Overhead Transmission Line Sag Estimation Using a Simple ... - MDPI

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Overhead Transmission Line Sag Estimation Using a Simple Optomechanical System with Chirped Fiber Bragg Gratings. Part 1: Preliminary Measurements Michal Wydra 1, * 1 2

*

ID

, Piotr Kisala 2 , Damian Harasim 2 and Piotr Kacejko 1

Department of Power Systems, Lublin University of Technology, 20-618 Lublin, Poland; [email protected] Institute of Electronics and Information Technology, Lublin University of Technology, 20-618 Lublin, Poland; [email protected] (P.K.); [email protected] (D.H.) Correspondence: [email protected]; Tel.: +48-815-384-738

Received: 27 November 2017; Accepted: 18 January 2018; Published: 20 January 2018

Abstract: A method of measuring the power line wire sag using optical sensors that are insensitive to high electromagnetic fields was proposed. The advantage of this technique is that it is a non-invasive measurement of power line wire elongation using a unique optomechanical system. The proposed method replaces the sag of the power line wire with an extension of the control sample and then an expansion of the attached chirped fiber Bragg grating. This paper presents the results of the first measurements made on real aluminum-conducting steel-reinforced wire, frequently used for power line construction. It has been shown that the proper selection of the CFBG (chirped fiber Bragg grating) transducer and the appropriate choice of optical parameters of such a sensor will allow for high sensitivity of the line wire elongation and sag while reducing the sensitivity to the temperature. It has been shown that with a simple optomechanical system, a non-invasive measurement of the power line wire sag that is insensitive to temperature changes and the influence of high electromagnetic fields can be achieved. Keywords: power system monitoring; power lines sag measurement; chirped fiber Bragg gratings; quasi-periodic waveguide structures; strain measurement; elongation measurement

1. Introduction Fiber Bragg grating (FBG) sensors can be used to measure many physical quantities, such as strain, stress, elongation, temperature [1], and refractive index [2]. The advantage of optical method based research is the lack of influence on the tested object, the ability to perform non-invasive measurements which can be performed in a wide variety of fields such as mechanical structures diagnostics or even medicine [3]. Among the FBG structures are some significant gratings in which the period is not uniform [4]. Many studies have been published demonstrating the promising properties of periodic structures with non-uniform periods, especially chirped fiber Bragg gratings [5]. These structures can be used for separated parameter monitoring [6], independent strain and temperature measurement [5,7,8], dispersion compensation [9,10], or structural health monitoring [11]. Tapered fibers with CFBG have significantly improved strain sensitivity [12]. The CFBG sensors can also be used with inexpensive interrogators [13] and their specially-designed structures can be used as optical filters [14–16]. The loads of the overhead power transmission lines can be measured using a few uniform FBGs. In some embodiments, each grating is bonded directly to the conductor with epoxy [17], which makes it difficult to disassemble when the sensor head cracks. There are also known systems for distributed monitoring of overhead transmission lines with fiber Bragg grating sensor networks [18]. Such systems are very promising because they can be used to provide multiple types of information for smart grids. FBG sensors can be fairly used to monitor the strain of transmission Sensors 2018, 18, 309; doi:10.3390/s18010309

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line wire. In this case, the strain of the conductor is directly proportional to the ampacity of the cable [19]. In such systems, the strain of the grating cannot be widely adjusted because the optical fiber extends equally with the power line conductor. In this paper, the authors would like to present the construction of sensing heads where the CFBG is attached to the so-called control sample steel plate whose dimensional adjustment allows for the control of the sensitivity and measuring range. Among the various methods of constructing these periodic structure based sensors, this is the first method proposed to the best of our knowledge in which the CFBG can be implemented with the strain and sag of power lines can be measured using a special optomechanical system and the control specimen. Today, modern power systems and smart grids are required to have the operational flexibility of electrical power transmission whilst preserving the appropriate safety margin [20,21]. In the context of overhead transmission lines (OTL), the above approach can be implemented by dynamic line rating (DLR) systems [22–25]. The DLR systems allow for the continuous monitoring of operating conditions and the electromechanical state of the OTL span [20,26] or of the whole line [27]. The most important parameters determining the safe operation of the OTL, among others, are the sag and strain of the wire, which are direct functions of its actual temperature resulting from a load of electric current and atmospheric conditions [28–30]. The unquestionable advantages of fiber-optic and FBG sensors are the insensitivity of the measurement to the strong electromagnetic field, the speed of measurement, the non-invasive installation of the sensor on the conductor, the small power demand for the supply of the measuring system, and not needed a complex sensor or radio [31]. At present, the dynamic development of the FBG based monitoring systems is observed [32,33]. Using OTL monitoring and its actual state [28], the current wire elongation sag is a critical parameter in determining the distance from the ground or obstacle [34] that is affecting the operational safety. This article aims to present the results of the application of the CFBG-based sensor for power line strain (relative elongation) to calculate its sag, as an alternative to the standard FBG sensors. 2. Materials and Methods The chirped gratings, compared to conventional FBGs where the period of the refractive index perturbations is constant along the grating length, are characterized by a variable period in the internal structure. Chirps in gratings may take many different forms. The period may vary linearly with the length of the grating, it may be quadratic, and so on. The chirp could also be symmetrical where the period varies by increasing or decreasing around the pitch in the middle of a grating. Generally, modifications applied to the internal structure of the gratings leads to a change of its spectral characteristic. The most widely used CFBGs have a widened spectrum which makes them possible to be used in many areas, including dispersion compensators, mirrors for specialized photonic sensing systems, and sensing elements replacing conventional FBGs. Their widened characteristics allow them to measure not only the wavelength shift, but also the width of the spectra [35]. The proposed method for the power line sag estimation utilizes a simple optomechanical system which allows for the line’s sag change to be converted to the CFBG optical parameter change. The idea of the system is presented in Figure 1. Similar solutions were presented in [17,18] where a sensing head was mounted on an energized power line conductor and the ground voltage was connected directly by fiber-optic cables in the light spectrum processing devices. The system shown in Figure 1 allows for the elongation and sag measurement of the OTL wire. The light source was a superluminescent light emitting diode (SLED). The Thorlabs S5FC1005S (Thorlabs, Newton, NJ, USA) was attached to a single-mode optical fiber used as a transmission light-guide. The light emitted from the SLED source illuminated the sensing CFBG with a 1 nm/cm chirp, inscribed on the hydrogen-loaded SMF-28 part at the end of the fiber. The optical fiber with the CFBG sensor was connected/glued to a thinned plate which was 1 mm in thickness and made of steel (1.0037 S235JR UNI according to the norm EN 10025). The shape of the control plate is shown in Figure 2. The plate is screwed to the semi-circular clamps fixing the control plate with the CFBG sensor to an OTL wire (Figure 2). The elongation of the OTL wire causes the clamps to move apart and

