capacitors is 0.324 MJ. Then, the switch is closed and the energies in capacitors are runs out.3. Behaviors and Characteristics of Long Free Burning Arc released to ignite the cooper wire. The arc will be formed and burns in open air freely until the energy runs out. 3.1. Behaviors of Long Free Burning Arc Free Burning Arc 3. Behaviors and Characteristics of Long

3. Behaviors andWaveforms Characteristics of Long Free Burning Arc 3.1.1. Typical 3.1. Behaviors of Long Free Burning Arc The typical and voltage 3.1. Behaviors of Longcurrent Free Burning Arc waveforms of a long free burning arc are shown in Figure 4. The

3.1.1. Typical Waveforms waveform of the arc current pulse is stable, which is caused by the smoothing effect of the circuit

inductance on the arc current. However, the waveform of the arc voltage is unstable with many

3.1.1.typical Typical Waveforms The current and voltage waveforms of a long free burning arc are shown in Figure 4. vibrations, which is caused by the instability of the long free burning arc. In the later Section 3.1.3, it The waveform of the arc pulse is stable, which isfree caused byrelated theare smoothing effect of the circuit typical current and voltage of a long burning arc in Figure 4. The isThe indicated that thecurrent instability of waveforms long free burning arc is closely toshown the local short circuit waveform thearc arccurrent. current pulse is noticed stable, which caused thearc smoothing of arc thevoltage circuit inductance on of the However, the waveform ofbythe voltage is unstable with many process of arc column. It should be that theisspike (0–0.1 ms) in the waveeffect front of inductance on arc current. the waveform of the arc voltage is the unstable many is caused byisthe the ignition of the fuse vibrations, which caused byprocess theHowever, instability ofwire. the long free burning arc. In later with Section 3.1.3, it is vibrations, which is causedofbylong the instability of the long free burning arc.to Inthe the local later Section 3.1.3, itprocess indicated that the instability free burning arc is closely related short circuit 3000 of long free burning arc is closely related3000 is indicated that the instability to the local short circuit of arc column. It should be noticed that the spike (0–0.1 ms) in the wave front of arc voltage is caused process of arc column. It should be noticed that the spike (0–0.1 ms) in the wave front of arc voltage by the ignition process of the fuse wire. is caused by the ignition process of the fuse wire. 2000

2000

1000

Voltage

Current (A)

2000

1000

2000 Current

0

1000 0

20

40

60

Voltage 80

0

1000

Voltage (V)

3000

Voltage (V)

Current (A)

3000

Time (ms)

Current

0 Figure 4.0 Typical current and voltage waveforms of a free burning arc. 0

20

40

60

80

Time (ms)

Figure 4. Typical current and voltage waveforms of a free burning arc.

Figure 4. Typical current and voltage waveforms of a free burning arc.

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3.1.2. Development Process of a Long Free Burning Arc Energies 11, x FOR PEER REVIEW 5 of 19 gap Figure2018, 5 shows the development process of a long free burning arc of which the discharge Energies 2018, 11, x FOR PEER REVIEW 5 of 19 length Lgap = 1000 mm. Figure 6 shows the variation of arc length with time. The whole development 3.1.2.of Development Processof ofaaLong Long Free Burning Arc process long free burning arc can be divided into four phases based on the shape of arc column, 3.1.2. Development Process Free Burning Arc Figure 5 shows the development process of a long free burning arcofofwhich whichthe thedischarge dischargegap gap the motion of arc and the expansion of arc (the variation of burning arc length): Figure 5 shows the development process of a long free arc

lengthLLgapgap==1000 1000mm. mm.Figure Figure66shows showsthe thevariation variationofofarc arclength lengthwith withtime. time.The Thewhole wholedevelopment development length

Phase I (0.1–3 ms):free Thisburning phase arc is called the slowinto expansion phase. The arc motion gentle, the arc process long canbe bedivided divided fourphases phases based onthe theshape shapeofofis arc column, process ofoflong free burning arc can into four based on arc column, expansion speed is slow and the arc column is stable with a clear shape. the motion of arc and the expansion of arc (the variation of arc length): the motion of arc and the expansion of arc (the variation of arc length): Phase II Phase (3–32 ms): This is called the fast expansion phase. The arcarc motion violent, the arc (0.1–3 ms):phase Thisphase phase called theslow slow expansion phase. The motionis gentle,the the Phase I I(0.1–3 ms): This isiscalled the expansion phase. The arc motion isisgentle, expansion speed is fast, and the arc column is relative stable. It can be seen that there are blurs around arcexpansion expansionspeed speedisisslow slowand andthe thearc arccolumn columnisisstable stablewith withaaclear clearshape. shape. arc the arc column making theThis shape of arc column unclear. The blurs areThe conductive, willthe induce Phase II (3–32 ms): phase is called the fast expansion phase. arcmotion motionwhich violent, Phase II (3–32 ms): This phase is called the fast expansion phase. The arc isisviolent, the arcexpansion expansion speed fast,and and thearc arccolumn columnisisrelative relativestable. stable.ItItcan canbe beseen seenthat thatthere thereare areblurs blurs the arc local short circuit processes ofthe arc columns. speed isisfast, around the arc column making the shape of arc column unclear. The blurs are conductive, which willmore Phase III (32–60 ms): This phase is called the violent motion phase. The arc motion becomes around the arc column making the shape of arc column unclear. The blurs are conductive, which will induce the local short circuit processes of arc columns. violent, however, arccircuit expansion slows down. The blurs around the arc column are diffused which induce the localthe short processes of arc columns. PhaseIII III(32–60 (32–60ms): ms):This Thisphase phaseisiscalled calledthe theviolent violentmotion motionphase. phase.The Thearc arcmotion motionbecomes becomesmore more Phase leads frequent local short circuit processes making the arc column unstable and without a clear shape. violent, however, the arc expansion slows down. The blurs around the arc column are diffused which violent, however, the arc expansion slows down. The blurs around the arc column are diffused which Phase IV (60–70 ms): This phase is called the extinction phase, in which both the arc motion and leadsfrequent frequentlocal localshort shortcircuit circuitprocesses processesmaking makingthe thearc arccolumn columnunstable unstableand andwithout withoutaaclear clearshape. shape. leads expansion cease, thems): arcThis is quenched to itsthe final extinction. Phase IV and (60–70 phase is called extinction phase, in which both the arc motion and

Phase IV (60–70 ms): This phase is called the extinction phase, in which both the arc motion and expansioncease, cease,and andthe thearc arcisisquenched quenchedtotoits itsfinal finalextinction. extinction. expansion It should be mentioned that the initial phase for the case of overvoltage breakdown is different should beof mentioned that theinitial initial phase forthe the caseofofovervoltage overvoltage breakdown different gap to that of the case fuse wire ignition. Inphase the case of case overvoltage breakdown, theisis discharge ItItshould be mentioned that the for breakdown different to that of the case of fuse wire ignition. In the case of overvoltage breakdown, the discharge gap is bridged streamer before the initial Since breakdown, the streamer hasgap a relative to that ofby thethe case of fuse wire ignition. In thearc caseformed. of overvoltage theusually discharge isis bridged by the streamer before the initial arc formed. Since the streamer usually has a relative curved bridged by the the streamer has a the relative curved curved shape, thestreamer shape ofbefore initialthe arcinitial may arc notformed. be verySince straight. On the usually other hand, huge amount of shape,the theshape shapeofofinitial initialarc arcmay maynot not bevery verystraight. straight.On Onthe the otherhand, hand,the thehuge hugeamount amountofof shape, molecules of the fuse wire guarantee the be high conductivity of theother arc column, and ambient air is not moleculesofofthe thefuse fusewire wireguarantee guaranteethe thehigh highconductivity conductivityofofthe thearc arccolumn, column,and andambient ambientair airisisnot not molecules warm enough to cause strong turbulence at the beginning. As a result, the arc column during phase warm enough to cause strong turbulence at the beginning. As a result, the arc column during phase enough to cause strong turbulence atand the beginning. As a result,the the following arc columnprocess during phase I forwarm the case of fuse wire ignition clear straight. However, should forthe thecase case fuse wire ignitionis clearand andstraight. straight.However, However, thefollowing followingprocess processshould should be be I Ifor ofoffuse wire ignition isisclear the be similar for the two cases. similarfor forthe thetwo twocases. cases. similar

