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sensors Article

Design of a Wireless Sensor Module for Monitoring Conductor Galloping of Transmission Lines Xinbo Huang 1, *, Long Zhao 2 and Guimin Chen 2 1 2

*

School of Electronics Information, Xi’an Polytechnic University, Xi’an 710048, China School of Electro-Mechanical Engineering, Xidian University, Xi’an 710070, China; [email protected] (L.Z.); [email protected] (G.C.) Correspondence: [email protected]; Tel.: +86-186-0296-5050

Academic Editor: Kemal Akkaya Received: 1 June 2016; Accepted: 27 September 2016; Published: 9 October 2016

Abstract: Conductor galloping may cause flashovers and even tower collapses. The available conductor galloping monitoring methods often employ acceleration sensors to measure the conductor translations without considering the conductor twist. In this paper, a new sensor for monitoring conductor galloping of transmission lines based on an inertial measurement unit and wireless communication is proposed. An inertial measurement unit is used for collecting the accelerations and angular rates of a conductor, which are further transformed into the corresponding geographic coordinate frame using a quaternion transformation to reconstruct the galloping of the conductor. Both the hardware design and the software design are described in details. The corresponding test platforms are established, and the experiments show the feasibility and accuracy of the proposed monitoring sensor. The field operation of the proposed sensor in a conductor spanning 734 m also shows its effectiveness. Keywords: wireless sensor module; transmission lines; conductor galloping; inertial measurement unit

1. Introduction Conductor galloping involving various voltage levels of transmission lines occurs frequently around the world [1–4]. It is considered as a self-excited vibration of low frequency and large amplitude caused by non-uniform icing and strong winds. The damages produced by conductor galloping may manifest in many ways, e.g., deformation of tower cross-arms, flashovers between conductors, and even tower collapse [4–7], as shown in Figure 1. The causes and the characteristics of conductor galloping are complicated due to the complexities related to system parameters, external environment parameters and various stochastic factors, which bring about many challenges to the research on conductor galloping. To date, much work has been focused on galloping prevention. For example, suspension clamps are often mounted on the transmission lines to prevent galloping. However, while this may be effective for some transmission lines, it may not work for others. Therefore, accurate simulation of the conductor galloping condition is necessary for the design of a satisfactory anti-galloping device. Dynamic tension variation is the most common feature of conductor galloping [8]. Some people have adopted the average method to get an analytical solution of galloping amplitude, and they found that the damping ratio, wind velocity and mass ratio were the three most important parameters of the conductor galloping model [9]. The Hamilton principle was also used for analyzing the galloping vertical amplitude and torsional angle with different influencing factors. It was shown that the most significant factors included wind velocity, flow density, span length, damping ratio, and initial tension [10].

Sensors 2016, 16, 1657; doi:10.3390/s16101657

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Figure 1. Damages caused by conductor galloping: (a) depiction of the damages caused by conductor Figure 1. Damages caused by conductor galloping: (a) depiction of the damages caused by conductor broken stocks; (b) depiction of the damages caused by tension fitting fracture, and suspension clamp broken stocks; (b) depiction of the damages caused by tension fitting fracture, and suspension clamp breakage; (c) depiction of the damages caused by tower collapses. breakage; (c) depiction of the damages caused by tower collapses.

