Design of a Wireless Sensor Module for Monitoring Conductor Galloping of Transmission Lines

Transcription

1 sensors Arile Design a Wireless Sensor Module for Monioring Conduor Galloping Transmission Lines Xinbo Huang 1, *, Long Zhao 2 and Guimin Chen 2 1 Shool Eleronis Informaion, Xi an Polyehni Universiy, Xi an 7148, China 2 Shool Elero-Mehanial Engineering, Xidian Universiy, Xi an 717, China; zhaolong@xpu.edu.n (L.Z.); gmhen@mail.xidian.edu.n (G.C.) * Correspondene: huangxinbo@xpu.edu.n; Tel.: Aademi Edior: Kemal Akkaya Reeived: 1 June 216; Aeped: 27 Sepember 216; Published: 9 Oober 216 Absra: Conduor galloping may ause flashovers and even ower ollapses. The available onduor galloping monioring mehods en employ aeleraion sensors o measure onduor ranslaions wihou onsidering onduor wis. In his paper, a new sensor for monioring onduor galloping ransmission lines based on an inerial measuremen uni and wireless ommuniaion is proposed. An inerial measuremen uni is used for olleing aeleraions and angular raes a onduor, whih are furr ransformed ino orresponding geographi oordinae frame using a quaernion ransformaion o reonsru galloping onduor. Boh hardware design and sware design are desribed in deails. The orresponding es plaforms are esablished, and experimens show feasibiliy and auray proposed monioring sensor. The field operaion proposed sensor in a onduor spanning 734 m also shows is effeiveness. Keywords: wireless sensor module; ransmission lines; onduor galloping; inerial measuremen uni 1. Inroduion Conduor galloping involving various volage levels ransmission lines ours frequenly around world [1 4]. I is onsidered as a self-exied vibraion low frequeny and large ampliude aused by non-uniform iing and srong winds. The damages produed by onduor galloping may manifes in many ways, e.g., deformaion ower ross-arms, flashovers beween onduors, and even ower ollapse [4 7], as shown in Figure 1. The auses and haraerisis onduor galloping are ompliaed due o omplexiies relaed o sysem parameers, exernal environmen parameers and various sohasi faors, whih bring abou many hallenges o researh on onduor galloping. To dae, muh work has been foused on galloping prevenion. For example, suspension lamps are en mouned on ransmission lines o preven galloping. However, while his may be effeive for some ransmission lines, i may no work for ors. Therefore, aurae simulaion onduor galloping ondiion is neessary for design a saisfaory ani-galloping devie. Dynami ension variaion is mos ommon feaure onduor galloping [8]. Some people have adoped average mehod o ge an analyial soluion galloping ampliude, and y found ha damping raio, wind veloiy and mass raio were hree mos imporan parameers onduor galloping model [9]. The Hamilon priniple was also used for analyzing galloping verial ampliude and orsional angle wih differen influening faors. I was shown ha mos signifian faors inluded wind veloiy, flow densiy, span lengh, damping raio, and iniial ension [1]. Sensors 216, 16, 1657; doi:1.339/s

