Impact of the DC cable models on the SVD analysis of a Multi-Terminal HVDC system

Abstract

Abstract-High Voltage Direct Current (HVDC) grids are complex Multi-Inputs Multi-Outputs (MIMO) systems whose dynamics are difficult to assess. This paper first describes the modelling of VSC-based Multi-Terminal HVDC systems (MTDC) using different existing cable models. It then recalls the benefits of the Singular Value Decomposition (SVD) approach for the frequency analysis of such systems, and describes how to perform an SVD analysis on a Multi-Terminal HVDC (MTDC) system from its state-space representation. The paper discusses the results of the SVD analysis with regards to the selection of the voltage-droop parameter and the DC voltage constraint of the DC grid. It then emphasises the impact of the choice of the DC cable model on the results of the SVD study and illustrates the cable model influence on the MTDC system through an ElectroMagnetic Transient (EMT) simulation.

Analysis of MMC Energy-Based Control Structures for VSC-HVDC Links

“…Linear models are useful for small-signal analysis (stability, eigenvalues, participation factors) [5], [12], [13] and for control design assessment by means of linear tools [14], [15]. Several efforts have been made regarding the linear modeling of the MMC, for both energy-controlled and non-energy-controlled approaches.…”

Disturbance attenuation of DC voltage droop control structures in a multi-terminal HVDC grid

“…In fact, it is necessary to verify them by an analysis of the transfer functions connecting the disturbances with the highest deviating output (MISO analysis) due to an uneven impact of the disturbances on the different outputs. [24] r dc,z1 = 1.1724 · 10 −1 Ω/km l dc,z1 = 2.2851 · 10 −4 H/km r dc,z2 = 8.2072 · 10 −2 Ω/km l dc,z2 = 1.5522 · 10 −3 H/km r dc,z3 = 1.1946 · 10 −2 Ω/km l dc,z3 = 3.2942 · 10 −3 H/km gcs = 7.6333 · 10 −11 S/km ccs = 1.9083 · 10 −7 F/km…”

“…Third, we point out that the maximum SV limits frequently used for multiple input multiple output (MIMO) analysis in literature (e.g. [23], [24]) are not sufficient to prove that the impact of specific disturbances on analyzed outputs is within a certain boundary. Due to the fact that these maximum SV limits implicitly assume the same amplification at every output, it is necessary to verify them by a multiple input single output (MISO) analysis of the transfer functions connecting the inputs with the highest amplified output.…”

“…The model parameters are chosen according to [23]. In [24], however, the authors argue that for SVD studies the conventional π model may not be accurate enough. Therefore, in a second step, the results are compared to the case where a 'frequency dependent π' cable model, introduced in [30], is implemented.…”

“…The model, shown in Fig. 5, is called 'frequency dependent π' since the additional parallel branches are calculated to fit the frequency response of a wide-band cable model [24], [31].…”