输电线路非线性脱冰耦合振动数学模型及振动响应参数优化

MATHEMATICAL MODEL OF NONLINEAR ICE-SHEDDING COUPLING VIBRATION FOR TRANSMISSION LINE AND PARAMETER OPTIMIZATION OF VIBRATION RESPONSE

为研究输电线路脱冰振动响应,基于能量法的拉格朗日动力方程,考虑输电线竖向、顺线路方向位移与绝缘子旋转角耦合,建立连续档输电线路非线性脱冰耦合振动数学模型用于描述输电线路脱冰振动。在不同档距、覆冰厚度、脱冰率作用的脱冰工况下,利用四阶Runge-Kutta方法求解非线性振动数学模型的数值解,得到输电线路脱冰振动动态位移和动态应力。对比数学模型和抛物线方程及状态方程求解的位移、应力,初步验证了数学模型的准确性。根据数学模型求解结果对输电线路脱冰振动响应参数进行优化,得出档距越小、覆冰厚度越大、脱冰率越大,输电导线脱冰振动响应中位移振幅越大。

In order to study the vibration response caused by transmission line ice-shedding, based on the Lagrangian dynamic equation of the energy method, considering the coupling of the vertical and forward direction displacement of the transmission line with the rotation angle of the insulators, a mathematical model for the nonlinear ice-shedding coupling vibration of the continuous transmission line was established to describe the ice-shedding vibration of the transmission line. Under the conditions of different spans, icing thickness and ice-shedding ratio, the fourth-order Runge-Kutta method was used to solve the numerical solution of the nonlinear vibration mathematical model, and the dynamic displacement and dynamic stress of the ice-shedding vibration of the transmission line were obtained. Comparing the displacement and stress of the mathematical model and ice-shedding parabolic equation and state equation, the accuracy of the mathematical model was preliminarily verified. According to the results of the mathematical model, the response parameters of the ice-shedding vibration of the transmission line were optimized. The smaller the span, the thicker the icing thickness, the larger the ice-shedding ratio, the greater the displacement amplitude of the transmission line ice-shedding vibration response.