5 ms 5 ms

15 ms 15 ms

32 ms 32 ms

45 ms 45 ms

60 ms 60 ms

Figure 5. Developmentprocess processof of long long free burning arc (L(L gap = 1000 mm). Figure 5. 5.Development freeburning burning = 1000 Figure Development process of long free arcarc (Lgap =gap 1000 mm).mm). 2000 2000

II

1750 1750

IIII

III III

3000 3000 2500 2500 2000 2000

1500 1500

1500 1500

1250 1250

1000 1000

1000 1000 Local short-circuit processes Local short-circuit processes

750 750 500 500

IV IV

Arc voltage (V) Arc voltage (V)

Arc length (mm) Arc length (mm)

0 ms 0 ms

0

0

10 10

20 20

30 40 30 40 Time (ms) Time (ms)

50 50

500 500

0 Arc length 0 Arc length Arc voltage Arc voltage -500 60 70 -500 60 70

Figure 6. Variation of arclength lengthand and voltage voltage with time (L(L gap = 1000 mm). Figure 6.6.Variation with time = 1000 Figure Variationof ofarc arc length and voltage with time (Lgap =gap 1000 mm).mm).

70 ms 70 ms

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According to the experimental results, the arc elongates rapidly at first, and then fluctuates around a stable length Lst much longer than the discharge gap length Lgp . Table 1 presents the average stable arc length for the arcing horns at vertical and horizontal configurations, at least 10 experiments have been carried out for each condition. Energies 2018, 11, x FOR PEER REVIEW

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Table 1. Average stable arc length of arcing horns at different configurations. According to the experimental results, the arc elongates rapidly at first, and then fluctuates around a stable length Lst much longer than the discharge gap length Lgp. Table 1 presents the average Average Stable Arc Length (mm) Gap (mm) stable arc length for theDistance arcing horns at vertical and horizontal configurations, at least 10 experiments Vertical Gap Horizontal Gap have been carried out for each condition.

450 600 1000 Gap Distance (mm) 1500

1083 1142 1313 1384 1762 1705 Average Stable Arc Length (mm) Vertical Gap Horizontal Gap 2454 2512

Table 1. Average stable arc length of arcing horns at different configurations.

450 1083 1142 600 1313 1384 Overall, the average stable arc1000 length increases with the discharge gap length, but the elongation 1762 1705 2454 2512 the elongation rate of vertical and αL = Lst /Lgp decreases from 2.41500 to 1.6. The difference between

rate horizontal gaps is not significant, and the result is similar to [5]. In [5], it is thought that magnetic force Overall, the average stable arc length increases with the discharge gap length, but the elongation is the dominating force at high current level therefore the influence of thermal buoyancy force can be rate αL = Lst/L gp decreases from 2.4 to 1.6. The difference between the elongation rate of vertical and ignored. horizontal However,gaps theisthermal turbulence canresult increase the instability arc andthat contribute not significant, and the is similar to [5]. In [5],ofit an is thought magneticto the arc force is usually the dominating at higharc current levelso therefore the influence thermal force motion which meansforce a longer length, the explanation ofof[5] is notbuoyancy very comprehensive. be ignored. it However, the thermal turbulence can increase the instability an arc and contribute In a latercan subsection, is indicated that the insignificant difference of arcoflength between the vertical to the arc motion which usually means a longer arc length, so the explanation of [5] is not very and horizontal gaps may be due to local short circuit processes. comprehensive. In a later subsection, it is indicated that the insignificant difference of arc length between the vertical and horizontal gaps may be due to local short circuit processes.

3.1.3. Instability of Long Free Burning Arc

Instability of Long Free Burning Arc The3.1.3. important characteristic of a long free burning arc is the strong instability of arc column. The important characteristic of a long free burninginstability arc is the strong of arc column. The instability of the arc column is composed of macro and instability micro instability. TheThe arc burning instability of the arc column is composed of macro instability and micro instability. The arc burning in open air without a confined container remains in motion and violent expansion, so the macro shape in open air without a confined container remains in motion and violent expansion, so the macro shape of the arcofvaries with time showing instability. On the other hand, the micro instability is related to the the arc varies with time showing instability. On the other hand, the micro instability is related to local short process, as shown in Figure 7. 7. the circuit local short circuit process, as shown in Figure Channel

A

B

B

A

Blur

B

A

A

B

(a)

A

A

B

A

B

A

B

B

(b) Figure 7. Local short circuit process of arc column: (a) high speed images of local short circuit process;

Figure 7.(b)Local short circuit process of arc column: (a) high speed images of local short circuit process; mechanism diagram of local short circuit process. (b) mechanism diagram of local short circuit process. For the short arc and arcs in a closed space, there is usually one continuous column channel. theand long arcs free burning arc, thespace, arc column notusually continuous rather segmented and channel. ForHowever, the shortforarc in a closed thereis is onebutcontinuous column composed of short channels and blurs. The blurs can be regarded as the products of cooled channel However, for the long free burning arc, the arc column is not continuous but rather segmented and segments. Hence the conductivity of blurs should be lower than that of the channel. The self-magnetic composed of short pressure channels blurs. The blurs can be regarded as the products of cooled channel compression Psmand of arc column equals:  segments. Hence the conductivity of blurs should be lower than that of the channel. The self-magnetic Psm = J × B (1) compression pressure Psm of arc column equals: →

→

Psm = J × B

(1)

