Studies on an Electromagnetic Transient Model of Offshore Wind Turbines and Lightning Transient Overvoltage Considering Lightning Channel Wave Impedance

energies

Article Studies on an Electromagnetic Transient Model of Offshore Wind Turbines and Lightning Transient Overvoltage Considering Lightning Channel Wave Impedance

Li Zhang 1, Shengwei Fang 1, Guozheng Wang 1 ID , Tong Zhao 2,* ID and Liang Zou 1 1 School of Electrical Engineering, Shandong University, Jinan 250061, China; [email protected] (L.Z.); [email protected] (S.F.); [email protected] (G.W.); [email protected] (L.Z.) 2 Shandong Provincial Key Lab of UHV Transmission Technology and Equipment, Jinan 250061, China * Correspondence: [email protected]; Tel.: +86-531-8169-6129

Received: 12 October 2017; Accepted: 24 November 2017; Published: 1 December 2017

Abstract: In recent years, with the rapid development of offshore wind turbines (WTs), the problem of lightning strikes has become more and more prominent. In order to reduce the failure rate caused by the transient overvoltage of lightning struck offshore WTs, the influencing factors and the response rules of transient overvoltage are analyzed. In this paper, a new integrated electromagnetic transient model of offshore WTs is established by using the numerical calculation method of the electromagnetic field first. Then, based on the lightning model and considering the impedance of the lightning channel, the transient overvoltage of lightning is analyzed. Last, the electromagnetic transient model of offshore WTs is simulated and analyzed by using the alternative transients program electro-magnetic transient program (ATP-EMTP) software. The influence factors of lightning transient overvoltage are studied. The main influencing factors include the sea depth, the blade length, the tower height, the lightning flow parameters, the lightning strike point, and the blade rotation position. The simulation results show that the influencing factors mentioned above have different effects on the lightning transient overvoltage. The results of the study have some guiding significance for the design of the lightning protection of the engine room.

Keywords: offshore wind turbines (WTs); electromagnetic transient model; lightning transient overvoltage; lightning channel wave impedance; lightning protection

1. Introduction With the increasingly serious energy problem, wind energy has gradually become the most rapidly developed and widely used renewable energy in the world [1,2]. As the direct generators of wind energy, wind power units are getting higher and higher as their capacity increases. In addition, the sea environment is wet and rainy, the grounding environment is complex, thunderstorm phenomena are frequent, so the probability of lightning strikes on offshore wind turbines (WTs) has increased considerably. According to the statistics of the International Electro Technical Commission, the damage rate of wind power units caused by lightning strikes is up to 14% in areas where thunderstorms are frequent. WTs are the most valuable components of wind farms, representing more than 60% of the total investment in wind power. Lightning strikes not only cause damage to the WTs themselves, but also cause the wind power to be shut down when serious, even threatening the safe operation of the power grid [3,4]. Therefore, the lightning protection of offshore WTs has become a major technical problem which needs to be urgently solved. When a wind turbine is struck by lightning, a thunderbolt that carries a huge amount of energy will be injected into the top of the unit’s blades, or a lightning rod in the rear of the nacelle. The current

Energies 2017, 10, 1995; doi:10.3390/en10121995 www.mdpi.com/journal/energies Energies 2017, 10, 1995 2 of 15

flows through the metal conductor inside the blade, the guide path of the engine room, the tower body, the grounding device of the WTs, and finally the discharge flow enters the ground. In the transient process of the whole discharge, the lightning flow can cause the potential jump of all parts of the WTs, which may cause a counterattack or insulation damage to the equipment [5]. Due to the power system and control system present in the engine room, it is very important to protect the engine room. At present, domestic and foreign scholars have mainly reported experimental research and theoretical analysis on the field of lightning over-voltage and electromagnetic effects. In an experimental study, the Japanese scientist Yamamoto built a scale model of a wind turbine, used the electrode simulated lightning generator to complete the lightning simulation test, and analyzed the potential rise of the bottom of the cylinder [6]. However, due to the huge cost of experimental research [7], the experimental model is not flexible. With its dual characteristic of voltage source and current source, lightning is difficult to simulate, so to date most research on the characteristics of lightning are based on computer theoretical analysis. At present, most research on lightning transient response is carried out for lightning protection of the steel structure model of buildings. Zhang at Beijing Jiao Tong University studied the distribution characteristics of lightning current in the lightning protection system when lightning strikes buildings [8]. The electromagnetic transient software EMTP (ATP, Bonneville Power Administration, Portland, OR, USA) is widely used in the lightning transient calculation of wind farms, and it is a powerful tool for designers and researchers [9]. Zhao and Wang, from the Chinese Academy of Sciences, have established a simplified “tower-transmission line” model for EMTP for the lightning transient potential problem [10]. The transient over-voltages of the tower and transmission lines have been calculated and analyzed. In the aspect of theoretical analysis, Harrington proposed the method of moment analysis of lightning electromagnetic induction [11]. Zhang discussed the influencing factors of the potential rise of the WTs grounding device by the moments method [12,13]. References [14–16] use the finite-difference time-domain (FDTD) method to analyze the WTs ring grounding pole. In [17–19], the lightning protection model of a power system is proposed. These works provide the reference for the establishment of offshore wind turbine lightning models. In [20], the influence of the tower and transmission line interdispersion capacitance is considered, and the induced overvoltage of the tower internal transmission line is analyzed. Although the lightning transient response to the WTs has been studied more, it is mainly based on onshore WTs. The influence of oceanic factors, especially the seawater layer, on the transient potential of the WTs, is not considered. Studies on the transient potential of the nacelle are limited. In addition, the traditional empirical formulae [21,22] cannot show the influence of blade rotation angle on the impedance model. The existing research lacks an analysis of the wave impedance characteristics of the unit, which affects the accurate calculation of the potential of each part and each point of the generator when the lightning current occurs in the unit. In this paper, a grounding model of offshore WTs is established firstly, and the numerical calculation method of the impact grounding resistance of the WTs is proposed. The wave impedance model of the blade and the tower is established according to the rotation characteristics and the conical antenna theory. Based on the wave impedance model, an alternative transients program electro-magnetic transient program (ATP-EMTP) simulation model of the lighting WTs is built and compared with the traditional impedance model. The influence of different factors on the transient overvoltage is analyzed. This has certain guiding significance for the design of offshore wind turbine lightning protection systems.