2 Sensors 216, 16, Sensors 216, 16, (a) (b) () Figure 1. Damages aused by onduor galloping: (a) depiion damages aused by onduor Figure 1. Damages aused by onduor galloping: (a) depiion damages aused by onduor broken soks; (b) depiion damages aused by ension fiing fraure, and suspension lamp broken soks; (b) depiion damages aused by ension fiing fraure, and suspension lamp breakage; () depiion damages aused by ower ollapses. breakage; () depiion damages aused by ower ollapses. Researh on onduor galloping monioring ehnology aims o obain key daa abou galloping Researh for sienifi on onduor researh galloping on galloping monioring mehanisms ehnology and is aims prevenion. o obainin key pas daa deades, abou galloping wih oninuous for sienifi improvemen researh on galloping oreial mehanisms galloping andmodels, is prevenion. sensor Inehnology pas deades, and wih ommuniaion oninuous ehnology, improvemen monioring oreialehnology galloping models, onduor sensorgalloping ehnology is developing and ommuniaion rapidly, ehnology, e.g., image/video monioring surveillane ehnology [4 7,11], onduor and aeleraion gallopingsensor is developing monioring rapidly, mehods e.g., image/video [7,11,12]. surveillane Alhough [4 7,11], image/video and aeleraion surveillane sensor mehod monioring is more mehods inuiive, [7,11,12]. onduors Alhough are en image/video oo long surveillane o be observed mehod using is video more or inuiive, image, espeially onduors sine are devie enmay oo long swing owhen be observed onduors using vibrae video or sharply. image, The espeially aeleraion sinesensor devie monioring may swing mehod when may onduors ause oupu vibraedaa sharply. o no The be in aeleraion same sensor referene monioring oordinaes mehod due o may ause ineviable oupu onduor daa orsion, no bewhih in brings same referene abou a large oordinaes deviaion due o from ineviable aual movemen. onduor Besides, orsion, whih maximum brings abou ampliude a large esimaed deviaion by from mamaial aual models movemen. has Besides, been pu forward maximum bu i sill ampliude needs o esimaed be verified by by mamaial examples [13]. models A monioring has been sheme pu forward based on bu i sill fiber needs Bragg ograing be verified sensor bywas examples also proposed [13]. A monioring onduor sheme based galloping on [14], fiber bu Bragg i suffered graing sensor from some was also diffiulies proposed in o praie. monior Meanwhile, onduor galloping Miro-Elero-Mehanial-Sysems [14], bu i suffered from some ehnology diffiuliesis in praie. araing Meanwhile, more and more Miro-Elero-Mehanial-Sysems aenion and provides smaller and ehnology heaper sensors is araing whih more an measure and more aenion physial quaniies and provides suh smaller as aeleraion and heaper and angular sensors veloiy, whih an allowing measure inerial physial sensors quaniies o be widely suh as aeleraion used in moion and angular analysis veloiy, and raking allowing appliaions inerial sensors [15,16]. o Using be widely inerial usedmeasuremen in moion analysis unis and o raking monior appliaions galloping an [15,16]. avoid Using errors inerial aused by measuremen onduor wis unis[17]. o monior However, galloping referene an[17] avoid did errors no aused menion byhow onduor deal wis wih [17]. rend However, iems whih referene en [17] appear did and no menion direly how influene o deal wih measuremen rend iems whih resuls. en appear and direly influene measuremen resuls. Aiming a monioring moionsae sae onduor galloping galloping and and using using i as a ibasi auni basi uni an inegraed an inegraed online-monioring online-monioring sysem sysem for ransmission for ransmission lines, a lines, wireless a wireless sensor sensor is proposed is proposed in his in his paper, paper, whih whih uilizes uilizes an inerial an inerial measuremen measuremen uni uni o olle o olle aeleraions aeleraions and and angular angular raes raes onduor moion moion and and n n reonsrus reonsrus onduor onduor galloping galloping 3D in spae 3D spae hrough hrough a series a series algorihms. algorihms. The The mehods mehods for for alulaing alulaing aeleraions, aeleraions, veloiy veloiy and and displaemen displaemen are dedued are dedued in in deails. deails. During During derivaion derivaion proedure, proedure, rend rendiems iems onduor gallopinghave havebeen been onsidered, and whole onduor galloping rajeoryis is obainedusing using Bezier Bezierurve urvefiing mehod for for firs ime. The orrespondinges plaformsare arese seup upand anda aseries series experimens experimensare are arried arried ou ou o o evaluae is feasibiliyand and auray. Moreover, Moreover, i iwas waspu puino inooperaion operaionin ina aonduor span span m, m, and and resuls resuls show show ha ha proposed proposed wireless wireless sensor module sensor module for monioring for monioring onduor galloping onduor galloping ransmission ransmission lines is boh lines feasible is boh and feasible effeive. and effeive. The The online online monioring monioring ehnology ehnology onduor onduor galloping galloping ransmission ransmission lines mainly lines omprises mainly omprises wireless sensor modules, a ondiion/sae monioring devie (CMD), and ondiion wireless sensor modules, a ondiion/sae monioring devie (CMD), and ondiion monioring monioring ener [12], as shown in Figure 2. The wireless sensor module is responsible for olleing ener [12], as shown in Figure 2. The wireless sensor module is responsible for olleing onduor onduor galloping daa and sending i o CMD using a ZigBee nework. The CMD is galloping daa and sending i o CMD using a ZigBee nework. The CMD is insalled on ower insalled on ower and reeives daa from wireless sensor modules and ransmis m o and reeives daa from wireless sensor modules and ransmis m o monioring ener by monioring ener by a GPRS nework. Exper sware insalled in monioring ener an display a GPRS nework. Exper sware insalled in monioring ener an display line saus informaion, line saus informaion, diagnose running saus, alarm, and foreas poenial breakdowns. diagnose running saus, alarm, and foreas poenial breakdowns.