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increase the tension of the control plate, which is monotonically extending the length of its measuring section with Sensors 2018, 18,the 309 CFBG attached. 3 of 14

Figure 1. The overhead transmission line wire sag measurement system where: 1: the ACSR 26/7 Hawk conductor; 2: the measuring clamps/sensing head; 3a: the optical fiber; 3b: the inscribed chirped fiber Bragg grating; 4: the light source with a stabilized super-luminescent diode; 5: the optical circulator; 6: the optical spectrum analyzer; and 7: the computer/gateway.

The idea of the whole optomechanical system is illustrated schematically in Figure 2 and the Figure 1. The The overhead transmission line2b wire sag measurement measurement system where: the ACSR ACSR 26/7 cross-section is shown in Figure 3. Figure shows the proposedsystem shape where: of the sensing plate26/7 which Figure 1. overhead transmission line wire sag 1:1: the Hawk conductor; 2: the measuring clamps/sensing head; 3a: the optical fiber; 3b: the inscribed chirped provides the non-uniform strain while the whole section is extended. The sensing grating was Hawk conductor; 2: the measuring clamps/sensing head; 3a: the optical fiber; 3b: the inscribed fiber Bragg grating; 4: the light source with a stabilized super-luminescent diode; 5: the optical attached theBragg plate grating; keeping4:the of with the chirp shownsuper-luminescent in the figure below. Grating sections chirpedtofiber thedirection light source a stabilized diode; 5: the optical circulator; 6: the the optical opticalperiods spectrum analyzer; and 7: the the computer/gateway. with the most extended are placed and on the plate segment which is mostly elongated which circulator; 6: spectrum analyzer; 7: computer/gateway. provides the best response to the spectrum FWHM in the case of wire elongation. The idea the the whole system is illustrated schematically Figure 2 and the The lightoffrom lightoptomechanical source (SLED) was directed to the CFBG sensor via anin optical circulator. The idea of the whole optomechanical system is illustrated schematically in Figure 2 and the cross-section is shown reflected in Figurefrom 3. Figure 2b shows the was proposed shape of the which The optical spectrum the elongated CFBG returned through thesensing optical plate circulator cross-section is shown in Figure 3. Figure 2b shows the proposed shape of the sensing plate which provides the non-uniform strain while the whole section is extended. The sensing grating was to the optical spectrum analyzer (OSA). Thermal expansion and additional mechanical loads on the provides the non-uniform strain while the whole section is extended. The sensing grating was attached OTL wire cause variations in the of the section surrounded by attached attached to the plate keeping the length direction of measured the chirp wire shown in the figure below. Gratingclamps sections to the plate keeping the direction of the chirp shown in the figure below. Grating sections with the as shown in Figure 2. Inperiods such cases, the response the single-mode fiber is with the inscribed CFBG with the most extended are placed on theofplate segment which mostly elongated which most extended periods are placed on the plate segment which is mostly elongated whichofprovides the results in the widening of the spectral characteristics which is caused by the nonlinearity the strain provides the best response to the spectrum FWHM in the case of wire elongation. best response to the spectrum FWHM in the case of wire elongation. applied to the transducer. The light from the light source (SLED) was directed to the CFBG sensor via an optical circulator.

The optical spectrum reflected from the elongated CFBG was returned through the optical circulator to the optical spectrum analyzer (OSA). Thermal expansion and additional mechanical loads on the OTL wire cause variations in the length of the measured wire section surrounded by attached clamps as shown in Figure 2. In such cases, the response of the single-mode fiber with the inscribed CFBG results in the widening of the spectral characteristics which is caused by the nonlinearity of the strain applied to the transducer.

Figure the optomechanicalsystem system using using aa chirped chirped fiber strain Figure 2. 2. (a)(a) the optomechanical fiberBragg Bragggrating gratingand anda amechanical mechanical strain transformer where: 1: the ACSR 26/7 (Hawk) conductor; 2a: the optical fiber; 2b: the chirped fiber transformer where: 1: the ACSR 26/7 (Hawk) conductor; 2a: the optical fiber; 2b: the chirped fiber Bragg grating; 3: the thinned steel plate; 4: the semi-circular screwed clamps, lref: reference sensing Bragg grating; 3: the thinned steel plate; 4: the semi-circular screwed clamps, lref : reference sensing head length; and (b) the strain distribution in the proposed steel testing plate while extending the head length; and (b) the strain distribution in the proposed steel testing plate while extending the measurement section. measurement section.

The light from the light source (SLED) was directed to the CFBG sensor via an optical circulator. Figure 2. (a) the optomechanical using a chirped grating and a the mechanical The optical spectrum reflected fromsystem the elongated CFBGfiber was Bragg returned through optical strain circulator transformer where: 1: the ACSR 26/7 (Hawk) conductor; 2a: the optical fiber; 2b: the chirped fiber Bragg grating; 3: the thinned steel plate; 4: the semi-circular screwed clamps, lref: reference sensing head length; and (b) the strain distribution in the proposed steel testing plate while extending the measurement section.

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to the optical spectrum analyzer (OSA). Thermal expansion and additional mechanical loads on the OTL wire cause variations in the length of the measured wire section surrounded by attached clamps as shown in Figure 2. In such cases, the response of the single-mode fiber with the inscribed CFBG results in the widening of the spectral characteristics which is caused by the nonlinearity of the strain applied to the transducer. Sensors 2018, 18, 309 4 of 14

Figure3.3.The Thecross-section cross-sectionofofthe thesensing sensinghead head power line measurement system where: 1, Figure ofof thethe power line sagsag measurement system where: 1, 2a, 2a, 3, and 4 are elements equivalent to those shown in Figure 2. 3, and 4 are elements equivalent to those shown in Figure 2.

