The calculation of frequency-dependent cable parameters is essential for simulations of transient phenomena in electrical power systems. The simulation of transients is more complicated than the calculation of currents and voltages in the nominal frequency range. The model has to represent the frequency dependency and the wave propagation behavior of cable lines. The introduced model combines an improved subconductor method for the determination of the frequency-dependent parameters and a PI section wave propagation model. The subconductor method considers the skin and proximity effect in all conductors for frequency ranges up to few megahertz. The subconductor method method yields accurate results. The wave propagation part of the cable model is based on a cascaded PI section model. A modal transformation technique has been used for the calculation in the time domain. The frequency-dependent elements of the related modal transformation matrices have been fitted with rational functions. The frequency dependence of cable parameters has been reproduced using a vector fitting algorithm and has been implemented into an resistor-inductor-capacitor network (RLC network) for each PI section. The proposed full model has been validated with measured data.

The knowledge about the behavior of cables is substantial in cases of transients or in cases of faults. However, there are only a few models that are tailored to the current requirements for calculations of transient phenomena in three-phase cable systems. These models are based on complex structures. PI-section cable models with simple structures were previously qualified only for calculations in the frequency domain. A new full frequency-dependent cable model to simulate transient phenomena is introduced and validated. The model is based on lumped parameters with cascaded frequency-dependent PI-sections. For the implementation and the integration in simulation tools, it is important to investigate the impact of the PI-section parameters to the accuracy, the stability and the mathematical robustness. In this work, the impact of the frequency dependence of cable parameters, the length distribution and the number of PI-sections on the results of the developed three-phase cable model have been discussed. For simulations in the time domain, two algorithms have been presented to optimize the number of PI-sections based on a specified accuracy.

Kabel sind ein wichtiger Bestandteil des Elektroenergiesystems. Für die Kenntnis des Verhaltens von Kabeln sind Modelle erforderlich, die ihr Verhalten im stationären Zustand und bei transienten Vorgängen hinreichend genau abbilden können. Eine Methode zur Modellierung von Kabeln basiert auf konzentrierten Parametern. Hierbei wird das Kabel durch eine Ersatzanordnung, in der Regel durch eine Kaskade von π-Gliedern, modelliert. Das Prinzip dieser Modelle ist relativ einfach. Allerdings vernachlässigt das bisher verwendete π-Glieder-Kabelmodell die Frequenzabhängigkeit der Kabelparameter. Deshalb wird dieses Modell nur im stationären Zustand verwendet. In dieser Arbeit erfolgt die Entwicklung eines auf π-Gliedern basierenden Kabelmodells, mit dem der stationäre Zustand und die transienten Vorgänge beschrieben werden können. Dabei wird der Einfluss unterschiedlicher Faktoren auf die Resultate des neu entwickelten Kabelmodells sowohl im Frequenz- als auch im Zeitbereich ausführlich untersucht. / Cables are an important part of the electrical energy system. Describing the cable behavior by stationary or transients phenomena requires cable models with proper accuracy. The simulation of transients is more complicated than the calculation of currents and voltages in the nominal frequency range. The model has to represent the frequency dependency and the wave propagation behavior of cable lines. The introduced model is based on a cascaded π-section. A modal transformation technique has been used for the calculation in the time domain. The frequency-dependent elements of the related modal transformation matrices have been fitted with rational functions. The frequency dependence of cable parameters has been reproduced using a vector fitting algorithm and has been implemented into a RLC-network for each π-section. The proposed full model has been validated with measured data.