3 Sensors 216, 16, Sensors 216, 16, Sensors 216, 16, Sensors 216, 16, Figure Figure 2. The funional The funional bloks bloks an an online online monioring monioring sysem sysem for onduor onduor galloping galloping ransmission ransmission lines. lines. Figure 2. The funional bloks an online monioring sysem for onduor galloping ransmission lines. 2. Hardware Design Wireless 2. Hardware Design Wireless Sensor Module 2. Hardware Design Wireless Sensor Module The wireless sensor module, as shown in Figure 3, inludes four unis: an inerial measuremen The wireless uni (IMU), The wireless sensor a maser sensor module, onroller, module, as a power as shown shown in supply in Figure Figure 3, uni, 3, inludes and inludes a wireless four four ommuniaion unis: unis: an an inerial inerial uni. measuremen measuremen Eah uni uni (IMU), will uni be (IMU), a briefly maser a maser inrodued onroller, onroller, as follows. a power a power supply uni, and a wireless ommuniaion uni. uni. Eah Eah uni uni will be will briefly be briefly inrodued as follows. as Figure 3. Design wireless sensor module. Figure 3. Design sensor module. The inerial measuremen Figure Figure uni Design Design measures wireless wireless veloiy, sensor sensor orienaion, module. module. and graviaional fores a poin The on inerial onduor, measuremen using a uni ombinaion measures aeleromeers veloiy, orienaion, and gyrosopes, and graviaional and someimes fores also a The magneomeers. poin inerial on measuremen onduor, The inerial using uni measuremen a ombinaion measures uni onsiss aeleromeers veloiy, a orienaion, hree-axis and gyrosopes, aeleraion and andgraviaional sensor, someimes a singleaxis magneomeers. on on gyrosope onduor, and The a using inerial dual-axis a measuremen aombinaion gyrosope. The uni hree-axis aeleromeers onsiss ADXL33 a hree-axis and gyrosopes, aeleraion sensor and sensor, produed someimes a single- by also magneomeers. Analog axis gyrosope Devies, The and In. inerial a (ADI dual-axis measuremen Company, gyrosope. Norwood, uni The onsiss hree-axis MA, USA) ADXL33 a a hree-axis employed in aeleraion his work sensor o sensor, produed measure a single-axis a by fores also a poin a axis gyrosope aeleraions Analog and Devies, and aalong a In. dual-axis (ADI X-, Y-, Company, gyrosope. and Z-axes. Norwood, The The A single-axis hree-axis MA, USA) Lpr53al ADXL33 is employed gyrosope aeleraion in and his a work dual-axis sensor o measure produed Ly53alh by Analog gyrosope aeleraions Devies, from In. along (ADI ST X-, Company, Y-, and Z-axes. (Geneva, Norwood, A Swizerland) single-axis MA, MA, USA) Lpr53al USA) were is employed hosen. isgyrosope They in and all his ina have his dual-axis work buil-in work o Ly53alh measure osignal measure ondiioning gyrosope from iruis ST and Company oupu (Geneva, volage signals. Swizerland) The Lpr53al were hosen. is used They for all measuring have buil-in signal aeleraions along along X-, Y-, X-, and Y-, Z-axes. and Z-axes. A single-axis A single-axis Lpr53al Lpr53al gyrosope gyrosope and a dual-axis and a angle Ly53alh dual-axis variaions ondiioning around iruis and Z-axis, oupu while volage Ly53alh signals. measuring The Lpr53al angle is variaions used for around measuring X- and angle Y- gyrosope Ly53alh gyrosope from ST fromcompany ST Company (Geneva, (Geneva, Swizerland) Swizerland) were hosen. were hosen. They all They have all buil-in have buil-in signal axes. variaions In praie, around sensiive Z-axis, while axes Ly53alh sensors measuring mus be orhogonally angle variaions insalled around o align X- and hree Y- ondiioning signal axes. ondiioning along In praie, iruis iruis oordinae and sensiive oupu and oupu frame axes volage volage measuring signals. sensors signals. uni. mus The The Lpr53al be orhogonally is used is used insalled for for measuring o align hree angle variaions axes Three along around axis oordinae aeleraions Z-axis, frame while and Ly53alh hree measuring axis angular measuring uni. raes under angle angle variaions arrier s oordinae around frame X- and X- are and Y-axes. axes. In praie, olleed In praie, Three by sensiive axis aeleraions IMU. sensiive axes Seen from axes and sensors hree direion axis sensors mus angular along bemus orhogonally raes line, be under orhogonally rajeory insalled arrier s o insalled any align oordinae poin o hree is align similar frame axes are o hree along axes oordinae along an olleed ellipse by when oordinae frame IMU. onduor Seen frame measuring from is galloping, measuring direion uni. wih along uni. ellipi line, plane rajeory perpendiular any o poin onduor, is similar as o Three shown an ellipse axis in Figure when aeleraions 4. onduor and is hree galloping, axis wih angular ellipi raes under plane perpendiular arrier s o oordinae onduor, frame as are olleed shown by in Figure IMU. 4. Seen from direion along line, rajeory any poin is similar o an ellipse when onduor is isgalloping, wih wih ellipi plane plane perpendiular o o onduor, as shown as shown in Figure in Figure Figure 4. Ellipial rajeory monioring nodes. Figure 4. Ellipial rajeory monioring nodes. Figure 4. Ellipial rajeory monioring nodes. Figure 4. Ellipial rajeory monioring nodes.

4 Sensors 216, 16, To avoid errors aused by onduor wising, all haraerisi quaniies are alulaed wih respe To avoid o errors geographial aused oordinae by onduor frame, wising, ha is allo say, haraerisi aeleraions quaniies (i.e., are ax, alulaed ay and az) wih Sensors 216, 16, respe o arrier s geographial oordinae oordinae frame frame, are ransformed ha is o say, ino aeleraions aeleraions (i.e., (i.e., axg, a x, a y and a z ) ayg and azg) wih wih respe respe o To avoid o geographial errors arrier s aused oordinae by onduor frame frame wising, are before ransformed all alulaion haraerisi ino(as aeleraions quaniies shown in are (i.e., Figure alulaed a xg, 5) a yg using wih and a zg ) wih following respe relaionships: o o geographial oordinae oordinae frame, frame ha before is o say, alulaion aeleraions (as shown (i.e., ax, in Figure 5) using ay and az) wih following respe relaionships: o arrier s oordinae frame are ransformed ino aeleraions (i.e., axg, ayg and azg) wih respe o geographial a oordinae axg, aframe x abefore xg, a x aalulaion xg xg, a x a (as shown x a in Figure 5) using x following relaionships: a xg axg,a x axg,a x axg,a x x a x a,, xg a x axg ax a yg a = yg axg,a x axg,a x a, axg xg a a x,a x y C a y = C ay y (1) (1) a zg aa zg axg a,aa x, axg,a x, axg,a, x a xg a x axg a a x a z a xg, a x axg, a xg x a, a x z xg a a x a x x z axg, a ayg x axg, a x axg, a x ay Cay (1) where C is referred o as aiude a marix, whih is ommonly used for an aiude desripor. Then zg axg, a x axg, a a x axg, a z a z x galloping displaemens are gained hrough wo inegral operaions, as illusraed in Figure where C is referred o as aiude marix, whih is ommonly used for an aiude desripor. Then galloping displaemens are gained hrough wo inegral operaions, as illusraed in Figure 6. a a Figure Transformaion oordinaes. Figure Figure 6. The 6. The diagram diagram o displaemen. hanging aeleraion o displaemen. Le s ake X direion for example. Inegraing aeleraion yields veloiy: Le s ake X direion for example. Inegraing aeleraion yields veloiy: v () v ( ) a xg() d (2) v () v ( ) a () xg d (2) and inegraing obained veloiy v() yields v( ) displaemen: = a xg ()d (2) and inegraing obained veloiy yields displaemen: and inegraing obained veloiy yields x() x displaemen: ( ) v() d (3) x() x( ) v() d (3) Veloiy and displaemen are alulaed wih following formula: x() x( ) = v()d (3) Veloiy and displaemen are alulaed v () v wih ( ) a following () d formula: (4) Veloiy and displaemen are alulaed v () wih v ( ) following axg() d formula: (4) s () x( ) v() d (5) x v() = v( in whih axg() is aeleraion a ime s x() (m/s x( ) 2 ) + a ); v() is xg ()d (4) v() veloiy d a ime (m/s); v() is iniial (5) veloiy (m/s); and sx() is displaemen a ime (m); in whih axg() is aeleraion a ime s (m/s 2 x () = x( ); ) v() + is v()d veloiy a ime (m/s); v() is iniial (5) veloiy (m/s); and sx() is displaemen a ime (m); xg

