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

Abstract

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.

Three-way Subsynchronous Torsional Interactions Between LCC HVDC, MMC HVDC and a Thermal Generator

“…The linearized state-space LCC HVDC analytical model employs the modeling approaches from [11] and it is outlined in [8]. The state-space DC cable model consists of 10 series π sections which represent well the dynamics up to 1 kHz [24].…”

“…The complete MMC HVDC model is of the 126 th order and includes 2 MMCs, their control systems, and the DC cable [12]. The DC cable is represented as the 50 th -order state-space model using frequency-dependent (wideband) vector fitting, and its accuracy is verified against the EMT model up to 1 kHz [24].…”

Analysis of potential low frequency resonance between a 1GW MMC HVDC and a nearby nuclear generator

“…The state space model of the subsea cable is assembled by performing direct vector fitting method on the wideband cable model [23]. This model is of the 50 th order, and accuracy is verified against the EMTP model in the frequency range up to 1 kHz.…”