覆冰导线舞动方程的建立及求解策略

架空导线的覆冰舞动是导致线路跳闸的重要因素，严重威胁着电力系统运行的安全性与稳定性，如何准确地描述其位移与频率的舞动规律就成为亟待解决的问题。基于拉格朗日原理建立了包括垂直、水平以及扭转的3自由度的舞动运动方程，使用模态摄动法描述导线舞动时各微元的相对位置关系，考虑到覆冰导线大幅舞动的几何非线性，使用Newmark-β法结合Newton-Raphson迭代求解覆冰导线舞动运动方程，并提出了有效的求解算法。由算例获得的舞动位移幅值及频率的数值解与实测值较为接近，从而证明了模型及算法的有效性。研究表明：覆冰导线舞动是一种以垂直运动为主的自激振动，其舞动频率十分接近于覆冰导线体系垂直振动的固有频率。在覆冰导线舞动的应变模型与气动力系数处理上有较大改进，且使用模态摄动法大大减少了计算量并提高了舞动位移的计算精度，从而为准确估计因舞动导致的线路跳闸概率计算奠定了良好的基础。

Establishment and Solution Strategy of Galloping Equation of Iced Conductors

The galloping of iced overhead conductors is one of the key factors for tripping fault of transmission lines, and threatens the security and stability of power system. It is thus needed to accurately capture such conductor’s galloping characteristics as displacement and frequency for solving the galloping problems. A 3-DOF (vertical, horizontal and torsional) galloping motion equation is established based on the Lagrange principle, and the modal perturbation method is used to describe the relative positions of the infinitesimals of galloping conductors. Considering the geometric nonlinearity of iced conductor’s galloping, the galloping motion equation is solved using the Newmark-β method combined with Newton-Raphson iteration, and an effective solving algorithm is proposed. The simulated displacement amplitude and frequency of the galloping in the case study are very close to the measured ones, which proves the effectiveness of the proposed model and algorithm. It is concluded that the galloping of iced conductors is a kind of self-excited vibration with vertical motion as principal and its frequency close to the natural frequency of the vertical vibration of the iced conductor system. The strain model and aerodynamic coefficients of the iced conductor galloping were improved significantly in this paper, and the modal perturbation method greatly reduced the calculation amount and improved the calculation accuracy of the galloping displacement, thus laying a good basis for accurate estimation of the line tripping probability caused by galloping.