Modelling and numerical solution of ungrounded DC rail traction system load flow using ladder circuit - part II: solution method

Accurate solution of dc ungrounded rail power system load flow requires detailed modelling of negative path components, resulting in large numbers of circuit nodes and branches. Such modelling complexity incurs heavy computational burden and potential ill numerical conditions when solved by nodal voltage equations. Part I of this study presented a ladder-circuit model for traction network between substations and a power flow formulation adopted from ac distribution load flow. Part II presents the solution algorithm that harnesses the ladder circuit models to achieve efficient load flow computation and numerical robustness for the entire dc traction system by sequentially solving for power flows of individual substations and wayside ladder circuits. The proposed algorithm requires computational burden linearly proportional to the number of substations, much less than those by nodal voltage equations. The computation results from two transit lines in Taiwan illustrate that the proposed algorithm accomplishes the objectives of computational proficiency, numerical robustness and versatility to train load models and various traction circuit configurations such as branch lines.