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where, J is the local current density, and B is the local magnetic field. Since the conductivity of blurs where, J is the local current density, and B is the local magnetic field. Since the conductivity of blurs is is lower, the local current density of blurs is lower as well. As a result, the self-magnetic compression lower, the local current density of blurs is lower as well. As a result, the self-magnetic compression pressure of blur is weak, and the shape of blurs is divergent. For the long curved channel segment A pressure of blur is weak, and the shape of blurs is divergent. For the long curved channel segment A (as shown in Figure 7b), the voltage drop on channel segment A is large, and the distance between (as shown in Figure 7b), the voltage drop on channel segment A is large, and the distance between the two terminals is short. Considering that channel segment A is surrounded by the conductive blurs, the two terminals is short. Considering that channel segment A is surrounded by the conductive there is possibility to form a new short pass channel segment B between the two terminals. Once the blurs, there is possibility to form a new short pass channel segment B between the two terminals. new short channel segment B is formed, the new short channel segment B will keep growing Once the new short channel segment B is formed, the new short channel segment B will keep growing meanwhile the old long channel segment A will be quenched afterwards forming new blurs. The meanwhile the old long channel segment A will be quenched afterwards forming new blurs. The whole whole process is called the local short circuit process. process is called the local short circuit process. The length as well as the resistance of the new channel segment is smaller than that of the old The length as well as the resistance of the new channel segment is smaller than that of the old one. one. Thus a sudden drop arc voltage will be observed, as shown in Figure 6. Besides, there can be Thus a sudden drop arc voltage will be observed, as shown in Figure 6. Besides, there can be more more than one channel segment during the local short circuit process, and the equivalent parallel than one channel segment during the local short circuit process, and the equivalent parallel resistance resistance of channel segments is smaller than single channel segments which will cause a sudden of channel segments is smaller than single channel segments which will cause a sudden drop of arc drop of arc voltage as well. voltage as well. As the blur area is expanded and diffused, the local short circuit process becomes more frequent, As the blur area is expanded and diffused, the local short circuit process becomes more frequent, enhancing the instability of the arc column. Although the local short circuit process can contribute to enhancing the instability of the arc column. Although the local short circuit process can contribute to the arc motion, it can shorten the arc length. That is the reason why the arc motion is violent but the the arc motion, it can shorten the arc length. That is the reason why the arc motion is violent but the arc length remains unchanged in Phase III. arc length remains unchanged in Phase III. A similar explanation can be used for the insignificant difference of arc length between vertical A similar explanation can be used for the insignificant difference of arc length between vertical and horizontal gaps. Although the thermal turbulence can make the arc motion more violent which and horizontal gaps. Although the thermal turbulence can make the arc motion more violent which usually means a longer arc length, however, the more frequent local short circuit processes can usually means a longer arc length, however, the more frequent local short circuit processes can shorten shorten the arc length. Consequently, the difference of arc length between vertical and horizontal the arc length. Consequently, the difference of arc length between vertical and horizontal arcing gaps arcing gaps may not be that significant as expected. Besides, the pulse duration in ours experiments may not be that significant as expected. Besides, the pulse duration in ours experiments is limited, is limited, the difference of arc length between vertical and horizontal gaps can be more significant the difference of arc length between vertical and horizontal gaps can be more significant at a longer at a longer pulse duration. pulse duration. 3.2. Electric Characteristic of Long Free Burning Arcs 3.2. Electric Characteristic of Long Free Burning Arcs 3.2.1. U-I Characteristic Long Free Burning Arc 3.2.1. U-I Characteristic of of Long Free Burning Arc The variation characteristic long free burning with time is shown in Figure The variation of of U-IU-I characteristic of of long free burning arcarc with time is shown in Figure 8. 8. 2000

Arc formation

0.1-5 ms 5-32 ms 32-60 ms >60 ms

Voltage (V)

1500

1000 Arc extinction

500

0

Local short-circuit processes

0

500

1000

1500

2000

2500

Current (A)

Figure Variation characteristic long free burning with time. Figure 8. 8. Variation of of U-IU-I characteristic of of long free burning arcarc with time.

The U-I characteristic can also be divided into four phases based on the arc development process: The U-I characteristic can also be divided into four phases based on the arc development process: Phase I (0.1–3 ms): In this phase, the arc current Iarc rises but the arc voltage Uarc falls off quickly. Phase I (0.1–3 ms): In this phase, arc current Iarc obeys rises but the arc power voltagefunction Uarc falls off quickly. The U-I characteristic curve Uarc(Ithe arc) approximately a negative law. The U-IPhase characteristic curveInUthis obeys a negative power function law. II (3–32 ms): the arc current remains at a high level, and on the other hand, arc (Iphase, arc ) approximately the arc voltage shows a slight uptrend with vibrations caused by the local short circuit processes.

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Phase II (3–32 ms): In this phase, the arc current remains at a high level, and on the other hand, the arc voltage shows a slight uptrend with vibrations caused by the local short circuit processes. Phase III (32–60 ms): In this phase, the arc current decreases continuously, the arc voltage vibrations Energies 2018, 11, x FOR PEER REVIEW 8 of 19 are more violent and frequent, which implies frequent local short circuit processes. Phase IV Phase (60–70IIIms): In this arc goes intocurrent the extinction state, and both the (32–60 ms):phase, In thisthe phase, the arc decreases continuously, the arc arc current voltage and vibrations are more violent and frequent, which implies frequent local short circuit processes. voltage are decreasing. Phase IV (60–70 ms): In this phase, the arc goes into the extinction state, and both the arc current

3.2.2.and E-Ivoltage Characteristic of Long Free Burning Arc are decreasing. The majority of arc voltage drops on the arc column for the free burning arc. Therefore, the voltage 3.2.2. E-I Characteristic of Long Free Burning Arc drop on the arc roots can be neglected. Then the electric field of arc column Earc equals: The majority of arc voltage drops on the arc column for the free burning arc. Therefore, the voltage drop on the arc roots can be neglected. ThenUthe arc electric field of arc column Earc equals:

Earc =

Earc =

L arc U arc

(2)

(2)

Larc length at the measured moment respectively. where Uarc (V) is the arc voltage and Larc (mm) is arc It was found that relation between electric field of arcatcolumn Earc (V/mm) the arc current (V)the is the arc voltage and the Larc (mm) is arc length the measured momentand respectively. It where Uarc Iarc (A) can be expressed in the following form [11]: was found that the relation between the electric field of arc column Earc (V/mm) and the arc current

Iarc (A) can be expressed in the following form [11]:

−n Earc = a + bI−arc n

Earc = a + bI arc

(3)

(3)

where, a, b and n are both positive constant resultsofof[6] [6]indicated indicated that = 0.95 V/mm, where, a, b and n are both positive constantcoefficients. coefficients. The The results that a = a0.95 V/mm, b = 5band n = n1 =for long airair gap. dataare arefitted fitted Equation assuming = 5 and 1 for long gap.Here, Here,the theexperimental experimental data byby Equation (3) (3) assuming n = 1,n = 1, andfitted the fitted results = 0.87 V/mm,bb== 5.77. Figure the variation of arc column electric and the results are are a =a0.87 V/mm, Figure99presents presents the variation of arc column electric field with the arc current (E-I characteristic). In [6], the arc elongation was not considered so their field with the arc current (E-I characteristic). In the arc elongation was not considered so their calculated electric field arc /L gp should be higher than thethe actual electric field field Earc = E Uarc arc/L . arc /Larc . calculated electric field EarcEarc = =UU /L should be higher than actual electric =arcU arc gp 1.6

Electric field (V/mm)

1.2

−1

U=0.95+5I

0.8

U=0.86+5.77I 0.4

0.0

−1

Experimental data Fitted result Ref.[6] 0

500

1000

1500

2000

2500

Current (A)

Figure 9. 9.E-I of long longfree freeburning burning arc. Figure E-Icharacteristic characteristic of arc.

4. Insulation Coordination ArcingHorns Hornson on HVDC HVDC Electrode 4. Insulation Coordination ofof Arcing ElectrodeLines Lines 4.1. Characteristic U-I Characteristic of HVDC ElectrodeLines Linesand and Fault Fault Arc 4.1. U-I of HVDC Electrode Arc U-I Characteristic HVDC ElectrodeLines Lines 4.1.1.4.1.1. U-I Characteristic of of HVDC Electrode power transfer ±800kV kVHVDC HVDC system system is bi-polar mode) andand its operating The The power transfer of aof±a 800 is5000 5000MW MW(at(at bi-polar mode) its operating current I dc is 3150 A. The lengths of electrode lines on each side is 100 km. The electrode lines are current Idc is 3150 A. The lengths of electrode lines on each side is 100 km. The electrode lines are double circuit transmission lines, and the resistance of each electrode line Rl is 4.885 Ω. The resistance double circuit transmission lines, and the resistance of each electrode line Rl is 4.885 Ω. The resistance of electrode Re is 0.5 Ω, and the tower footing resistance Rt is 15 Ω. of electrode Re is 0.5 Ω, and the tower footing resistance Rt is 15 Ω. Figure 10 shows the equivalent circuit of a grounding fault on the electrode lines operated in Figure 10 shows the equivalent circuitfault of aongrounding fault thenot electrode operated in mono-polar mode. Usually the grounding the electrode lineson does influencelines the operation mono-polar mode. Usually the grounding fault on the electrode lines does not influence the current and only the static stability of system is of concern, hence the station can be regarded asoperation a DC current source.

