Analysis of accuracy versus model order for frequency-dependent Pi-model of HVDC cables

Accurate eigenvalue analysis of High Voltage Direct Current (HVDC) transmission systems depends on state-space models that are accounting for the frequency-dependent characteristics of the dc cables. A classical simplified model with cascaded pi-sections can be enhanced to capture the frequency dependency of cable parameters by adding parallel RL branches for representing the longitudinal impedances. This paper analyzes the performances in terms of accuracy that can be achieved with such a frequency-dependent pi-section (FD-π) representation. The obtained results are used to identify the number of cascaded sections and the number of parallel branches that will ensure a model configuration with the maximum accuracy for a specific model order. Furthermore, the presented analysis is utilized to identify what model order and model configuration are needed for ensuring a specified accuracy over a given frequency range, depending on the cable length. Based on the presented analysis, clear guidelines can be derived for selecting the most suitable model of an HVDC cable with a certain length, depending on the required accuracy and frequency range.