Research on conductor galloping monitoring technology aims to obtain the key data about Research on conductor galloping monitoring technology aims to obtainInthe about galloping for scientific research on galloping mechanisms and its prevention. thekey pastdata decades, galloping for scientific research on galloping mechanisms and its prevention. In the past decades, with continuous improvement of theoretical galloping models, sensor technology and with continuous technology, improvement theoretical technology galloping models, sensorgalloping technology and communication communication theofmonitoring of conductor is developing rapidly, technology, the monitoring technology of conductor galloping is developing rapidly, e.g., image/video e.g., image/video surveillance [4–7,11], and acceleration sensor monitoring methods [7,11,12]. surveillance [4–7,11], and acceleration sensor monitoring Although image/video Although the image/video surveillance method is moremethods intuitive,[7,11,12]. the conductors arethe often too long surveillance method more the conductors are oftenmay too long be observed using video to be observed using is video orintuitive, image, especially since the device swingtowhen conductors vibrate or image, especially since the device may swing when conductors vibrate sharply. The acceleration sharply. The acceleration sensor monitoring method may cause the output data to not be in the same sensor monitoring method may the output data to not bewhich in the brings same reference coordinates due reference coordinates due to thecause inevitable conductor torsion, about a large deviation to the the inevitable conductor Besides, torsion, which brings about a large deviation the actualmodels movement. from actual movement. the maximum amplitude estimated byfrom mathematical has Besides, maximum amplitude has been put forward been putthe forward but it still needs toestimated be verifiedbybymathematical examples [13].models A monitoring scheme based onbut theit still be verified bywas examples [13]. A monitoring scheme based on the[14], fiberbut Bragg grating fiberneeds Braggtograting sensor also proposed to monitor conductor galloping it suffered sensor was also proposed monitor conductor the galloping [14], but it suffered from some difficultiesisin from some difficulties in to practice. Meanwhile, Micro-Electro-Mechanical-Systems technology practice. the Micro-Electro-Mechanical-Systems technology is attracting and more attractingMeanwhile, more and more attention and provides smaller and cheaper sensors whichmore can measure physical quantities suchsmaller as acceleration and angular allowing inertial sensors to be widely attention and provides and cheaper sensors velocity, which can measure physical quantities such as used in motion analysisvelocity, and tracking applications [15,16]. inertial units and to acceleration and angular allowing inertial sensors to Using be widely usedmeasurement in motion analysis monitor applications galloping can[15,16]. avoid Using errors inertial caused by conductor twist However, reference diderrors not tracking measurement units[17]. to monitor galloping can[17] avoid mention to dealtwist with[17]. trendHowever, items which often[17] appear directly how influence thewith measurement caused byhow conductor reference did and not mention to deal trend items results.often appear and directly influence the measurement results. which Aiming at monitoring state of conductor galloping and and usingusing it as aitbasic of unit an Aiming monitoringthe themotion motion state of conductor galloping as aunit basic integrated online-monitoring systemsystem for transmission lines, alines, wireless sensorsensor is proposed in thisin of an integrated online-monitoring for transmission a wireless is proposed paper, which utilizes an inertial measurement unit unit to collect accelerations and and angular ratesrates of this paper, which utilizes an inertial measurement to collect accelerations angular conductor motion and then reconstructs the conductor galloping in 3D space through a series of of conductor motion and then reconstructs the conductor galloping in 3D space through a series algorithms. TheThe methods for for calculating accelerations, velocity andand displacement are deduced in of algorithms. methods calculating accelerations, velocity displacement are deduced details. During thethe derivation procedure, thethe trend items in details. During derivation procedure, trend itemsofofthe theconductor conductorgalloping gallopinghave havebeen been considered, and the whole conductor galloping trajectory is obtained using the Bezier curve fitting considered, and the whole conductor galloping trajectory is obtained using the Bezier curve fitting method for for the the first first time. time. The method The corresponding corresponding test test platforms platformsare areset setup upand andaaseries seriesofofexperiments experimentsare are carried out to evaluate its feasibility and accuracy. Moreover, it was put into operation in a conductor carried out to evaluate its feasibility and accuracy. Moreover, it was put into operation in a conductor spanofof734 734 results thatproposed the proposed wireless sensor module for monitoring span m,m, andand the the results showshow that the wireless sensor module for monitoring conductor conductor galloping of transmission lines is both feasible and effective. galloping of transmission lines is both feasible and effective. The online onlinemonitoring monitoring technology of conductor galloping of transmission linescomprises mainly The technology of conductor galloping of transmission lines mainly comprises wireless sensor modules, a condition/state monitoring device (CMD), and condition wireless sensor modules, a condition/state monitoring device (CMD), and condition monitoring monitoring center [12], as shown in Figure 2. The wireless sensor module is responsible for collecting center [12], as shown in Figure 2. The wireless sensor module is responsible for collecting the conductor the conductor galloping data and sending it to the CMD using a ZigBee network. The CMD is galloping data and sending it to the CMD using a ZigBee network. The CMD is installed on the tower installed on the tower and receives data from the wireless sensor modules and transmits them to the and receives data from the wireless sensor modules and transmits them to the monitoring center by monitoring center by a GPRS network. Expert software installed in the monitoring center can display a GPRS network. Expert software installed in the monitoring center can display line status information, line status information, diagnose running status, alarm, and forecast potential breakdowns. diagnose running status, alarm, and forecast potential breakdowns.

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Figure 2.2.functional The blocks of online monitoring system for for conductor conductor galloping oftransmission transmission lines. Figure Thefunctional functional blocks of an an online monitoringsystem system of lines. Figure 2. The blocks of an online monitoring for conductorgalloping galloping of transmission lines. Figure 2. The functional blocks of an online monitoring system for conductor galloping of transmission lines.

2. Hardware Design of WirelessSensor Sensor Module Module 2. Hardware Hardware Design Wireless 2. Design ofofWireless Sensor Module 2. Hardware Design of Wireless Sensor Module The wireless sensor module, as shown in Figure 3, includes four units: an inertial measurement The wireless wireless sensor sensor module, module, as as shown shown in in Figure Figure 3, 3, includes includes four four units: units: an inertial inertial measurement measurement The The wireless sensor module, as shown in Figure includes fourcommunication units: anan inertialunit. measurement unit (IMU), a master controller, a power supply unit, 3, and a wireless Each unit unit (IMU), (IMU), a master controller, a power supply unit, and communication unit. Each unit unit a master controller, a power supply unit, and a wireless communication unit. Each unit be (IMU), a master controller, a power supply unit, and a wireless communication unit. Each unit unit will briefly introduced as follows. will be briefly introduced as follows. will bewill briefly introduced be briefly introduced as follows.

Figure 3. Design of the wireless sensor module. Figure Designof ofthe the wireless wireless sensor Figure 3. 3. Design sensormodule. module.