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current and only the static stability of system is of concern, hence the station can be regarded as a DC Energies 2018, 11, x FOR PEER REVIEW 9 of 19 current source. Rl kRl

(1-k)Rl + _

Igp Ugp

Re

Idc

Rt

Figure 10. Equivalent circuit of single line grounding fault on electrode line system.

Figure 10. Equivalent circuit of single line grounding fault on electrode line system. Here, k represents for the relative fault location:

Here, k represents for the relative fault location: k=

Df

(4)

Ds D f k= Dselectrode, Ds is the distance from the station to where Df is the distance from the fault location to the

(4)

the electrode as well as the length of electrode line. The fault location lie between the electrode and

wherethe Df station, is the distance from the fault location to the electrode, D is the distance from the station to so the value of k should limit in the range from 0 to 1. s the electrode as well to asKirchhoff’s the lengthlaw, of electrode line. The fault location lie between electrode According the U-I characteristic of external system Ugp(Igp) isthe expressed as: and the station, so the value of k should limit in the range from 0 to 1.   1 − cn 2 k According to Kirchhoff’s U gplaw, = ( Rthe + U-I Rl )characteristic ⋅ I dc −  Re + Rt + (of external k + k ) ⋅system Rl  ⋅ I gp Ugp (Igp ) is expressed (5) as: e cn

cn





 k 12−forcnthis 2 case). Equation (5) is a linear where cn is theUconductor number of electrode lines (c n = Rl ) · Idc − Re + Rt + ( k + k) · Rl · Igp gp = ( Re + cn as: cn function which can be simplified 

(5)

U gp = lines A − B ⋅(c I gp = 2 for this case). Equation (5) is(6)a linear where cn is the conductor number of electrode n function which can be simplified as: Here, the coefficients A and B stand for: Ugp = A − B · Igp (6)

A ≡ ( Re +

Here, the coefficients A and B stand for:

k R )⋅ I cn l dc

(7)

  1 −kcn 2 + R +( B ≡A R≡ ) ⋅ Rl  Rkl ) +· Ikdc e ( Rt e + c cnn  

1 − cn 2 k + k ) · Rl B≡ 4.1.2. U-I Characteristic of Fault Arc Re + Rt + ( cn 

(7)

(8)

 (8)

From Equations (2) and (3), the U-I Characteristic of Fault arc Uarc(Iarc) is expressed as:

4.1.2. U-I Characteristic of Fault Arc U =aL

+

bLarc

arc arc Iof From Equations (2) and (3), the U-I Characteristic arc Fault arc Uarc (Iarc ) is expressed as:

(9)

where a = 0.87 and b = 5.77. Equation (9) is a negative power bL function which can be simplified as: arc

Uarc = aL arc +

D Iarc Uarc =C + I arc

(9)

(10)

where a = 0.87 and b = 5.77. Equation (9) is a negative power function which can be simplified as: Here, the coefficients C and D stand for:

Uarc C=≡CaL+arc Here, the coefficients C and D stand for:

D Iarc

D ≡ bLarc

(11)

(10)

(12)

It is supposed that the arc on the arcing horns will elongate from the discharge gap length Lgp to the final stable arc length Lst which is much larger than C ≡ aL arc initial arc length. The stable arc length Lst is

(11)

D ≡ bL arc

(12)

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It is supposed that the arc on the arcing horns will elongate from the discharge gap length Lgp to the final stable arc length Lst which is much larger than initial arc length. The stable arc length Lst is taken as the arc length for calculation, the arcing horns with gap lengths of 450, 600, 1000, 1500 mm correspond to the final stable arc lengths Lst of 1100, 1350, 1700, 2500 mm, respectively. 4.2. Protection Region of Arcing Horns 4.2.1. Solutions of State Equation There is only one solution point for the critical burning state. It is assumed that the current of critical burning state is Icr and the correlated relative fault location is kcr . Combine Equations (6) and (10) and let Ugp = Uarc , Igp = Iarc = Icr , it yields the state equation: A − BIcr = C +

D Icr

(13)

Then rewrite Equation (13) in the form of quadratic equation: 2 BIcr + (C − A) Icr + D = 0

(14)

Hence the general solutions of Equation (14) are: Icr =

  q 1 A − C ± ( A − C )2 − 4BD 2B

(15)

Considering that there is only solution of Icr for the critical burning state, thus:

( A − C )2 − 4BD = 0 Icr =

A−C 2B

(16) (17)

Noticing that A and B are functions of kcr , the full expression of Equation (16) as a function of kcr is deduced as: 

( Re +

k cr R ) · Idc − aL arc cn l

2

  1 − cn 2 − 4bL arc · Re + Rt + ( k cr + k cr ) · Rl = 0 cn

(18)

Then rewrite Equation (18) in the form of quadratic equation: A0 k2cr + B0 k cr + C 0 = 0

(19)

where, A0 , B0 and C0 stands for:

( Rl Idc )2 − 4cn · (1 − cn ) · bL arc Rl c2n

(20)

2Rl Idc · ( Re Idc − aL arc ) − 4cn bL arc Rl cn

(21)

C 0 ≡ ( Re Idc − aL arc )2 + 4bL arc · ( Re + Rt )

(22)

A0 ≡ B0 ≡

Finally, the general solutions of kcr are: k cr =

 p 1  0 2 − 4A0 C 0 B − B ± 2A0

(23)

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Since there may be two solutions of kcr , there may be two solutions of Icr as well. In the next subsection, it is indicated that not all the solutions of kcr and Icr are reasonable. Energies 2018, 11, x FOR PEER REVIEW

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4.2.2. Protection Region of Arcing Horns 4.2.2. Protection Region of Arcing Horns The protection region of arcing hornshorns is related to to kcrkcronly realsolution solution kcr and Icr exists. onlyifif the the real of of kcr and Icr exists. The protection region of arcing is related Figure 11 shows the possible real solutions of and kcr and forcritical critical burning in real plane. Figure 11 shows the possible real solutions of kcr IcrIcrfor burningstates states in real plane. 2000

kcr,1=kcr,2 Igp=0

Voltage (V)

1500

1000

Uarc

Icr,2>0

Ugp

k=kcr,2 Icr,1=±∝

kcr,1=kcr,2

500

Ugp=C

Icr,1<0 k=kcr,1

0

-500

Icr,1=Icr,2=0

-400

-200

0

200

400

Current (A)

Figure 11. Possible real solutions of kcr and Icr for critical burning states in real plane.