The full-width half-maximum (FWHM) comparison of the spectral characteristics of the signals The full-width half-maximum (FWHM) comparison of the spectral characteristics of the signals reflected from the Bragg sensor with the value assigned to the reference length of the segment gives reflected from the Bragg sensor with the value assigned to the reference length of the segment gives information on the current elongation of the OTL wire. At the same time, changes in the wire information on the current elongation of the OTL wire. At the same time, changes in the wire surrounding temperature cause spectral shifts to the whole CFBG spectrum and do not affect the surrounding temperature cause spectral shifts to the whole CFBG spectrum and do not affect the FWHM. The linear relationship between the elongation of the conductor, its temperature, and its FWHM. The linear relationship between the elongation of the conductor, its temperature, and its stress stress allow for the determination of the elongation value. In the case of this sensor, the matrix allow for the determination of the elongation value. In the case of this sensor, the matrix equation of equation of the processing can be written as: the processing can be written as: "

# 1 "  SC11 SC12 #  " T  #  OP OP1 SC SC  11 12 ×  Tl  =  SC OP2OP2  SC  21 21 SCSC 22 22   ∆l

(1) (1)

where SC SCij (i(i == 1–2, 1–2, jj == 1–2) 1–2) is is the the sensitivity sensitivity coefficients coefficients that that are are defining defining the the optical optical parameters parameters where ij sensitivity of of the theCFBG CFBGsensor sensorOP OPi on on the the temperature temperature TT along along with with the theelongation elongation∆l. Δl. Let Let us us denote denote sensitivity i the matrix of coefficients SC as: the matrix of coefficients SC as: " # SC SC SC 11 SC 12  11 12 (lT, T) ) (2) MM =  (2) = f f(∆l, SC SC 22 22  2121 SC SC The The optical optical parameter parameter OP OP11 denotes denotes the the full-width full-width at at half half maximum maximum (FWHM) (FWHM) of of the the measured measured CFBG reflects thethe spectral shift (SSH). Thus, it can that CFBGspectrum, spectrum,while whilethe theOP OP 2 parameter reflects spectral shift (SSH). Thus, it be canassumed be assumed 2 parameter OP and OP depend upon the relative elongation ∆l and temperature T (Equations (3) and (4)): that OP 1 and OP 2 depend upon the relative elongation Δl and temperature T (Equations (3) and (4)): 1 2



OP Tl ,]T OP 1 1=f 1f[1∆l,



(3) (3)

OP2 = f 2 [∆l, T ]

OP2  f 2  l , T 

(4) (4) In this case, we will look for the temperature values and maximum stress without knowing the case,M. weLet will for the and values maximum stress knowing the the valueIn ofthis matrix uslook denote the temperature vector of thevalues searching as sv. Thiswithout vector contains valueof ofthe matrix M. Let us denote the of the searching values sv. This vector contains the value engineering strain e and thevector temperature T so that we can as write: value of the engineering strain e and the temperature T so that we can write:

sv  [l , T ]

(5)

The measurement values vector mv can be defined as follows:

mv  [OP1 , OP2 ]  FWHM CFBG , SSH CFBG 

(6)

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sv = [∆l, T ]

(5)

The measurement values vector mv can be defined as follows: mv = [OP1 , OP2 ] = [ FW HMCFBG , SSHCFBG ]

(6)

where FWHMCFBG is the full-width at half maximum of the CFBG spectrum and SSHCFBG denotes its spectral shift. Equation (1) can be written in the matrix form as follows: mv = Msv

(7)

The matrix M has 2 × 2 dimensions, is symmetrical for all vectors x ∈ R2 , and is real. As a result of the measurements, the sensitivity matrix M is determined and the vector of searching values sv can be calculated based on the measured magnitude vector mv. Measuring the optical parameters of the CFBG, such as FWHMCFBG and SSHCFBG allows for the determination of the fiber temperature T and elongation ∆l according to the matrix equation below: "

OP1 OP2

#

"

=

CSC11 CSC21

CSC12 CSC22

#

"

×

T ∆l

# (8)

where CSCij are the complex sensitivity coefficients (i = 1, 2, j = 1, 2). The value ∆l which appears in Equation (8) is the relative elongation length measured between the clamps of sensing head (lref ) mounted on the conductor. The conductor sag D can be calculated as a function of ∆l, according to the reference conductor length Lref . The overhead transmission line conductor’s sag-tension calculations are typically based on the catenary equation, which describes an entirely flexible rope rigidly fixed at both ends. The catenary equation is defined using hyperbolic sine or cosine functions. However, it can be reliably approximated by a parabola. The main difference between a catenary equation and the parabolic approximation is that catenary assumes a constant weight per unit length through the conductor while the parabolic equation assumes an invariable weight per unit horizontal length. This simplification causes the sag calculation with the parabolic approximation to be smaller than when it is estimated with the catenary equation. The shape of a catenary is a function of the conductor weight per unit length weight w, the horizontal component of tension H, span length S, and the maximum sag of the conductor D. The exact catenary equation uses hyperbolic functions, as shown in Equation (9). The right side of the Equation (9) is an approximation of the hyperbolic cosine using the Maclaurin series expansion: y( x ) =


 w   w x2 H cosh x −1 = . w H 2H

(9)

For a flat span, the low point is at the center and the wire sag D is found by substituting x = S/2. Exact and approximate formulas for the sag calculations is shown in Equation (10):     H wS wS2 D= cosh −1 = . w 2H 8H

(10)

The parabolic approximation is sufficiently accurate as long as the sag in the span does not exceed 5% of its length [36]. The power line sag D varies with the conductor temperature, ice, wind loading, and time as the conductor creeps. The horizontal tension H is equal to the conductor tension in the middle of the span shown in Figure 4. At the endpoints where the wire is fixed to the insulators, the conductor tension F is equal to the horizontal tension H plus the conductor weight per unit length w multiplied by the sag D, according to Equation (11) [36]:

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F = H + wD.

