Research On Perturbation Method In Un-transposed Transmission Lines Of Power System

More and more high voltage transmission lines are being used because of the fast development of the economic and the growing demand for electricity.The technology of multi-circuit transmission lines on same tower has the advantages of large transmission power per unit area,saving the transmission corridor and better economic.Therefore,it is widely used now.However,multi-circuit transmission lines on same tower may be un-transposed sometimes because of the cost or technology,which makes it difficult to analysis or calculate the fault in the un-transposed transmission lines.Traditional symmetrical component method or six-sequence component method only works under the condition of symmetrical parameters of transposed transmission lines.The error can't be ignored if the transmission lines are un-transposed.So study the analysis method of un-transposed transmission lines has certain practical significance.The theory of modal analysis can be used to analysis the un-transposed transmission lines because of its multiple phase-mode transformation matrices.The key of the modal analysis is to get a sufficiently accurate phase-mode transformation matrix which can decouple the impedance matrix of the un-transposed transmission lines.This paper builds a perturbation made by un-transpose to get more accurate results.It uses perturbation theory to expand the eigenvalues and eigenvectors of the transmission line's impedance matrix and then get phase-mode transformation matrix of different precisions by satisfying different order's equations,which realizes the decoupling of the impedance matrix of the un-transposed single-circuit transmission lines.By calculating a real example,it proves that the phase-mode transformation matrix has high accuracy.Applying the obtained matrix to the theory of modal analysis in fault location,we find that the calculated results have small error compared with the real results,which verifying the feasibility of the method in this paper.At last,we study further the applicability of perturbation theory in un-transposed double-circuit transmission lines on the basis of the phase-mode transformation of un-transposed single-circuit transmission lines based on perturbation method in the previous text.By calculating a real example,it proves that the phase-mode transformation matrix of un-transposed double-circuit transmission lines still has high accuracy.Applying the obtained matrix to the theory of modal analysis in fault location,we find that the calculated results also have small error compared with the real results,which verifying the applicability of perturbation theory in un-transposed double-circuit transmission lines.