2. Modeling of Offshore WT Lightning Transient Effect When the offshore WT is struck by lightning, the lightning current will ﬂow through the lightning channel wave impedance, and will form a certain circulation path on the WT at the same time. The lightning current goes through the blade, tower, grounding device, and ﬁnally into the ground. Energies 2017, 10, 1995 3 of 15

Energies 2017, 10, 1995 3 of 15 In order to accurately analyze the transient overvoltage of the WT, an accurate calculation model of Energies 2017, 10, 1995 3 of 15 each2.1. Numerical part should Calculation be established. of Offshoree Wind Turbines Grounding Resistance 2.1. Numerical Calculation of Offshoree Wind Turbines Grounding Resistance 2.1. NumericalThe design Calculation of the offshore of Offshoree wind Wind turbine Turbines groundin Groundingg system Resistance is different from that of traditional onshoreThe WTs.design The of thepipe offshore rack structure wind turbine is used groundin as the foundationg system is of different offshore from WTs. that Considering of traditional the The design of the offshore wind turbine grounding system is different from that of traditional onshoreeconomy WTs. and theThe ease pipe of rack construction, structure isthe used general as the engineering foundation uses of offshore the foundation WTs. Considering as the natural the onshore WTs. The pipe rack structure is used as the foundation of offshore WTs. Considering the economygrounding and body. the At ease present, of construction, the basic forms the general of offshore engineering wind turbine uses thecan foundationbe subdivided as the into natural single economy and the ease of construction, the general engineering uses the foundation as the natural groundingpile foundations, body. Atgravity present, foundations, the basic forms suction of offshore foundations, wind turbinemulti-pile can foundationsbe subdivided and into floating single grounding body. At present, the basic forms of offshore wind turbine can be subdivided into pilefoundations foundations, [23]. Amonggravity them, foundations, the most suctionwidely usedfoundations, is the single multi-pile pile foundation, foundations and andits structural floating single pile foundations, gravity foundations, suction foundations, multi-pile foundations and ﬂoating foundationsdiagram is shown [23]. Among in Figure them, 1. the most widely used is the single pile foundation, and its structural foundations [23]. Among them, the most widely used is the single pile foundation, and its structural diagram is shown in Figure 1. diagram is shown in Figure1.

Figure 1. Single foundation schematic. Figure 1. Single foundation schematic. The grounding resistance is calculated by point current source Green function in the soil. The LaplaceThe equation grounding grounding of cylindricalresistance resistance isc is oordinatecalculated calculated system by by point point is solvedcurrent current by source Fourier source Green transform Green function function and in separationthe in soil. the soil.The of TheLaplacevariables Laplace equation [24]. equation The of potentialcylindrical of cylindrical function coordinate coordinate of thesystem systemmidp is ointsolved is solved current by byFourier source Fourier transform is transform obtained, and and separationas separationshown ofin ofvariablesEquation variables (1):[24]. [ 24 The]. The potential potential function function of ofthe the midp midpointoint current current source source is is obtained, obtained, as as shown in Equation (1): −λλrr ϕφλ=+()J ( λre ) γλ () J ( λ re ) (1) 00−λr λr ϕϕφλ==+φ(()λ)JJ0( (λ λrre) )e −λλrr+ γλγ ()(λ) JJ0 (( λλ rer )e (1) 00 (1) In Equation (1), φ(λ) and γ(λ) are undetermined coefficients, and J0(λr) is the first class of zeroth In Equation (1), ϕ(λ) and γ(λ) are undetermined coefﬁcients, and J0(λr) is the ﬁrst class of zeroth orderIn Bessel Equation functions, (1), φ( λλ) isand an γarbitrary(λ) are undetermined constant. The coefficients, ground environment and J0(λr) ofis theoffshore first class wind of turbine zeroth order Bessel functions, λ is an arbitrary constant. The ground environment of offshore wind turbine is orderis divided Bessel into functions, sea water λ layer is an andarbitrary soil layer. constant. The grounding The ground body environment is divided ofinto offshore the upper wind and turbine lower divided into sea water layer and soil layer. The grounding body is divided into the upper and lower istwo divided sections, into and sea waterthe potential layer and function soil layer. should The grounding be calculated body respectively is divided into [25]. the The upper mathematical and lower two sections, and the potential function should be calculated respectively [25]. The mathematical twomodel sections, is shown and in theFigure potential 2. function should be calculated respectively [25]. The mathematical model is shown in Figure2. model is shown in Figure 2.

1 ρ1 h 1 l ρ1 h l

ρ2 ρ2 2a 2a Figure 2. Grounding model of offshore WT. Figure 2. Grounding model of offshore WT. Figure 2. Grounding model of offshore WT. where l is the total length of grounding, a is based radius, h1 is the upper water depth, ρ1 is the upper whereseawater l is resistivity, the total length ρ2 is the of grounding,lower resistivity a is based of seabed radius, sand. h1 is The the current upper waterdensity depth, of the ρ ground1 is the upper body seawater resistivity, ρ2 is the lower resistivity of seabed sand. The current density of the ground body

Energies 2017, 10, 1995 4 of 15

Where l is the total length of grounding, a is based radius, h1 is the upper water depth, ρ1 is the upper seawater resistivity, ρ2 is the lower resistivity of seabed sand. The current density of the ground body in the upper seawater and the lower soil is δ1 and δ2 respectively, and the relation is as shown in Equation (2): ( ρ2 I δ1 = [ρ2h1+ρ1(l−h1)] (2) ρ1 I δ2 = [ρ2h1+ρ1(l−h1)]

The potential functions of the upper seawater and the underlying soil φδ1 and φδ2 can be calculated by using Equations (1) and (2), respectively. Based on the superposition principle, the numerical expression of the impulse grounding resistance of the single pile wind turbine in the double deck grounding environment of the ocean can be obtained, as shown in Equation (3):

= αρ1ρ2 × R 2π[ρ h +ρ (l−h )] √ 2 1 1 1 √ 2 2 ∞ + + 2+( + )2 (3) ln l+ a +l + kn ln 2nh1 l √a 2nh1 h1 a ∑ 2 2 n=0 2nh1−h1+ a +(2nh1+h1)

In Equation (3), α is the impulse factor. Considering that the single pile foundation is a vertical tube, its radius is much larger than the radius of ﬂat steel in the common grounding device. The spark discharge around the grounding body is not obvious [26]. The approximate value of α is 1.