(11)

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Figure 4. The The conductor conductor length, length, sag, sag, clearance, and tension in a transmission line span. Figure

It common to to perform performsag-tension sag-tensioncalculations calculationsusing usingonly onlythe thehorizontal horizontal tension component It is is common tension component H, H, but the average of the horizontal and support point tension F is usually shown. The conductor but the average of the horizontal and support point tension F is usually shown. The conductor length length in the span can be calculated the application of a catenary using Equation (12). in the span can be calculated with thewith application of a catenary equation equation using Equation (12). The right The side of (12) Equation (12) corresponds to a approximation parabolic approximation of thefunction: catenary function: side right of Equation corresponds to a parabolic of the catenary 2 2  2 H  Sw  Sw    S2Sw2w  2H sinh  1  2 2.  . LL= sinh =  S S1+ ww 2H 24 H   2H   24H

(12)

The total total conductor conductor length length can can be be expressed expressed as as aa function function of of sag sag D D as as shown shown in in the the Equation Equation (13): (13): The 8D2 2 LL=SS+ 8D. 3S .

(13) (13)

3S

Using Equation (13), we can write the formula for the conductor sag dependence D upon the span Using Equation (13), we can write the formula for the conductor sag dependence D upon the length S and the conductor length L, shown below: span length S and the conductor length L, shown below: r 3S( L − S) D= (14) 3S 8L  S. (14) D . 8 The difference between the conductor length L and span length S is defined as the conductor slack.The Equation (14)between shows that changes in the slackspan givelength significant changes as in the the conductor conductor difference thesmall conductor length L and S is defined sag. As it was mentioned above, conductor sag depends mainly on the total conductor length L when slack. Equation (14) shows that small changes in the slack give significant changes in the conductor the span S remains above, constant. The temperature dependency ofthe thetotal conductor length L is typically sag. As itlength was mentioned conductor sag depends mainly on conductor length L when calculated using Equation (15): the span length S remains constant. The temperature dependency of the conductor length L is





typically calculated using Equation (15): L2 = α AS L1 ( T2 − T1 ) + β L1 (σ2 − σ1 ),

(15) L2   AS L1 T2  T1   L1  2  1 , (15) where index 1 and 2 are the beginning and end states, respectively; L1 , L2 : the conductor length in the span; Tindex the2conductor temperature; αASstates, is the respectively; thermal elongation coefficient for ACSR; σ1,the σ2 where 1 and are the beginning and end L1, L2: the conductor length in 1 , T 2 are are the conductor stress; and β and the wire elastic elongation coefficient. span; T1, T2 are the conductor temperature; αAS is the thermal elongation coefficient for ACSR; σ1, σ2 The typicallystress; temperature-tension calculation of the power line span is performed using are the conductor and β and the wire elastic elongation coefficient. Equation (16) [36] and solved using iterative methods: The typically temperature-tension calculation of the power line span is performed using









Equation (16) [36] and solved using iterative methods: S2 g12 S2 g22 α σ2 − ( T2 − T1 ), 2 22 = σ1 − 22 − 2 S gσ22 24β 24βSσ1g1 β 

2 

24  22

 1 

24  12





T2  T1  ,

(16)

(16)

where S is the span length; σ1, σ2 = H/A is the wire stress; g = w/A is volumetric weight; A is the wire cross-sectional area; and β = 1/γ is the wire elastic elongation coefficient. For ACSR 26/7 Hawk conductors, typically α = 18.7 × 10−6 1/K, γ = 75,000 MPa, A = 276.2 mm2, w = 9.52 N/m, and g = 34.47 N/(m.mm2) [37]. In such cases, we need to measure tension, stress, or the wire

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where S is the span length; σ1 , σ2 = H/A is the wire stress; g = w/A is volumetric weight; A is the wire cross-sectional area; and β = 1/γ is the wire elastic elongation coefficient. For ACSR 26/7 Hawk Sensors 2018, 18, 309 7 of 14 conductors, typically α = 18.7 × 10−6 1/K, γ = 75,000 MPa, A = 276.2 mm2 , w = 9.52 N/m, and g = 34.47 N/(m·mm2 ) [37]. In such cases, we need to measure tension, stress, or the wire temperature temperature to estimate the total length of the wire in the span and then calculate sag. Sometimes, a to estimate the total length of the wire in the span and then calculate sag. Sometimes, a calculation of calculation of the bare conductor temperature can be done using the methods presented in [28–30] the bare conductor temperature can be done using the methods presented in [28–30] based on weather based on weather parameters, electric current, or conductor tension measurements. The algorithm for parameters, electric current, or conductor tension measurements. The algorithm for conductor sag conductor sag calculation was investigated by [26] and is presented in Figure 5. calculation was investigated by [26] and is presented in Figure 5. Tension Measurements

Weather Parameters

Conductor Temperature Calculation

Conductor Current

Mechanical State Estimation

Sag Estimation

Check for Clearance Violiations

Operator Dispaly

Figure 5. The sag estimation process reproduced from [26]. Figure 5. The sag estimation process reproduced from [26].

