A full multi-span two-degree-of-freedom (2-DOF) iced transmission line model is presented .Taking multi-span conductors as the research object, based on Hamiltonian principle, a nonlinear galloping model of multi-span conductors considering the influence of insulator string is established and its galloping equation is derived. Based on the theoretical formula, the modes and frequencies in-plane and out-of-plane the multi-span conductors plane were obtained. After the partial differential equation was transformed into ordinary differential equation by Galerkin discrete method, the multiple scale method was used to solve the dynamic response of the multi-span conductors.The influence of parameters such as number of spans, length of spans and tension on the characteristics of in-plane and out-of-plane movement of multi-span conductors is systematically analyzed by numerical examples.The research results of this paper have certain reference value for practical engineering and preventing multi-span conductors galloping.
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