2.2. Modeling of Propeller Blade Wave Impedance Considering Rotation Factor The rotation of the blade will change the capacitance, inductance and other parameters of the blade. From the deﬁnition of wave impedance, it can be seen that the blade wave impedance changes with the increase of blade length. Therefore, in order to accurately establish the blade wave impedance model, the simultaneous effects of rotation angle, height of tower and blade length should be taken into account. Because of the good conductivity of sea water, the sea surface can be considered as a good conductor. Calculation of wind turbine and its mirror is shown in Figure3, where l1, l2, l3, h 0 0 0 0 respectively represent three blades and tower, l1 , l2 , l3 , h respectively represent the mirror images of Energiesthe wind 2017, turbine 10, 1995 blades and the tower. 6 of 15

l1 L

l3 l2

H h

地面 Ground

l2' l3'

l1'

FigureFigure 3. 3. SchematicSchematic of of a aWT WT and and its its mirror mirror image. image.

dh Rdθ H

θ1 h

Figure 4. Conical antenna model of an offshore WT tower.

The wave impedance of the differential element dh Z’ can be obtained from the cone antenna theory, as shown in Equation (11):

1 μ r Z′ = ln  (11) 2πε rhh22+−  The equivalent wave impedance of the whole offshore wind turbine tower Z can be derived by finding the integral and averaging along the tower body, as shown in Equation (12):

1 μ H r Z = ln dh 0 22 (12) 2πεH rhh+− 

Energies 2017, 10, 1995 5 of 15

The blade capacitance is calculated by the mean potential method. Considering that the height of the offshore wind turbine is much larger than the radius of the tower, the radius of the tower can be neglected. It is assumed that the blade and tower are uniformly charged and the charge is concentrated on the axis, and the charge linear density is τ. As shown in Figure3, the blade to ground capacitance Cg, the blade to column capacitor Clh and the blade capacitance Cl1/2 can be obtained:

4πεL2 Cg = (4) R R 1 R 1 0 dl − 0 dl dl l1 l1 Dl l 1 l1 D 0 1 1 1 1 l1l1

4πεL2 Clh = (5) R R 1 R 1 0 dh − 0 dh dl l h Dl h h D 0 1 1 1 l1h 4πεL2 Cl1/2 = (6) R R 1 R 1 0 dl2 − 0 dl2 dl l1 l2 Dl l l2 D 0 1 1 2 l1l2 In Equations (4)–(6), L is the blade length, ε is the space conductivity, and D is the distance between the two micro units. The inductance of a conductor consists of two parts, the inner inductance and the outer inductance, but considering that lightning current changes rapidly and the lightning transient process time is short, it is generally recognized that the internal inductance is negligible in the calculation of lightning electric parameters, and only the external inductance should be considered [27]. For space conductors, the inductance is the sum of inductance and mutual inductance. At present, Neumann integral method in electromagnetic ﬁeld theory is widely used to calculate self-inductance and mutual inductance in domestic and foreign scholars [28]. According to the geometrical relationship of the blade, the self-inductance Lg, the mutual inductance Llh and the mutual inductance between blades Ll1/2 can be obtained:

µ cos θ1 Lg = (7) R R 1 R 1 0 4π dl − 0 dl dl l1 l1 Dl l 1 l1 D 0 1 1 1 1 l1l1

µ cos θ = 2 Ll1h (8) R R 1 R 1 0 4π dh − 0 dh dl l h Dl h h D 0 1 1 1 l1h

µ cos θ3 Ll1/2 = (9) R R 1 R 1 0 4π dl2 − 0 dl2 dl l1 l2 Dl l l2 D 0 1 1 2 l1l2

In Equations (7)–(9), θ1, θ2, θ3 respectively is the angle between the blade and blade, blade and mirror tower, the blade and blade. µ is the spatial permeability. From the above analysis, the total capacitance and total inductance of a single blade can be obtained. According to the deﬁnition of wave impedance, the wave impedance of the blade can be obtained, as shown in Equation (10): s Lg + 2Ll1/2 + Llh Zb = (10) Cg + 2Cl1/2 + Clh

In this paper, the blade wave impedance model is compared with the conventional fan blade wave impedance model. Not only the blade length and the height of the drum are taken into account, but also the rotation angle of the blade is taken into account. Energies 2017, 10, 1995 6 of 15

l1 L

l3 Energies 2017, 10, 1995 l2 6 of 15

H 2.3. Modeling of Offshore Wind Turbines Tower Impedanceh When the lightning current passes through the wind turbine tower, the wind turbine tower is 地面 made into a vertical tower, ignoring the difference betweenGround the radius of the upper and the lower parts. The process of lightning passing through the tower of a wind turbine can be regarded as the propagation in the form of spherical wave [29]. Thish' is similar to the wave process of conical antenna. The wave impedance can be obtained by using the cone antenna theory [30–32]. Figure4 is a conical antenna equivalent model of an offshore wind turbine tower. The height of l ' the tower is H, and the radius of the upper2 and lowerl3' bottom is r. A differential element dh on wind turbine tower is selected, the height from the ground is h, the inverted cone vertex O is the projection point of the center of the tower on the ground, and θ1 is half of the cone vertex angle. The arbitrary l1' micro angle dθ is selected, R is the distance between the O and theouter boundary of the inﬁnitesimal segment, then the arc√ length of the micro arc is Rdθ. According to the geometric relation of the graph, 2 2Figure 3. Schematic of a WT and its mirror image. r = R × sinθ1, R = h + r can be obtained.

dh Rdθ H

θ1 h

O Figure 4. Conical antenna model of an offshore WT tower. Figure 4. Conical antenna model of an offshore WT tower.

0 The wave impedance of the differential element dh Z’ can be obtained from the cone antenna theory, asas shownshown inin EquationEquation (11):(11): r 0 11 µμ rr Z Z=′ = lnln √ (11)(11) 22ππεε rhhr222++−h2 − h  The equivalent wave impedance of th thee whole offshore wind turbine tower Z can be derived by ﬁndingfinding the integral and averaging along thethe towertower body,body, asas shownshown inin EquationEquation (12):(12): r 1 1 µμZ HH rr Z =Z = ln√ dhdh (12) 0 222 2 (12) 2π2πεHH ε 0 rhhr +−+ h − h  2.4. Offshore Wind Turbine Integrated Electromagnetic Transient Model According to the wind turbine blade, the tower body wave impedance and the offshore wind turbine impact grounding resistance model, the integrated model of the offshore wind turbine lightning transient integration can be obtained, as shown in Figure5. Energies 2017, 10, 1995 7 of 15

2.4. Offshore Wind Turbine Integrated Electromagnetic Transient Model According to the wind turbine blade, the tower body wave impedance and the offshore wind turbine impact grounding resistance model, the integrated model of the offshore wind turbine Energies 2017, 10, 1995 7 of 15 lightning transient integration can be obtained, as shown in Figure 5.