Figureunit 3. Design of the module. The inertial measurement measures thewireless velocity,sensor orientation, and gravitational forces of a inertial measurement measuresofthe velocity, orientation, and gravitational forces also of a pointThe on the conductor, using a unit combination accelerometers and gyroscopes, and sometimes The inertial measurement unit measures velocity, orientation, andgravitational gravitational forces The inertial unit measures the velocity, and forces a point on the measurement conductor, using a combination ofthe accelerometers and gyroscopes, andsensor, sometimes also of of magnetometers. The inertial measurement unit consists of aorientation, three-axis acceleration a singlea point the conductor, usinga measurement acombination combination accelerometers and gyroscopes, and sometimes also point onon the conductor, ofofthree-axis accelerometers and gyroscopes, and sometimes magnetometers. Theausing inertial unit consists of a three-axis acceleration sensor, a singleaxis gyroscope and dual-axis gyroscope. The ADXL330 acceleration sensor produced by also axis gyroscope a(ADI dual-axis gyroscope. Theconsists three-axis acceleration sensor produced by Analog Devices, Inc. Company, Norwood, MA, USA) employed in this work tosensor, measure magnetometers. inertial measurement unit ofofADXL330 a three-axis acceleration sensor, a single-axis magnetometers. Theand inertial measurement unit consists ais three-axis acceleration a the singleAnalog Devices, Inc. (ADI Company, Norwood, MA, USA) is employed in this work to measure the accelerations along the X-, Y-, and Z-axes. A single-axis Lpr530al gyroscope and a dual-axis Ly530alh gyroscope andand a dual-axis gyroscope. The by axis gyroscope a dual-axis gyroscope. Thethree-axis three-axisADXL330 ADXL330acceleration acceleration sensor sensor produced by accelerations along the Y-, and Z-axes. A Switzerland) single-axis Lpr530al dual-axis gyroscope from ST X-, Company (Geneva, were chosen. They all built-in Analog Devices, Inc.the (ADI Company, Norwood, MA, USA) isgyroscope employed inahave this work tosignal measure Analog Devices, Inc. (ADI Company, Norwood, MA, USA) is employed inand this work to Ly530alh measure the gyroscope from the ST Company (Geneva, Switzerland) were chosen. They all have built-in conditioning and output voltage signals. TheLpr530al Lpr530al is used for measuring thea signal angle the accelerations along the Y-,Z-axes. and Z-axes. A single-axis Lpr530al gyroscope and dual-axis accelerations alongcircuits the X-, Y-,X-, and A single-axis gyroscope and a dual-axis Ly530alh conditioning circuits output signals. The Lpr530al used for around measuring theand angle variations around the and Z-axis, whilevoltage Ly530alh measuring the angleisvariations the XYgyroscope from the ST Company (Geneva,(Geneva, Switzerland) were chosen. They allThey haveall built-in signal Ly530alh gyroscope from the ST Company Switzerland) were chosen. have built-in variations aroundthe thesensitive Z-axis, while Ly530alh measuring angle variations around the XYaxes. In practice, axes of the sensors must bethe orthogonally installed to align theand three conditioning circuits and output voltage signals. The Lpr530al is used for measuring the angle signalaxes. conditioning circuits and output voltage signals. The Lpr530al is used for measuring the angle In practice, the sensitive of measuring the sensorsunit. must be orthogonally installed to align the three axes along the coordinate frameaxes of the variations around the Z-axis,frame while Ly530alh measuring the angle variations around X- are and Yvariations Z-axis, while Ly530alh the angle variations thethe X- and Y-axes. axes Three along the coordinate the measuring unit. axisthe accelerations andof three axismeasuring angular rates under the carrier’saround coordinate frame axes. In practice, the sensitive axes of the sensors must be orthogonally installed to align the three In practice, the sensitive axes of the sensors must be orthogonally installed to align the three axes along Three axis accelerations and three axis angular rates under the carrier’s coordinate frame are collected by the IMU. Seen from the direction along the line, the trajectory of any point is similar to axes along the by coordinate frame of unit. the coordinate frame ofconductor the measuring unit. with collected the the IMU. Seen from the measuring direction along the line, the trajectory of any is similar as to an ellipse when is the galloping, the elliptic plane perpendicular to point the conductor, an ellipse when the conductor is galloping, with the elliptic plane perpendicular to the conductor, as shownaxis in Figure 4. Three accelerations and Three axis accelerations and three three axis axis angular angular rates rates under under the the carrier’s carrier’s coordinate coordinate frame frame are are shown Figure 4.Seen collected by the IMU. collected byin the IMU. Seen from from the the direction direction along along the the line, line, the the trajectory trajectory of of any any point point is is similar similar to to

an with thethe elliptic plane perpendicular to the conductor, as an ellipse ellipsewhen whenthe theconductor conductorisisgalloping, galloping, with elliptic plane perpendicular to the conductor, shown in Figure 4. 4. as shown in Figure

Figure 4. Elliptical trajectory of monitoring nodes. Figure 4. Elliptical trajectory of monitoring nodes.

Figure Figure 4. 4. Elliptical Ellipticaltrajectory trajectoryof ofmonitoring monitoring nodes. nodes.

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To avoid errors caused by conductor twisting, all the characteristic quantities are calculated with To caused coordinate by conductor twisting, alltothe characteristic quantities with respect avoid to the errors geographical frame, that is say, the accelerations (i.e., are axc, acalculated yc and azc) with Sensors 2016, 16, 1657 4 of 15 respect to the geographical coordinate frame, that is to say, the accelerations (i.e., a , a and azc ) yc azg) with respect to the carrier’s coordinate frame are transformed into accelerations (i.e., axg, aygxc and with respect to geographical theerrors carrier’s coordinate frame are transformed into (as accelerations axg ,5)ayg and athe zg ) respect toTothe coordinate frame before calculation shown in Figure using avoid caused by conductor twisting, all the characteristic quantities are(i.e., calculated with with respect to the geographical coordinate frame before calculation (as shown in Figure 5) using the respect to the geographical coordinate frame, that is to say, the accelerations (i.e., axc, ayc and azc) with following relationships: following relationships: respect to the carrier’s coordinate frame are transformed into accelerations (i.e., axg, ayg and azg) with

  (as shown caxgbefore respect to the geographical   caxg ,aframe , a xc cacalculation a xc in  a xgcoordinate  Figure 5) using the xc xg , a xc a xc     caxg ,axc caxg ,axc caxg ,axc  a xc  a xg following relationships:  a xc

a   a yg   caxg , axc caxg , axc caxg , axc  (1) yc   aayc  =CC (1)  ayg  =  c axg ,axc c axg ,axc c axg ,axc     aycyc  a a xg   ccaxg ,axc ccaxg , axc caxg ,axc   a a    a a  azg  zg  c axg,aaxcxg , axc c axg ,aaxgxc, axc ccaxg   xcazczc   xc azczc a xg,a, axcxc    c c (1) a xg , a xc ca xg , a xc   a yc   C  a yc   a yg    axg , axc    used foran attitude descriptor.  where which is commonly descriptor. Then  a  matrix, where C C is referred referred to to as the attitude  a zc   zg   caxg , axc caxg , axc caxg ,axc   a zc  the galloping displacements displacements are are gained gained through through two two integral integral operations, operations, as asillustrated illustratedin inFigure Figure6.6. where C is referred to as the attitude matrix, which is commonly used for an attitude descriptor. Then the galloping displacements are gained through two integral operations, as illustrated in Figure 6.





a

a

Figure 5.5.Transformation ofcoordinates. coordinates. Figure5. Transformation of Figure Transformation of coordinates.





