The safe operation of power transmission lines is seriously threatened by galloping. In Hubei on January 28,2015,the galloping has caused severe accidents of shut down,partial discharge and disconnection on several 500 kV extreme-high-voltage lines. In light of the climatic change process,structure of transmission lines,ice formation and arrangements of anti-galloping fittings,an average equation for the galloping of Jinlin I,II,III Circuits,Sanjiang II Circuits and Nanjing I Lines was established and detailedly based on a three degrees of freedom nonlinear dynamic curved beam model. By virtue of the equation,the dynamic behaviors of the circuits and lines were detailedly analysed and the nonlinear dynamic properties,such as the conditions and processes of gallopings occurrence and development were revealed. For improving the theoretical cognition on galloping,and raising the power grids ability against icing galloping, the following conclusions are beneficial: the accident happened in Hubei belongs to the typical Nigol galloping and a reasonable arrangement of anti-galloping devices can effectively improve the conductorsability of anti-vibration. Some suggestions based on the theoretical computations were provided to make the arrangements of anti-galloping fittings more reasonable.