## Calculation Program of Effective Impedances, Magnetic and Electric Field Distribution of Catenary Lines

 The SIGNON IMAfeb program is used to calculate the effective impedance of the contact lines of single-phase AC railways and the cross-sectional magnetic and electric field distribution around contact lines and overhead lines. The magnetic field emissions of a railway track with given load flows can be assessed with this program. Knowledge of the contact line impedances is one of several important prerequisites for carrying out electrical load flow calculations with the SIGNON WEBAnet simulation system.

SIGNON IMAfeb user interface^(click to enlarge)

## Initial data

 Structure and material properties of electric conductors (cross section, radius, equivalent radius - grouping, conductance, permeability) Geometrical layout of the overhead and/or energy transmission line in cross section (conductor coordinates). Operation frequency, earth conductance and leakage of return current system

## Calculation method

 The impedance calculation is carried out according to the principle of the conductor-earth-loops coupled inductively with the consideration of the skin effects in the ferromagnetic conductors. The electromagnetic field calculation follows according to the Biot-Savart law. The magnetic field strength value depends on the conductor currents proportionally and the inverse proportion of the distance between the conductor and the coordinate to be calculated in the cross section. The mutual geometric conductor layout and the phase displacement are very important for the addition of the magnetic field strengths. The electric field strength is calculated on the basis of the method “mirror charges” with the terrestrial surface as mirror surface. The relative space permittivity of 1 is accepted for this calculation. The priority of the operation functionality of each considered conductors is necessary for the calculation. Conductors: contact wires, messenger wires, feeders, negative feeder, third rails Return conductors: rails, return wires, grounded band wires, tunnel armour Neutral conductors: cable sheath etc.

Example magnetic flux density (click to enlarge)

## Results

 Currents, longitudinal voltages and effective impedances of all defined conductors Currents, longitudinal voltages and effective impedances of all defined circuits (conductor parallel connection) in table form Induced voltages in the conductors laid in parallel Total impedance of the return current system and earth current Maximum track-earth-voltage (outside of the transition sections) for a defined leakage of the return current system Calculation of the magnetic field strength distribution in all possible areas around the electrical conductors (absolute value and polarization of the magnetic strength) Calculation of the profiles for the magnetic field strength, flux density, polarization angle and induced voltage in different horizontal and vertical cuts or versus predefined coordinate line Calculation of the electric field strength distribution in air above of the terrestrial surface in all possible areas around the electrical energy transmission lines

rel. Rail impedance UIC 60 (click to enlarge)