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.

This paper adds some new contributions to the unified alternating current/direct current (ac/dc) power-flow method that is applied to railway power supply systems. These contributions are mainly focused on the way that the unified power-flow problem is implemented. The authors propose a new technique based on graph theory to model the motion of the trains without varying the system topology and dimensions, as well as the solution vector. Furthermore, a new matrix formulation is developed to provide an easy way of setting out the problem. The combination of these techniques makes the unified ac/dc power flow easier to implement, and the comparison among different instants can directly be done, representing the major contribution of this paper. Finally, as a minor contribution, a new technique based on previous matrix formulation is developed to easily obtain all active and reactive power magnitudes in compact form.

This paper presents three new contributions to power flow analysis of unbalanced three-phase distribution systems. First, a complex vector based model in αβ0 stationary reference frame is developed to state the power flow equations using a compact matrix formulation. The proposed model is based on Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). Then, a general and exact power transformer model in the αβ0 reference frame is proposed. Finally, this transformer model is incorporated into the power flow problem. It will be shown that the use of an orthogonal reference frame simplifies the modeling of the distribution network components. In this work, both the network and the power transformer, as well as PQ type loads, PQ and PV type generators and a slack bus are modeled. By using the node incidence matrix instead of the admittance matrix, the information about the grid topology and the grid parameters (including power transformers) is separately organized. As it will be demonstrated, the proposed formulation is ready to incorporate other complex models of loads, generators or storage devices. The model is tested by using the IEEE 4-Node and the IEEE 123-Node Test Feeders with different transformer connections and balanced and unbalanced lines and loads.

This paper proposes a Modified Current Injection method for power flow analysis, bespoke for the specific features of dc traction networks. It introduces major contributions when compared with the state-of the-art solution. In addition to simulating the nonlinear and nonsmooth behavior of the trains, the proposed algorithm can simulate reversible IGBT-based and nonreversible diode-based substations present in the system. These latter substations are the most common type and they supply unidirectional power flow from the ac distribution network to the dc traction subsystem. Depending on the voltage level at the dc side, the substations will be either blocked or conducting. This nonlinear behavior increases significantly the system complexity. Another key aspect of the proposed method is that it is also valid for heavily meshed networks. Even when the dc systems are usually radial or weakly meshed, the connections between the dc and the ac systems create multiple meshes, increasing the network topological complexity. In order to validate the performance of the proposed solution, the behavior of the algorithm is compared with the conventional derivative-based Trust Region Dogleg and the backward/forward sweep algorithm. This comparison shows convergence and speed improvements in the performance of the proposed algorithm.