Modelling and numerical solution of ungrounded DC rail traction system load flow using a ladder circuit – part I: circuit modelling

Abstract

Accurate solution of DC ungrounded rail power system load flow requires detailed modelling of the negative path, resulting in large numbers of circuit nodes and branches. The solution of the associate nodal voltage equations not only requires a heavy computational effort, but could also encounter ill numerical conditions. This two-part study presents a novel methodology utilising the longitudinal configuration of rail traction power networks to derive a ladder-circuit model and to devise an efficient solution algorithm. This method belongs to the so-called sequential methods yet goes a step further to divide a DC traction power system into substations and ladder circuits between them. The modelling of individual substations makes it easier to incorporate detailed characteristics of receptive substations and various train load models, while the generic ladder-circuit topology paves the way for simple and efficient numerical solutions. The proposed load flow solution requires manipulation of small-dimensional matrices and equations, making it suitable for either manual or computer calculations of the DC portion of the sequential method for the load flow analysis of the entire traction system.