Mathematical Model of Pantograph Arc Based on Probability Distribution of Arc Parameters

Abstract

Pantograph arc has become a potential hazard for the safe running of electric locomotive. It is essential to build an accurate mathematical model of pantograph arc for arc simulation. Pantograph arc experiments were carried out. And the probability distribution characteristics of arc parameters such as arc ignition moment, arc extinction moment and arc duration were analyzed. A mathematical model of pantograph arc was established. Firstly, Habedank model was selected as an initial mathematical model. The model parameters were optimized by using particle swarm optimization algorithm. Secondly, the initial mathematical model was preliminarily improved by using time-varying model parameters. Thirdly, taking into account the randomness of arc phenomenon, the model was further improved by adding a pulse function, and then the final mathematical model of pantograph arc was obtained. The pulse generation time and pulse width of the pulse function vary along with uniform distribution function and truncated normal distribution function, respectively. Finally, a simulation module of pantograph arc was designed with MATLAB software, and the effectiveness of the mathematical model was proved. The proposed model can describe the electrical characteristics of pantograph arc more accurately, and it can be used to further analyze the evolution of pantograph arc.