This paper introduces a direct method for calculation of the sag D based on a single spot conductor This paper introduces a direct method for calculation of the sag D based on a single spot elongation measurement with a CFBG sensor. Assuming that the horizontal tension H and conductor conductor elongation measurement with a CFBG sensor. Assuming that the horizontal tension H and thermal elongation is constant over the span, the relative elongation measurement ∆l of the selected conductor thermal elongation is constant over the span, the relative elongation measurement Δl of 10 cm wire segment covered with the sensing head clamps provides the data required for the calculation the selected 10 cm wire segment covered with the sensing head clamps provides the data required of the total wire length L, as described with Equations (17)–(20). According to previous considerations, for the calculation of the total wire length L, as described with Equations (16)–(19). According to the relative wire elongation ∆l could be appointed as a function of the sensor FWHM spectral width as previous considerations, the relative wire elongation Δl could be appointed as a function of the sensor shown below: FWHM spectral width as shown below: ∆l = COP1 · ∆FW HMCFBG , (17) E=

l  C COP1  FWHM CFBG , ∆l = OP1 · ∆FW HMCFBG , lre f lre f

(16) (18)

l COP1 where E is the relative elongation coefficient FWHM function; COP1 is the experimentally E  as a measured  FWHM (17) CFBG , evaluated elongation sensor sensitivity coefficient; lref lreflref is the reference distance of the installed sensor clamps on the conductor; and ∆l is the elongation of the wire segment covered by the sensing head where E is by thethe relative elongation coefficient as a measured FWHM function; COP1 is the and measured CFBG sensor. experimentally evaluated elongation sensor lref is the reference distance of the L =sensitivity Lre f (1 + E)coefficient; . (19) installed sensor clamps on the conductor; and Δl is the elongation of the wire segment covered by theand above (Equation the conductor the Assuming sensing head measured by(19)), the CFBG sensor. sag dependence D (Equation (14)) we acquire the following form: v  u L  L 1 E .  (18) u 3S L ref t re f (1 + E ) − S D= . (20) 8 sag dependence D (Equation (14)) we acquire Assuming the above (Equation (18)), the conductor the According following form: to Equations (14) and (19), it is shown that for OTL wire sag calculation is enough to





3S  Lref 1  E   S 

measure an elongation of a particular section of the wire.

D

8

.

(19)

According to Equations (14) and (18), it is shown that for OTL wire sag calculation is enough to measure an elongation of a particular section of the wire.

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3. Results 3.3.Results Results The surveys were performed on a real overhead power transmission line. The measurement The surveys were performed on overhead power transmission line. The were performed on akV a real real overhead power transmission The measurement measurement system The was surveys mounted directly on a 110 OTL power line wire which wasline. energized. The proper system was mounted directly on a 110 kV OTL power line wire which was energized. The proper system was mounted directly on a 110 kV OTL power line wire which was energized. The proper construction of the optomechanical system, provided its compact size and weight, makes it negligible construction of the optomechanical system, provided its compact size and weight, makes ititnegligible construction of the optomechanical system, provided its compact size and weight, makes negligible to to thethe mechanical workings of the power line. Figure 66 shows shows a photographofofthe the measurement to the mechanical mechanical workings workings of of the the power power line. line. Figure Figure 6 shows aa photograph photograph of the measurement measurement system mounted on an ACSR 26/7 Hawk wire. system systemmounted mountedon onan anACSR ACSR26/7 26/7Hawk Hawkwire. wire.

Figure 6. The CFBG based optomechanical system for the power line sag estimation in real conditions. Figure 6. The CFBG based optomechanicalsystem systemfor forthe the power line Figure 6. The CFBG based optomechanical line sag sagestimation estimationininreal realconditions. conditions.

The The influence influence of of temperature temperature variations variations on on the the measurement measurement system system described described above above was was The influence of temperature variations online the measurement system described above was(clamps, measured measured for a short segment of the power wire with the mounted complete system measured for a short segment of the power line wire with the mounted complete system (clamps, forsteel a short segment of the power line wire with the mounted complete system (clamps, steel plate steel plate plate with with attached attached optical optical fiber). fiber). The The OTL OTL wire wire segment segment was was placed placed in in aa climate-control climate-control with attached optical fiber). The OTL wire segment was placed in a climate-control chamber with chamber at chamber with with aa temperature temperature range range established established at 10–90 10–90 °C. °C. Figure Figure 7a 7a shows shows the the spectral spectral ◦ a temperature rangethe established at 10–90 C. Figure 7a shows the spectralofcharacteristics of the characteristics characteristics of of the CFBG CFBG reflected reflected signal signal measured measured for for border border cases cases of the the surrounding surrounding ◦ C and 90 ◦ CFBG reflected signal measured for border cases of the surrounding temperature: 10 temperature: 10 °C and 90 °C. The increase of the surrounding temperature of the wire changes temperature: 10 °C and 90 °C. The increase of the surrounding temperature of the wire changesthe the C. CFBG spectral characteristic by the spectrum to wavelengths. The The increase of the surrounding temperature of the wire changes the CFBG spectral characteristic CFBG spectral characteristic byshifting shifting thewhole whole spectrum tolonger longer wavelengths. Thespectrum spectrumisis widened so FWHM characteristics has bynot shifting the whole to longer of wavelengths. The spectrum is not widened so the FWHM not widened so the thespectrum FWHM parameter parameter of the the sensor sensor output output characteristics has aa quasi-constant quasi-constant character. However, the shift of the spectrum could be distinguished and measured and in paper parameter of the sensor output characteristics has a quasi-constant character. However, the shift of the character. However, the shift of the spectrum could be distinguished and measured and inthis this paper is called SSH (spectral shift). spectrum be distinguished is calledcould SSH (spectral shift). and measured and in this paper is called SSH (spectral shift).

Figure 7. (a) a comparison of the spectra measured for the CFBG mounted in the proposed OTL wire Figure 7. (a) a comparison thespectra spectrameasured measuredfor for the the CFBG mounted Figure 7. (a) a comparison ofofthe mountedin inthe theproposed proposedOTL OTLwire wire monitoring system for 10◦ °C and 90◦°C surrounding temperatures; (b) a comparison of the spectra monitoring system and9090 C °Csurrounding surrounding temperatures; temperatures; (b) monitoring system forfor 1010C°Cand (b) aa comparison comparisonofofthe thespectra spectra measured for CFBG: FWHM_1 refers to the measurement directly after mounting the system on the measured CFBG: FWHM_1refers referstotothe themeasurement measurement directly directly after measured forfor CFBG: FWHM_1 after mounting mountingthe thesystem systemononthe the wire and FWHM_2 refers to the measurement after 0.1% relative elongation. wire and FWHM_2 refers to the measurement after 0.1% relative elongation. wire and FWHM_2 refers to the measurement after 0.1% relative elongation.

