Insulation Coordination of Arcing Horns on HVDC Electrode Lines: Protection Performance Evaluation, Inﬂuence Factors and Improvement Method

energies

Article Insulation Coordination of Arcing Horns on HVDC Electrode Lines: Protection Performance Evaluation, Inﬂuence Factors and Improvement Method

Xiandong Li 1,2,3,* ID , Hua Li 1,2,3,*, Yi Liu 1,2,3 and Fuchang Lin 1,2,3 1 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.) 2 School of Electrical and Electronic Engineering, Huazhong University of Science & Technology, Wuhan 430074, China 3 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 Figure1a, 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 Figure1b, the operation

Energies 2018, 11, 430; doi:10.3390/en11020430 www.mdpi.com/journal/energies Energies 2018, 11, 430 2 of 19 Energies 2018, 11, x FOR PEER REVIEW 2 of 19 currentoperation on the current electrode on the lines electrode is rather lines large. is rather If ala lightningrge. If a lightning fault happens, fault happens, the fault the fault arc arc may may not be extinguished,not be extinguished, then both then the arcingboth the horns arcing and horns insulator and insulator strings strings will be will burned be burned and and destroyed. 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 optimizedTo solve insulation this problem, coordination the characteristicsscheme should be of studied fault based arcs the should characteristics be investigated of fault arcs. firstly, andThus, an optimized the whole insulation problem involves coordination two aspects: scheme the shouldcharacteristics be studied of fault based arcs and the characteristicsthe insulation of faultcoordination arcs. Thus, scheme. the whole problem involves two aspects: the characteristics of fault arcs and the insulationThe coordination fault arcs in scheme.HVDC systems are long free burning arcs. The long free burning arc (>100 mm) 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 ofAs its for complex the insulation behavior. coordinati The existingon scheme, studies some aboutstudies long have arcs been are carried mainly out concerned [12–14]. Those with its movementworks can [1– 5be] andclassified electrical by their [4– methods11] characteristics. into two kinds: the maximum arc extinction current method andAs the for U-I the characteristic insulation method. coordination scheme, some studies have been carried out [12–14]. Those worksCanellas can [12] be classified carried out by studies their methodson the extinction into two of kinds:direct current the maximum (DC) arcs arc on extinctionlong electrode current methodlines and based the on U-I the characteristic experimental method. results of the Itaipu group, and gave the relations between the maximumCanellas [ 12arc] carriedextinction out current studies and on thethe extinctiongap length of of direct arcing current horns. (DC)However, arcs onthe long maximum electrode arc lines basedextinction on the experimental current is only results few hundreds of the Itaipu (≤400 group, A) and and the gavemaximum the relations gap length between is less thethan maximum 500 mm, arc extinctionwhich currentare not suitable and the for gap the length HVDC of systems arcing horns.with large However, operation the currents maximum used arc today. 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 horns.Jankov In [ 13our] discussedprevious works. about th thee protection protection performance performance of arcing of arcing horns horns in HVDC on the electrode HVDC lines system withwas neutral investigated conductor. also based The staticon the stabilityU-I characterist criterionic method, Voltage-Current and the influence characteristic factors were method analyzed (or U-I characteristicpreliminarily method [14]. Although, as usually the called) U-I characteristic was adopted method to find has the been maximum proved to protection be an effective region way of arc horns.for Inthe our insulation previous coordination works. the of protection arcing horns performance by [13,14], none of arcing of them horns provided in HVDC a comprehensive electrode lines was investigatedstudy on the influence also based factors on theand U-I the characteristicprotection performance method, improvement and the influence strategy factors for arcing were horns. 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. Energies 2018, 11, 430 3 of 19

EnergiesIn this 2018 paper,, 11, x FOR the PEER insulation REVIEW coordination of arcing horns on the electrode lines of a3 5000 of 19 MW, ±800 kV HVDC system is studied. The U-I characteristic method is used to evaluate the protection performanceIn this of paper, arcing the horns. insulation Since coordination the protection of arcing performance horns on the of electrode arcing horns lines of is adecided 5000 MW, 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 tocharacteristics investigate of the not characteristics only electrode ofline long system free but burning also the arcs. fault The arc, factorsexperiments inﬂuencing have been the carried protection performanceout to investigate of arcing the horns characteristics are analyzed of long theoretically.free burning arcs. Finally, The factors the improvement influencing the strategy protection for the protectionperformance performance of arcing of horns arcing are horns analyzed is proposed theoretically. based Finally, on the the theoretical improvement analysis. 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 HVDC system.U-I characteristic As shown method in Figure [13,14]2, can the be U-I used characteristic as the static stability of fault criterion arc in static for the state fault Uarcarc on(I ) has a negativeHVDC powersystem. function As shown form in Figure [11], on2, the the U-I other characteristic hand, the of U-I fault characteristic arc in static ofstate external Uarc (I)DC has systema 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 (P , with the fault location. Therefore, the possible number of cross point would be zero, one (P) or two 1 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 U I U I arc (equation) = ex U( arc), which(I) = Uex actually(I), which stands actually for stands the possible for the possi burningble burning state forstate the for fault the fault arc. arc.

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, theIf there U-I characteristic is no cross point,of the fault which arc means is higher the than arc the would U-I characteristic go into the extinction of the external state. system, In this so situation, the the U-Iexternal characteristic system cannot of the provide fault arc sufficient is higher energy than theto keep U-I characteristicthe fault arc burning. of the externalThe area system,which is so the externallower system than the cannot U-I characteristic provide sufﬁcient of fault energyarc is called to keep the protected the fault arczone. 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-Ithan characteristic the U-I characteristic of fault of arcfault is arc lower is called than the the unprotected U-I characteristic zone of the external system, so the external systemIt should can be providementioned sufﬁcient that only energy P1 is a to stable keep burning the fault point arc burning.(state), while, The P area2 is an which unstable is higher thanburning the U-I characteristicpoint (state) in ofwhich fault any arc disturbance is called the will unprotected lead to a deviation zone from P2 and a transit to P1 eventually.It should beThe mentioned critical burning that state only occursP1 is when a stable P2 and burning P1 are overlapped point (state), at P. In while, fact, theP2 maximumis an unstable burningprotection point zone (state) is indetermined which any by disturbancethe U-I characteristic will lead curve to a deviationof the external from systemP2 and where a transit P is to P1 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 protectionhappens, zone and is can determined be used to byevaluate the U-I the characteristic protection performance curve of the of externalarcing horns. 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 2. Experimental(total equivalent Settings capacitance Ceq = 18 mF) is chosen as the power source whose maximum pulse width is 70 ms and peak current is 2500 A. Two steel arcing horns are used as electrodes of which the dischargeFigure3 shows gap length the diagram Lgap is from of our 400 experimental mm to 1500 system.mm, and A the cascade arcing circuit horns pulse-waveare installed generatorboth (totalvertically equivalent and capacitancehorizontally inC eqthe= experiments. 18 mF) is chosen The fault as arc the is powerignited sourceby a ϕ 0.05 whose mm maximumcooper 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 Energies 2018, 11, 430 4 of 19