FigureFigure 5.5.Integrated Integrated wavewave impedanceimpedance model model of of offshore offshore WT. WT.

In Figure 5, Zb1, Zb2, Zb3 respectively represent the impedance of the three blades of the wind In Figure5, Zb1, Zb2, Zb3 respectively represent the impedance of the three blades of the wind turbine. Zt represents the wave impedance of the wind turbine tower, Rg denotes the equivalent turbine. Zt represents the wave impedance of the wind turbine tower, Rg denotes the equivalent impactimpact resistance resistance of of the the offshore offshore wind wind turbine. turbine.

3.3. LightningLightning ParametersParameters InfluenceInfluence Offshore Offshore WT WT Lightning Lightning Transient Transient Characteristics Characteristics InIn this this paper, paper, the the lightning lightning current current channel channel is is simplified simplified according according to to [ 28[28],], ignoring ignoring the the influence influence ofof the the pilotpilot and and thethe distortiondistortion of of thethe lightninglightning current current waveform waveform in in the the discharge discharge channel. channel.Assuming Assuming thethe discharge discharge channel channel is is perpendicular perpendicular to to the the ground ground and and the the current current is concentrated is concentrated on the on axisthe axis of the of channel,the channel, the lightning the lightning transport transport process process utilizes utilizes the Petersen the Petersen current current source equivalentsource equivalent circuit instead. circuit instead. 3.1. Lightning Parameter Model 3.1. Lightning Parameter Model Lightning is a discharge phenomenon in the atmosphere that occurs randomly between clouds and cloudsLightning or between is a discharge clouds andphenomenon the ground. in the Lightning atmosphere in nature that hasoccurs a polarity. randomly In order between to express clouds theand convenience, clouds or between it is set clouds as positive and the polarity ground. in Lightn the research.ing in nature Since has the a doublepolarity. exponential In order to express model ofthe lightning convenience, flow canit is beset conveniently as positive polarity differentiated in the research. and integrated, Since the a doubledouble exponentialexponential modelmodel isof adoptedlightning to flow simulate can lightningbe conveniently current. differentiated Its mathematical and expression integrated, is a shown double in Equationexponential (13): model is adopted to simulate lightning( current. Its mathematical expression is shown in 0, t ≤ 0 Equation (13): i(0, t) = (13) I0 [exp(−αt) − exp(−βt)], t > 0 η0,t ≤ 0  I it()0, =  I (13) where 0 is the peak of the lightning current,0 expη is()−− theαβttt peak exp correction() − , > factor 0 of the lightning current. η  In the following calculations, I0 = 120 kA, η = 0.92; α(s) and β(s) are the time constants determined by the wave head time and the wave duration. whereBased I0 is onthe lightningpeak of the observation lightning current, and previous η is the research peak correction [13,33], thisfactor paper of the uses lightning 8/20 µ current.s, 120 kA In standardthe following lightning calculations, current I waveform0 = 120 kA, toη = simulate 0.92; α(s) the and lightning β(s) are the current time sufferedconstants by determined a wind turbine. by the Thewave parameters head timeα andand theβ were wave 7.713 duration.× 104 s and 2.484 × 105 s. InBased addition on lightning to the parameters observation mentioned and previous above, research this paper [13,33], also considersthis paper the uses lightning 8/20 μs,120 channel kA standard lightning current waveform to simulate the lightning current suffered by a wind turbine. wave impedance ZM. The integrated model of the offshore wind turbine lightning transient integration 4 5 consideringThe parameters lightning α and channel β were wave7.713 × impedance 10 s and 2.484 can be× 10 obtained,s. as shown in Figure6. In many papers, for example, [34], ZM ≈ 300 Ω, but, through the observation and analysis of former Soviet Union scientists [35], the value of the wave impedance of the lightning channel is not constant, and its value is related to the magnitude of the lightning current. The impedance of the lightning channel varied from 300 to 3000 Ω. When the lightning current amplitude is 30–200 kA, the value of the wave impedance of the lightning channel is relatively stable, about 300–600 Ω. Energies 2017, 10, 1995 8 of 15 Energies 2017, 10, 1995 8 of 15 In addition to the parameters mentioned above, this paper also considers the lightning channel In addition to the parameters mentioned above, this paper also considers the lightning channel wave impedance ZM. The integrated model of the offshore wind turbine lightning transient wave impedance ZM. The integrated model of the offshore wind turbine lightning transient integration considering lightning channel wave impedance can be obtained, as shown in Figure 6. integration considering lightning channel wave impedance can be obtained, as shown in Figure 6. In many papers, for example, [34], ZM ≈ 300 Ω, but, through the observation and analysis of In many papers, for example, [34], ZM ≈ 300 Ω, but, through the observation and analysis of former Soviet Union scientists [35], the value of the wave impedance of the lightning channel is not former Soviet Union scientists [35], the value of the wave impedance of the lightning channel is not constant, and its value is related to the magnitude of the lightning current. The impedance of the constant, and its value is related to the magnitude of the lightning current. The impedance of the lightning channel varied from 300 to 3000 Ω. When the lightning current amplitude is 30–200 kA, the Energieslightning2017 ,channel10, 1995 varied from 300 to 3000 Ω. When the lightning current amplitude is 30–200 kA,8 of the 15 value of the wave impedance of the lightning channel is relatively stable, about 300–600 Ω. According value of the wave impedance of the lightning channel is relatively stable, about 300–600 Ω. According to the data in [36], the relation between the lightning current amplitude and the wave impedance of to the data in [36], the relation between the lightning current amplitude and the wave impedance of theAccording lightning to channel the data is inobtained, [36], the as relation shown betweenin Figure the7. lightning current amplitude and the wave impedancethe lightning of thechannel lightning is obtained, channel as is shown obtained, in Figure as shown 7. in Figure7.

FigureFigure 6. IntegratedIntegrated wave wave impedance impedance mode modell of of offshore offshore WT considering ZM.. Figure 6. Integrated wave impedance model of offshore WT considering ZM.

