Abstract
Eigenvalue-based analysis of small-signal dynamics in high-voltage direct current (HVdc) transmission systems requires cable models that are compatible with a state-space representation. While distributed parameter models accounting for frequency-dependent effects are inherently incompatible with a state-space representation, a conventional $\pi $ model can only represent the cable behavior accurately at a single frequency. Instead, a frequency-dependent $\pi $ (FD- $\pi $ ) model consisting of a lumped circuit representation with multiple parallel $RL$ branches in each $\pi $ -section can be utilized to reproduce the frequency dependence of the cable characteristics in a specified frequency range. Based on an evaluation of relevant error metrics for FD- $\pi $ models, this article demonstrates how the number of sections and the number of parallel branches in each section will influence the accuracy. From this starting point, an optimization algorithm for identifying the configuration that fulfills a specified set of accuracy requirements with the lowest possible model order is introduced. A similar algorithm for identifying the most accurate FD- $\pi $ model within a specified maximum model order is also proposed. Examples of numerical results for different cable lengths and cross sections are presented to highlight their effect on the model, and it is demonstrated how the cable model configuration can influence the results from small-signal eigenvalue analysis of HVdc transmission systems.
Highlights
A SSESSING the small-signal dynamics and stability by eigenvalue analysis is common practice for large-scale ac power systems
The parameter sensitivity of the optimal frequency-dependent π (FD-π) models is evaluated by considering a range of cable lengths and various cable cross sections. These results provide a basis for indicating general guidelines and practical recommendations for selecting suitable model configurations for a small-signal analysis of high-voltage direct current (HVdc) transmission systems
Sheath along the entire length of the cable. This reduction only applies when the voltages in armor and sheath remain small compared with the conductor voltage [27], which is a realistic assumption for the analysis of small-signal dynamics in HVdc transmission systems
Summary
A SSESSING the small-signal dynamics and stability by eigenvalue analysis is common practice for large-scale ac power systems. Ladder-type networks are included in the RTDS real-time simulation library for modeling frequency-dependent inductances and resistances [21] Even though they are mainly developed for the purpose of time-domain simulations, such lumped-parameter models are directly applicable to state-space modeling and eigenvalue-based analysis. The parameter sensitivity of the optimal FD-π models is evaluated by considering a range of cable lengths and various cable cross sections These results provide a basis for indicating general guidelines and practical recommendations for selecting suitable model configurations for a small-signal analysis of HVdc transmission systems. The results serve to illustrate how inaccurate representation of the HVdc cables can cause misleading results from a small-signal eigenvalue-based analysis and even lead to false prediction of instability This serves as a clear illustration of the practical importance of the analysis presented in this article and the proposed methods for selecting the cable model configuration
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