# Power Flow Analysis of the Swedish Railway Electrical System

Sammanfattning: This thesis deals with analysis of the steady state power flow in the Swedish railway electrical system. Finding the steady state of the system means that all voltages and power flows in the system are known. The trains are supplied from the public grid using frequency converters. This is the major difference compared with ordinary power systems fed from tur­bine-driven generators. The output voltage phase shift function for the con­verters is important in the mathematical formulation of the problem. In the system, the locomotives are almost entirely of the Re-type, having a rectifier and d.c.-motors. The fundamental frequency reactive power need is thereby dependent on the train speed, wheel power and line voltage.In this thesis, the converters and thyristor locomotives are modelled and included in the load flow formulation. The method is shown to have good convergence properties. An approximate and fast method for the calculation of the power injections from converters is presented. A necessary condition for this approximate method to be valid is that the converters are strongly interconnected. The construction of a new 130 kV line brings the converters close to each other electrically. Energy input from each of the converters in­the system can be simulated calculating repeated load flows.Measurements in a real system have verified the applicability of the proposed load flow method. Examples of areas where the method can be used are sys­tem studies and optimal control of the system.The locomotives act as sources of harmonic currents. In an extended load flow formulation this is taken into account. The fundamental idea behind the method is that harmonic powers caused by the thyristor bridges at first are transferred as fundamental frequency active power from the sinusoidal volt­age sources. The method thus gives the fundamental frequency powers injected from the sinusoidal voltage sources to the network. Comparisons with time simulations with detailed models show good agreement.

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