3000 3000 Ω / M Ω / Z M

2000 2000

1000 1000

Lightning channel wave impedance wave Lightning channel 0

Lightning channel wave impedance wave Lightning channel 00 50 100 0Lightning current 50 I/kA 100 Lightning current I/kA

FigureFigure 7.7. RelationshipRelationship between between lightning lightning current current amplitude amplitude and waveand impedancewave impedance of lightning of lightning channel. Figure 7. Relationship between lightning current amplitude and wave impedance of lightning channel. channel. When the other parameters remain unchanged, the lightning channel impedance is 300 Ω, as shownWhen in Figure the other8, the parameters transient response remain unchange of the WTd, lightning the lightning impulse channel is signiﬁcantly impedance different is 300 Ω from, as When the other parameters remain unchanged, the lightning channel impedance is 300 Ω, as shownwhen the in ZFigureis not 8, the considered transient in response the model of (ignore the WTZ lightning),as shown impulse in Figure is significantly5. The model different considers fromZ , shown in MFigure 8, the transient response of the WTM lightning impulse is significantly different fromM whenwhich the is very ZM is different not considered from not in considering the model (ignoreZM. Therefore, ZM),as shown it is of somein Figure value 5. toThe study model the considers inﬂuence when the ZM is not considered in the model (ignore ZM),as shown in Figure 5. The model considers ZofM, the which actual is valuevery ofdifferent lightning from channel not considering wave impedance ZM. Therefore, on the transient it is of response. some value to study the ZM, which is very different from not considering ZM. Therefore, it is of some value to study the influence of the actual value of lightning channel wave impedance on the transient response. influence of the actual value of lightning channel wave impedance on the transient response.

Energies 2017, 10, 1995 9 of 15 EnergiesEnergies 20172017,, 1010,, 19951995 99 ofof 1515

Z 6.06.0 IgnoreIgnore ZMM Z =300Ω ZMM=300Ω 4.04.0 /MV /MV U(t) U(t)

2.02.0

0.00.0 Transient voltage Transient voltage -2.0-2.0

-4.0-4.0 00 10203040506070 10203040506070 TimeTime tt//μμss

FigureFigureFigure 8.8. 8. TheTheThe influenceinfluence inﬂuence ofof of thethe the wavewave wave impedanceimpedance impedance onon on thethe the transienttransient transient potentialpotential potential ofof of thethe the nacelle.nacelle. nacelle.

3.2.3.2.3.2. LightningLightning Lightning ChannelChannel Channel WaveWave Wave ImpedanceImpedance Impedance ThisThisThis paperpaper paper usesuses uses 8/208/20 8/20 μμssµ standardsstandard standard lightninglightning lightning currentcurrent current waveformwaveform waveform toto to simulatesimulate simulate thethe the lightninglightning lightning currentcurrent current sufferedsufferedsuffered byby by windwind wind turbine.turbine. turbine. TheThe The lightninglightning lightning currentcurrent current amplitudeamplitude amplitude rangerange range 5–1005–100 5–100 kAkA kA isis is usedused used toto to studystudy study thethe the lightninglightninglightning transienttransient transient responseresponse response ofof of didi differentfferentfferent lightning lightning channelchannel impedanceimpedancimpedancee parametersparametersparameters (the (the(the actual actualactual value valuevalue of ofofZ ZZMMMcan cancan be bebe obtained obtainedobtained from fromfrom Figure FigureFigure7 ),7),7), the thethe results resultsresults shown shownshown in inin Figure FigureFigure9. 9.9.

4040 TheThe actualactual valuevalue ofof ZZMM 44 ZZMM=300=300ΩΩ /MV /MV P P U U 33

2020 22

1 error(%) Relative

1 error(%) Relative Transient peak voltage voltage peak Transient Transient peak voltage voltage peak Transient

00 00 00 20406080100120 20406080100120 00 20 20 40 40 60 60 80 80 100 100 120 120 LightningLightning currentcurrent amplitudeamplitude ii/kA/kA LightningLightning currentcurrent amplitudeamplitude ii//kAkA ((aa)) ((bb))

FigureFigureFigure 9.9. 9. TransientTransientTransient potentialpotential potential peakpeak peak curvecurve curve ofof of thethe the nacenace nacellellelle underunder under differentdifferent different lightlight lightningningning channelschannels channels wavewave wave impedanceimpedanceimpedance andand and relativerelative relative error,error, error, ((aa ()a) )ContrastContrast Contrast chart;chart; chart; ((bb (b)) )RelativeRelative Relative error.error. error.

ItIt cancan bebe seenseen fromfrom FigureFigure 99 thatthat whenwhen thethe lighlightningtning currentcurrent isis relativelyrelatively small,small, thethe resultresult willwill It can be seen from Figure9 that when the lightning current is relatively small, the result will greatlygreatly deviatedeviate whenwhen ZZMM ≈≈ 300300 ΩΩ isis usedused inin thethe calculations.calculations. WithWith thethe increaseincrease ofof lightninglightning current,current, greatly deviate when Z ≈ 300 Ω is used in the calculations. With the increase of lightning current, thethe relativerelative errorerror decreasesdecreasesM gradually.gradually. InIn thisthis papaper,per, thethe valuevalue ofof lightninglightning channelchannel wavewave impedanceimpedance the relative error decreases gradually. In this paper, the value of lightning channel wave impedance correspondscorresponds toto thethe amplitudeamplitude ofof thethe lightninglightning current,current, whichwhich isis moremore inin lineline withwith thethe actualactual situation.situation. corresponds to the amplitude of the lightning current, which is more in line with the actual situation. InIn thethe calculationcalculation ofof lightninglightning protection,protection, lightninglightning wavewave impedanceimpedance valuesvalues generallygenerally choosechoose In the calculation of lightning protection, lightning wave impedance values generally choose 300300 ΩΩ,, however,however, throughthrough thethe analysisanalysis ofof thisthis section,section, itit cancan bebe foundfound thatthat ifif thethe lightninglightning channelchannel 300 Ω, however, through the analysis of this section, it can be found that if the lightning channel impedanceimpedance valuevalue isis simulatedsimulated inin thethe normalnormal lightninglightning protectionprotection standardstandard (300(300 ΩΩ),), thethe resultresult isis thatthat impedance value is simulated in the normal lightning protection standard (300 Ω), the result is that thethe transienttransient voltagevoltage peakpeak inin thethe nacellenacelle isis smallersmaller ththanan thethe actualactual peak.peak. IfIf thethe lightninglightning protectionprotection isis the transient voltage peak in the nacelle is smaller than the actual peak. If the lightning protection is implementedimplemented accordingaccording toto ZZMM ≈≈ 300300 ΩΩ,, thisthis willwill greatlygreatly increaseincrease thethe probabilityprobability ofof lightninglightning damagedamage implemented according to Z ≈ 300 Ω, this will greatly increase the probability of lightning damage thethe windwind turbine.turbine. TheThe nacellenacelle canMcan bebe penetrated,penetrated, whichwhich willwill bringbring seriousserious consequences,consequences, endangeringendangering the wind turbine. The nacelle can be penetrated, which will bring serious consequences, endangering thethe safesafe operationoperation ofof thethe fanfan andand cacauseuse significantsignificant economiceconomic losses.losses. the safe operation of the fan and cause signiﬁcant economic losses. Therefore,Therefore, thethe analysisanalysis resultsresults ofof thisthis sectionsection willwill havehave certaincertain guidingguiding significancesignificance forfor thethe Therefore, the analysis results of this section will have certain guiding signiﬁcance for the lightning lightninglightning protectionprotection calculationcalculation ofof offshoreoffshore WTs.WTs. AtAt thethe samesame time,time, thethe lightninglightning modelmodel mustmust bebe protection calculation of offshore WTs. At the same time, the lightning model must be improved. improved.improved.