Figure The 6. The diagramof of changing acceleration to displacement. Figure diagram Figure 6. 6. The diagram of changing changing acceleration acceleration to to displacement. displacement.

Let’s take the X direction for example. Integrating the acceleration yields the velocity:

direction for for example. example. Integrating the acceleration acceleration yields yields the the velocity: velocity: Let’s take the X direction

 v (t )  v (t0 ) wt tt0 axg (t ) dt v ( t ) − v ( t ) = a xg (t)dt and integrating the obtained velocity yields the0 displacement: t t0

v (t )  v (t 0 ) 

axg (t ) dt

(2)

(2) (2)

t0

and integrating the obtained velocity yields the displacement: x (tthe )  xdisplacement: (t0 )   tt v (t ) dt and integrating the obtained velocity yields x (t )  x (t0 )   tt0 v (t ) dt w tfollowing formula: Velocity and displacement are calculated with the x (t) − x (t0 ) = t v(t)dt Velocity and displacement are calculated formula: v (t )  vwith (t0 ) the xg (t ) dt  t ta0following 0

0



Velocity and displacement are calculated the tt following v (t )  with v (t0 )  a xg (t ) dt formula: s x (t )  x (t0 )   tt0 v (t ) dt

v(t) = v(t ) +

wt

0

a (t)dt



(3)

(3) (3) (4) (5)

txg in which axg(t) is the acceleration at times xt ((m/s velocity at time t (m/s); v(t0) is the initial t )  20x);(v(t) t0 ) ist0 the t0 v (t ) dt velocity (m/s); and sx(t) is the displacement at time t (m);

(4) (4) (5)

wt in which axg(t) is the acceleration at time at time t (m/s); v(t0) is the initial s x (tt) (m/s = x (2);t0 )v(t) + is the v(t)velocity dt (5) t velocity (m/s); and sx(t) is the displacement at time t (m);0

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in which axg16, (t)1657 is the acceleration at time t (m/s2 ); v(t) is the velocity at time t (m/s); v(t0 ) is the initial Sensors 2016, 5 of 15 velocity (m/s); and sx (t) is the displacement at time t (m). Similarly, Similarly, the the YYand andZZdirection directiondisplacements displacementsssyy(t), (t), sszz(t) (t) can can be be calculated calculated and and the the conductor conductor trajectory trajectorycould couldbe befit fitaccording accordingto to(s(sxx(t), (t),ssyy(t), (t), sszz(t)). Figure 7 shows the plots of changing changing acceleration acceleration into into displacement. displacement.

Figure 7. 7. The The plots plots of of changing changing acceleration acceleration to to displacement. displacement. Figure

The communication unit utilizes a short-distance ZigBee network, which is implemented by a The communication unit utilizes a short-distance ZigBee network, which is implemented by CC2430 at 2.4 GHz radio frequency. A MSP430F247 microprocessor (TI company, Dallas, TX, a CC2430 at 2.4 GHz radio frequency. A MSP430F247 microprocessor (TI company, Dallas, TX, USA) is USA)is selected as the master controller. Furthermore, considering that the wireless sensor module selected as the master controller. Furthermore, considering that the wireless sensor module is installed is installed on the conductor, the power supply module is designed through an open-loop on the conductor, the power supply module is designed through an open-loop transformer installed on transformer installed on the conductor. The current obtained by mutual inductance is then rectified, the conductor. The current obtained by mutual inductance is then rectified, filtered, and regulated to filtered, and regulated to form stable output voltage. The CMD receives the timing command after form stable output voltage. The CMD receives the timing command after the wireless sensor module the wireless sensor module is powered on and sends a response to the sensors if the timing succeeds. is powered on and sends a response to the sensors if the timing succeeds. Then the sensors begin to Then the sensors begin to collect motion states of the conductor and send the results to the CMD. If collect motion states of the conductor and send the results to the CMD. If the value exceeds the set the value exceeds the set threshold of the monitoring centre, the CMD will trigger an alarm. threshold of the monitoring centre, the CMD will trigger an alarm. 2.1. Structure Design of Wireless Sensor Module 2.1. Structure Design of Wireless Sensor Module To avoid corona discharge and improve the aerodynamic characteristics, the wireless sensor To avoid corona discharge and improve the aerodynamic characteristics, the wireless sensor shell shell has a smooth spherical structure made from aluminum. The shell was designed to be waterproof has a smooth spherical structure made from aluminum. The shell was designed to be waterproof without affecting its normal operation. without affecting its normal operation. The current transformer is embedded into a ring-type structure whose width is 27 mm, outer The current transformer is embedded into a ring-type structure whose width is 27 mm, diameter is 150 mm and inner diameter is 55 mm. The sensor module can easily be installed and outer diameter is 150 mm and inner diameter is 55 mm. The sensor module can easily be installed and uninstalled, as shown in Figure 8. Through running on site, the wireless sensor module can meet the uninstalled, as shown in Figure 8. Through running on site, the wireless sensor module can meet the requirements of HV electrical characteristics and security. requirements of HV electrical characteristics and security.