Figure 11. Possible real solutions of kcr and Icr for critical burning states in real plane. From Figure 11, it is known that there are two solutions Icr,1 < 0 and Icr,2 > 0 except the situation = Icr,2 =11, 0 when Igp = 0. Inthat a practical case,two Icr should be a limited value. Icr,2situation is a FromIcr,1 Figure it is known there are solutions Icr,1 < 0positive and Icr,2 > 0Therefore, except the special situation Igp should = 0 and be Ugpa=limited C should also be value. excluded. The Icr,1 = Icr,2 reasonable = 0 whensolution Igp = 0.and In the a practical case, Icr positive Therefore, corresponded relative fault location of Icr,2 is kcr,2: Icr,2 is a reasonable solution and the special situation Igp = 0 and Ugp = C should also be excluded. 1 The corresponded relative fault location kof Icr,2 = is k−cr,2 B ' +: B '2 − 4 A ' C ' (24) cr ,2

2A'

)

(

 p 1  cannot 0 02 − the 0electrode 0 arcing horns protect lines. If kcr,2 > 1 which means (24) If kcr,2 < 0 which meanskthe B 4A C − B + cr,2 = 2A0 lines. If 0 < kcr,2 < 1 which means the arcing horns protect part the arcing horns protect all the electrode of the electrode lines. Finally, the (relative) protection region of arcing horns kp is:

If kcr,2 < 0 which means the arcing horns cannot protect the electrode lines. If kcr,2 > 1 which means 0 0 < kcr,2 <when kcr ,2 <means 0  the arcing horns protect all the electrode lines. If 1 which the arcing horns protect  1 (relative) part of the electrode lines. Finally,k the protection region of arcing horns kp is: 2 = − B ' + B ' − 4 A ' C ' when 0 < k < 1 P

  



)

(

  2A'  0 

√

cr ,2

(25)

when kkcr ,2 > 1< 0 when cr,2

1



1 0 02 0 0 when 0 < k cr,2 < 1 2A0 − B + B − 4A C   5. Influence Factors on Protection Performance of Arcing Hornsk 1 when cr,2 > 1

kP =

(25)

5.1. Analysis Method of Influence Factors Based on Power Balance

5. Influence Factors on Protection Performance of Arcing Horns 5.1.1. Relations between Power Balance, Protection Performance and U-I Characteristics

5.1. Analysis Method of Influence Factors Based on Power Balance

The essential of static stability of fault arcs is the power balance between the power supplied by

external system and the power consumed by thePerformance fault arc. If theand power by external system 5.1.1. Relations between Power Balance, Protection U-Isupplied Characteristics

is less than the power consumed by the fault arc, then the fault arc will cool down and be extinguished

The essential ofInstatic is the powerperformance balance between thehorns, power eventually. otherstability words, if of wefault wantarcs a better protection for arcing wesupplied should by reduce the power supplied by the external system and increase the power consumed by the fault arc. external system and the power consumed by the fault arc. If the power supplied by external system is This idea is inspired that the analysis of the factors influencing the protection region that can be less than the power consumed by the fault arc, then the fault arc will cool down and be extinguished converted to the analysis of the factors influencing the power balance between the external system eventually. In other words, if we want a better protection performance for arcing horns, we should and the fault arc. reduce the power supplied by the external system and increase the power consumed by the fault arc. This idea is inspired that the analysis of the factors influencing the protection region that can be converted to the analysis of the factors influencing the power balance between the external system and the fault arc.

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For a given point on the U-I characteristic, the power P = U·I consumed or released is decided For a givenparameters point on the U-I U. characteristic, thepower powerofPa=given U ·I consumed decided by by its position I and Therefore the point can or be released increasedis(or reduced) its position parameters I and U. Therefore the power of a given point can be increased (or reduced) by lifting (or lowering) the U-I characteristic. In the end, the analysis of the influence factors on the by lifting (or lowering) thefurther U-I characteristic. end, the of thefactors influence protection region can be converted to In thethe analysis of analysis the influence on factors the U-I on the protection region can be further converted to the analysis of the influence factors on the characteristic. U-I characteristic. 5.1.2. Influence of Circuit Parameters on U-I Characteristics 5.1.2. Influence of Circuit Parameters on U-I Characteristics The U-I characteristic of fault arc is in form of Equation (9). According to Equation (9), The U-I The U-I characteristic of fault arc is in form of Equation (9). According to Equation (9), The U-I characteristic of fault arc can be lifted by increasing the arc length Larc. characteristic of fault arc can be lifted by increasing the arc length Larc . On the other hand, the U-I characteristic of external system is in form of Equation (6) which is a On the other hand, the U-I characteristic of external system is in form of Equation (6) which linear function. In fact, A is the vertical intercept and B is the slope of Equation (6). The U-I is a linear function. In fact, A is the vertical intercept and B is the slope of Equation (6). The U-I characteristic of external system can be lowered by reducing the vertical intercept or increasing the characteristic of external system can be lowered by reducing the vertical intercept or increasing slope. the slope. 5.2.Variation VariationofofProtection ProtectionPerformance PerformanceofofArcing ArcingHorns Hornswith withCircuit CircuitParameters Parameters 5.2. 5.2.1.Arc ArcLength Length 5.2.1. Althoughit it is the length notdischarge the discharge gap distance arcing horns which directly Although is the arc arc length not the gap distance of arcingofhorns which directly influence influence the protection region according to the state equations, the discharge gap distance of arcing the protection region according to the state equations, the discharge gap distance of arcing horns can horns can have an stable arc length. Figure 12 shows of thearc influence of still have anstill influence byinfluence deciding by thedeciding stable arcthe length. Figure 12 shows the influence length on arc length on the protection region of arcing horns. The protection region increases almost linear with the protection region of arcing horns. The protection region increases almost linear with the arc length. the arcarc length. arc length larger energy of arc, so that the arc U-I Longer lengthLonger means larger energymeans consumption of arc, soconsumption that the U-I characteristic of fault characteristic of fault arc will be lifted,ofand thehorns protection region ofthe arcing horns increases with the will be lifted, and the protection region arcing increases with arc length. The arcing horns arc length. The arcing horns can protect the electrode line only if the stable arc length is more than can protect the electrode line only if the stable arc length is more than 1100 mm. For the arcing horns 11001500 mm.mm For discharge the arcinggap horns withwhose 1500 mm discharge gap length whose stable arc length with length stable arc length is 2500 mm, the protection region is is 2500 just mm, the protection region is just 20.1%. It can be concluded that the arcing horns has poor protection 20.1%. It can be concluded that the arcing horns has poor protection performance for electrode lines of performance forcurrent electrode larger operation current and long distance. larger operation andlines longofdistance.

Protection region (%)

40

30

20

10

0 0

500

1000

1500

2000

2500

3000

3500

4000

Arc length (mm)

Figure12. 12.Influence Influenceof ofarc arclength lengthon onprotection protectionregion regionofofarcing arcinghorn. horn. Figure

5.2.2.Tower TowerFooting FootingResistance Resistance 5.2.2. Figure13 13and and Table Table 22 show show the the influence of Figure influence of of tower towerfooting footingresistance resistanceon onthe theprotection protectionregion region arcing footing resistance, resistance, but but the theinfluence influence of arcinghorns. horns.The Theprotection protectionregion regionincreases increaseswith with the the tower tower footing decreases as the tower footing resistance increases. decreases as the tower footing resistance increases. Sincethe theslope slopeBBincreases increaseswith withthe thetower towerfooting footingresistance, resistance,the theU-I U-Icharacteristic characteristicofofexternal external Since systemwill willbe belowered loweredwhich whichmeans meansthe theenergy energysupplied suppliedby bythe theexternal externalsystem systemwill willdecrease decreaseas aswell. well. system Finally, the protection region of arcing horns increases with the tower footing resistance. Finally, the protection region of arcing horns increases with the tower footing resistance.