Energies 2017, 10, 1995 10 of 15 Energies 2017, 10, 1995 10 of 15

4.4. Factors Factors Influencing Influencing Offshore Offshore WT WT Lightning Lightning Transient Transient Characteristics Characteristics TheThe single single pilepile offshoreoffshore wind wind turbine turbine is used is used as the as standard the standard model in model the simulation in the simulation (parameters (parametersshown inTable shown1), in and Table the 1), transient and the potential transient of po thetential offshore of the wind offshore turbine wind nacelle turbine is nacelle analyzed. is analyzed.The internal The equipment internal equipment circuit adopts circuit separate adopts grounding separate system,grounding the transientsystem, the potential transient of the potential internal ofequipment the internal is muchequipment less than is much the transient less than potential the transient of the nacelle,potential and of thethe potential nacelle, and difference the potential between differencethe equipment between and the the equipment nacelle can and be the approximately nacelle can be equal approximately to the nacelle equal potential to the [nacelle5]. Therefore, potential the [5].transient Therefore, potential the transient analysis potential in the nacelle analysis is the in mainthe nacelle factor. is the main factor. AfterAfter simulation simulation calculation, calculation, the the rotation rotation angl anglee has has less less influence influence on on the the lightning lightning transient transient responseresponse of of the the offshore offshore wind wind turbine, turbine, and and the the influence influence of of rotation rotation angle angle can can be be neglected neglected in in the the simulationsimulation process. process. Therefore, Therefore, this this section section is is not not ta takingking into into account account the the impact impact of of the the rotation rotation angle. angle.

TableTable 1. 1. StandardStandard model model parameters parameters in in simulation. simulation. Wind Power Unit Parameters (Unit) Parameter Selection HeightWind of tower Power body Unit H (m) Parameters (Unit) Parameter120 Selection The average radiusHeight of the of towertower bodyrt (m)H (m) 1202.3 The average thicknessThe average of the radius tower of wall the towerdt (m) rt (m) 0.0257 2.3 TheThe length average of the thickness blade L of (m) the tower wall dt (m) 0.025770 L ReferralThe radius length rb (m) of the blade (m) 700.001 Referral radius r (m) 0.001 The depth of the sea h1 (m) b 15 The depth of the sea h1 (m) 15 Seawater resistivity ρ1 (Ω·m) 5 Seawater resistivity ρ1 (Ω·m) 5 Sand soil resistivity ρ2 (Ω·m) 1500 Sand soil resistivity ρ2 (Ω·m) 1500 Ground base radius rg (m) 3 Ground base radius rg (m) 3 2 Extend theExtend length theof the length seabed of the h (m) seabed h2 (m) 10 10 Length of Lengthgrounding of grounding lg (m) lg (m) 25 25

4.1.4.1. Seawater Seawater Depth Depth Influence Inﬂuence on on Transi Transientent Response Response of of WT WT Lightning Lightning Impulse Impulse ForFor an an offshore offshore WT, WT, the the depth depth of of the the sea sea layer layer is is an an important important factor factor affecting affecting the the grounding grounding parameters.parameters. According According toto EquationEquation (3), (3), with with the th decreasee decrease of the of sea the water sea layer,water the layer, impulse the groundingimpulse groundingresistance resistance of the offshore of the windoffshore turbine wind will turbine increase. will increase. When the When sea the water sea layerwater is layer 0 m, is it 0 canm, it be canapproximately be approximately regarded regarded as a land as WT.a land According WT. Accord to theing different to the different soil layer soil resistivity, layer resistivity, the grounding the groundingresistance changesresistance in changes the range in of the 0–20 rangeΩ [37 of]. 0–20 At different Ω [37]. oceanAt different depths, ocean the transient depths, potential the transient of the potentialwind turbine of the nacelle wind turbine is obtained nacelle from is theobtained integrated from model,the integrated as shown model, in Figure as shown 10. in Figure 10.

15m 10m 4 5m

/MV 0m U(t)

2 Transient voltage 0

0 102030405060 Time t/μs

FigureFigure 10. 10. EffectEffect of of ocean ocean depth depth on on the the transient transient potential. potential.

