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

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.