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25 450 mm 600 450mm mm 600 mm 1000 1000mm mm 1500

25

20 Protection region (%)

Protection region (%)

20

15

1500 mm

15

10 10 5 5 0 0 0 0

33

66

99

1212

15 15

Tower footing resistance (Ω) Tower footing resistance (Ω)

FigureInfluence 13. Influence of tower footing resistanceon on protection region of arcing horns. Figure Figure13. 13. Influenceofoftower towerfooting footingresistance resistance onprotection protectionregion regionofofarcing arcinghorns. horns. Table 2. Influence of tower footing resistance on protection region of arcing horns.

Table Table2.2.Influence Influenceofoftower towerfooting footingresistance resistanceononprotection protectionregion regionofofarcing arcinghorns. horns. Protection Region (%)

Rt (Ω)

450 mm Rt (Ω) Rt (Ω) 3 0 450 mm 450 mm 3 6 00 3 0 00 6 9 6 0 00 12 9 9 0 0 15

12 12 15 15 5.2.3. Electrode Resistance

0 0 0 0

Protection Region (%)1500 mm 600 mm Region 1000 mm(%) Protection 4.8mm 1500 13.8 mm 600 0mm 1000 600 mm 1000 mm 1500 mm 5.3 14.4 00 4.8 13.8 00 0.7 6.0 15.2 5.34.8 14.413.8 0 5.3 1.8 7.3 16.7 0.7 6.0 15.214.4 0.7 4.4 10.26.0 20.1 15.2 1.8 7.3 16.7 1.8 7.3 16.7 4.4 10.2 20.120.1 4.4 10.2

Figure 14 and Table 3 show the influence of electrode resistance on the protection region of 5.2.3. Electrode Resistance 5.2.3. arcing Electrode Resistance horns. As the result shown, the protection region decreases almost linearly with the electrode Figure 14and and Table 3 horns show isthe influence of electrode resistance on the protection region of resistance, arcing for protection at large electrodeon resistance. Figure 14 and the Table 3 show theinvalid influence of electrode resistance the protection region of arcing horns. result shown, almost linearly with the electrode Both As the the vertical intercept A the andprotection the slope B region increasedecreases with the electrode resistance Re. However arcing horns. As the result shown, the protection region decreases almost linearly with the electrode resistance, and arcing hornsbecause is invalid for R protection atmuch largelarger electrode the effect of the Re on B is limited Rt and l are usually than resistance. Re, hence the effect of Re resistance, and the arcing horns is invalid for protection at large electrode resistance. on A isthe dominant. a consequence, theslope U-I characteristic of external system will be raised Both vertical As intercept A and the B increase with the electrode resistance Re.which However Both thethe vertical intercept A and the slope B increase with the electrode resistance Reof. However means energy supplied by the external system will increase, and the protection region arcing the effect of Re on B is limited because Rt and Rl are usually much larger than Re, hence the effect of Re the effect ofdecreases Re on B iswith limitedelectrode because resistance. Rt and Rl are usually much larger than Re , hence the effect of Re on Ahorns is dominant. As a the consequence, the U-I characteristic of external system will be raised which on A is dominant. As a consequence, the U-I characteristic of external system will be raised which means the energy supplied by the external system will increase, and the protection region of arcing means the energy supplied by50the external system will increase, and the protection region of arcing horns decreases with the electrode resistance. horns decreases with the electrode resistance. 450 mm Protection region (%)

50

600 mm 1000 mm 1500 mm

40

450 mm 600 mm 1000 mm 1500 mm

30

Protection region (%)

40 20

30 10

20 0

10 0.0

0.2

0.4

0.6

0.8

1.0

Electrode resistance (Ω)

0

Figure 14. Influence of electrode resistance on protection region of arcing horns. 0.0

0.2

0.4

0.6

0.8

1.0

Electrode resistance (Ω)

Figure14. 14.Influence Influenceofofelectrode electroderesistance resistanceon onprotection protectionregion regionofofarcing arcinghorns. horns. Figure

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Table 3. Influence of electrode resistance on protection region of arcing horns. Energies 2018, 11, x FOR PEER REVIEW

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Protection Region (%)

Re3.(Ω) Table Influence of electrode resistance on protection region of arcing horns. 450 mm 0.1 0.2 0.3 0.4 0.5

Re (Ω)14.9 450 mm 0.1 13.9 14.9 0.2 12.2 13.9 0.3 8.8 12.2 0.4 0 8.8 0.5 0

600 mm

1000 mm

1500 mm

Protection Region (%) 20.9mm 100026.7 36.6 600 mm 1500 mm 19.9 25.7 20.9 26.7 36.6 35.5 18.2 24.0 19.9 25.7 35.5 33.8 14.7 20.5 18.2 24.0 33.8 30.4 4.4 10.2 14.7 20.5 30.4 20.1 4.4 10.2 20.1

5.2.4. Line Resistance 5.2.4. Line Resistance

Figure 15 and Table 4 show the influence of line resistance on the protection region of arcing horns. Figure 15 and Table 4 show the influence of line resistance on the protection region of arcing The protection region decreases with the line resistance, but the rate of decline falls off with the line horns. The protection region decreases with the line resistance, but the rate of decline falls off with resistance. A full protection can be realized at small line resistance which demonstrates that arcing the line resistance. A full protection can be realized at small line resistance which demonstrates that horns arcing are very effective foreffective short HVDC electrode lines. Forlines. the line resistance Rl , both vertical horns are very for short HVDC electrode For the line resistance Rl,the both the intercept A and the slope B increase Rl . When small,Rthe effect of Rl on AofisRdominated, l lis . When l is small, the effect l on A is vertical intercept A and the slopewith B increase withRR and the U-I characteristic of external system be lifted which means energy supplied by the dominated, and the U-I characteristic of will external system will be liftedthe which means the energy external systembywill Thus the region with the line resistance. As Rl supplied the increase. external system willprotection increase. Thus the decreases protection region decreases with the line resistance. As R l increases, the effect of R l on B becomes stronger, so that the rate of decline of the increases, the effect of Rl on B becomes stronger, so that the rate of decline of the protection region protection region falls off. falls off.

Protection region (%)

100

450 mm 600 mm 1000 mm 1500 mm

80 60 40 20 0 0

1

2

3

4

5

Line resistance (Ω)

Figure 15. Influence of line resistance on protection region of arcing horns.

Figure 15. Influence of line resistance on protection region of arcing horns. Table 4. Influence of line resistance on protection region of arcing horns.

