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Presents a method to use linear analysis to capture the frequency coupling of nonlinear and time-varying components. System stability is analyzed by connecting the harmonic transfer functions of the different component models. This facilitates an object-oriented approach to modeling, which supports reuse of models. An analysis of the complete railway system is, of course, difficult. Several locomotives can be moving along the power distribution line at the same time, and depending on the distance between them, the interaction changes. The power consumption also changes, depending on operating modes. During normal operation, energy is consumed from the network, but as modern locomotives use electrical braking, the power flow changes direction during deceleration, and energy is delivered back to the grid. The inverter trains are not passive systems. The converters are controlled with only limited system knowledge (local measurements of currents and voltages), making analysis and control design an even bigger challenge.
Möllerstedt et al. (2000) studied this question.