verticallyEnergies and 2018 horizontally, 11, x FOR PEER in REVIEW the experiments. The fault arc is ignited by a ϕ 0.05 mm cooper4 of 19 wire connected to the edge of arcing horns. A 500 MHz oscilloscope (TDS3052C, Tektronix, Beaverton, OR, USA) andconnected a high-speed to the edge camera of arcing (FASTCAM horns. A 500 SA5, MHz Motion oscilloscope Engineering (TDS3052C, Company, Tektronix, Chicago, Beaverton, IL, OR, USA) are Energies 2018, 11, x FOR PEER REVIEW 4 of 19 appliedUSA) to record and a thehigh-speed voltage, camera current (FASTCAM and development SA5, Motion process Engineering of fault Company, arc, respectively. Chicago, IL, USA) 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,1.5Ω current and developmentSwitch process of fault arc, respectively.Voltage Probe 7.2mF Arcing Horns (vertical) 1.5Ω Switch Voltage 5.4mF Probe

3.5mH 7.2mF ArcingFuse Horns (vertical)wire 3.6mF

3.5mH5.4mF 14mH 3.5mH High-speed Fuse Camera wire 1.8mF 3.5mH 3.6mF 3.5mH 14mH High-speed Current Support Pulse-wave Generator Camera Probe 1.8mF 3.5mH Figure 3. Diagram of experimental system. Figure 3. Diagram of experimental system. Current Support Pulse-wave Generator In the experiment, the capacitors are charged firstlyProbe to the voltage U0 = 6000 V, and the total energy stored in capacitors is 0.324 MJ. Then, the switch is closed and the energies in capacitors are In the experiment, the capacitorsFigure 3. areDiagram charged of experimental ﬁrstly to system. the voltage U0 = 6000 V, and the total 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. released toIn ignitethe experiment, the cooper the wire. capacitors The arc are will charged be formed firstly to and the burns voltage in U open0 = 6000 air freelyV, and until the total 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 3. Behaviorsruns3.1. out. Behaviors and Characteristics of Long Free Burning of LongArc Free Burning Arc

3.1. Behaviors3. Behaviors3.1.1. Typical of Long and Waveforms Characteristics Free Burning Arcof Long Free Burning Arc 3.1. BehaviorsThe typical of Long current Free Burning and voltage Arc waveforms of a long free burning arc are shown in Figure 4. The 3.1.1. Typicalwaveform Waveforms 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 The3.1.1. typicalTypical Waveforms current and voltage waveforms of a long free burning arc are shown in Figure4. vibrations, which is caused by the instability of the long free burning arc. In the later Section 3.1.3, it The waveformisThe indicated typical of the that current arc the current instabilityand voltage pulse of waveformslong is stable, free burning of which a long arc is free causedis closelyburning by related arc the are smoothing to shown the local in Figure effectshort circuit of4. The the circuit inductancewaveformprocess on of the arcthe arc column.arc current.current It should pulse However, be is noticedstable, the whichthat waveform th eis spike caused (0–0.1 of by the ms)the arc smoothingin the voltage wave effect front is unstable ofof arcthe voltage circuit with many vibrations,inductanceis caused which on by is thethe caused ignitionarc current. by process the However, instability of the fuse the of wire. wave the longform freeof the burning arc voltage arc. Inis theunstable later with Section many 3.1.3 , it is indicatedvibrations, that thewhich instability is caused of by long the instability free burning of the arc long is closelyfree burning related arc. to In thethe locallater Section short circuit 3.1.3, it process is indicated that the instability3000 of long free burning arc is closely related3000 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 theis ignitioncaused by process the ignition of the process fuse of wire. the fuse wire. 2000 2000 3000 3000

1000 Voltage 1000 Voltage (V) Voltage 2000Current (A) 2000

Current 0 0

1000 Voltage 1000 Voltage (V) Voltage

Current (A) 0 20406080 Time (ms) Current Figure 4.0 Typical current and voltage waveforms of a free burning0 arc.

0 20406080 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.

