A Non-linear Analytical Analysis Model For Shielding Performance Estimation Of Transmission Lines And Its Application On The Differentiated Lightning Protection

The EHV (Extra High voltage) transmission lines have been operated many yearsin China. The operation experience show that the trip-out caused by shielding failure isone of the important factors which influences the safe running of EHV transmissionlines. As a normal voltage class in China, the safe and stable running of EHVtransmission line is the fundamental for persist power supply in power grid. In thedesign and reform procedure of lightning protection for a transmission line, in order toensure the lightning protection to be effective, some shielding failure methods will beadopted to obtain the shielding performance of the transmission line. Thus, shieldingperformance estimation attracts much attentions from lightning protection researchers.Due to the limitation of lightning measuring technology and parameter acquisitiontechnology of transmisison lines, the parameters used in shielding performanceestimation of a transmission line have to adopt one unique value. Study show that thismethod can reflect the shielding performance of a entire tranmission line and made agreat contribution to the current study on shielding performance of EHV tranmissionlines. For the lightning protection, trip-out events usually occur in the weakest point of atransmission line. Thus, the differentiated lightning protection idea, which considers thedifferent tranmission line parameter and different tranmission line corridor, is proposed.The differentiated shielding performatnce of tranmission line is the fundamental fordifferentiated lightning protection. At present, many study on differentiated shieldingperformance estimation of tranmission lines have been conducted.Based on those models, some key methods in those models have been studiedsufficiently in this dissertation. Some methods which limit their practical engineeringapplication are improved. Furthermore, a differentiated shielding performanceestimation model for EHV transmission lines application is proposed.The high-spatial precision of ground flash density map in differentiated shieldingperformance estimation method is required. The disadvantage of classical grid methodto calculate the high-spatial precision ground flash density map is analyzed. However,the classical grid method cannot obtain a high-spatial precision ground flash densitymap with a high credibility. Thus, a new method, neighborhood grid method is proposedbased on the classical grid method. The neighborhood grid method separates the gridand statistical area in the statistiacal procedure, which ensures that the high-spatial precision ground flash density map can be obtained with a high reliability. From twoaspects, ground flash sample size and ground flash locating error, the advantages anddisadvantages of two gridding methods are analyzed in detail. Results show that whenthe grid size is large the ground flash density obtained by the two methods are bothcredible, while when the grid size is small the ground flash density obtained byneighborhood grid method is credible and the one obtained by classical grid method ishard to be credible. Besides, the ground flash density on the basis of the Chongqinglightning location data verifies this results. In addition, using the neighborhood gridmethod, a high-spatial precision ground flash density map (0.01°×0.01°) is obtained.Some study show that, for a EHV transmission line, the leader progression modelis suggested in the shielding performance estimation. Although the leader progressionmodel can effectively reflect the entire procedure of shielding failure for a transmissionline, the huge computation load and time-consuming problem is an obstruction for itsengineering application.The key steps for this problem are analyzed and the development of upward anddownward leaders are deemed as one of the most huge computation load parts. Thus,based on the widely used Rizk assumptions on the developing direction of upwardleader and downward leader, a governing equation for description for development ofleaders is proposed by using differential equations. Further, the analytical solution (agroup of nonlinear equations) for the differential equations is obtained. And thetrajectories of upward and downward leaders’ tips can be expressed by the group ofnonlinear equations. Validation experiment shows that this group of nonlinear equationseffectively reflects the Rizk assumptions on developing direction of upward anddownward leaders. In the practical engineering application, the traditional numericalmethod for the development of leaders can be substituted by the group of equations.By dividing the lightning strike procedure to earthed object in to two key stages,first location of downward leader and second location of downward leader, thecomplicated lightning strike procedure is simplified to solve the servaral nonlinearequations. The widely adopted linear decay assumption on the charge density indownward leader is used to establish the nonlinear equation model for potentialcalculation. The first location of downward leader is obtained by solving the nonlinearequations for the potential calculation. By combing the nonlienar equations for leaders’developing direction and the nonlinear equations for potential as well as voltage drop ofupward leader, a nonlinear model for positioning the second location of downward leader is established. Thus, the lightning strike point can be obtained rapidely bycomparing the different second location of downward leader of conductors, overheadground wires and ground. The compariosn of different attractive distances of conductorsshow that the attractive distances obtained by this study are similar to the ones obtainedby the Dellera-Garbagnati model, which indicates the model in this study is reasonable.Futhermore, a nonlinear analysis model for leader progression model is proposedfor multi-conductors tranmisison lines. And with the help of the lasted global elevationmodel ASTER GDEM, by combining the high-spatial precision ground flash densitycalculation model and analytical leader progression model, a shielding performanceestimation model for EHV transmission line is proposed. By combining the groundflash density map in Chongqing, the shielding performance of a500kV transission lineis estimated.