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Figure8.8.Structure Structuredesign designofofthe thewireless wirelesssensor sensormodule. module. Figure

2.2.Localization LocalizationAlgorithm AlgorithmofofWireless WirelessSensor SensorModule Module 2.2. The conductor galloping gallopingprocess processisisdifficult difficulttotoavoid, avoid, which causes Theconductor conductor torsion torsion in the conductor which causes the the acceleration values collected at different times a same coordinate frame, thekey keyto acceleration values collected at different times to to notnot bebe in in a same coordinate frame, sosothe torealize realizethe thesoftware softwareisisthe the calculation calculation of of the attitude matrix matrix [17]. [17]. The The sensor sensor chooses choosesthe thecarrier carrier coordinate reference system of of a measured value, andand thethe geographic coordinate frame as coordinateframe frameasasthe the reference system a measured value, geographic coordinate frame the uniform reference system. The conversion between the carrier coordinate frameframe and as transformed the transformed uniform reference system. The conversion between the carrier coordinate the geographic coordinate frame isframe completed by the attitude built on the theory body and the geographic coordinate is completed by thematrix, attitude matrix, built on of thea rigid theory of a rotating about a fixedabout pointainfixed mechanics, which the common describing thedescribing relationship rigid body rotating point ininmechanics, in which methods the common methods the ofrelationship motion coordinate frame and reference frame are Eulerframe angles, andquaternion direction of motion coordinate frame coordinate and reference coordinate arequaternion Euler angles, cosine. However, due toHowever, the linearity no singularity of differential equations, no trigonometrics and direction cosine. dueand to the linearity and no singularity of differential equations, in no the integral program (asintegral opposedprogram to Euler angles), and the (relative to theparameters direction trigonometrics in the (as opposed to fewer Euler parameters angles), and the fewer cosine), the is chosen the premier application method. (relative toquaternion the direction cosine),as the quaternion is chosen as the premier application method. According AccordingtotoEuler’s Euler’srotation rotationtheorem, theorem,ininthree-dimensional three-dimensionalspace, space,any anydisplacement displacementofofaarigid rigid bodysuch suchthat thataapoint pointon onthe therigid rigidbody bodyremains remainsfixed, fixed,can canbe berepresented representedby byaasingle singlerotation rotationabout about body someaxis axisthat thatruns runsthrough throughthe thefixed fixedpoint. point.The Theaxis axisofofrotation rotationisisknown knownasasthe theEuler Euleraxis axisdenoted denoted some → andthe therotation rotationangle angleisiscalled calledthe theEuler Eulerangle angledenoted denotedby byζζ(Rodrigues-Hamilton (Rodrigues-Hamiltonparameters). parameters). asasn , ,and → → → → → → a vector referencesystem systemwhose whose three three unit unit vectors j and, when InInaareference vectors are are i, , and k , when a vector=Z =+x i + + y j rotates +zk an angle the instantaneous axis, the new can becan calculated as: as: rotates an around angle around the instantaneous axis, thecoordinates new coordinates be calculated

   1 ZC D→ x1i →y1 j  → z1k D=C− D = x1 i + y1 j + z1 k D = C 1 ZC

(6) (6)

where Z is the carriers coordinate frame, and C is the geographic coordinate frame: where Z is the carriers coordinate frame, and C is the geographic coordinate frame: 

1 1 C  cos   n sin  1 2 → 1 2 C = cos ζ + n sin ζ

2 Equation (7) can be rewritten as a quaternion: Equation (7) can be rewritten as a quaternion: 

2

 1  1 1 1 C  cos   nxi sin   ny j sin   nz k sin  → → 1 2 → 1 2 12 12

(7) (7)

(8)

(8) C = cos ζ + n x i sin ζ + ny j sin ζ + nz k sin ζ 2 2 2 2 = , = ∙ , = ∙ sin and = ∙ sin , Equation (3) can By denoting 1 1 1 By denoting c = cos c = n · sin c = n · sin and c = nz ·sin 21 ζ, Equation (3) can be ζ, ζ, ζ be simply expressed x y 2 3 1 as: 2 4 2 2  simply expressed as:   (9) c1 →c2i → c3 j  c→4 k , c1 + c2 i + c3 j + c4 k , (9)

SubstitutingEquation Equation(9) (9)into into(6) (6)yields: yields: Substituting

      D  (c1 →  c2 i →c3 j  → c4 k )(→xi  yj →  zk→)  C ,

D = (c1 − c2 i − c3 j − c4 k )( x i + y j + z k )·C, which can be rewritten in a matrix form as:

(10) (10)

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which can be rewritten in a matrix form as:    2(c2 c3 +c1 c4 ) c1 2 + c2 2 − c3 2 − c4 2 x1    2( c2 c3 − c1 c4 ) c1 2 + c3 2 − c2 2 − c4 2  y1  =  2(c2 c4 +c1 c3 ) 2( c3 c4 − c1 c2 ) z1

  x 2( c2 c4 − c1 c3 )   2(c3 c4 +c1 c2 )  y z c1 2 + c4 2 − c2 2 − c3 2

(11)

From the above equation the attitude matrix can be known: 

c1 2 + c2 2 − c3 2 − c4 2  2( c2 c3 − c1 c4 )  2(c2 c4 +c1 c3 )

 2( c2 c4 − c1 c3 )  2(c3 c4 +c1 c2 ) , c1 2 + c4 2 − c2 2 − c3 2

2(c2 c3 +c1 c4 ) c1 2 + c3 2 − c2 2 − c4 2 2( c3 c4 − c1 c2 )

(12)

From the above equation, we know that as long as the four elements c1 , c2 , c3 and c4 are obtained, and the attitude matrix can be derived, which can then be used to realize the conversion from the carrier’s coordinate frame to the geographic coordinate frame. What’s more, the angular rate w and quaternion C have the following relationship in quaternions: C0 =

1 A·w 2

(13)

In the above formula, w is the angular rate matrix. Substituting the quaternion and angular rate component into the above equation, the following matrix form can be obtained:   c1 0 c1 c 0  c 1  2  2  0 =  2  c3  c3  c4 0 c4 

− c2 c1 c4 − c3

− c3 − c4 c1 c2

   0 − c4 0 w  w 1 c3    x  x   =  − c2   w y  2  w y wz c1 wz

−wx 0 − wz wy

− wy wz 0 −wx

  c1 − wz c  − wy    2   w x   c3  c4 0

(14)

C can be obtained when the above equation is solved. There are many analytical methods for solving differential equations. Commonly used methods include the Euler method, second-order Runge-Kutta method, fourth-order Runge-Kutta method, etc. Through a comparative analysis, the fourth-order Runge-Kutta method that produces smaller errors was adopted in this work. Combined with the fourth-order Runge-Kutta classic formula of numerical analysis, the simplified formula of Equation (9) is given as:  Cn+1       k1 = k2 =    k3 =    k4 =