Energies 2018, 11, 430 5 of 19

3.1.2. Development Process of a Long Free Burning Arc

Energies 2018, 11, x FOR PEER REVIEW 5 of 19 EnergiesFigure 20185 ,shows 11, x FOR the PEER development REVIEW process of a long free burning arc of which the discharge5 of 19 gap length Lgap = 1000 mm. Figure6 shows the variation of arc length with time. The whole development process3.1.2.3.1.2. ofDevelopment Development long free burning Process Process of arcof a a Long canLong be Free Free divided Burning Burning into Arc Arc four phases based on the shape of arc column, the motionFigureFigure of arc5 5 shows shows and thethe the expansiondevelopment development of process arcprocess (the of of variation a a long long free free of burning arcburning length): arc arc of of which which the the discharge discharge gap gap length Lgap = 1000 mm. Figure 6 shows the variation of arc length with time. The whole development length Lgap = 1000 mm. Figure 6 shows the variation of arc length with time. The whole development Phase I (0.1–3 ms): This phase is called the slow expansion phase. The arc motion is gentle, the arc processprocess of of long long free free burning burning arc arc can can be be divided divided into into four four phases phases based based on on the the shape shape of of arc arc column, column, expansion speed is slow and the arc column is stable with a clear shape. thethe motion motion of of arc arc and and the the expansion expansion of of arc arc (the (the variation variation of of arc arc length): length): Phase II (3–32 ms): This phase is called the fast expansion phase. The arc motion is violent, the arc PhasePhase I I(0.1–3 (0.1–3 ms): ms): This This phase phase is is called called the the slow slow expansion expansion phase. phase. The The arc arc motion motion is is gentle, gentle, the the expansion speed is fast, and the arc column is relative stable. It can be seen that there are blurs around arcarc expansion expansion speed speed is is slow slow and and the the arc arc column column is is stable stable with with a a clear clear shape. shape. the arc column making the shape of arc column unclear. The blurs are conductive, which will induce PhasePhase II II (3–32 (3–32 ms): ms): This This phase phase is is called called the the fast fast expansion expansion phase. phase. The The arc arc motion motion is is violent, violent, the the thearc localarc expansion expansion short circuit speed speed processes is is fast, fast, and and of the arcthe arc columns.arc column column is is re relativelative stable. stable. It It can can be be seen seen that that there there are are blurs blurs Phasearoundaround III (32–60 the the arc arc ms):column column This making making phase the the is shape calledshape of of the arc arc violentcolumn column unclear. motion unclear. The phase.The blurs blurs The are are arcconductive, conductive, motion which becomeswhich will will more violent,induceinduce however, the the local local the short short arc circuit circuit expansion processes processes slows of of arc down.arc columns. columns. The blurs around the arc column are diffused which leads frequentPhasePhase III III local (32–60 (32–60 short ms): ms): circuit This This phase phase processes is is called called making the the viol viol theentent arcmotion motion column phase. phase. unstable The The arc arc andmotion motion without becomes becomes a clear more more shape. violent, however, the arc expansion slows down. The blurs around the arc column are diffused which Phaseviolent, IV (60–70 however, ms): the Thisarc expansion phase is slows called down. the extinctionThe blurs around phase, the in arc which column both are thediffused arc motion which and leads frequent local short circuit processes making the arc column unstable and without a clear shape. expansionleads frequent cease, local and short the arc circuit is quenched processes tomaking its ﬁnal the extinction. arc column unstable and without a clear shape. PhasePhase IV IV (60–70 (60–70 ms): ms): This This phase phase is is called called the the extinction extinction phase, phase, in in which which both both the the arc arc motion motion and and expansion cease, and the arc is quenched to its final extinction. expansionIt should cease, be mentioned and the arc that is quenched the initial to its phase final for extinction. the case of overvoltage breakdown is different to that ofItIt should theshould case be be ofmentioned mentioned fuse wire that that ignition. the the initial initial In phase phase the casefor for the the of case overvoltagecase of of overvoltage overvoltage breakdown, breakdown breakdown the is is discharge different different gap is bridgedtoto that that of of by the the the case case streamer of of fuse fuse wire beforewire ignition. ignition. the initial In In the the arccase case formed. of of overvoltage overvoltage Since breakdown, thebreakdown, streamer the the usually discharge discharge has gap gap a relativeis is curvedbridgedbridged shape, by by the thethe streamer shapestreamer of before before initial the the arc initial initial may arc notarc formed formed be very. .Since Since straight. the the streamer streamer On the usuallother usually hand,y has has a a therelative relative huge curved curved amount of shape, the shape of initial arc may not be very straight. On the other hand, the huge amount of moleculesshape, the of theshape fuse of wireinitial guarantee arc may not the be high very conductivity straight. On of the the other arc column,hand, the and huge ambient amount air of is not molecules of the fuse wire guarantee the high conductivity of the arc column, and ambient air is not warmmolecules enough of to the cause fuse wire strong guarantee turbulence the high at the cond beginning.uctivity of Asthe aarc result, column, the and arc columnambient air during is not phase warmwarm enough enough to to cause cause strong strong turbulence turbulence at at the the be beginning.ginning. As As a a result, result, the the arc arc column column during during phase phase I forI thefor casethe case of fuseof fuse wire wire ignition ignition is is clear clear andand straight.straight. However, However, the the following following process process should should be be similarI for forthe thecase two of fuse cases. wire ignition is clear and straight. However, the following process should be similarsimilar for for the the two two cases. cases.

0 ms 5 ms 15 ms 32 ms 45 ms 60 ms 70 ms 0 ms 5 ms 15 ms 32 ms 45 ms 60 ms 70 ms

Figure 5. Development process of long free burning arc (Lgap = 1000 mm). FigureFigure 5. 5.Development Development processprocess of of long long free free burning burning arc arc (Lgap (L =gap 1000= 1000 mm). mm).

2000 3000 2000 3000 I II IV I II IIIIII IV 1750 2500 1750 2500 2000 1500 2000 1500 1500 1500 1250 1250 1000 1000 1000 Arc voltage voltage (V) Arc Arc length (mm) 1000 500 Arc voltage voltage (V) Arc Arc length (mm) 500 Local short-circuit processes 750 Local short-circuit processes 750 Arc length 0 Arc length 0 Arc voltage Arc voltage 500 -500 500 0 10203040506070-500 0 10203040506070 Time (ms) Time (ms)

Figure 6. Variation of arc length and voltage with time (Lgap = 1000 mm). FigureFigure 6. 6.Variation Variationof of arcarc lengthlength and and voltage voltage with with time time (Lgap (L =gap 1000= 1000 mm). mm).

Energies 2018, 11, 430 6 of 19

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. Table1 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 6 of 19 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) stable arc length forGap the Distance arcing horns (mm) at vertical and horizontal configurations, at least 10 experiments have been carried out for each condition. Vertical Gap Horizontal Gap 450 1083 1142 Table 1. Average600 stable arc length of arcing 1313 horns at different configurations. 1384 1000Average 1762 Stable Arc Length (mm) 1705 Gap Distance (mm) 1500Vertical 2454 Gap Horizontal Gap 2512 450 1083 1142 600 1313 1384 Overall, the average stable arc1000 length increases1762 with the discharge1705 gap length, but the elongation rate αL = Lst/Lgp decreases from 2.41500 to 1.6. The difference2454 between2512 the elongation rate of vertical and 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/Lgp decreases from 2.4 to 1.6. The difference between the elongation rate of vertical and ignored.horizontal However, gaps the is thermal not significant, turbulence and the can result increase is similar the instabilityto [5]. In [5], of it anis thought arc and that contribute magnetic to the arc motion whichforce is usuallythe dominating means force a longer at high arc current length, level so therefore the explanation the influence of of [ 5thermal] is not buoyancy very comprehensive. force In a latercan subsection, be ignored. itHowever, is indicated the thermal that theturbulence insignificant can increase difference the instability of arc of length an arc and between contribute 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 The3.1.3. important Instability characteristic of Long Free Burning of a long Arc free burning arc is the strong instability of arc column. The instabilityThe of important the arc column characteristic is composed of a long free of macroburning instability arc is the strong and instability micro instability. of arc column. The The arc burning in open airinstability without of the a confined arc column container is composed remains of macr ino instability motion and and violentmicro instability. expansion, The soarc theburning macro shape in open air without a confined container remains in motion and violent expansion, so the macro shape of the arc varies with time showing instability. On the other hand, the micro instability is related to the of the arc varies with time showing instability. On the other hand, the micro instability is related to local shortthe circuitlocal short process, circuit process, as shown as shown in Figure in Figure7. 7.