Energies 2017, 10, 1995 11 of 15

It can be seen from Figure 10 that the transient overvoltage of the lightning impact of the offshore WT and the onshore WT is different, the transient voltage of the land WT is obviously larger than that Energies 2017, 10, 1995 11 of 15 of the offshore WT, so it is very necessary to model and analyze the offshore WT separately. It can be seen that the maximum value of transient potential in the nacelle is related to the depth It can be seen that the maximum value of transient potential in the nacelle is related to the depth of the seawater layer, and the maximum value appears in the first oscillation period. of the seawater layer, and the maximum value appears in the first oscillation period. The complex environment of offshore WTs makes them very different from onshore WTs. The complex environment of offshore WTs makes them very different from onshore WTs. The The greater the depth of the sea, the smaller the impulse grounding resistance, the peak value of the greater the depth of the sea, the smaller the impulse grounding resistance, the peak value of the transient voltage of the nacelle decrease. Under the premise of ensuring the normal operation of the transient voltage of the nacelle decrease. Under the premise of ensuring the normal operation of the equipment, the deeper the sea water, the more conducive to lightning protection design. This has equipment, the deeper the sea water, the more conducive to lightning protection design. This has guiding significance for the site selection of offshore WT. In full consideration of other conditions, the guiding significance for the site selection of offshore WT. In full consideration of other conditions, WT should be selected in deep seawater. the WT should be selected in deep seawater. 4.2. Influence of Blade Length and Tower Height on WT Lightning Impulse Transient Response 4.2. Influence of Blade Length and Tower Height on WT Lightning Impulse Transient Response The other parameters are kept unchanged, and the length of the blades (L = 40 m, L = 70 m and The other parameters are kept unchanged, and the length of the blades (L = 40 m, L = 70 m and L = 100 m) and the height of the tower (H = 90 m, H = 120 m and H = 150 m) are simulated. The L = 100 m) and the height of the tower (H = 90 m, H = 120 m and H = 150 m) are simulated. The influence of the blade length and the tower height on the transient potential of the nacelle (Figure 11) influence of the blade length and the tower height on the transient potential of the nacelle (Figure 11) and the oscillation frequency (as shown in Table2) are analyzed. The transient voltage peak of the and the oscillation frequency (as shown in Table 2) are analyzed. The transient voltage peak of the nacelle can be approximated in Equation (14): nacelle can be approximated in Equation (14):

Up ==+Uh + Ug (14) UUUphg (14)

where Up isis the the voltage voltage peak peak in in the the nacelle, nacelle, UUh andh and UgU areg are the the voltage voltage drops drops on the on thetower tower and andthe theground. ground.

3.9

5 /MV /MV P P

U 3.8 U

3.7

3 Transient voltage peak Transient peak voltageTransient peak 3.6

2 80.0 100.0 120.0 140.0 160.0 40 50 60 70 80 90 100 Tower hight H/m Blade length L/m (a) (b)

Figure 11.11. EffectEffectof of blade blade length length and and tower tower height height on transienton transient potential potential peak, peak, (a) Effect (a) Effect of tower of heighttower onheight transient on transient potential potential peak, ( bpeak,) Effect (b) of Effect blade of length blade onlength transient on transient potential potential peak. peak.

Table 2. Effect of blade length and tower height on transient potential oscillation frequency. Table 2. Effect of blade length and tower height on transient potential oscillation frequency. Leaf Blade Length L/m Tower Height H/m Oscillation Frequency/MHz Leaf Blade40 Length L/m Tower Height90 H/m Oscillation Frequency/MHz2.5936 70 40 9090 2.59362.4593 100 70 9090 2.45932.3584 40 100 90120 2.35843.8370 70 40 120120 3.83703.7073 100 70 120120 3.70733.5882 40 100 120150 3.58825.0767 40 150 5.0767 70 150 4.9643 70 150 4.9643 100 100 150150 4.84254.8425

Energies 2017, 10, 1995 12 of 15

It can be seen that as the tower height increases, the transient potential of the WT nacelle shows an upward trend. With the increase of blade length, the transient potential of the WT nacelle is decreasing. When the WT is struck by lightning, a high tower and short blades will increase the probability of damageEnergies to the2017,nacelle. 10, 1995 12 of 15 The simulation results have guiding signiﬁcance for selecting the height of the tower and the The simulation results have guiding significance for selecting the height of the tower and the length of the blade when constructing an offshore WT. Short towers and long blades are good for WT length of the blade when constructing an offshore WT. Short towers and long blades are good for WT lightninglightning protection. protection.

4.3. Lightning4.3. Lightning Parameters Parameters Inﬂuence Influence on on WT WT Lightning Lightning Impulse Transient Transient Response Response The timeThe time of theof the wave wave front front and and the the time time ofof the wave tail tail are are the the two two main main parameters parameters of the of the lightninglightning current current waveform. waveform. Figure Figure 1212 is is a aschemati schematicc diagram diagram of three of threekinds of kinds lightning of lightning current, 4/20 current, 4/20μµs,s, 8/20 8/20 μsµ ands and 8/50 8/50 μs. Usingµs. Using the three the different three different wave fronts wave and fronts wave and times, wave the lightning times, the current lightning currentwaveform waveform is simulated is simulated to get tothe get transient the transient potential potential at the nacelle, at the as nacelle, shown in as Table shown 3. in Table3.

1.5x105 4/20μs 8/20μs 8/50μs

A 1.0x105

5.0x104 Electric currentI/

0.0 0 1x10-5 2x10-5 3x10-5 4x10-5 5x10-5 Time t/s

FigureFigure 12. 12.Comparison Comparisonof of differentdifferent lightning lightning current current waveform. waveform.

TableTable 3. Transient 3. Transient potential potential of of different different lightninglightning parameters parameters at atWT WT nacelle. nacelle.

Lightning Parameters Peak Transient Voltage at the Engine Room/MV Lightning4/20 Parameters μs Peak Transient Voltage4.9 at the Engine Room/MV 4/208/20µ sμs 3.7 4.9 8/208/50µ sμs 3.6 3.7 8/50 µs 3.6 The overall impedance of the wind turbine is perceptive, so the voltage value in the nacelle is available in Equation (14) [12]: The overall impedance of the wind turbine is perceptive, so the voltage value in the nacelle is di available in Equation (14) [12]: UL=+ iR (14) didt U = L + iR (14) where L is the wind turbine equivalent inductance,dt R is the wind turbine equivalent resistance, i is wheretheL islightning the wind current. turbine di/dt equivalent is the suminductance, of the changesR isof thethe windlightning turbine flow equivalentitself and the resistance, variation ofi is the lightningthe current current. reflection.di/dt is the sum of the changes of the lightning flow itself and the variation of the current reflection.It can be seen that the wave front time has a great influence on the transient process of the Itlightning can be stroke seen offshore that the wind wave turbine. front Since time the has wa ave great front influencetime is much on smaller the transient than the wave process wake of the time, when the wave front time decreases, the high frequency component obviously increases, and lightning stroke offshore wind turbine. Since the wave front time is much smaller than the wave wake the di/dt value becomes larger, then the transient potential peak value is higher obviously. The time, when the wave front time decreases, the high frequency component obviously increases, and the lightning current wave steepness in front of the wave is very big. U is mainly decided by the first di/dtitemvalue in becomesEquation (14). larger, The then gradient the transientof the double potential exponential peak current valueis wave higher in front obviously. of the wave The is lightning the currenthigher, wave the steepness overvoltage in maximum front of theusua wavelly occurs is very in the big. first Uperiod.is mainly decided by the first item in EquationLightning (14). The gradientcurrents tail of thegently, double the wave exponential tail time current change wavehas little in fronteffect ofon the the wavedi/dt, then is the the higher, the overvoltageimpact on the maximum nacelle transient usually potential occurs is in also the smaller. first period.

