In the world of DC railway trains nowadays, asynchronous-traction machine with traction controllers, i.e. an inverter with variable output frequency, is implemented. This controller changes the incoming DC voltage into an AC voltage of a variable frequency and RMS amplitude. The disadvantages of switching inverters, compared to a pure sine wave source, are the harmonics they inject in both the output as in the input of the inverters connection. At the incoming power line, it is necessary to damp these harmonics, in order to avoid resonance issues or issues regarding other systems, for instance, train detection. For this purpose of harmonic and transient filtering, generated within as well as outside the train, an LC filter is utilised. However, this LC-filter has also influence on stability. Due to the resulting impedance to current variation in the inductance of the LC-filter, the power flow dynamics towards the train are decreased. When applying a certain amount of power, the voltage over the capacitance can become unstable very quickly. In this thesis, a graphical user interface simulation model is made to simulate these stability phenomena in Simulink in order to find the optimum size of the LC-filter in a train on the Dutch DC railway. The simulations are achieved with a model representing a generalised train. The model is simple to modify, and consists of the important parts for determining the stability of the system. Different simulations have been carried out, in order to examine the effect certain parameter variations have on the stability. Two systems have been considered, a constant power controlled system and a system where the motors had no controlling regime. An important factor is the value of the capacitance and inductance. A larger filter inductor results in an unstable system. Likewise, implementing a higher value capacitance will cause the system to be more stable. Simulations have shown that a motor controller with a simple constant power control regime is unstable with normal values for the inductance and capacitance. However a damping branch can solve this problem up to an extent. A system without any controlling regime has proven to be more stable with smaller capacitance. By utilising the model presented in this thesis, the stability of the system, consisting purely of a controlled constant power load or as a non-controlled load, can be investigated, and the impact of the LC-filter can be determined.