= Cn + 6h (k1 + 2k2 1 2 w ·Cn 1 h 2 w ·(Cn + 2 · k 1 ) 1 h 2 w ·(Cn + 2 · k 2 ) 1 2 w ·(Cn + h · k 3 )

+ 2k3 + k4 ) (15)



0 w  x In the above equation, h is the sampling interval, W =   wy wz   k n0  k   n1  and k n =  . Then the first item is derived as:  k n2  k n3     

c1 c2 c3 c4





   

  =  n +1

c1 c2 c3 c4





 t    +  6  n

k10 k11 k12 k13





    +2  

k20 k21 k22 k23



−wx 0 − wz wy

− wy wz 0 −wx





    +2  

k30 k31 k32 k33

  − wz  − wy    , Cn =   wx  0



    +  

k40 k41 k42 k43

c1 c2 c3 c4

    ,  n

    

(16)

 kn 3 

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 c1   c1   k10   k20   k30   k40  k  k      c  c   2    2   t  11   2  21   2  k31    k41   c3   c3  6  k12   k22   k32   k42              c4  n 1 c4  n  k13   k23   k33   k43 

(16) 8 of 15

kknn can be solved according to the following three equations. This is the solution procedure of C, and and then then attitude attitude matrix matrix is is obtained obtained after after CC is is directly directlysubstituted substitutedinto intoEquation Equation(10). (10). Once Once C C is is worked worked out, out, we we can can get get the the accelerations accelerations with with respect respect to to the the geographical geographical coordinate coordinate frame frame using using Equation Equation (1). (1). Figure 9 is is the the accelerations accelerations with with respect respect to to the the carrier’s carrier’s coordinate coordinate frame frame measured measured by by the the IMU. Figure Figure 10 is the angular rates measured by the IMU. Finally, Finally, the the accelerations accelerations with with respect respect to to the the geographical geographicalcoordinate coordinateframe frameon onthe theYYaxis axiscan canbe beseen seenin inFigure Figure11. 11.

Figure 9. The accelerations with respect to the carrier’s coordinate frame.

Sensors 2016, 16, 1657 Figure 9. The accelerations with respect to the carrier’s coordinate frame.

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In this paper, the conductor galloping trajectory is obtained using the Bezier curve fitting method through the displacements measured by the sensors installed on the conductor. Suppose that n galloping sensors were installed on a span. For a Bezier curve, n control points are obtained, with each sensor position given as:

sk  ( skx , sky , skz ) k  0,1,..., n  1

Figure 10. 10. The angular rate. Figure

(17)

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Figure 10. The angular rate.

Figure 11. 11. Y-axes Y-axes accelerations accelerations with with respect respect to to the the geographical geographical coordinate coordinateframe. frame. Figure

The conductor galloping wave S(u) can be written as: In this paper, the conductor galloping trajectory is obtained using the Bezier curve fitting method n 1 through the displacementsS (measured n  the conductor. Suppose that u )  [ x  u  by y  uthe u ]   installed skx sky son  z sensors (18) kz  BEZ k , n 1 (u ) k 0 curve, n control points are obtained, with each galloping sensors were installed on a span. For a Bezier sensor given ( ) =as: ( − 1, ) (1 − ) where position = (1 − ) , and u is the ratio of , sky , skz ) k = 0, 1, ..., n − 1 (17) k = ( skx , towers: installation location and distancesbetween The conductor galloping wave S(u) can be written d as: u i , (19) i n−1dh S(u) = [ x (u) y (u) z (u) ] = ∑ skx sky skz BEZk,n−1 (u) (18) where di is the horizontal distance between the i-th sensor and the small side of tower and d is the k =0

span. where BEZk,n−1 (u) = C (n − 1, k) uk (1 − u)n−1−k = Cnk −1 uk (1 − u)n−1−k , and u is the ratio of installation location and distance between towers: 2.3. Other Considerations d During the data collection process of the sensors, due to temperature drift and outside u = i, (19) interference, the received signals often contain DCd components and trend items, whose existence have a large influence on the subsequent integral operations, and may even yield distortions. where di is the horizontal distance between the i-th sensor and the small side of tower and d is the span. Therefore, the mean method and the least squares method are used to remove the DC components andOther the trend items. Figure 12 compares a set of measured data, of which the data contain the DC 2.3. Considerations During the data collection process of the sensors, due to temperature drift and outside interference, the received signals often contain DC components and trend items, whose existence have a large influence on the subsequent integral operations, and may even yield distortions. Therefore, the mean method and the least squares method are used to remove the DC components and the trend items. Figure 12 compares a set of measured data, of which the data contain the DC component and the trend items are represented by the red line, and the processed data are represented by the blue line. This shows that the processing effect is good. Selecting acceleration data of one direction in the reciprocating trial in one period as an example, Figure 13 illustrates the effect of low-pass filtering. The first plot is the waveform simulation of the original measured acceleration, and the second plot shows the signal after low pass filtering. The original measured acceleration signal showing high frequency interference get smoother after low-pass filtering, which makes the acquired data more accurate and easier to use for subsequent processing. When the frequency of galloping ranges from 0.1 to 3 Hz, it may cause the measured amplitude to be inconsistent with the actual data, and distortions can even occur when the cut-off frequency is set too low, and the interference signal will not be filtered out well if set too high. In this paper, the cut-off frequency is set in the software at 5 Hz and the effect is good.

