The measurement of overhead conductor s sag with DLT method

Transcription

1 Advaces i Egieerig Research (AER), volume 7 2d Aual Iteratioal Coferece o Electroics, Electrical Egieerig ad Iformatio Sciece (EEEIS 206) he measuremet of overhead coductor s sag with DL method Fag Ye, Meg ia2, Xig Zhag2, Zhi-Yog Ga3, Xi He3 ad Zhag-Qi Wag2 Electric Power Research Istitute, State Grid iaji Electric Power Compay, iaji, , Chia @63.com 2Departmet of Mechaical Egieerig, North Chia Electric Power Uiversity, Baodig, 07003, Chia 3Electric power sciece ad echology Developmet Co., Ltd. of iaji city, iaji , Chia he overhead coductor sag calculatio is put forward combied with image aalysis techology based o DL theory i this paper. Moreover, the simulatio experimet is carried o ad the measuremet error is also aalyzed. he attetios eeded i practical operatio are also provided. he result shows that the method provided i this paper is a quick, efficiet ad practical measuremet method for trasmissio lie ispectio. Keywords: Direct Liear rasformatio; Overhead Coductor; Sag.. Itroductio he electric power system is the foudatio of Chia's ecoomic costructio, ad it is also a importat guaratee for the atioal life. Sag is oe of the importat parameters for operatio ad maiteace of trasmissio lies, so it is ecessary to cotrol the sag of overhead coductor withi the allowable rage. If the sag is too small, the wire stress will be icreased, which will cause more vibratio ad the break of trasmissio lie, ad eve the damage of electric power tower. If the sag is too large, the safe distace betwee the wire ad the groud is ot eough, ad the discharge pheomeo will be take place, ad eve the pheomeo of short twist is occurred to coductor gallopig. Ad furthermore, sag is oe of the limitig factors to icrease the trasmissio capacity of overhead trasmissio lies. he trasmissio capacity ca be adjusted by the real-time dyamic measuremet of the sag, which could release the coservative trasmissio capacity to achieve the purpose of dyamic capacity icrease []. herefore, it is of great sigificace to measure the sag of overhead trasmissio lies regularly to esure the safe operatio of the whole power grid. he traditioal methods of sag measuremet iclude agle method, equal Copyright 207, the Authors. Published by Atlatis Press. his is a ope access article uder the CC BY-NC licese ( 365

2 Advaces i Egieerig Research (AER), volume 7 legth method ad relaxatio plate observatio method, etc, but these methods are very icoveiet to operate, ad have large huma error ad low measuremet efficiecy. I referece [2], the local meteorology parameters are cosidered as the cotrol coditio, ad the wire sag is calculated by measurig the stress or icliatio of coductor i combiatio with the coductor state equatio, but this method requires a large ivestmet ad has high cost. Chris Measha Bous i [3] studies DGPS techology for coductor sag measuremet. his method uses four satellites to locate the positio of Rover that ca be used i ay eviromet hagig fixed poit for overhead coductor sag measuremet, however, the price of this measuremet method is very expesive, ad the power cosumptio is also high. he referece [4] shows that the spacer is used as a template to match the spacer of the coductor through image processig, the three-dimesioal coordiate trasformatio is carried out for the match poit, the coductor sag is calculated by curve fittig of world coordiates of the match poit. As the spacer could be out of shape i differet positios ad is easily affected by the eviromet durig the matchig procedure, it is also difficult to measure trasmissio lies sag i practical applicatio. I this paper, a ew method is put forward to measure the overhead coductor sag based o two-dimesioal plae image aalysis. I the preset method, a marker o the measurig spot is used ad the coordiates of the marked poit is obtaied by a photograph aalysis method. 2. Director Liear rasformatio 2.. Camera imagig model he camera imagig model is a importat part of the measuremet system. I the moocular visio, accordig to requiremets of the measuremet ad the actual situatio, the camera imagig model ca be divided ito vertical projectio model, weak perspective imagig model, pihole imagig model, ad so o. Amog of them, the pihole imagig model is the closest to the actual situatio [5-7]. So this paper selects the pihole model as camera imagig model. he priciple of pihole imagig model is show i the Fig.. Spatial poit P passes through the optical ceter O, ad PO itersect at p poit with i the projectio plae. he camera coordiate of spatial poit P is deoted as XC, YC, Z C, the space coordiate of space coordiates system O w X W Y w Z w is P X, Y, Z, correspodig to the image pixel coordiate of the projectio poit p ( uv, ). 366