Channel

B B B B A A A A Blur

(a)

A A B A B A BB

(b)

Figure 7. Local short circuit process of arc column: (a) high speed images of local short circuit process; Figure 7. a (bLocal) mechanism short diagram circuitprocess of local short of arc circuit column: process. ( ) high speed images 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. ForHowever, the short for arc the andlong arcsfree burning in a closed arc, the space, arc column there is isnot usually continuous one but continuous rather segmented column and channel. 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 composedcompression of short pressure channels Psm and of arc blurs. column The equals: blurs can be regarded as the products of cooled channel   segments. Hence the conductivity of blurs should=× be lower than that of the channel. The self-magnetic PJBsm (1) compression pressure Psm of arc column equals:

→ → Psm = J × B (1) Energies 2018, 11, 430 7 of 19 Energies 2018, 11, x FOR PEER REVIEW 7 of 19

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 Figure7b), 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 Figure6. 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.

3.2.3.2. Electric Electric Characteristic Characteristic of Longof Long Free Free Burning Burning Arcs Arcs

3.2.1.3.2.1. U-I U-I Characteristic Characteristic of of Long Long Free Free Burning Burning Arc Arc TheThe variation variation of of U-I U-I characteristic characteristic of of long long free free burning burning arc arc with with time time is shownis shown in Figurein Figure8. 8.

2000 Arc formation 0.1-5 ms 5-32 ms 32-60 ms 1500 >60 ms

1000

Voltage (V) Voltage Arc extinction

500 Local short-circuit processes

0 0 500 1000 1500 2000 2500 Current (A)

FigureFigure 8. 8.Variation Variation of of U-I U-I characteristic characteristic of of long long free free burning burning arc arc with with time. 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. PhaseThe U-I I (0.1–3 characteristic ms): In this curve phase, Uarc(I thearc) approximately arc current Iarc obeysrises buta negative the arc power voltage functionUarc falls law. off quickly. The U-IPhase characteristic II (3–32 ms): curve InU thisarc( Iphase,arc) approximately the arc current obeys remains a negative at a high power level, function and on law. the other hand, the arc voltage shows a slight uptrend with vibrations caused by the local short circuit processes.

Energies 2018, 11, 430 8 of 19

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 IVPhase (60–70 III ms): (32–60 In thisms): phase, In this the phase, arc goes the arc into current the extinction decreases state, contin anduously, both thethe arcarc currentvoltage and voltagevibrations are decreasing. are more violent and frequent, which implies frequent local short circuit processes. 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-I voltage Characteristic are decreasing. of Long Free Burning Arc 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. ThenU thearc electric field of arc column Earc equals: Earc = (2) ULarc E = arc (2) arc L where Uarc (V) is the arc voltage and Larc (mm) is arcarc length at the measured moment respectively.

It waswhere found Uarc that (V) theis the relation arc voltage between and theLarc (mm) electric is arc field length of arc at column the measuredEarc (V/mm) moment and respectively. the arc current It Iarc (A)was can found be expressedthat the relation in the between following the form electric [11 field]: of arc column Earc (V/mm) and the arc current Iarc (A) can be expressed in the following form [11]: E = a + bI−n (3) arc =+ −arcn EabIarc arc (3) where,where,a, b and a, b andn are n are both both positive positive constant constant coefficients. coefficients. The results results of of [6] [6 indicated] indicated that that a = a0.95= 0.95 V/mm, V/mm, b = 5b and = 5 andn = n 1 = for 1 for long long air air gap. gap. Here, Here, the the experimentalexperimental data data are are fitted fitted by by Equation Equation (3) (3)assuming assuming n = 1,n = 1, and theandfitted the fitted results results are area = a 0.87 = 0.87 V/mm, V/mm,b b= = 5.77. Figure Figure 99 presentspresents the the variation variation of ofarc arc column column electric electric fieldfield with with the the arc arc current current (E-I (E-I characteristic). characteristic). InIn [[6],6], the the arc arc elongation elongation was was not not considered considered so their so their calculatedcalculated electric electric field fieldEarc Earc= =U Uarcarc//Lgp shouldshould be be higher higher than than thethe actual actual electric electric field fieldEarc = EUarcarc/L=arcU. arc/Larc.

1.6

1.2 −1 U=0.95+5I

0.8

− U=0.86+5.77I 1

Electric field(V/mm) 0.4 Experimental data Fitted result Ref.[6] 0.0 0 500 1000 1500 2000 2500 Current (A)

FigureFigure 9. 9.E-I E-I characteristic characteristic of long long free free burning burning arc. arc.

4. Insulation4. Insulation Coordination Coordination of of Arcing Arcing Horns Horns onon HVDCHVDC Electrode Electrode Lines Lines

4.1. U-I4.1. CharacteristicU-I Characteristic of HVDCof HVDC Electrode Electrode Lines Lines andand Fault Arc Arc

4.1.1.4.1.1. U-I CharacteristicU-I Characteristic of of HVDC HVDC Electrode Electrode Lines Lines TheThe power power transfer transfer of aof± a 800±800 kV kV HVDC HVDC system is is 5000 5000 MW MW (at (at bi-polar bi-polar mode) mode) and and its operating its operating current Idc 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 R is 0.5 Ω, and the tower footing resistance R is 15 Ω. Figuree 10 shows the equivalent circuit of a groundingt fault on the electrode lines operated in mono-polarFigure 10 shows mode. Usually the equivalent the grounding circuit fault of aon grounding the electrode fault lines on does the not electrode influence lines the operation operated in mono-polarcurrent and mode. only Usually the static the stability grounding of system fault ison of concern, the electrode hencelines the station does notcan inﬂuencebe regarded the asoperation a DC current source.