5 Sensors 216, 16, in Sensors whih 216, a xg 16, () 1657 is aeleraion a ime (m/s 2 ); v() is veloiy a ime (m/s); v( ) is iniial 5 15 veloiy (m/s); and s x () is displaemen a ime (m). Similarly, Y and Z direion displaemens ssy(), y ssz() z an be alulaed and onduor rajeory ould be fi aording o o (s(sx(), x (), ssy(), y ssz()). z Figure 7 shows plos hanging aeleraion ino displaemen. Figure Figure The The plos plos hanging hanging aeleraion aeleraion o o displaemen. displaemen. The ommuniaion uni uilizes a shor-disane ZigBee nework, whih is implemened by a The ommuniaion uni uilizes a shor-disane ZigBee nework, whih is implemened by CC243 a 2.4 GHz radio frequeny. A MSP43F247 miroproessor (TI ompany, Dallas, TX, a CC243 a 2.4 GHz radio frequeny. A MSP43F247 miroproessor (TI ompany, Dallas, TX, USA) is USA)is seleed as maser onroller. Furrmore, onsidering ha wireless sensor module seleed as maser onroller. Furrmore, onsidering ha wireless sensor module is insalled is insalled on onduor, power supply module is designed hrough an open-loop on onduor, power supply module is designed hrough an open-loop ransformer insalled on ransformer insalled on onduor. The urren obained by muual induane is n reified, onduor. The urren obained by muual induane is n reified, filered, and regulaed o filered, and regulaed o form sable oupu volage. The CMD reeives iming ommand afer form sable oupu volage. The CMD reeives iming ommand afer wireless sensor module wireless sensor module is powered on and sends a response o sensors if iming sueeds. is powered on and sends a response o sensors if iming sueeds. Then sensors begin o Then sensors begin o olle moion saes onduor and send resuls o CMD. If olle moion saes onduor and send resuls o CMD. If value exeeds se value exeeds se hreshold monioring enre, CMD will rigger an alarm. hreshold monioring enre, CMD will rigger an alarm Sruure Design Wireless Sensor Module 2.1. Sruure Design Wireless Sensor Module To avoid orona disharge and improve aerodynami haraerisis, wireless sensor To avoid orona disharge and improve aerodynami haraerisis, wireless sensor shell shell has a smooh spherial sruure made from aluminum. The shell was designed o be waerpro has a smooh spherial sruure made from aluminum. The shell was designed o be waerpro wihou affeing is normal operaion. wihou affeing is normal operaion. The urren ransformer is embedded ino a ring-ype sruure whose widh is 27 mm, ouer The urren ransformer is embedded ino a ring-ype sruure whose widh is 27 mm, diameer is 15 mm and inner diameer is 55 mm. The sensor module an easily be insalled and ouer diameer is 15 mm and inner diameer is 55 mm. The sensor module an easily be insalled and uninsalled, as shown in Figure 8. Through running on sie, wireless sensor module an mee uninsalled, as shown in Figure 8. Through running on sie, wireless sensor module an mee requiremens HV elerial haraerisis and seuriy. requiremens HV elerial haraerisis and seuriy.

