Small signal state space model of the frequency-dependent DC cable based on direct vector fitting

This paper proposes a new method to represent transmission lines and cables in state space. The method accounts for the frequency dependency of line parameters and essentially translates the state of the art time-domain universal line model into state space. The proposed model is compared against the latest state space model for single DC cable and a bipolar DC cable and it shows certain advantages. DC cables are represented without applying Kron reduction which means that a higher accuracy can be achieved. Single DC cable is represented with a lower model order and higher accuracy for a wide spectre of upper frequency limits and cable lengths. The longer the cable and the higher the upper frequency limit, the more pronounced is the model order reduction. The two state space models are also compared for a 70km bipolar DC cable in the frequency range up to 1 kHz and the proposed model achieves higher accuracy with a slightly lower model order. More importantly, the proposed model succeeds at representing the effect of mutual coupling within the desired accuracy criteria. Furthermore, based on the analysis of the two-conductor DC cable (bipolar cable), it is shown that the proposed method overcomes the issue to represent unbalanced multi-conductor lines and cables in state space. The reason is that it avoids modal transformation. Moreover, in case of multi-conductor lines and cables, it is expected that the proposed method is beneficial for longer systems, higher upper frequency limits and for more mutually coupled conductors.