Energies 2018, 11, 430 9 of 19 current and only the static stability of system is of concern, hence the station can be regarded as a DC currentEnergies source. 2018, 11, x FOR PEER REVIEW 9 of 19

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: D k = f (4) D Dsf k = (4) where Df is the distance from the fault location to theDs electrode, Ds is the distance from the station to the electrode as well as the length of electrode line. The fault location lie between the electrode and D D wherethef station,is the distance so the value from of k the should fault limit location in the torange the from electrode, 0 to 1. s is the distance from the station to the electrodeAccording as well to as Kirchhoff’s the length law, of electrode the U-I characteristic line. The fault of external location system lie between Ugp(Igp) is the expressed electrode as: and the station, so the value of k should limit in the range from 0 to 1. 1− c =+k ⋅−++n 2 +⋅⋅ According to Kirchhoff’sURgpe law,() the U-I RIRR ldcet characteristic ( of external kkRI ) system lgp Ugp(Igp) is expressed(5) as: ccnn k 1 − cn where cn is the conductor number of electrode lines (cn = 2 for this2 case). Equation (5) is a linear Ugp = (Re + Rl) · Idc − Re + Rt + ( k + k) · Rl · Igp (5) function which can be simplifiedcn as: cn

UABI=−⋅ where cn is the conductor number of electrodegp lines (c gpn = 2 for this case). Equation (5) is(6) a linear function whichHere, canthe coefficients be simpliﬁed A and as: B stand for: Ugp = A − B · Igp (6) ≡+k ⋅ A ()RRIeldc (7) Here, the coefﬁcients A and B stand for: cn

 1− c  ≡++k n 2 +⋅ BRRA ≡et(Re +()R kkRl) · Idc l (8) (7)  ccn  1 − cn 2 4.1.2. U-I Characteristic of FaultB ≡Arc Re + Rt + ( k + k) · Rl (8) cn 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 bL + arc UaLarc= arc (9) From Equations (2) and (3), the U-I CharacteristicI ofarc Fault arc Uarc(Iarc) is expressed as: where a = 0.87 and b = 5.77. Equation (9) is a negative power function which can be simplified as: bLarc Uarc = aLarc + (9) D Iarc UC= + (10) arc I where a = 0.87 and b = 5.77. Equation (9) is a negative powerarc function which can be simpliﬁed as: Here, the coefficients C and D stand for: ≡ D Uarc CaL= C +arc (11) (10) Iarc DbL≡ (12) Here, the coefﬁcients C and D stand for: arc 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 largerC ≡ aL thanarc initial arc length. The stable arc length Lst is (11)

D ≡ bLarc (12) Energies 2018, 11, 430 10 of 19

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:

D A − BIcr = C + (13) Icr

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:

1 q I = A − C ± (A − C)2 − 4BD (15) cr 2B

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

(A − C)2 − 4BD = 0 (16)

A − C I = (17) cr 2B

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

2 kcr 1 − cn 2 (Re + Rl) · Idc − aLarc − 4bLarc · Re + Rt + ( kcr + kcr) · Rl = 0 (18) cn cn

Then rewrite Equation (18) in the form of quadratic equation:

0 2 0 0 A kcr + B kcr + C = 0 (19) where, A0, B0 and C0 stands for:

(R I )2 − 4c · (1 − c ) · bL R 0 ≡ l dc n n arc l A 2 (20) cn

2R I · (R I − aL ) − 4c bL R B0 ≡ l dc e dc arc n arc l (21) cn 0 2 C ≡ (Re Idc − aLarc) + 4bLarc · (Re + Rt) (22)

Finally, the general solutions of kcr are:

1 p k = −B0 ± B2 − 4A0C0 (23) cr 2A0 Energies 2018, 11, 430 11 of 19

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 11 of 19 4.2.2. Protection Region of Arcing Horns 4.2.2. Protection Region of Arcing Horns

The protectionThe protection region ofregion arcing of arcing horns horns is related is related to tokcr kcronly onlyif if thethe real solution solution of ofkcr andkcr and Icr exists.Icr exists. Figure 11 showsFigure 11 the shows possible the possible real solutions real solutions of k crof andkcr andIcr Icrfor for critical critical burning burning states states in real in real plane. plane.

2000 k =k cr,1 cr,2 U arc I =0 I >0 gp cr,2 U 1500 gp k=k cr,2

I =±∝ 1000 cr,1

k =k cr,1 cr,2 500 U =C Voltage (V) Voltage gp I <0 cr,1 k=k 0 cr,1

I =I =0 cr,1 cr,2 -500 -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 FromIcr, Figure1 = Icr,2 =11 0 ,when it is knownIgp = 0. In that a practical there arecase, two Icr should solutions be a limitedIcr,1 < 0positive and Icr, value.2 > 0 Therefore, except the Icr,2 situation is a reasonable solution and the special situation Igp = 0 and Ugp = C should also be excluded. The Icr,1 = Icr,2 = 0 when Igp = 0. In a practical case, Icr should be a limited positive value. 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 locationkBBAC of Icr,=−2 is (kcr,2'+: '2 − 4 ' ') (24) cr ,2 2'A 1 p If kcr,2 < 0 which means the arcing horns cannot0 protect02 the 0electrode0 lines. If kcr,2 > 1 which means kcr,2 = 0 −B + B − 4A C (24) the arcing horns protect all the electrode2A lines. If 0 < kcr,2 < 1 which means the arcing horns protect part 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  < the arcing horns protect all the electrode lines. If00 0 < kcr,  0 when kcrcr,2 ,2 < 0  √ = 1 − 0 + 02 − 0 0 < < kP 2A0 B B 4A C when 0 kcr,2 1 (25) 5. Influence Factors on Protection Performance of Arcing Horns 1 when kcr,2 > 1

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 5.1.1. Relationsexternal between system and Power the power Balance, consumed Protection by the Performance fault arc. If the andpower U-I supplied Characteristics by external system is less than the power consumed by the fault arc, then the fault arc will cool down and be extinguished The essentialeventually. of In static other stabilitywords, if ofwe fault want arcsa better is the protection power performance balance between for arcing the horns, power we supplied should by external systemreduce andthe power the power supplied consumed by the external by the system fault an arc.d increase If the powerthe power supplied consumed by by external the fault system arc. is less than theThis power idea is consumedinspired that by the the analysis fault arc,of the then factors the faultinfluencing arc will the coolprotection down region and be that extinguished can be 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. EnergiesEnergies2018 2018,,11 11,, 430x FOR PEER REVIEW 1212 of of 19 19

For a given point on the U-I characteristic, the power P = U·I consumed or released is decided P U·I by itsFor position a given parameters point on the I and U-I U characteristic,. Therefore the the power power of a= givenconsumed point can orbe releasedincreased is (or decided reduced) by I U itsby position lifting (or parameters lowering) theand U-I. characteristic. Therefore the In power the end, of a giventhe analysis point canof the be influence increased factors (or reduced) on the byprotection lifting (or region lowering) can be the further U-I characteristic. converted to Inthe the analysis end, the of analysisthe influe ofnce the factors influence on factorsthe U-I oncharacteristic. the protection region can be further converted to the analysis of the influence factors on the 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.