6 Sensors 216, 16, Sensors 216, 16, Figure Sruure design wireless sensor module Loalizaion Algorihm Wireless Sensor Module The onduor orsion in onduor galloping proessis is diffiulo o avoid, whih auses aeleraion values values olleed a a differen imes imes o o no no be be in in a a same oordinae frame, so so key keyo o realize swareis is alulaion aiude marix [17]. The sensor hooses arrier oordinae frame as as referene sysem a measured a value, value, and and geographi oordinae frame frame as as ransformed uniform uniform referene referene sysem. sysem. The onversion The onversion beween beween arrier arrier oordinae oordinae frame frame and and geographi geographi oordinae oordinae frame isframe ompleed is ompleed by aiude by marix, aiude buil marix, on buil ory on a rigid ory body a roaing rigid body abou roaing a fixedabou poina infixed mehanis, poin in inmehanis, whih ommon in whih mehods ommon desribing mehods desribing relaionship relaionship moion oordinae moion frame oordinae and referene frame oordinae and referene frame oordinae are Eulerframe angles, are quaernion Euler angles, andquaernion direion osine. and direion However, osine. due ohowever, lineariy due and o no singulariy lineariy and differenial no singulariy equaions, differenial no rigonomeris equaions, ino rigonomeris inegral program in (asinegral opposedprogram o Euler angles), (as opposed and o fewer Euler parameers angles), and (relaive fewer o parameers direion osine), (relaive o quaernion direion is hosen osine), as quaernion premier appliaion is hosen as mehod. premier appliaion mehod. Aording o o Euler s roaion orem, in in hree-dimensional spae, any displaemen aa rigid body suh ha aa poin on on rigid body remains fixed, an be be represened by by aa single roaion abou some axis ha runs hrough fixed poin. The axis roaion is is known as as Euler axis denoed as as n,, and roaion angle is is alled Euler angle denoed by ζ (Rodrigues-Hamilon parameers). In In aa referene sysem whose hree uni veors are, i, and j and, when k, when a veor a veor =++ Z = x i + y j roaes + z k roaes an angle around angle around insananeous insananeous axis, axis, new oordinaes an be alulaed as: D xi 1 y new 1j zk oordinaes an be alulaed as: 1 1 D=C ZC (6) D = x 1 i + y1 j + z1 k D = C 1 ZC (6) where Z is arriers oordinae frame, and C is geographi oordinae frame: where Z is arriers oordinae frame, and C is geographi oordinae frame: 1 1 C os nsin (7) 2 2 C = os 1 2 ζ + n sin 1 2 ζ (7) Equaion (7) an be rewrien as a quaernion: Equaion (7) an be rewrien as a quaernion: Cos ni x sin n yjsin nk z sin (8) C = os 1 By denoing =, 2 ζ + n 1 x i sin =, 2 ζ + n 1 y j sin 2 ζ + n 1 = sin z k sin and 2 ζ (8) = sin, Equaion (3) an be simply By denoing expressed 1 = as: os 1 2 ζ, 2 = n x sin 2 1 ζ, 3 = n y sin 1 12i 2 ζ and 3j4k 4 = n z sin 1 2 ζ, Equaion (3) an be simply expressed as:, (9) i + 3 j + 4 k, (9) Subsiuing Subsiuing Equaion Equaion (9) (9) ino ino (6) (6) yields: yields: D ( 1 2i 3j 4k)( xi yj zk ) C, (1) D = ( 1 2 i 3 j 4 k )(x i + y j + z k ) C, (1) whih an be rewrien in a marix form as:

7 Sensors 216, 16, whih an be rewrien in a marix form as: x 1 y 1 z 1 = ( ) 2( ) 2( ) ( ) 2( ) 2( ) From above equaion aiude marix an be known: ( ) 2( ) 2( ) ( ) 2( ) 2( ) x y (11) z, (12) From above equaion, we know ha as long as four elemens 1, 2, 3 and 4 are obained, and aiude marix an be derived, whih an n be used o realize onversion from arrier s oordinae frame o geographi oordinae frame. Wha s more, angular rae w and quaernion C have following relaionship in quaernions: C = 1 A w (13) 2 In above formula, w is angular rae marix. Subsiuing quaernion and angular rae omponen ino above equaion, following marix form an be obained: w x w y w z = w x w y = 1 w x w z w y 2 w y w z w x w z w z w y w x C an be obained when above equaion is solved. There are many analyial mehods for solving differenial equaions. Commonly used mehods inlude Euler mehod, seond-order Runge-Kua mehod, fourh-order Runge-Kua mehod, e. Through a omparaive analysis, fourh-order Runge-Kua mehod ha produes smaller errors was adoped in his work. Combined wih fourh-order Runge-Kua lassi formula numerial analysis, simplified formula Equaion (9) is given as: C n+1 = C n + h 6 (k 1 + 2k 2 + 2k 3 + k 4 ) k 1 = 1 2 w C n k 2 = 1 2 w (C n + h 2 k 1) k 3 = 1 2 w (C n + h 2 k 2) k 4 = 1 2 w (C n + h k 3 ) w x w y w z w In above equaion, h is sampling inerval, W = x w z w y w y w z w x, C n = w z w y w x k n k and k n = n1. Then firs iem is derived as: k n2 k n n+1 = n + 6 k 1 k 11 k 12 k k 2 k 21 k 22 k k 3 k 31 k 32 k 33 + k 4 k 41 k 42 k (14) (15), n (16)

8 k n3 1 1 k1 k2 k3 k4 2 2 k 11 k 21 k 31 k k k k k k k k k Sensors 216, 16, n1 4n kkn n an be solved aording o following hree equaions. This is soluion proedure C, and n aiude marix is obained afer C is direly subsiued ino Equaion (1). One C is worked ou, we an ge aeleraions wih respe o geographial oordinae frame using Equaion (1). Figure 9 is aeleraions wih respe o arrier s oordinae frame measured by IMU. Figure 1 is angular raes measured by IMU. Finally, aeleraions wih respe o geographial oordinae frame on Y axis an be seen in Figure 11. (16) Figure 9. The aeleraions wih respe o arrier s oordinae frame. Sensors 216, 16, 1657 Figure 9. The aeleraions wih respe o arrier s oordinae frame In his paper, onduor galloping rajeory is obained using Bezier urve fiing mehod hrough displaemens measured by sensors insalled on onduor. Suppose ha n galloping sensors were insalled on a span. For a Bezier urve, n onrol poins are obained, wih eah sensor posiion given as: s ( s, s, s ) k,1,..., n 1 (17) k kx ky kz Figure 1. The angular rae. Figure 1. The angular rae.

