This work presents a comprehensive set of steady state models to be included in power flow simulation studies of DC railway networks. This simulation framework covers all important aspects and features of each element of modern DC railways. The proposed models are simplified to achieve the maximum simulation speed while keeping the required accuracy. Not only non-reversible, controlled and uncontrolled reversible substations are considered, but also on-board and off-board accumulation systems. The train model can consider the low network receptivity (overvoltage protection for trains equipped with regenerative braking) and overcurrent protection. It is also possible to include in the simulation DC/DC links between nodes of the railway network at the same or different voltage. To date, there is no other work able to conjugate all the mentioned models in a complex multi-train scenario.

Abstract-In this paper a new procedure based on a Backward/forward sweep (BFS) algorithm for solving power flows in weakly meshed DC traction networks is presented. The proposed technique is able to consider the trains as non-linear and nonsmooth (non-differentiable) voltage dependent loads or generators. This feature permits the inclusion of the trains overcurrent protection and the squeeze control. With the use of the mentioned controls, the conventional power flow problem becomes a voltage constrained power flow problem, and the interaction between the trains and the network can be accurately modeled. However, the train control induces a highly non-smooth voltage dependent load characteristics, causing convergence problems in most of the derivative based algorithms. The proposed algorithm is faster, more robust and stable than the derivative based ones. In addition, the authors present all the formulation in a compact matrix based form by means of the graph theory application and the node incident matrix.

In this paper, a decoupled model of a train including an on-board hybrid accumulation system is presented to be used in DC traction networks. The train and the accumulation system behavior are modeled separately, and the results are then combined in order to study the effect of the whole system on the traction electrical network. The model is designed specifically to be used with power flow solvers for planning purposes. The validation has been carried out comparing the results with other methods previously developed and also with experimental measurements. A detailed description of the power flow solver is beyond the scope of this work, but it must be remarked that the model must by used with a solver able to cope with the non-linear and non-smooth characteristics of the model. In this specific case, a modified current injection-based power flow solver has been used. The solver is able to incorporate also non-reversible substations, which are the most common devices used currently for feeding DC systems. The effect of the on-board accumulation systems on the network efficiency will be analyzed using different real scenarios.

Simulation is a valuable way to develop efficient design of the infrastructure and operations of electrical railway systems. Nevertheless, the size of such systems and the complexity of the power flows lead to complex models that require simplifications. A specific scenario has been identified as particularly difficult to study with most of the existing simulation tools. This scenario consists in a line with low energy recovery capacity in which all the substations are blocked. In such case, the railway system is disconnected from the AC grid and becomes an islanded system in which the braking trains, and eventually energy storage subsystems, supply other trains in traction mode. This paper aims to compare different modelling approaches to simulate DC railway systems in this specific scenario. The results highlight that conventionnal approach is not able to deal with this scenario. Another approach, based on a dynamic model from previous research works, is well able to estimate the system behavior with this scenario, but it leads to long computational time. Finally, an intermediary approach is proposed to simplify the model in such scenario and potentially reduce the computation time.

Abstract-In this paper a new procedure based on a Backward/forward sweep (BFS) algorithm for solving power flows in weakly meshed DC traction networks is presented. The proposed technique is able to consider the trains as non-linear and nonsmooth (non-differentiable) voltage dependent loads or generators. This feature permits the inclusion of the trains overcurrent protection and the squeeze control. With the use of the mentioned controls, the conventional power flow problem becomes a voltage constrained power flow problem, and the interaction between the trains and the network can be accurately modeled. However, the train control induces a highly non-smooth voltage dependent load characteristics, causing convergence problems in most of the derivative based algorithms. The proposed algorithm is faster, more robust and stable than the derivative based ones. In addition, the authors present all the formulation in a compact matrix based form by means of the graph theory application and the node incident matrix.