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In the case of chirped Bragg gratings, distinguishing the center wavelength is difficult because of SensorsIn 2018, 309 of chirped Bragg gratings, distinguishing the center wavelength is difficult because of 14 the18, case the non-regular character of its spectra. In the processing characteristics shown in this paper,9 the SSH of the non-regular character of its spectra. In the processing characteristics shown in this paper, the parameter is calculated based on the half spectral width of the appointed FWHM. Another situation the case of Bragg gratings, the center wavelength difficult Another because SSH In parameter is chirped calculated based on thedistinguishing half spectral width of the appointedis FWHM. occurs when the wirecharacter length changes due toInthe mechanical elongation which is in shown in Figure 7b. of the non-regular of its spectra. the processing characteristics shown this paper, situation occurs when the wire length changes due to the mechanical elongation which is shownthe in The SSH FWHM value sharply increases with the growth of the measured elongation, which promises that parameter is calculated based on the halfwith spectral width of appointed elongation, FWHM. Another Figure 7b. The FWHM value sharply increases the growth of the the measured which in the described measurement system it could be used as a determinant of the power line shown sag. Figure situation occurs when the wire length changes due to the mechanical elongation which in 8 promises that in the described measurement system it could be used as a determinant ofisthe power shows the characteristics of the dependency of SSH on the wire elongation and the surrounding Figure 7b. The FWHM value sharply increases with the growth of the measured elongation, which line sag. Figure 8 shows the characteristics of the dependency of SSH on the wire elongation and the promises thattemperature in the described measurement systemranges. it could be used as a determinant of the power temperature variations in thevariations selected ranges. surrounding in the selected line sag. Figure 8 shows the characteristics of the dependency of SSH on the wire elongation and the surrounding temperature variations in the selected ranges.

Figure 8. The comparison SSHdependency dependency on on (a) testing plate; andand (b) the Figure 8. The comparison ofofSSH (a) the the elongation elongationofofthe the testing plate; (b) the changes of the CFBG sensor surroundingtemperature. temperature. changes of the CFBG sensor surrounding

Figure 8. The comparison of SSH dependency on (a) the elongation of the testing plate; and (b) the changes of the CFBG sensor The graph depicted abovesurrounding shows thattemperature. the spectral shift calculated as a half wavelength width of

The graph depicted above shows that the spectral shift as a half wavelength width FWHM depends on both elongation and temperature. In thecalculated case of temperature variations, the The graph depicted above shows that the spectral shift calculated as a half wavelength width of of FWHM depends on both elongation and temperature. In the case of temperature variations, transformation of the measured temperature to SSH has a linear character. The temperature depends on both elongation and temperature. In the case of temperature variations, the the FWHM transformation of the measured temperature to SSH has a linear character. The temperature sensitivity of the considered monitoring system configuration is associated with a thermal expansion transformation ofmaterial the measured to SSH has aislinear character. temperature sensitivity of the considered monitoring system associated with aThe thermal expansion coefficient of the which thetemperature testing plateconfiguration is made of along with the material of the OTL wire. sensitivity of the considered monitoring system configuration is associated with a thermal expansion The shift the different elongation results directly from the widening of thewire. coefficient of determined the materialfor which the testing plate isvalues made of along with the material of the OTL of the material testing platevalues is made of along with the material of theonly OTL wire. signal spectrum. As to the theelongation SSH parameter, theresults FWHM spectral width the The coefficient shift determined foropposed the which different directly from thedepends widening of on the signal The shift determined for the different elongation values results directly from the widening of the elongation of the measurement section and is practically insensitive to the temperature changes. spectrum. As opposed to the SSH parameter, the FWHM spectral width depends only on the elongation signal spectrum. As tocharacteristics the SSH parameter, FWHM spectral width depends on the Figure 9 shows section the opposed changing of thethe FWHM width dependent on Figure the only changes of the of the measurement and is practically insensitive to the temperature changes. 9 shows elongation of the measurement section and is practically insensitive to the temperature changes. elongation and temperature in the same ranges as in the case shown in Figure 8. changing of the FWHM width dependent on thewidth changes of elongation and temperature Figurecharacteristics 9 shows the changing characteristics of the FWHM dependent on the changes of in the same ranges as in the case shown in Figure 8. elongation and temperature in the same ranges as in the case shown in Figure 8.

Figure 9. The characteristics of the FWHM spectral width dependency on (a) the relative elongation; and (b) the ambient temperature of the proposed system. Figure 9. The characteristicsofofthe theFWHM FWHM spectral spectral width onon (a)(a) thethe relative elongation; Figure 9. The characteristics widthdependency dependency relative elongation; and (b) the ambient temperature of the proposed system. and (b) the ambient temperature of the proposed system.

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According to Figure 9, the total wire elongation in the span and the wire sag can be anticipated as a function of FWHM and the initial state span parameters. Let us assume that the power line span to constructed Figure 9, thewith total ACSR wire elongation in conductors the span andthat thehave wire asag can be length anticipated as is S =According 300 m and 26/7 Hawk per unit weight awfunction of FWHM and the initial state span parameters. Let us assume that the power line span = 9.75 N/m [37]. The mechanical characteristics of the span describe that, for a wire temperature of is = 300 and constructed HawkEquation conductors per unitto length weight 10S°C, them horizontal tension with is H =ACSR 14,60026/7 N. Using (12),that it ishave thenapossible calculate the w = 9.75 N/m [37]. The mechanical characteristics of the span describe that, for a wire temperature of reference wire length Lref (Equation (20)) and reference sag Dref (Equation (21)): 10 ◦ C, the horizontal tension is H = 14,600 N. Using Equation (12), it is then possible to calculate the 2 3002  9.75 reference wire length Lref (Equation (21)) and reference sag Dref (Equation (22)): Lref  300 1  (20)   300.502 m , 242146002 2   300 · 9.75 Lre f = 300 1 + = 300.502 m, (21) 24 · 14, 6002

3  300  (300.502  300) Dref  r 3 · 300 · (300.502 − 300)  7.514 m . Dre f = = 7.514 m. 8 8

(21) (22)