9 Sensors 216, 16, Figure 1. The angular rae. Figure 11. Y-axes aeleraions wih respe o o geographial oordinae frame. frame. The onduor galloping wave S(u) an be wrien as: In his paper, onduor galloping rajeory is obained using Bezier urve fiing mehod n1 hrough displaemens Su ( measured ) [ xu by yu zu sensors ] insalled skx sky s on kz BEZ onduor. k, n1( u) Suppose ha n (18) galloping sensors were insalled on a span. For a Bezier k urve, n onrol poins are obained, wih eah sensor where posiion given, () =( 1,) as: (1 ) = (1 ), and u is raio insallaion loaion and disane s beween k = (s kx, owers: s ky, s kz ) k =, 1,..., n 1 (17) The onduor galloping wave S(u) an be wrien d as: u i, (19) n 1d [ ] S(u) = [ x (u) y (u) z (u) ] = where di is horizonal disane beween i-h s sensor kx s and ky s kz BEZ small side k,n 1 (u) (18) ower and d is k= span. where BEZ k,n 1 (u) = C (n 1, k) u k (1 u) n 1 k = Cn 1 k uk (1 u) n 1 k, and u is raio insallaion 2.3. Or Consideraions loaion and disane beween owers: During daa olleion proess sensors, due o emperaure drif and ouside u = d i inerferene, reeived signals en onain DC d omponens, and rend iems, whose exisene (19) have a large influene on subsequen inegral operaions, and may even yield disorions. where d i is horizonal disane beween i-h sensor and small side ower and d is span. Therefore, mean mehod and leas squares mehod are used o remove DC omponens 2.3. and Or rend Consideraions iems. Figure 12 ompares a se measured daa, whih daa onain DC During daa olleion proess sensors, due o emperaure drif and ouside inerferene, reeived signals en onain DC omponens and rend iems, whose exisene have a large influene on subsequen inegral operaions, and may even yield disorions. Therefore, mean mehod and leas squares mehod are used o remove DC omponens and rend iems. Figure 12 ompares a se measured daa, whih daa onain DC omponen and rend iems are represened by red line, and proessed daa are represened by blue line. This shows ha proessing effe is good. Seleing aeleraion daa one direion in reiproaing rial in one period as an example, Figure 13 illusraes effe low-pass filering. The firs plo is waveform simulaion original measured aeleraion, and seond plo shows signal afer low pass filering. The original measured aeleraion signal showing high frequeny inerferene ge smoor afer low-pass filering, whih makes aquired daa more aurae and easier o use for subsequen proessing. When frequeny galloping ranges from.1 o 3 Hz, i may ause measured ampliude o be inonsisen wih aual daa, and disorions an even our when u-f frequeny is se oo low, and inerferene signal will no be filered ou well if se oo high. In his paper, u-f frequeny is se in sware a 5 Hz and effe is good.

10 Seleing aeleraion daa one direion in reiproaing rial in one period as an example, Figure 13illusraes effe low-pass filering. The firs plo is waveform simulaion original measured aeleraion, and seond plo shows signal afer low pass filering. The original measured aeleraion signal showing high frequeny inerferene ge smoor afer lowpass filering, whih makes aquired daa more aurae and easier o use for subsequen proessing. Sensors 216, 16, Figure 12. Comparison signals before and afer being proessed. Figure 13. Comparison signals before and afer low-pass filering. Figure 13. Comparison signals before and afer low-pass filering. When frequeny galloping ranges from.1 o 3 Hz, i may ause measured ampliude 3. Experimenal Tes and Analysis o be inonsisen wih aual daa, and disorions an even our when u-f frequeny is 3.1. se oo Auray low, and Tes inerferene Single Sensor signal Based will onno Tesbe Plaform filered ou well if se oo high. In his paper, u-f frequeny is se in sware a 5 Hz and effe is good. A es plaform, as shown in Figure 14, was buil o es measuring auray proposed onduor galloping sensor. The onduor galloping sensor was insalled on es equipmen wih X-axis parallel o fixed axis and Z-axis perpendiular o ground. As shaf performs a reiproaing movemen, aeleraions and angular rae measured by onduor galloping monioring sensor were ransmied o a ompuer wih sware insalled espeially for es insalled by a ZigBee nework. Afer being proessed, resuls displaemens along X-, Y- and Z-axes are shown in Figure 15. In addiion, known bigges swing ampliude is 1 m. The es resuls show ha maximum displaemens along Y- and Z- axis are 1.95 m and.889 m, respeively, whih agree well wih aual onduor movemen.

11 A es plaform, as shown in Figure 14, was buil o es measuring auray proposed onduor galloping sensor. The onduor galloping sensor was insalled on es equipmen wih onduor galloping sensor. The onduor galloping sensor was insalled on es equipmen wih o ground. ground.as As shaf shafperforms performs x-axis x-axisparallel paralleloo fixed fixedaxis axisand and z-axis z-axis perpendiular perpendiular o a areiproaing movemen, aeleraions and angular rae measured by onduor galloping reiproaing movemen, aeleraions and angular rae measured by onduor galloping monioring wih sware sware insalled insalledespeially espeiallyfor for es es monioringsensor sensorwere wereransmied ransmied o o aa ompuer ompuer wih insalled by a ZigBee nework. Afer being proessed, resuls displaemens along Sensors 216, 16,by insalled a ZigBee nework. Afer being proessed, resuls displaemens along 11 x-,x-, y-y-and known bigges biggesswing swingampliude ampliudeisis1 1m. m. andz-axes z-axesare areshown shownin infigure Figure In In addiion, addiion, known Figure 14. Auray es seup. Figure es seup. seup. Figure Auray Auray es Figure15. Colleed daa auray es. Figure15. Colleed daa Figure 15. Colleed daa auray aurayes. es. The es resuls show ha maximum displaemens along Y- and Z- axis are 1.95 m and The resuls show haagree maximum displaemens alongmovemen. Y- and Z- axis are 1.95 m and.889 m,es respeively, whih well wih aual onduor 3.2. Auray Tes Single Sensor Based on Conduor.889 m, respeively, whih agree well wih aual onduor movemen. An experimen seup was buil o es feasibiliy monioring sensors, as illusraed in Figure 16. One end onduor is fixed, and or end is fixed on handle a mahine. The mahine an exie onduor o perform an ellipial moion in one direion by driving handle vibraion. A mirowave radar meer is used as benhmark for measuring lengh semi-major axis and semi-minor axis [18]. The olleed daa ri-axial aeleraions and angular raes are sen o a ompuer wih a sware insalled espeially for es using ZigBee. Then relaive displaemen urves were obained hrough fiing. In experimens, semi-major axis ellipial moion ranges from abou.5 m o abou 2 m, and semi-minor axis ranges from abou.3 m o abou 1.3 m. Figure 17 shows how o ge ellipial moion parameers aording o a se ondiion where lengh semi-major axis is.5 m and lengh semi-minor axis is.3 m. Then many differen moions were measured by boh designed sensor and radar meer, and resuls are shown in Table 1. I an be seen ha maximum relaive error semi-major axis is 8.11%, and maximum relaive error semi-minor axis is 8.35%.