3 Advaces i Egieerig Research (AER), volume 7 Ow Yw Zw Xw P(Xc,Yc,Zc) Zc P u o x O v y Xc Fig.. his is the priciple of pihole imagig model. Yc 2.2. DL mathematical model Direct liear trasformatio is obtaied by the colliear equatio of image poit, optical ceter ad spatial poit. he trasformatio relatioship betwee image coordiates ad spatial coordiates is established through DL. Durig the calculatio, the iteral ad exteral parameters of the camera are ot required, ad the features of the DL are simple ad stable. hus, the followig relatioship ca be obtaied accordig to DL theory: L X L2Y L3 Z L4 u L9 X L0Y L Z L5 X L6Y L7 Z L8 v L9 X L0Y L Z () Here, the space coordiate of object poits is ( X, Y, Z ), the coordiate of image pixel coordiate system is ( uv, ). Ad L i is the elemet of the trasformatio matrix L. It is very easy to derive the two-dimesioal DL method from the threedimesioal DL solutio, that is, Z is appoited as zero, the two-dimesioal DL mathematical model ca be obtaied from, L X L2Y L4 u L9 X L0Y L5 X L6Y L8 v L9 X L0Y (2) 367

4 Advaces i Egieerig Research (AER), volume 7 Note that there are oly 8 variables i the two-dimesioal DL mathematical model, while the 3D DL mathematical model has variables, so the twodimesioal DL has the advatages of small amout of calibratio poits, simple operatio ad less computatio. From the two-dimesioal DL model, if the coordiates of 4 poits i pace scee ad their correspodig pixel coordiates are available, 8 equatios ca be obtaied ad the trasformatio matrix L ca be kow by solvig these 8 equatios. 3. Object Spatial Coordiates Calculatio I the calculatio of the coordiates of spatial poit, the trasform matrix L should be calculated first, the the object coordiates ca be obtaied by L, fially, the coductor sag ca be obtaied by fittig the object coordiates. 3.. Resolutio of trasformatio matrix Whe the spatial coordiates of ladmarks ad correspodig pixel coordiates are available, 2 equatios ca be obtaied as i followig, X Y u X uy u X Y Xv vy v L (3) X Y u X uy u X Y X v vy v where L L L L L L L L L he, the trasform matrix is u X Y u X uy v X Y Xv vy L A A A, A u X Y u X uy v X Y X v vy (4) I order to calculate the 8 variables of the trasformatio matrix L, the spatial coordiates of at least 4 marker poits ad the correspodig pixel coordiates should be kow Calculatio of object poit coordiate Whe the trasformatio matrix ad the spatial coordiates of ladmarks ad the correspodig pixel coordiates are kow, the spatial coordiates of the 368

5 Advaces i Egieerig Research (AER), volume 7 object ca be calculated accordig to, X u L4 L ul9 L2 ul0 Y v L 8 L5 vl9 L6 vl 0 B B B, B (5) X u L4 L ul9 L2 ul0 Y v L L v L L v L Overhead lie curve fittig he two-dimesioal spatial coordiates of each poit of the overhead coductor ca be obtaied by the Eq. (5), ad the the calculatio model of the coductor ca be calculated by the method of data regressio. he calculatio model of overhead coductor ca be described as cateary or parabolic equatio [8]. I order to avoid the hyperbolic fuctio ad simplify the calculatio, this paper adopts parabolic equatio. he quadratic parabolic equatio model of overhead coductor is show as y k k x k x (6) Here, xy, is the spatial coordiate of a poit o the overhead lie, ad k 0, k, k2 are udetermied coefficiets. Usig the oliear regressio algorithm of least square to fit the feature poits of the coductor, the value of the udetermied coefficiets ca be calculated, ad the the sag of overhead coductor also ca be obtaied easily. 4. Simulatio Experimet Research I order to verify the accuracy ad feasibility of the overhead lie sag calculatio method, the simulatio experimet is carried o. For coveiece, the height betwee the groud ad the coductor ear stadia rod is take as the measurig object. I additio, the ifluece of distributio of the idetificatio poits o the measuremet accuracy has also bee aalyzed. Sice the smooth cable, with the characteristics of uiform load, iextesibility ad fully flexibility, is accord with the state of overhead lie, it is used to carry o the experimet istead of overhead lie. he experimetal image is show i Fig.2. he simulatio coductor of this experimet is a costat height suspesio, ad the related parameters are measured by the stadia rod. he groud clearace of coductor is 200cm, ad the side legth value of checkerboard is 5cm square. 369