The initial initial conditions conditions shown shown above above are are matched matched for for an an OTL OTL span span right right after after installing installing the the wire wire The on the the poles. poles. Weather Weather conditions conditions cause cause changes changes in in the the elongation elongation of of the the wire wire due due to to icing, icing, ambient ambient on temperature, wind wind speed speed and and angle, angle, and and solar solar radiation. radiation. The The elongation elongation is is also also associated associated with with the the temperature, conductor temperature temperature arising from the electric current flow. flow. As a result of the total wire length L, conductor changes in the power line the variations of changes line sag sag D Dalso alsovary. vary.In Inthe theproposed proposedoptomechanical optomechanicalsystem, system, the variations thethe length measuredCFBG CFBGFWHM FWHM spectral width. width. Characteristics Characteristics of lengthofofthe themeasured measuredsection section affect the measured shownin inFigures Figures10 10and and1111present present how power line be influenced by the elongation of shown how thethe power line sagsag willwill be influenced by the elongation of the the testing OTL wire segment and how the FWHM spectral width is affected by sag changes of the testing OTL wire segment and how the FWHM spectral width is affected by sag changes of the power power line theparameters initial parameters described by Equations line with thewith initial described by Equations (21) and(20) (22).and (21).

Figure 10. (a) The dependency of the OTL wire sag related with the elongation of the proposed Figure 10. (a) The dependency of the OTL wire sag related with the elongation of the proposed measurement system plate calculated for the initial conditions described in Equations (21) and (22); measurement system plate calculated for the initial conditions described in Equations (20) and (21); and (b) the dependency of the measured FWHM for different sag values of the monitored OTL line. and (b) the dependency of the measured FWHM for different sag values of the monitored OTL line.

The two different parameters of the Bragg grating spectrum that will 1 1and 2 are Thecoefficients coefficientsOP OP andOP OP 2 are two different parameters of the Bragg grating spectrum that change due to the induced elongation or temperature changes. The matrixThe equation of the temperature will change due to the induced elongation or temperature changes. matrix equation of the and elongation sensor processing will take the form of Equation (8). Taking into account the results temperature and elongation sensor processing will take the form of Equation (8). Taking into account obtained the measurements, it allows us to writeusthe matrix equation in the form below: the resultsfrom obtained from the measurements, it allows to write the matrix equation in the form below: FW HM 0.000100.00603 0.00603 T CFBG  FWHM  0.00010  T CFBG = ×   , SSHCFBG  0.02261 0.00484  SSH    ∆l  0.02261 0.00484  l  CFBG   "

#

"

#

"

# ,

(23) (22)

where CSC11 is the sensitivity of FWHMCFBG to temperature (CSC11 = 0.1 pm/K), CSC21 is the sensitivity where CSC11 is the sensitivity of FWHMCFBG to temperature (CSC11 = 0.1 pm/K), CSC21 is the sensitivity of SSHCFBG to the temperature (CSC21 = 22.61 pm/K), CSC12 is the sensitivity of FWHMCFBG to the of SSHCFBG to the temperature (CSC21 = 22.61 pm/K), CSC12 is the sensitivity of FWHMCFBG to the elongation of testing section (CSC12 = 6.03 pm/µm), and CSC22 is the sensitivity of SSHCFBG to the elongation of testing section (CSC12 = 6.03 pm/μm), and CSC22 is the sensitivity of SSHCFBG to the elongation of the testing section (CSC22 = 4.84 pm/µm). elongation of the testing section (CSC22 = 4.84 pm/μm).

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OTL wire sag (m)

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1.9

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2.3

2.5

2.7

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FWHM (nm) Figure 11. The dependency of the OTL wire sag as a function of the measured FWHM. Figure 11. The dependency of the OTL wire sag as a function of the measured FWHM.

By analyzing it could be seen thethat simultaneous measurement of the temperature By analyzingEquation Equation(23), (22), it could be that seen the simultaneous measurement of the and elongation possible if, for the proposed system, we designate two different temperature and iselongation is possible if, for the monitoring proposed monitoring system, we designate two parameters of the CFBG which show different sensitivities for the measured quantities. It is only possible different parameters of the CFBG which show different sensitivities for the measured quantities. It is if the possible inequalityif condition OP1 6= condition OP2 is alsoOP met, which is fulfilled because FWHMCFBG 6= SSH CFBG . only the inequality 1 ≠ OP2 is also met, which is fulfilled because Analysis of Equation (23) allows us to conclude that with the known (determined experimentally) FWHM CFBG ≠ SSHCFBG. Analysis of Equation (22) allows us to conclude that with the known sensitivities FWHMCFBG andsensitivities SSHCFBG for of theFWHM temperature and elongation, the measured quantities (determined ofexperimentally) CFBG and SSHCFBG for the temperature and of CSC , CSC , CSC , and CSC could be determined simultaneously. matrix of algebraic 11 12 22 elongation, the21 measured quantities of CSC11, CSC21, CSC12, and CSC22 The could be determined complements of The all sensor CSCsensitivities calculated 11 , CSC12 along 21 , CSC22 have simultaneously. matrixsensitivities of algebraicCSC complements of allwith sensor CSCbeen 11, CSC12 along using Equation (24) and the received values have been shown in Equation (25): with CSC21, CSC22 have been calculated using Equation (23) and the received values have been shown in Equation (24): d11 = (−1)1+1 · CSC22 = CSC22 , d12 = (−1)1+2 · CSC21 = −CSC21 . (24) 1 2 · CSC d111)2(+11)·1CSC  CSC  CSC2212,, dd1222= ( (− 1)1 12)2 + CSC d21 = (− = CSC 12 = 11CSC 11 22 − 21   21 . (23) d 21  ( 1)2  1  CSC12  CSC12 , d 22  ( 1)2  2  CSC11  CSC11 By the condition of the non-zero matrix determinant of Equation (24), it is possible to construct its complementary matrix on Equation (24), which we of will now write initthe form: to construct By the condition ofbased the non-zero matrix determinant Equation (23), is possible its complementary (23), which we will form: " matrix # based on Equation " # now " write in the # 1 T 0.00484 −0.00603 FW HMCFBG , (25) 0.00603 × FWHM ∆lT  = −0, 100014  0.00484 SSHCFBG −0.02261 0.00010 CFBG    , (24)      

