Mathematical modeling of road heating system with underground distribution line based on nonlinear ODE model

Abstract

In regions with heavy snowfall, there has long been a serious problem of great inconvenience and danger to people's lives caused by the snowfall. To tackle this problem, a novel framework for efficient snowmelting should be proposed, which can be useful in the control systems design for the considered road healing systems. In this paper, we propose a road heating system using underground power distribution lines. As a main result, we derive a mathematical model of the system. The nonlinear ordinary differential equation (ODE) model is introduced to describe the spatial and temporal variation of the voltage of the distribution line. The validity of the model is verified by numerical simulations using actual data of solar radiation and PV power generation of Toyama Prefecture, Japan in winter.