6 Advaces i Egieerig Research (AER), volume 7 Fig. 2. his is the simulatio of experimetal based o DL. If the checkerboard is placed i the coductor plae, the spatial coordiate of each poit of the coductor ca be calculated accordig to the DL theory. he flowchart of the procedure is preseted i Fig. 3. Layout idetificatio poit Image acquisitio he computatio of projectio matrix Fig. 3.his is the flow chart of the experimetal procedure. Coductor spatial coordite calculatio First, the calibratio poits o the checkerboard is chose ad the trasformatio matrix L is calculated accordig to the Eq. (4). he, the measuremet poit i the coductor is selected, ad the two-dimesioal spatial coordiates is calculated accordig to the Eq. (5). I the experimet, the calibratio poits of differet distributio forms are selected ad divided ito six groups, that is, A- A4, B-B4, C-C4, D-D4, E-E4, F-F4, respectively correspodig, 2 2, 4 4, 6 6, 8 8, 0 0 square. he distributio of calibratio poits are show i Fig. 4: Fig. 4. his is the distributio of calibratio poits o the checkerboard he actual value of the distace betwee coductor ad groud is 200 cm, while the calculatio results of the idetificatio poits with differet distributio 370

7 Advaces i Egieerig Research (AER), volume 7 coditios are show i table. able. his is the experimetal result ad the measuremet error. Size of calibratio grid Measured value(cm) Relative error( ) 29.38% 6.75% 7.07% 6.57%.60%.09% From the above results, it shows that the larger the surrouded area of calibratio poits i the image proportio is, the smaller the measuremet error is. Moreover, the measured values are less tha the actual value, which meas there are some system errors. 5. Coclusios A measuremet method for overhead coductor sag is put forward usig twodimesioal image measuremet based o the DL theory. he ifluece of the distributio of the calibratio poits o the measurig accuracy is aalyzed, which shows the measuremet accuracy is higher whe the idetificatio poit is larger tha /4 i the image. he proposed method ca calculate the coductor sag with the characteristics of simple operatio, good accuracy, high efficiecy ad practicability, which avoids the disadvatages of the traditioal maual measuremet method. Refereces. Forbes, Blake, D. Bradshow, ad F. Campbell, Fidig hidde capacity i trasmissio lies. rasmissio & Distributio World, 2002, 54, (9). 2. Wei Kog, Xiao-Guag Dai, Zhe-Wei Yag, Matlab realizatio of stress sag curve of overhead lie. Electric Power, 2009, 42 (7): Mesah-Bosu C, Krekeler U F, Heydt G, etc, Applicatio of the global positioig system to the measuremet of overhead power trasmissio coductor sag. IEEE rasactios o Power Delivery, 2002, 7(): Wei-Guo og, Bao-Shu Li, Ji-Sha Yua, etc. Method of trasmissio lie sag measuremet based o aerial image sequece. Proceedigs of the CSEE, 20, 6: D.A.Forsyth, J.Poce. Forsyth. Computer Visio: A Moder Approach. Pretice Hall Professioal echical Referece, R. Szeliski, Richard. Computer Visio: Algorithms ad Applicatios. Joural of Polymer Sciece Polymer Chemistry Editio 2.8 (20): M.S.Nixo, A.S.Aguado. Feature extractio ad image processig. Beijig: Electroic Idustry Publishig House, 20: Dia-Sheg Zhag. Desig Maual of High Voltage rasmissio Lie i Power Egieerig. Beijig: Chia Power Press,