Optimization approach to unified AC/DC power flow applied to traction systems with catenary voltage constraints

Abstract

This paper presents two innovative contributions related to the combined AC/DC power flow in railway power supply systems (RPSS). First, most of the power flow equations (the linear ones) are expressed in a compact matrix form by using graph theory based protocol. Such approach simplifies the statement of the unified power flow problem and allows the train motion to be modeled without varying the system topology. Second, the problem is formulated as an Optimization Problem (OP) instead of using the non-constrained power flow approach. This technique allows the authors to simulate the effect of trains regenerative braking, considering system constraints such us the catenary voltage limit, which determines the amount of available regenerated energy injected to the network, and burned through the resistors.

On the Use of Graph Theory for Railway Power Supply Systems Characterization

“…The edges existing for each case are depicted. It can be observed that the edge representing the adjacency (6,7), is e 19 in both cases. Furthermore, the adjacencies appearing in both cases ((1, 5), (3,5) and (2, 7)) are represented by the same edges (e 4 , e 13 and e 11 ).…”

“…For instance, by means of the matrix, all current and voltage Kirchhoff laws can be expressed in a compact form as follows [2,6]:…”

BFS algorithm for voltage-constrained meshed DC traction networks with nonsmooth voltage-dependent loads and generators

“…Some of these works consider the DC system and also the AC system feeding the DC one [1], [2], [5]- [8] and others consider only the DC subsystem [4], [9]. The former provide a more accurate solution because the effect of the AC subsystem is considered, but the latter are faster, and for most applications they have enough accuracy.…”

“…], [4], [9] . Others use Newton based methods [1], [2], [10]. One of the drawbacks of these last iterative methods is the lack of robustness [11].…”

“…With these two mechanisms, all trains collaborate to maintain the grid voltages within the limits. In [2] an optimal power flow approach was used to simulate these controls and add the voltage constrains to the problem.…”