12 Figure 16. One end onduor is fixed, and or end is fixed on handle a mahine. The mahine an exie onduor o perform an ellipial moion in one direion by driving handle vibraion. A mirowave radar meer is used as benhmark for measuring lengh semi-major axis and semi-minor axis [18]. The olleed daa ri-axial aeleraions and angular Sensors raes 216, are 16, sen 1657 o a ompuer wih a sware insalled espeially for es using ZigBee. Then relaive displaemen urves were obained hrough fiing. Figure 16. Experimen seup a single sensor. In experimens, semi-major axis ellipial moion ranges from abou.5 m o abou 2 m, and semi-minor axis ranges from abou.3 m o abou 1.3 m. Figure 17 shows how o ge ellipial moion parameers aording o a se ondiion where lengh semi-major axis is.5 m and lengh semi-minor axis is.3 m. Then many differen moions were measured by boh designed sensor and radar meer, and resuls are shown in Table 1. I an be seen ha maximum relaive error semi-major axis is 8.11%, and maximum relaive error Figure 16. Experimen seup a single sensor. semi-minor axis is 8.35%. Figure 16. Experimen seup a single sensor. In experimens, semi-major axis ellipial moion ranges from abou.5 m o abou 2 m, and semi-minor axis ranges from abou.3 m o abou 1.3 m. Figure 17 shows how o ge ellipial moion parameers aording o a se ondiion where lengh semi-major axis is.5 m and lengh semi-minor axis is.3 m. Then many differen moions were measured by boh designed sensor and radar meer, and resuls are shown in Table 1. I an be seen ha maximum relaive error semi-major axis is 8.11%, and maximum relaive error semi-minor axis is 8.35%. Sensors 216, 16, (A) (A) (B) Figure 17. The displaemen fiing a a single monioring poin: (A) Moion displaemens a Figure single node; 17. The (B) displaemen Trajeory fiing a single a apoin single in monioring a yle (view poin: from (A) Moion Z-axis). displaemens a single node; (B) Trajeory a single poin in a yle (view from Z-axis). Table 1. Experimenal daa ellipial moion. Semi-Major Axis Measured by Sensor (m) Semi-Minor Axis Measured by Sensor (m) Semi-Major Axis by Radar (m) Semi-Minor Axis by Radar (m) Relaive Error Semi-Major Axis Relaive Error Semi-Minor Axis % 5.99%

13 (B) SensorsFigure 216, 16, The displaemen fiing a a single monioring poin: (A) Moion displaemens a single node; (B) Trajeory a single poin in a yle (view from Z-axis). Table 1. Experimenal daa ellipial moion. Semi-Major Semi-Major Semi-Minor Semi-Minor Axis Semi-Major Semi-Major Semi-Minor Semi-Minor Relaive Relaive Error Error Relaive Relaive Error Error Axis AxisMeasured Axis Measured Measured by Axis Axis by by Axis by Semi-Major Semi-Minor by bysensor (m) bysensor (m) Radar (m) (m) Radar (m) Axis Axis % 5.99% % 5.99% % 4.9% 5.14% 5.14% % 4.82% % 4.78% % 8.35% % 5.1% % 7.81% % 8.24% 8.24% 3.3. Appliaion Single Sensor The wireless sensor module has been esed in in Guizhou power grid. Three sensors were insalled on a onduor spanning 734 m. The field insallaion is is shown in in Figure 18. (a) (b) Figure 18. Field insallaion wireless sensor module. (a) CMD; (b) wireless sensor. Figure 18. Field insallaion wireless sensor module. (a) CMD; (b) wireless sensor. Figure 19 plos daa obained by wireless sensor module whose ID is 2 desribing onduor Figure 19 plos galloping saus daa in a obained period on by 28 May wireless 213. I sensor an be module learly whose seen from ID is his 2 desribing figure ha onduor displaemen galloping along saus x-axis in a is period smalles, on 28 May while 213. I displaemen an be learly along seen from z-axis his figure is ha larges. displaemen The resuls agree along well wih X-axis hose is reorded smalles, by while video amera. displaemen along Z-axis is larges. Sensors The resuls 216, 16, agree 1657 well wih hose reorded by video amera Figure 19. The runime daa urve Conlusions Conlusions Wih higher sae grid sale, monioring ehnologies for ransmission lines are beoming more and and more more imporan. Akind kind wireless wirelesssensor sensor module module for for monioring monioring onduor onduor galloping galloping ransmission ransmission lines lines has has been beenproposed proposedand andrealized realizedin inhis hiswork. The Thefeasibiliy feasibiliyand and auray wireless sensor module were verified on orresponding es plaform. In general, proposed wireless sensor module appears o be very useful for monioring galloping. Furr work will fous on how many sensors should be insalled beween wo onseuive owers o ahieve opimal monioring performane. Aknowledgmens: This work was suppored in par by Naional Naural Siene Foundaion China