 l 

0, 00014  0.02261

0.00010   SSH CFBG 

where det: the matrix determinant form of Equation (23) moreover, equals: where det: the matrix determinant form of Equation (22) moreover, equals: det = CSC11 CSC22 − CSC21 CSC12 . (26) det  CSC11CSC22  CSC21CSC12 . (25) The fulfilled condition of the various sensitivity ratios of FWHMCFBG and SSHCFBG for the temperature The fulfilled condition of the of various sensitivity ratios of FWHM CFBG and SSHCFBG for the and elongation gives the possibility simultaneous determination of both quantities by measuring temperature and elongation gives the possibility of simultaneous determination of both quantities by the spectrum shift (SSHCFBG ) and the spectral width of the CFBG characteristic (FWHM CFBG ). measuring the spectrum shift (SSHCFBG) and the spectral width of the CFBG characteristic (FWHM CFBG). 4. Discussion The proposed method has a low cross-sensitivity, as seen in the final matrix of the processing 4. Discussion system in Equation (25). An analytical determination of the OTL sag was proposed based on the CFBG Themeasurements proposed method has a directly low cross-sensitivity, seen in the matrix of the processing spectra mounted on the Hawk as wire using thefinal special semicircular screwed system Equation An sensing analytical determination the OTL sagconfirmed was proposed based on the CFBG clampsin forming the(24). whole head. Empirical of studies have the low cross-sensitivity spectra measurements mounted directly onpm/K, the Hawk wire using the special semicircular screwed values (CSC CSC21 = 22.61 CSC12 = 6.03 pm/µm and CSC 11 = 0.1 pm/K, 22 = 4.84 pm/µm). clamps forming the whole sensing head. Empirical studies have confirmed the low cross-sensitivity We have shown that such use of CFBGs and the suitable optomechanical system allows for the values (CSC11 = 0.1 pm/K, CSC21 = 22.61 pm/K, CSC12 = 6.03 pm/μm and CSC22 = 4.84 pm/μm). We have shown that such use of CFBGs and the suitable optomechanical system allows for the monitoring of

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monitoring of the relative wire elongation and the OTL sag D. The presented method is non-sensitive to temperature changes (the FWHM width used for the determination of elongation is practically insensitive to thermal variations), provides repeatability of measurements (by the mechanical construction of clamps and the whole sensing head) and it is non-invasive . It is also worth mentioning that the design of the sensing head protects the optical fiber because changing the wire length within the possible elongation range does not damage the optical fiber. Additionally, the mass of the sensing head is negligible relative to the mass of the entire wire in the span so the sensor does not affect the object being measured. Figure 11 shows the dependency of the calculated sag of the power line with the assumed initial parameters on the measured FWHM spectral width. The potential of the method is increased by the use of a chirped fiber Bragg grating CFBG whose spectral characteristics are broader (more extensive) than in the case of a conventional FBG. If the spectral response of the CFBG/FBG were to be measured using an interrogator (for example, based on an FBG optical filter) and not using an OSA, the measurement would be more accurate since the measured spectra would be broader and changes in its width would be measured more accurately by the interrogator. 5. Conclusions In this article, we have presented a method that monitors the state of an OTL and measures its relative elongation and its actual sag. It is based on the new construction of CFBG sensors and is insensitive to the ambient temperature, the electromagnetic field and any other external typically influencing parameters. Insensitivity has been achieved by the structure of the sensing head that consists of clamps and the special monotonically, non-uniformly extendable steel plate that the CFBG is attached to. The proposed system can be non-invasively and directly embedded on the power line wire. The use of the Bragg grating with a linearly variable period allows for more considerable variation in the optical spectrum than standard FBGs, which translates into an increased sensitivity and accuracy. The obtained sensitivity of the FWHM width to elongation was 0.00603 nm/µm, and at the same time, the FWHM is practically insensitive to temperature changes (sensitivity coefficient reduced to 0.0001 nm/K). This condition allows for the determination of the wire elongation independently of temperature variations. In addition to the determination of the OTL wire extension, the proposed method also allows for the measuring of the temperature around of power line wire by meeting the conditions of the sensitivity matrix equation. Furthermore, the use of chirped fiber Bragg grating with a broad spectrum is advantageous because its spectrum is approximately ten times wider than the usual FBG. The measurements using a CFBG will be more precise than the standard FBG which has a much narrower range. Thus, the proposed system is entirely applicable in a configuration in which the spectra of the grating are interrogated with an optical filter (for example, a filter based on homogeneous FBG). Such a combination can be very interesting because it offers the possibility to eliminate the OSA and use a simple interrogator based on an optical filter. The measurement point fixing system is designed for use for an indefinite time, which is of crucial economic importance. Additionally, such a designed system ensures the stability of its components on the OTL wire without any adverse effect on its strength, mainly due to the non-invasive fixing method. In the case of possible damages to the delicate components of the sensor system, it is possible to replace them with new ones with the same parameters. An important feature is the independence of the measurement from the influence of the outside temperature and the unavoidable electromagnetic field at the measurement site. It should be noted that all determined sensitivity coefficients and final results are also dependent on the geometry of the transducer and the initial parameters of the CFBG sensor together with the control plate. Future work will involve an investigation into a sensitivity analysis for the function of changes of the parameters mentioned above and on the metrological conditions of the whole system.

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Author Contributions: This work was realized with the collaboration of all authors. Michal Wydra, Piotr Kisala and Piotr Kacejko contributed to the idea of this work. Michal Wydra, Piotr Kisala and Damian Harasim conceived and designed the experiments; Damian Harasim and Michal Wydra performed the experiments; Piotr Kisala, Michal Wydra and Damian Harasim analyzed the data. Michal Wydra wrote the biggest part of the article and contributed all the work referred to the transmission lines and sag-tension calculations using presented optomechanical measuring system designed by Piotr Kisala. Mechanical simulations and all the optical part of the manuscript was contributed by Piotr Kisala and Damian Harasim. Piotr Kacejko provided the funding. All the authors contributed to the production of the paper, the discussion of the results and the reviewing process of the intellectual content of the article and finally approved the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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