5.2.5.2. VariationVariation ofof ProtectionProtection Performance Performance of of Arcing Arcing Horns Horns with with Circuit Circuit Parameters Parameters

5.2.1.5.2.1. ArcArc Length Length AlthoughAlthough it it is theis the arc arc length length not thenot discharge the discharge gap distance gap distance of arcing of horns arcing which horns directly which influence directly theinfluence protection the protection region according region toaccording the state to equations, the state theequations, discharge the gapdischarge distance gap of distance arcing horns of arcing can stillhorns have can an still influence have an by influence deciding by the deciding stable arc the length. stable Figure arc length. 12 shows Figure the influence12 shows ofthe arc influence length on of thearc protection length on the region protection of arcing region horns. of The arcing protection horns. The region protection increases region almost in linearcreases with almost the linear arc length. with Longerthe arc arc length. length Longer means largerarc length energy means consumption larger energy of arc, soconsumption that the U-I characteristicof arc, so that of faultthe arcU-I willcharacteristic be lifted, and of fault the protection arc will be region lifted, of and arcing the hornsprotection increases region with of thearcing arc length.horns increases The arcing with horns the canarc protectlength. theThe electrode arcing horns line onlycan protect if the stable the electrode arc length line is more only thanif the 1100 stable mm. arc For length the arcingis more horns than with1100 1500 mm. mm For dischargethe arcing gap horns length with whose 1500 mm stable discharg arc lengthe gap is 2500length mm, whose the protectionstable arc length region is 2500 just 20.1%.mm, the It canprotection be concluded region that is just the 20.1%. arcing It horns can be has concluded poor protection that the performance arcing horns for has electrode poor protection lines of largerperformance operation for current electrode and lines long of distance. larger operation current and long distance.

10 Protection region (%) region Protection

0 500 1000 1500 2000 2500 3000 3500 4000 Arc length (mm)

FigureFigure 12.12.Inﬂuence Influence of of arc arc length length on on protection protection region region of of arcing arcing horn. horn.

5.2.2.5.2.2. TowerTower Footing Footing Resistance Resistance FigureFigure 13 13 andand TableTable2 2 show show thethe inﬂuenceinfluence ofof tower footing resistance resistance on on the the protection protection region region of ofarcing arcing horns. horns. The The protection protection region region increases increases wi withth the the tower footing resistance,resistance, butbut thethe inﬂuenceinfluence decreasesdecreases as as the the tower tower footing footing resistance resistance increases. increases. SinceSince thethe slopeslopeB Bincreases increases with with the the tower tower footing footing resistance, resistance, the the U-I U-I characteristic characteristic of of external external systemsystem will will be be lowered lowered which which means means the the energyenergy supplied supplied by by thethe externalexternal systemsystem willwill decreasedecrease asas well.well. Finally,Finally, the the protection protection region region of of arcing arcing horns horns increases increases with with the the tower tower footing footing resistance. resistance.

Energies 2018, 11, x FOR PEER REVIEW 13 of 19 Energies 2018, 11, 430 13 of 19 Energies 2018, 11, x FOR PEER REVIEW 13 of 19 25 25 450 mm 600 450 mm mm 20 1000 600 mmmm 20 1500 1000 mm mm 1500 mm 15 15

10 10

5 Protection region (%) Protection 5 Protection region (%) Protection

0 0

0369121503691215 Tower footing resistance (Ω) Tower footing resistance (Ω)

Figure 13. Influence of tower footing resistance on protection region of arcing horns. FigureFigure 13. 13.Influence Influence of of tower tower footing footing resistance resistance on on protection protection region region of of arcing arcing horns. horns. Table 2. Influence of tower footing resistance on protection region of arcing horns. TableTable 2. 2.Influence Influence of of tower tower footing footing resistance resistance on on protection protection region region of of arcing arcing horns. horns. Protection Region (%) Rt (Ω) 450 mmProtection 600 mm Region1000 mm (%) 1500 mm R (ΩR) t (Ω) t 3 450 mm0 600 0 mm 1000 4.8 mm 150013.8 mm 450 mm 600 mm 1000 mm 1500 mm 3 6 0 0 0 0 5.3 4.8 14.413.8 36 9 00 0 0.7 0 6.0 5.3 4.8 15.214.4 13.8 69 12 00 0 0.7 1.8 0 7.36.0 5.3 16.715.2 14.4 915 00 0.7 4.4 10.2 6.0 20.1 15.2 12 0 1.8 7.3 16.7 12 0 1.8 7.3 16.7 15 0 4.4 10.2 20.1 5.2.3. Electrode Resistance15 0 4.4 10.2 20.1 5.2.3. ElectrodeFigure 14Resistance and Table 3 show the influence of electrode resistance on the protection region of 5.2.3.arcing Electrode horns. Resistance As the result shown, the protection region decreases almost linearly with the electrode Figure 14 and Table 3 show the influence of electrode resistance on the protection region of Figureresistance, 14 andand the Table arcing3 show horns the is invalid influence for protection of electrode at large resistance electrode on resistance. the protection region of arcing horns.Both Asthe thevertical result intercept shown, A theand protection the slope B regionincrease decreases with the electrode almost linearly resistance with Re. Howeverthe electrode arcing horns. As the result shown, the protection region decreases almost linearly with the electrode resistance,the effect and of theRe on arcing B is limited horns because is invalid Rt and for Rprotectionl are usually at much large larger electrode than resistance.Re, hence the effect of Re resistance, and the arcing horns is invalid for protection at large electrode resistance. onBoth A isthe dominant. vertical Asintercept a consequence, A and the the slope U-I characteri B increasestic with of external the electrode system willresistance be raised Re .which However Both the vertical intercept A and the slope B increase with the electrode resistance Re. However the effectmeans of the Re energyon B is supplied limited becauseby the external Rt and system Rl are usuallywill increase, much and larger the protectionthan Re, hence region the of effectarcing of Re the effect of R on B is limited because R and R are usually much larger than R , hence the effect of R on Ahorns is dominant. decreasese Aswith a theconsequence, electrode resistance. tthe U-Il characteristic of external systeme will be raised whiche 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 by the external system will increase, and the protection region of arcing horns decreases with the electrode50 resistance. horns decreases with the electrode resistance. 450 mm 40 600 mm 50 1000 mm 1500 mm 30 450 mm 40 600 mm 1000 mm 20 1500 mm 30 10 Protection region (%)

20 0

10 Protection region (%) 0.0 0.2 0.4 0.6 0.8 1.0 Ω Electrode resistance ( ) 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)

FigureFigure 14. 14.Inﬂuence Influence of of electrode electrode resistance resistance on on protection protection region region of of arcing arcing horns. horns.

