  Proper traffic simulation of electric vehicles, which draw energy from
overhead wires, requires adequate modeling of traction infrastructure. Such
vehicles include trains, trams or trolleybuses. Since the requested power
demands depend on a traffic situation, the overhead wire DC electrical circuit
is associated with a non-linear power flow problem. Although the Newton-Raphson
method is well-known and widely accepted for seeking its solution, the
existence of such a solution is not guaranteed. Particularly in situations
where the vehicle power demands are too high (during acceleration), the
solution of the studied problem may not exist. To deal with such cases, we
introduce a numerical method which seeks maximal suppliable power demands for
which the solution exists. This corresponds to introducing a scaling parameter
to reduce the demanded power. The interpretation of the scaling parameter is
the amount of energy which is absent in the system, and which needs to be
provided by external sources such as on-board batteries. We propose an
efficient two-stage algorithm to find the optimal scaling parameter and the
resulting potentials in the overhead wire network. We perform a comparison with
a naive approach and present a real-world simulation of part of the Pilsen city
in the Czech Republic. These simulations are performed in the traffic
micro-simulator SUMO, a popular open-source traffic simulation platform.