Table 4. Influence of line resistance on protection region of arcing horns. Protection Region (%) 450 mm Protection 600 mm Region 1000 mm (%)1500 mm 0.977 0 22.2 51.0 99.8 450 mm0 60017.7 mm 1000 1500 mm 1.954 40.8 mm 80.0 2.931 0 0 13.3 30.7 60.1 99.8 22.2 51.0 3.908 0 0 8.9 20.5 40.1 80.0 17.7 40.8 4.885 0 0 4.4 10.2 20.1 60.1 13.3 30.7

Rl (Ω)

Rl (Ω) 0.977 1.954 2.931 3.908 4.885 5.2.5. Operation Current

0 0

8.9 4.4

20.5 10.2

40.1 20.1

Figure 16 and Table 5 show the influence of operation current on the protection region of arcing

5.2.5. Operation Current region decreases with the operation current, but the rate of decline falls off with horns. The protection the operation current. A full protection can be realized at low operation current which demonstrates

Figure 16 and Table 5 show the influence of operation current on the protection region of arcing that arcing horns are very effective for HVDC electrode lines with small operation currents. For the horns. operation The protection region decreases with the operation current, but the rate of decline falls off with current Idc, the vertical intercept A increases with Idc, and the U-I characteristic of external the operation current. A full protection can be realized at low operation current which demonstrates that arcing horns are very effective for HVDC electrode lines with small operation currents. For the

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operation current Idc , the vertical intercept A increases with Idc , and the U-I characteristic of external system system will bewill lifted whichwhich means the energy supplied byby the external increase.Therefore Therefore be lifted means the energy supplied the externalsystem system will will increase. Energies 2018, 11, x FOR PEER REVIEW 15 of 19 the protection regionregion of arcing hornshorns decreases with thethe operation current. the protection of arcing decreases with operation current.

Protection region (%) Protection region (%)

system will be lifted which means the energy supplied by the external system will increase. Therefore 100 horns decreases with the operation current. the protection region of arcing 450 mm 100 80 60 40

600 mm 1000 mm 1500 mm 450 mm 600 mm 1000 mm 1500 mm

80 60 40 20

20

0 0

500

1000

1500

2000

2500

3000

Operation current (A)

0

0 500of operation 1000 1500 2000 2500 region 3000of arcing horns. 16. Influence current protection FigureFigure 16. Influence of operation current on on protection region of arcing horns. Operation current (A)

Table Influence operation current on protection regionofofarcing arcinghorns. horns. Table 5. Influence of operation current onon protection region arcing horns. Figure 16.5.Influence ofofoperation current protection region Protection Region (%) Idc (A) Region (%) 450 mmProtection 600 mm 1000 mm 1500ofmm Table Influence of operation current on protection region arcing horns. Idc5.(A) 630 100.0mm 100.0 450 mm77.1 600 100.0 mm 1000 1500 mm (%) 1260 57.3 Protection 81.6 Region 100.0 100.0 630 Idc (A) 77.1 100.0 100.0 100.0 450 mm 600 mm 1000 mm mm 1890 37.5 55.8 73.4 1500100.0 1260 630 57.377.1 81.6 100.0 100.0 100.0 100.0 100.0 2520 17.8 29.9 41.7 61.6 1890 1260 37.557.3 55.8 73.4 100.0 81.6 100.0 100.0 3150 0 4.4 10.2 20.1 2520 1890 17.837.5 29.9 41.7 55.8 73.4 100.0 61.6 3150 2520 0 17.8 4.4 29.9 41.710.2 61.6 20.1 5.2.6. Conductor Number 3150 0 4.4 10.2 20.1

Figure 17 and Table 6 show the influence of conductor number on the protection region of arcing 5.2.6. Conductor Number horns. The protection region increases almost linearly with the conductor number. For the conductor 5.2.6. Conductor Number

Figure 17 and Table 6 show the influence ofslope conductor number theRprotection regionpart of arcing number cn, both vertical intercept A and the B decrease with on cn. As t counts majority of B, Figure 17 and Table 6 show the influence of conductor number on the protection region of arcing the effect of cn onregion B is limited, in turn, the effect of cnwith on A the is dominant, so number. the U-I characteristic of the horns. The protection increases almost linearly conductor For the conductor horns. The protection region increases almost linearly with the conductor number. For the conductor external system will be lowered which slope meansBthe energywith supplied byRthe external systempart will number cn , both vertical intercept AAand decrease majority n . As t counts number cn, both vertical intercept andthe the slope B decrease with cn.cAs Rt counts majority part of B, of decrease, and the arcing horns protection region will increase. B, thethe effect ofofcncnon limited,ininturn, turn, effect A is dominant, so characteristic the U-I characteristic effect onBB is is limited, thethe effect of cnofoncnAon is dominant, so the U-I of the of theexternal externalsystem systemwill willbebelowered loweredwhich which means the energy supplied by the external system means the energy supplied by the external system willwill 80 decrease, and the horns protection region will increase. decrease, andarcing the arcing horns protection region will increase. 450 mm 600 mm 1000 mm 1500 mm 450 mm 600 mm 1000 mm 1500 mm

Protection region (%) Protection region (%)

80 60

60 40

40 20

20 0 1 0

2

3

4

5

6

Conductor number

1 3 on protection 4 5region of 6 arcing horns. Figure 17. Influence of2 conductor Conductor number

Figure Influence conductoron onprotection protection region Figure 17. 17. Influence of of conductor regionof ofarcing arcinghorns. horns.

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Table 6. Influence of conductor on protection region of arcing horns. Protection Region (%)

n 450 mm

600 mm

1000 mm

1500 mm

0 0 0 0 0 0

2.2 4.4 6.7 9.0 11.3 13.6

5.1 10.2 15.5 20.7 26.0 31.4

10.0 20.1 30.3 40.6 50.8 61.0

1 2 3 4 5 6

5.3. Analysis on Influence Factors Based on Approximation Solution of State Equation 5.3.1. Approximation Solution of State Equation The full expression of Equation (25) is quite complex for analysis. In this subsection, the approximation solution of state equation will be proposed for further analysis on influence factors. Generally, the total resistance of whole electrode lines should be as small as possible to ensure they are well grounded, otherwise a relatively high voltage will drop on the electrode lines which is not expected. In addition, large tower footing resistance can improve the performance of arcing horns. Therefore, it is proper to suppose that Rt >> Rl and Re , and Equation (18) can be simplified into: 

( Re +

k cr R ) · Idc − aL arc cn l

2

− 4bL arc Rt = 0

(26)

and then the approximation solutions of kcr are: k0cr =

 p cn  aL arc − Re Idc ± 4bL arc Rt Rl Idc

(27)

On the basis of the analysis in Section 4.2.2, the reasonable solution of k0cr for Icr > 0 is: k0cr,2 =

 p cn  aL arc − Re Idc + 4bL arc Rt Rl Idc

(28)

Finally, the approximation protection region of arcing horns k0 p is:

k0P

=

    

cn Rl Idc

0
√ aL arc − Re Idc + 4bL arc Rt 1

when k0cr,2 < 0 when 0 < k0cr,2 < 1 when k0cr,2 > 1

(29)

5.3.2. Analysis on Influence of Circuit Parameters Based on Approximation Solutions The derivatives of approximation protection region k0 p with respect to Larc , Re , Rl , Rt , Idc and cn are: s ! dk0p cn bRt = a+ (30) dL arc Rl Idc L arc dk0p dRe dk0p dRl

=−

=−

cn Rl

 p cn  aL arc − Re Idc + 4bL arc Rt 2 Rl Idc s dk0p cn bL arc = dRt Rl Idc Rt

(31) (32)

(33)

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dk0p dIdc dk0p dcn

=

=−

 p cn  aL + 4bL R arc arc t 2 Rl Idc

 p 1  aL arc − Re Idc + 4bL arc Rt Rl Idc

(34)

