A Generalized mathematical model of dc catenary lines

Sezgin, Mustafa Erdem
Most of the subway systems are powered by electricity around the world. Although both AC and DC systems can be employed for energization, DC electrified systems are commonly preferred. The DC catenary line voltage can be calculated trivially for stationary systems at steady state. However, accurate modeling of the catenary voltage during the movement of the subway trains is cumbersome, as it requires solution of differential equation systems. This thesis proposes a generalized model for catenary voltage variation of DC powered systems. One of the challenges of modeling problem is calculation of the electrical parameters of the system, because of the non-regular shape of the rails, on which the electric current flows. The thesis firstly develops an analytical method for accurate computation of electrical parameters of the system, and validates it using finite elements analysis. After that, by using the electrical parameters the voltage and current variations through the catenary line are investigated analytically for different mode of operations of the subway trains, such as constant speed and accelerating/decelerating operations. Because of the dynamical behavior of the system, both time and position dependent differential equations are defined during the analytical derivations. The solution of the system based on differential equations is not trivial, and requires significant computational burden, Therefore, this work, proposes a linearized method in order to improve the computational performance of the derived model. The proposed linear method enables solution of the system with improved computational performance, while maintaining a high accuracy. Moreover, the effect of the regenerative braking and the effect of multiple substation and train are investigated. The results of the analytical solution of voltage variation are compared with the real life test results.