Energies 2017, 10, 1995 13 of 15

Lightning currents tail gently, the wave tail time change has little effect on the di/dt, then the impact on the nacelle transient potential is also smaller. ThereEnergies is2017 no, 10 ﬁxed, 1995 waveform in the nature of lightning, but through this section analysis,13 of it 15 can be concluded that when other parameters are the same, the smaller the time of the wave front, the greater There is no fixed waveform in the nature of lightning, but through this section analysis, it can be the possibility of damage to the WT. In the design of lightning protection, priority should be given to concluded that when other parameters are the same, the smaller the time of the wave front, the the lightninggreater the wave possibility with less of damage front time. to the WT. In the design of lightning protection, priority should be given to the lightning wave with less front time. 4.4. Lightning Point Inﬂuence on WT Lightning Impulse Transient Response The4.4. Lightning offshore Point WT isInfluence struck on by WT lightning, Lightning andImpulse the Transient lightning Response current may be injected from the tip of the windThe turbine offshore blade WT is tipstruck or theby lightning, rear of the and engine the lightning room. current Therefore, may thebe injected different from lightning the tip of point positionsthe wind will leadturbine to theblade change tip or ofthe lightning rear of the current engine on room. the windTherefore, turbine, the anddifferent then lightning have an impactpoint on the transientpositions processwill lead of to lightningthe change stroke. of lightning In this current paper, on thethe transientwind turbine, potential and then response have an ofimpact the wind turbineon nacellethe transient is studied process by of analyzinglightning stroke. the two In this different paper, lightningthe transient strike potential points. response of the wind turbine nacelle is studied by analyzing the two different lightning strike points. As shown in Figure 13, due to the change of the current path, when lightning strikes the lightning As shown in Figure 13, due to the change of the current path, when lightning strikes the lightning rod of nacelle, the transient potential peak is about 11.6% higher than when lightning strikes blades. rod of nacelle, the transient potential peak is about 11.6% higher than when lightning strikes blades. Therefore,Therefore, emphasis emphasis should should be be placed placed onon the nacell nacellee lightning lightning protection. protection. The nacelle The nacelle is the focus is the of focus of lightninglightning protection, protection, inin orderorder to prevent lightning lightning damage damage to toall allkinds kinds of equipment of equipment in the in cabin, the cabin, causingcausing major major accidents. accidents.

Lightning stricks lightning rod of nacelle Lightning stricks blade 4.0 /MV U(t)

2.0 Transient voltage Transient 0.0

0.0 20.0 40.0 60.0 Time t/μs

FigureFigure 13. 13.Effect Effect of of lightning lightning strikestrike po pointint on on the the transient transient potential. potential.

5. Conclusions 5. Conclusions After lightning current strikes the tower of a wind turbine, the tower body becomes in an instant Aftera high lightningvoltage equipotential current strikes body. the The tower instantaneous of a wind voltage turbine, rise thecan towerreach several body becomeshundred kilovolts in an instant a highor voltage even a few equipotential MV, the tower body. body The moment instantaneous potential voltageuplift is riselikely can to reachcause insulation several hundred breakdown, kilovolts or evendamage a few fire MV, automatic the tower control body system moment and communica potentialtions uplift equipment, is likely toelectric causeal insulationequipment, breakdown,but also damagethe power ﬁre automatic line and the control signal system line of andthe tower communications body voltage equipment,can induce a electricaldangerous equipment, anti-strike. but also theTherefore, power in line the and lightning the signal protection line ofdesign the tower of wind body turbine, voltage it is necessary can induce to fully a dangerous analyze the anti-strike. fan Therefore,and lightning in the lightning parameters, protection try to reduce design the ofharm wind of lightning turbine, itto isthe necessary unit, and toensure fully the analyze safe and the fan reliable operation of the unit. The research of this paper has guiding significance for this problem, and lightning parameters, try to reduce the harm of lightning to the unit, and ensure the safe and the main features of this paper are as follows: reliable operation of the unit. The research of this paper has guiding signiﬁcance for this problem, the main(1) features According of this to paper the characteristics are as follows: of the offshore WT environment and lightning parameter, the integrated multi-wave impedance model of the offshore wind turbine is established. (1) (2)According Considering to the that characteristics the lightning ofchannel the offshore impedance WT can environment effectively reduce and lightning the transient parameter, voltage the integratedand oscillation multi-wave frequency, impedance the actual model peak ofvalue the of offshore transient wind overvoltage turbine is is higher established. than when ZM (2) Consideringis 300 Ω. This that requires the lightning the improvement channel impedance of lightning canprotection effectively levels. reduce the transient voltage (3) There are significant transient overvoltage differences between offshore and onshore WTs. The and oscillation frequency, the actual peak value of transient overvoltage is higher than when ZM peak value of transient overvoltage in the nacelle increases with the decrease of seawater depth is 300 Ω. This requires the improvement of lightning protection levels.

Energies 2017, 10, 1995 14 of 15

(3) There are significant transient overvoltage differences between offshore and onshore WTs. The peak value of transient overvoltage in the nacelle increases with the decrease of seawater depth when the WT is struck by lightning. This has a certain guiding significance for the location of offshore WT and selection of equipment. (4) When building an offshore WT, the tower height should be relatively small, and the blade length should be relatively large. The smaller the wave front time, the greater the harm caused by lightning current. In the design of lightning protection, emphasis should be placed on the lightning protection of the nacelle. The blade rotation angle has less influence on the transient voltage peak of the nacelle and can be neglected.

Acknowledgments: This work was supported by the National Science Foundation of China under Grant Nos. 51677110 and 51420105011, and State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (LAPS16018). Author Contributions: Li Zhang was in charge of theoretical guidance as the first author. Shengwei Fang was responsible for the simulation and prepared the manuscript. Tong Zhao assisted the project and research. All authors discussed the results and approved the final publication version. Conflicts of Interest: The authors declare no conflict of interest.

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