Energies 2018, 11, 430 14 of 19

Table 3. Inﬂuence of electrode resistance on protection region of arcing horns. Energies 2018, 11, x FOR PEER REVIEW 14 of 19 Protection Region (%) TableR e3.( ΩInfluence) of electrode resistance on protection region of arcing horns. 450 mm 600 mm 1000 mm 1500 mm Protection Region (%) Re (Ω) 0.1 14.9450 mm 600 20.9 mm 1000 26.7 mm 1500 mm 36.6 0.20.1 13.914.9 19.9 20.9 26.7 25.7 36.6 35.5 0.30.2 12.213.9 18.2 19.9 25.7 24.0 35.5 33.8 0.40.3 8.812.2 14.7 18.2 24.0 20.5 33.8 30.4 0.50.4 08.8 4.4 14.7 20.5 10.2 30.4 20.1 0.5 0 4.4 10.2 20.1 5.2.4. Line Resistance 5.2.4. Line Resistance Figure 15 and Table4 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 are very effective for short HVDC electrode lines. For the line resistance R , both the vertical arcing horns are very effective for short HVDC electrode lines. For the line resistancel Rl, both the interceptverticalA and intercept the slope A andB increase the slope with B increaseRl. When withR Rl lis. When small, R thel is effectsmall, oftheR effectl on A ofis R dominated,l on A is and thedominated, U-I characteristic and the U-I of externalcharacteristic system of willexternal be liftedsystem which will be means lifted the which energy means supplied the energy by the externalsupplied system by will the increase.external system Thus thewill protectionincrease. Thus region the decreasesprotection region with the decreases line resistance. with the line As Rl increases,resistance. the effect As R ofl increases,Rl on B becomesthe effect stronger,of Rl on B sobecomes that the stronger, rate of so decline that the of rate the of protection decline of region the falls off.protection region falls off.

100 450 mm 600 mm 80 1000 mm 1500 mm

Protection (%) region 20

012345 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 (%) Rl (Ω) 450 mmProtection 600 mm Region 1000 mm (%) 1500 mm Rl (Ω) 0.977 0 22.2 51.0 99.8 1.954450 mm0 600 17.7 mm 1000 40.8 mm 80.0 1500 mm 0.9772.931 00 22.2 13.3 30.7 51.0 60.1 99.8 1.9543.908 00 17.78.9 20.5 40.8 40.1 80.0 2.9314.885 00 13.34.4 10.2 30.7 20.1 60.1 3.908 0 8.9 20.5 40.1 5.2.5. Operation Current4.885 0 4.4 10.2 20.1 Figure 16 and Table 5 show the influence of operation current on the protection region of arcing 5.2.5. Operationhorns. The protection Current region decreases with the operation current, but the rate of decline falls off with the operation current. A full protection can be realized at low operation current which demonstrates Figure 16 and Table5 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. The protection region decreases with the operation current, but the rate of decline falls off with operation 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

Energies 2018, 11, 430 15 of 19

Energies 2018, 11, x FOR PEER REVIEW 15 of 19 operation current Idc, the vertical intercept A increases with Idc, and the U-I characteristic of external systemsystem will be will lifted be lifted which which means means the energythe energy supplied supplie byd by the the external external system system will increase. increase. Therefore Therefore the protectionEnergiesthe protection 2018 region, 11, x FOR region of PEER arcing of REVIEW arcing horns horn decreasess decreases with with the the operation operation current. current. 15 of 19

system will be lifted which means the energy supplied by the external system will increase. Therefore the protection region of arcing100 horns decreases with the operation current. 450 mm 600 mm 80 1000 mm 1500 mm 100 450 mm 600 mm 60 80 1000 mm 1500 mm

40 60 Protection region (%) region Protection

20 40

Protection region (%) region Protection 20 0 500 1000 1500 2000 2500 3000 0 Operation current (A)

FigureFigure 16. Influence 16. Influence0 of operation500 of operation 1000 current current 1500 on on protection 2000 protection 2500 region region 3000 of of arcingarcing horns. Operation current (A) TableFigureTable 5. Influence 16. 5. Influence Influence of operation of of operation operation current current current on on on protection pr protectionotection regionregion region of of arcing arcing horns. horns.horns. Protection Region (%) Idc (A) 450 mmProtection 600 mm Region 1000 mm (%) 1500 mm TableIdc 5.(A) Influence of operation current on protection region of arcing horns. 630450 mm77.1 600100.0 mm 1000100.0 mm 100.0 1500 mm 1260 57.3 Protection81.6 Region100.0 (%) 100.0 630Idc (A) 77.1 100.0 100.0 100.0 1890 450 mm37.5 600 mm55.8 1000 73.4 mm 1500 100.0 mm 1260 57.3 81.6 100.0 100.0 6302520 77.117.8 100.0 29.9 100.0 41.7 100.0 61.6 1890 37.5 55.8 73.4 100.0 12603150 57.30 81.64.4 100.010.2 100.020.1 25201890 17.837.5 29.9 55.8 73.4 41.7 100.0 61.6 3150 0 4.4 10.2 20.1 5.2.6. Conductor Number 2520 17.8 29.9 41.7 61.6 3150 0 4.4 10.2 20.1 5.2.6. ConductorFigure Number 17 and Table 6 show the influence of conductor number on the protection region of arcing 5.2.6.horns. Conductor The protection Number region increases almost linearly with the conductor number. For the conductor Figurenumber 17 andcn, both Table vertical6 show intercept the influence A and the of slope conductor B decrease number with on cn. theAs R protectiont counts majority region part of arcing of B, Figure 17 and Table 6 show the influence of conductor number on the protection region of arcing horns. Thethe effect protection of cn on region B is limited, increases in turn, almost the effect linearly of cnwith on A theis dominant, conductor so number.the U-I characteristic For the conductor of the horns. The protection region increases almost linearly with the conductor number. For the conductor numberexternalc , both system vertical will intercept be loweredA and which the slopemeansB thdecreasee energy withsuppliedc . As byR thecounts external majority system part will of numbern cn, both vertical intercept A and the slope B decrease with cn. Asn Rt countst majority part of B, decrease, and the arcing horns protection region will increase. B, thethe effect effect of ofcn cnon on BB isis limited, limited, in in turn, turn, the the effect effect of cn of onc nAon is dominant,A is dominant, so the U-I so characteristic the U-I characteristic of the of the external system will be lowered which means the energy supplied by the external system will external system will be lowered80 which means the energy supplied by the external system will decrease,decrease, and theand arcingthe arcing horns horns protection protection 450 region mmregion will will increase. increase. 600 mm 8060 1000 mm 1500 mm 450 mm 600 mm 6040 1000 mm 1500 mm

4020

Protection region (%) region Protection

20 0 Protection region (%) region Protection 123456 0 Conductor number

Figure 17. Influence123456 of conductor on protection region of arcing horns. Conductor number

FigureFigure 17. 17.Inﬂuence Influence of of conductor conductor on on protection protection region of of arcing arcing horns. horns.