Selecting acceleration acceleration data data of of one one direction direction in in the the reciprocating reciprocating trial trial in in one one period period as as an an example, example, Selecting Figure 13illustrates 13illustrates the the effect effect of of low-pass low-pass filtering. filtering. The The first first plot plot is is the the waveform waveform simulation simulation of of the the Figure original measured acceleration, and the second plot shows the signal after low pass filtering. The original measured acceleration, and the second plot shows the signal after low pass filtering. The original measured measured acceleration acceleration signal signal showing showing high high frequency frequency interference interference get get smoother smoother after after lowloworiginal pass filtering, which makes the acquired data more accurate and easier to use for subsequent pass filtering, which makes the acquired data more accurate and easier to use for subsequent Sensors 2016, 16, 1657 10 of 15 processing. processing.

Figure 12. Comparison of of the the signals signals before processed. 12. Comparison before and and after Figure after being being processed. processed.

Figure 13. 13. Comparison Comparison of of the the signals signals before before and and after after low-pass low-pass filtering. filtering. Figure Figure 13. Comparison of the signals before and after low-pass filtering.

When the the frequency frequency of of galloping galloping ranges ranges from from 0.1 0.1 to to 33 Hz, Hz, it it may may cause cause the the measured measured amplitude amplitude When 3. Experimental Test and Analysis to be inconsistent with the actual data, and distortions can even occur when the cut-off frequency is to be inconsistent with the actual data, and distortions can even occur when the cut-off frequency is set too low, and the interference signal will not be filtered out well if set too high. In this paper, the set too low, and interference signal will filtered out well if set too high. In this paper, the 3.1. Accuracy Testthe of the Single Sensor Based onnot Testbe Platform cut-off frequency is set in the software at 5 Hz and the effect is is good. good. cut-off frequency is set in the software at 5 Hz and the effect A test platform, as shown in Figure 14, was built to test the measuring accuracy of the proposed conductor galloping sensor. The conductor galloping sensor was installed on the test equipment with the X-axis parallel to the fixed axis and the Z-axis perpendicular to the ground. As the shaft performs a reciprocating movement, the accelerations and angular rate measured by the conductor galloping monitoring sensor were transmitted to a computer with software installed especially for the test installed by a ZigBee network. After being processed, the results of the displacements along the X-, Y- and Z-axes are shown in Figure 15. In addition, the known biggest swing amplitude is 1 m. The test results show that the maximum displacements along the Y- and Z- axis are 1.095 m and 0.889 m, respectively, which agree well with the actual conductor movement.

A test platform, as shown in Figure 14, was built to test the measuring accuracy of the proposed conductor galloping sensor. The conductor galloping sensor was installed on the test equipment with conductor galloping sensor. The conductor galloping sensor was installed on the test equipment with the to the theground. ground.As Asthe theshaft shaftperforms performs thex-axis x-axisparallel paralleltotothe thefixed fixedaxis axisand and the the z-axis z-axis perpendicular perpendicular to a areciprocating movement, the accelerations and angular rate measured by the conductor galloping reciprocating movement, the accelerations and angular rate measured by the conductor galloping monitoring with software software installed installedespecially especiallyfor forthe thetest test monitoringsensor sensorwere weretransmitted transmitted to to aa computer computer with installed by a ZigBee network. After being processed, the results of the displacements along the Sensors 2016, 16,by 1657 of 15 installed a ZigBee network. After being processed, the results of the displacements along the 11 x-,x-, y-y-and known biggest biggestswing swingamplitude amplitudeisis1 1m. m. andz-axes z-axesare areshown shownin inFigure Figure15. 15. In In addition, addition, the the known

Figure 14. Accuracy test setup.

Figure test setup. setup. Figure14. 14. Accuracy Accuracy test

Figure15. Collected data of the accuracy test. Figure15. Collected data Figure 15. Collected data of of the theaccuracy accuracytest. test.

The test results show that the maximum displacements along the Y- and Z- axis are 1.095 m and The results show thatagree the maximum displacements alongmovement. the Y- and Z- axis are 1.095 m and 0.889 m,test respectively, which well with the actual conductor 3.2. Accuracy Test of the Single Sensor Based on Conductor 0.889 m, respectively, which agree well with the actual conductor movement.

An experiment setup was built to test the feasibility of the monitoring sensors, as illustrated in Figure 16. One end of the conductor is fixed, and the other end is fixed on the handle of a machine. The machine can excite the conductor to perform an elliptical motion in one direction by driving the handle vibration. A microwave radar meter is used as benchmark for measuring the length of the semi-major axis and semi-minor axis [18]. The collected data of the tri-axial accelerations and angular rates are sent to a computer with a software installed especially for the test using ZigBee. Then the relative displacement curves were obtained through fitting. In the experiments, the semi-major axis of elliptical motion ranges from about 0.5 m to about 2 m, and the semi-minor axis ranges from about 0.3 m to about 1.3 m. Figure 17 shows how to get elliptical motion parameters according to a set condition where the length of the semi-major axis is 0.5 m and the length of the semi-minor axis is 0.3 m. Then many different motions were measured by both the designed sensor and the radar meter, and the results are shown in Table 1. It can be seen that the maximum relative error of the semi-major axis is 8.11%, and the maximum relative error of the semi-minor axis is 8.35%.

Figure 16. One end of the conductor is fixed, and the other end is fixed on the handle of a machine. The machine can excite the conductor to perform an elliptical motion in one direction by driving the handle vibration. A microwave radar meter is used as benchmark for measuring the length of the semi-major axis and semi-minor axis [18]. The collected data of the tri-axial accelerations and angular Sensors 1657 of 15 rates2016, are16, sent to a computer with a software installed especially for the test using ZigBee. Then12 the relative displacement curves were obtained through fitting.

Figure 16. Experiment setup of a single sensor.