14 Sensors 216, 16, wireless sensor module were verified on orresponding es plaform. In general, proposed wireless sensor module appears o be very useful for monioring galloping. Furr work will fous on how many sensors should be insalled beween wo onseuive owers o ahieve opimal monioring performane. Aknowledgmens: This work was suppored in par by Naional Naural Siene Foundaion China ( ) and Key Tehnology Innovaion Team Proje Shaanxi Provine (214KCT-16). Auhor Conribuions: All auhors read and approved manusrip. Xinbo Huang provided main idea his work and performed experimenal sudy and wroe his arile. Long Zhao horoughly reviewed lieraure and provided preious advie on sruure his arile. Guimin Chen made some simulaions and prepared manusrip. Conflis Ineres: The auhors delare no onfli ineres. Referenes 1. Huang, X.B. Conduor galloping monioring. In Transmission Line On-Line Monioring and Faul Diagnosis; China Eleri Power Press: Beijing, China, 28; pp (In Chinese) 2. Zhu, K.J.; Liu, B.; Niu, H.J.; Li, J.H. Saisial Analysis and Researh on Galloping Charaerisis and Damage for Ied Conduors Transmission Lines in China. In Proeedings 21 Inernaional Conferene on Power Sysem Tehnology, Hangzhou, China, Oober 21; pp Jiang, X.L.; Shu, L.C.; Sima, W.X.; Xie, S.J.; Hu, J.L.; Zhang, Z.J. Chinese Transmission Lines Iing Charaerisis and Analysis Severe Ie Aidens. In Proeedings foureenh Inernaional Offshore and polar Engineering Conferene, Toulon, Frane, May 24; p Tadano, S.; Takeda, R.; Miyagawa, H. Three Dimensional Gai Analysis Using Wearable Aeleraion and Gyro Sensors Based on Quaernion Calulaions. Sensors 213, 13, [CrossRef] [PubMed] 5. Wang, J.J. Overhead Conduor Vibraions and Conrol Tehnologies. In Proeedings Inernaional Conferene on Power Sysem Tehnology, Chongqing, China, Oober 26; pp (In Chinese) 6. Whapham, R. Aeolian Vibraion Conduors: Theory, Laboraory Simulaion & Field Measuremen. In Proeedings 212 Elerial Transmission and Subsaion Sruures Conferene, Columbus, OH, USA, 4 8 November 212; pp Dyke, P.V.; Laneville, A.; Bouhard, D. Galloping experimenal analysis onduors overed wih a D-seion on a high-volage overhead es line. ASME 26, 9, Liu, C.Q.; Liu, B.; Chen, H. A sudy on dynami ension galloping onduors based on energy balane mehod. J. Vibroeng. 214, 16, Xu, H.; Zhu, K.; Liu, B.; Liu, C.; Yang, J. A sudy influening parameers on onduor galloping for ransmission lines. J. Vibroeng. 214, 16, Liu, B.; Zhu, K.J.; Sun, X.Q.; Huo, B.; Liu, X. A onras on onduor galloping ampliude alulaed by hree mamaial models wih differen DOFs. Shok Vib. 214, 214, [CrossRef] 11. Aoa, H.; Yaguhi, Y.; Oka, R. Feaure Deeion Elerial Feeder Lines wih Galloping Moion. In Proeedings 8h IEEE Inernaional Conferene on Compuer and Informaion Tehnology, Sydney, Ausralia, 8 11 July 28; pp Huang, X.B.; Tao, B.Z.; Feng, L. Transmission Lines Galloping On-Line Monioring Sysem Based on Aeleromeer Sensors. In Proeedings 211 IEEE Power Engineering and Auomaion Conferene, Wuhan, China, 8 9 Sepember 211; pp Egber, R.I. Esimaion maximum ampliudes onduor galloping by desribing funion analysis. IEEE Trans. Power Deliv. 1986, 1, [CrossRef] 14. Chen, Y.; Zhang, Z.; Chen, X. Novel monioring mehod power ransmission line galloping based on fiber Bragg graing sensor. Op. Eng. 211, 5, [CrossRef] 15. Nakao, T.; Han, H.; Koshimoo, Y. Fundamenal Sudy Magneially Leviaed Cona-Free Miro-Bearing for MEMS Appliaions. In. J. Smar Sens. Inell. Sys. 21, 3, Sanhiranayagam, B.K.; Lai, D.T.H.; Begg, R.K.; Palaniswami, M. Correlaions beween end poin foo rajeories and inerial sensor daa. In Proeedings 6h Inernaional Conferene on Inelligen Sensors, Sensor Neworks and Informaion, Queensland, Ausralia, 7 1 Deember 21; pp

15 Sensors 216, 16, Lv, Z.B.; Li, Q.; Ni, Y.Q.; Huang, Q.; Wu, W.L.; Zhang, C. An Effiien Mehod for Galloping Prile Monioring Power Transmission Lines by Use an Inerial Uni: Theoreial and Experimenal Invesigaion. In Proeedings 215 World Congress on Advanes in Sruural Engineering and Mehanis, Inheon, Korea, Augus Xiao, J.; Huang, X.B. The on-line monioring radar agains exernal fore damage on eleri ransmission line. J. Xi an Polyeh. Univ. 216, 137, by auhors; liensee MDPI, Basel, Swizerland. This arile is an open aess arile disribued under erms and ondiions Creaive Commons Aribuion (CC-BY) liense (hp://reaiveommons.org/lienses/by/4./).