(35)

when 0 ≤ k0 p ≤ 1. It is obvious that: dk0 p /dRe and dk0 p /dcn are constants; dk0 p /dLarc and dk0 p /dRt are positive; dk0 p /dRe and dk0 p /dIdc are negative. The signs of dk0 p /dRl and dk0 p /dcn are decided by the specific circuit parameters. Under our conditions that Idc = 3150 A, Re = 0.5 Ω, Rt = 15 Ω, a = 0.87 V/mm, b = 5.77 and Larc = 1100~2500 mm, dk0 p /dRl < 0 and dk0 p /dcn > 0. For the arc length Larc , when Larc is very large, dk0 p /dLarc ≈ αcn /Rl Idc > 0 can be assumed a constant. Therefore, the protection region increases linearly with the arc length. For the electrode resistance Re and the conductor number cn , considering that dk0 p /dRe is a negative constant while dk0 p /dcn is a positive constant, which implies that the protection region will decrease with the electrode resistance but increase linearly with the conductor number. For the line resistance Rl and the operation current Idc , both of dk0 p /dRl and dk0 p /dIdc are negative with a saturation trend according to Equations (32) and (34). Therefore, the protection region will decrease with the line resistance and the operation current, but the rate of decline falls off gradually. For the tower footing resistance Rt , dk0 p /dRt are positive and decreases with Rt according to Equation (33). Consequently, the protection region will increase with the tower footing resistance, but the influence decreases as the tower footing resistance increases. The above theoretical analysis based on the approximation solutions coincides well with the results calculated by the state equations shown in Section 5.2. It is proved that the approximation solutions (Equations (30)–(35)) can be a useful tool for the fast evaluation of influence factors on the protection performance of arcing horns. 6. Protection Performance Improvement Methods for Arcing Horns 6.1. Protection Performance Improvement by Adjusting Circuit Parameters The efficient ways to improve the protection performance of arcing horns is increasing the arc voltage and tower footing resistance, and reducing the total resistance of electrode line system (including the line resistance and electrode resistance). According to Equation (10), the arc voltage Uarc can be elevated by elongating the arc length Larc or cooling the arc to increase the arc constants a and b. Increasing the discharge gap length of arcing horns is the simplest way to elongate the arc length. Auxiliary devices for arc extinction are also recommended to improve the protection performance. In [15–17], a gas jet was used to elongate the arc and promote the arc cooling process. Increasing the diameter of the conductor and conductor number can reduce the line resistance, however, extra expense is required. In [14], neutral conductor was used as additional ground return which can reduce the total resistance of electrode line system, so that a better protection performance is achieved. 6.2. Protection Performance Improvement by Diffirential Arcing Horns Configuration Strategy Figure 18 shows the variation of U-I characteristic of external system with the fault location. The U-I characteristic of the place near the station is higher than that of the place near the electrode. That is to say, arc extinction is harder for a place near the station. In the place near the electrode, the arcing horns with short discharge gap length is enough for full protection. Wherever, in the place near the station, even the arcing horns with long discharge gap length may not achieve full protection, and auxiliary devices for arc extinction are needed as well. Considering that the arc extinction devices will incur extra expenses, it is unnecessary to install the arc extinction devices all along the electrode lines. Therefore, the diversified configuration strategy

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of arcing horns is recommended for cost savings, which means arcing horns of short discharge gap length are sufficient and recommended for the place near the electrode, meanwhile, arcing horns of long discharge gap length with additional arc extinction devices are recommended for the places near Energies 2018, 11, x FOR PEER REVIEW 18 of 19 the station. 10000 10,000 k=1

Voltage (V)

8000

k=0.8 k=0.6

6000

k=0.4

4000

k=0.2

2000

0

k=0

0

100

200

300

400

500

600

Current (A)

Figure18. 18.U-I U-Icharacteristic characteristicofofexternal externalsystem systematatdifferent differentfault faultlocation. location. Figure

In the place near the electrode, the arcing horns with short discharge gap length is enough for 7. Conclusions full protection. Wherever, in the place near the station, even the arcing horns with long discharge gap In this paper, experiments were carried to studydevices the characteristics of longare free burning length may not achieve full protection, andout auxiliary for arc extinction needed as arcs well. and the insulation coordination of arcing horns on the electrode lines of a 5000 MW, ± 800 kV HVDC Considering that the arc extinction devices will incur extra expenses, it is unnecessary to install the system. The factors influencing protection of arcing horns are analyzed theoretically. arc extinction devices all alongthe the electrodeperformance lines. Therefore, the diversified configuration strategy The main conclusions are summarized as follows: of arcing horns is recommended for cost savings, which means arcing horns of short discharge gap sufficient and recommended for burning the placearcs nearcan thebe electrode, arcing horns (1)length Theare development process of long free divided meanwhile, into slow expansion, fastof longexpansion, discharge gap length with additional arc extinction devices are recommended for the places near violent motion and extinction phases. The long free burning arc column is very the station. unstable and made up of segments of short channels and conductive blurs. The local short circuit is thought to be the main cause of the instability of arc column. 7. Conclusions (2) The arcing horns are only suitable for the HVDC electrode lines systems of low operation current In this paper, experiments carried out tolines study the characteristics of longcurrent free burning arcs and short distance. For the were HVDC electrode systems of high operation and long anddistance, the insulation coordination of arcingof horns onhorns the electrode lines a 5000 MW, ±800 kV HVDC the protection performance arcing is limited, andofadditional auxiliary devices system. Theextinction factors influencing for arc are neededthe to protection realize fullperformance protection. of arcing horns are analyzed theoretically. main conclusions as follows: improvement of arcing horns are increasing the (3)TheThe effect ways forare thesummarized protection performance voltage and tower footing and reducing thebe total resistance HDVC electrode The development process of resistance, long free burning arcs can divided into of slow expansion, fast (1) arc line system. Differential arcing horns configuration strategy is recommended for cost saving. expansion, violent motion and extinction phases. The long free burning arc column is very unstable and made up of segments of short channels and conductive blurs. The local short circuit Acknowledgments: This work was supported by Central Southern China Electric Power Design Institute is thought be the main cause of the instability of arc column. (CSEPDI) of China to Power Engineering Consulting Group Corporation (DG1-A04-2013). (2) The arcing horns are only suitable for the HVDC electrode lines systems of low operation current Author Contributions: Xiandong Li analyzed the data, performed the experiment, and wrote the paper; Hua Li andand short distance. For the HVDC electrode linesLin systems of high operation current and long conceived designed the experiments; Yi Liu and Fuchang gave suggestions on the experiments. distance, the protection performance of arcing horns is limited, and additional auxiliary devices Conflicts of Interest: The authors declare no conflict of interest. for arc extinction are needed to realize full protection. (3) The effect ways for the protection performance improvement of arcing horns are increasing the References arc voltage and tower footing resistance, and reducing the total resistance of HDVC electrode 1. Gu, He, J.L.; Zeng, R.;arcing Zhang,horns B.; Xu, G.Z.; Chen, strategy W.J. Motion characteristics of arcs in lineS.Q.; system. Differential configuration is recommended forlong costac saving. atmospheric air. Appl. Phys. Lett. 2007, 90, 051501. [CrossRef] 2.Acknowledgments: Li, Q.M.; Cong, H.X.; Q.Q.; J.Y.; Chen, Q. Characteristics Secondary Arc Column This Sun, work wasXing, supported by Central Southern of China ElectricAC Power Design Motion Institute Near Power Transmission Line Insulator String. IEEE Trans. Power Deliv. 2014, 29, 2324–2331. [CrossRef] (CSEPDI) of China Power Engineering Consulting Group Corporation (DG1-A04-2013).

Author Contributions: Xiandong Li analyzed the data, performed the experiment, and wrote the paper; Hua Li conceived and designed the experiments; Yi Liu and Fuchang Lin gave suggestions on the experiments. Conflicts of Interest: The authors declare no conflict of interest.

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