Energies 2018, 11, 430 16 of 19

Table 6. Inﬂuence of conductor on protection region of arcing horns.

Protection Region (%) n 450 mm 600 mm 1000 mm 1500 mm 1 0 2.2 5.1 10.0 2 0 4.4 10.2 20.1 3 0 6.7 15.5 30.3 4 0 9.0 20.7 40.6 5 0 11.3 26.0 50.8 6 0 13.6 31.4 61.0

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:

2 kcr (Re + Rl) · Idc − aLarc − 4bLarcRt = 0 (26) cn and then the approximation solutions of kcr are:

0 cn p kcr = aLarc − Re Idc ± 4bLarcRt (27) Rl Idc

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

0 cn p kcr,2 = aLarc − Re Idc + 4bLarcRt (28) Rl Idc

0 Finally, the approximation protection region of arcing horns k p is:  0 when k0 < 0  √ cr,2 0 cn 0 k = aLarc − Re I + 4bLarcRt when 0 < k < 1 (29) P Rl Idc dc cr,2  0 1 when kcr,2 > 1

5.3.2. Analysis on Inﬂuence of Circuit Parameters Based on Approximation Solutions 0 The derivatives of approximation protection region k p with respect to Larc, Re, Rl, Rt, Idc and cn are: 0 s ! dkp c bR = n a + t (30) dLarc Rl Idc Larc 0 dkp c = − n (31) dRe Rl 0 dk c p = − n − + p 2 aLarc Re Idc 4bLarcRt (32) dRl Rl Idc 0 s dkp c bL = n arc (33) dRt Rl Idc Rt Energies 2018, 11, 430 17 of 19

0 dk c p = − n + p 2 aLarc 4bLarcRt (34) dIdc Rl Idc 0 dkp 1 p = aLarc − Re Idc + 4bLarcRt (35) dcn Rl Idc 0 0 0 0 0 when 0 ≤ k p ≤ 1. It is obvious that: dk p/dRe and dk p/dcn are constants; dk p/dLarc and dk p/dRt 0 0 0 0 are positive; dk p/dRe and dk p/dIdc are negative. The signs of dk p/dRl and dk p/dcn are decided by the specific circuit parameters. Under our conditions that Idc = 3150 A, Re = 0.5 Ω, Rt = 15 Ω, 0 0 a = 0.87 V/mm, b = 5.77 and Larc = 1100~2500 mm, dk p/dRl < 0 and dk p/dcn > 0. 0 For the arc length Larc, when Larc is very large, dk p/dLarc ≈ αcn/RlIdc > 0 can be assumed a constant. Therefore, the protection region increases linearly with the arc length. 0 For the electrode resistance Re and the conductor number cn, considering that dk p/dRe is 0 a negative constant while dk 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. 0 0 For the line resistance Rl and the operation current Idc, both of dk p/dRl and dk 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. 0 For the tower footing resistance Rt, dk 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 Energies 2018, 11, 430 18 of 19 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 theEnergies station. 2018, 11, x FOR PEER REVIEW 18 of 19

10,00010000 k=1

8000 k=0.8

6000 k=0.6

k=0.4 4000 Voltage (V) k=0.2 2000 k=0

0 0 100 200 300 400 500 600 Current (A)

FigureFigure 18. 18.U-I U-I characteristic characteristic of of external external system system at at different different fault fault location. location.

7. ConclusionsIn 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 lengthIn this may paper, not achieve experiments full protection, were carried and out auxiliar to studyy devices the characteristics for arc extinction of long are free needed burning as arcswell. andConsidering the insulation that coordinationthe arc extinction of arcing devices horns will on incur the electrode extra expenses, lines of it a 5000is unnecessary MW, ±800 to kV install HVDC the system.arc extinction The factors devices influencing all along the th protectione electrode performance lines. Therefore, of arcing the diversified horns are analyzedconfiguration theoretically. strategy Theof arcing main conclusions horns is recommended are summarized for cost as follows: savings, which means arcing horns of short discharge gap (1)lengthThe are development sufficient and process recommended of long free for burningthe place arcs near can the be electrode, divided meanwhile, into slow expansion, arcing horns fast of longexpansion, discharge gap violent length motion with additional and extinction arc exti phases.nction devices The long are free recommended burning arc for column the places is very near 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 andIn this short paper, distance. experiments For the were HVDC carried electrode out to lines study systems the characteristics of high operation of long current free burning and long arcs anddistance, the insulation the protection coordination performance of arcingof horns arcing on horns the electrode is limited, lines and of additional a 5000 MW, auxiliary ±800 kV devices HVDC system.for arc The extinction factors influencing are needed the to protection realize full performance protection. of arcing horns are analyzed theoretically. (3)The Themain effect conclusions ways for are the summarized protection performance as follows: improvement of arcing horns are increasing the (1) arcThe voltage development and tower process footing of resistance,long free burning and reducing arcs can the be total divided resistance into ofslow HDVC expansion, electrode fast lineexpansion, system. Differentialviolent motion arcing and horns extinction configuration phases. strategy The long is recommendedfree burning arc for column cost saving. 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 (CSEPDI)is thought of China to Power be the Engineering main cause Consulting of the instability Group Corporation of arc column. (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 conceivedand and short designed distance. the experiments;For the HVDC Yi Liu electrode and Fuchang lines Lin systems gave suggestions of high operation on the experiments. current and long 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.

References(3) The effect ways for the protection performance improvement of arcing horns are increasing the arc voltage and tower footing resistance, and reducing the total resistance of HDVC electrode 1. Gu,line S.Q.; system. He, J.L.;Differential Zeng, R.; arcing Zhang, horns B.; Xu, configuration G.Z.; Chen, st W.J.rategy Motion is recommended characteristics offor long cost acsaving. arcs in atmospheric air. Appl. Phys. Lett. 2007, 90, 051501. [CrossRef] 2.Acknowledgments:Li, Q.M.; Cong,H.X.; This Sun,work Q.Q.; was Xing, supported J.Y.; Chen, by Central Q. Characteristics Southern ofChina Secondary Electric AC Power ArcColumn Design MotionInstitute (CSEPDI)Near Powerof China Transmission Power Engineering Line Insulator Consulting String. GroupIEEE Trans.Corporation Power Deliv.(DG1-A04-2013).2014, 29, 2324–2331. [CrossRef]

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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Energies 2018, 11, 430 19 of 19

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