In the experiments, the semi-major axis of elliptical motion ranges from about 0.5 m to about 2 m, and the semi-minor axis ranges from about 0.3 m to about 1.3 m. Figure 17 shows how to get elliptical motion parameters according to a set condition where the length of the semi-major axis is 0.5 m and the length of the semi-minor axis is 0.3 m. Then many different motions were measured by both the designed sensor and the radar meter, and the results are shown in Table 1. It can be seen that the maximum relative error of the semi-major axis is 8.11%, and the maximum relative error of Figure 16. Experiment setup of a single sensor. the semi-minor axis is 8.35%.Figure 16. Experiment setup of a single sensor. In the experiments, the semi-major axis of elliptical motion ranges from about 0.5 m to about 2 m, and the semi-minor axis ranges from about 0.3 m to about 1.3 m. Figure 17 shows how to get elliptical motion parameters according to a set condition where the length of the semi-major axis is 0.5 m and the length of the semi-minor axis is 0.3 m. Then many different motions were measured by both the designed sensor and the radar meter, and the results are shown in Table 1. It can be seen that the maximum relative error of the semi-major axis is 8.11%, and the maximum relative error of the semi-minor axis is 8.35%.

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(A)

(A)

(B) Figure 17. The displacement fitting at a single monitoring point: (A) Motion displacements of a Figure 17. The at apoint single point: single node; (B)displacement Trajectory offitting a single in monitoring a cycle (view from(A) theMotion Z-axis).displacements of a single node; (B) Trajectory of a single point in a cycle (view from the Z-axis). Table 1. Experimental data of the elliptical motion. Semi-Major Axis Measured by Sensor (m) 0.473

Semi-Minor Axis Measured by Sensor (m) 0.267

Semi-Major Axis by Radar (m) 0.497

Semi-Minor Axis by Radar (m) 0.284

Relative Error of Semi-Major Axis 4.83%

Relative Error of Semi-Minor Axis 5.99%

(B) 17.1657 The displacement fitting at a single monitoring point: (A) Motion displacements of a SensorsFigure 2016, 16,

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single node; (B) Trajectory of a single point in a cycle (view from the Z-axis). Table 1. Table 1. Experimental Experimental data data of of the the elliptical elliptical motion. motion.

Semi-Major Semi-Major Axis AxisMeasured Measured by bySensor Sensor(m) (m) 0.473 0.473 0.492 0.492 0.906 0.906 1.029 1.029 1.431 1.431 1.483 1.483 2.026 2.026 2.156 2.156

Semi-Minor Axis Semi-Major Semi-Major Semi-Minor Measured by Axisby by Axis Axis Measured Radar(m) (m) Radar bySensor Sensor(m) (m) 0.267 0.497 0.267 0.497 0.295 0.513 0.295 0.513 0.593 0.986 0.593 0.986 0.678 1.114 0.678 1.114 0.757 1.538 0.757 1.538 0.874 1.585 0.874 1.585 1.215 2.109 1.215 2.109 1.281 2.253 1.281 2.253

Semi-Minor Semi-Minor Axis by by Axis Radar (m) 0.284 0.284 0.311 0.311 0.623 0.623 0.712 0.826 0.921 1.318 1.318 1.396 1.396

Relative Relative Error Error of of Semi-Major Semi-Major Axis 4.83% 4.83% 4.09% 4.09% 8.11% 8.11% 7.63% 6.96% 6.44% 3.94% 3.94% 4.31% 4.31%

RelativeError Error Relative of Semi-Minor of Semi-Minor Axis Axis 5.99% 5.99% 5.14% 5.14% 4.82% 4.82% 4.78% 4.78% 8.35% 8.35% 5.10% 5.10% 7.81% 7.81% 8.24% 8.24%

3.3. Application of the Single Sensor The The wireless wireless sensor sensor module module has has been been tested tested in in the the Guizhou Guizhou power power grid. grid. Three Three sensors sensors were were installed on a conductor spanning 734 m. The field installation is shown in Figure 18. installed on a conductor spanning 734 m. The field installation is shown in Figure 18.

(a)

(b)

Figure 18. Field installation of the wireless sensor module. (a) CMD; (b) wireless sensor. Figure 18. Field installation of the wireless sensor module. (a) CMD; (b) wireless sensor.

Figure 19 plots the data obtained by the wireless sensor module whose ID is 2 describing the Figuregalloping 19 plotsstatus the data by28the wireless ID is 2 describing conductor in aobtained period on May 2013. Itsensor can bemodule clearly whose seen from this figure that the the conductor galloping status in a period on 28 May 2013. It can be clearly seen from this figure that the displacement along the x-axis is the smallest, while the displacement along the z-axis is the largest. displacement along thewith X-axis is the smallest, while the camera. displacement along the Z-axis is the largest. The results agree well those recorded by the video Sensors 2016, 16, 1657 well with those recorded by the video camera. 14 of 15 The results agree

Figure Figure 19. 19. The The runtime runtime data data curve. curve.

4. 4. Conclusions Conclusions With the higher higher state state grid grid scale, scale, monitoring monitoring technologies technologies for transmission lines becoming With the for transmission lines are are becoming more and more important. A kind of wireless sensor module for monitoring conductor galloping of more and more important. A kind of wireless sensor module for monitoring conductor galloping transmission lines has been proposed and realized in this work. The feasibility and accuracy of transmission lines has been proposed and realized in this work. The feasibility and accuracy of of wireless sensor module were verified on the corresponding test platform. In general, the proposed wireless sensor module appears to be very useful for monitoring galloping. Further work will focus on how many sensors should be installed between two consecutive towers to achieve the optimal monitoring performance. Acknowledgments: This work was supported in part by National Natural Science Foundation of China

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wireless sensor module were verified on the corresponding test platform. In general, the proposed wireless sensor module appears to be very useful for monitoring galloping. Further work will focus on how many sensors should be installed between two consecutive towers to achieve the optimal monitoring performance. Acknowledgments: This work was supported in part by National Natural Science Foundation of China (51177115) and Key Technology Innovation Team Project of Shaanxi Province (2014KCT-16). Author Contributions: All authors read and approved the manuscript. Xinbo Huang provided the main idea of this work and performed experimental study and wrote this article. Long Zhao thoroughly reviewed literature and provided precious advice on the structure of this article. Guimin Chen made some simulations and prepared the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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