Integration of long transmission lines in large-scale dq0 dynamic models

Abstract

The dq0 transformation is increasingly used today to model distributed sources, complex loads, renewable generators, and power electronics-based devices. This paper presents a dynamic model of long transmission lines that is based entirely on dq0 quantities, and demonstrates how such a model may be integrated with emerging dq0 models of large-scale networks. The model is first developed in the frequency domain and then converted to the time domain, using a state-space representation which inputs and outputs are dq0 signals. The proposed approach may be used to evaluate the stability and dynamic behavior of power systems that include long transmission lines, taking advantage of the dq0 reference frame inherent benefits. This is demonstrated on the basis of a 7-bus network, which shows how long transmission lines influence the network dynamics and stability. The proposed models and examples are provided as a part of an open-source software.

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Notes

  1. 1.

    To simplify notation sometimes the time argument t is omitted.

  2. 2.

    Further discussion on the selection of \(\omega _s\) may be found in [16]. In brief, if there is an infinite bus in the system, \(\omega _s\) is selected as the frequency of the infinite bus. If no generator is large enough to be modeled as an infinite bus, then \(\omega _s\) should be equal to the steady-state system frequency.

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Correspondence to Juri Belikov.

Additional information

The work was partly supported by Grand Technion Energy Program (GTEP) and a Technion fellowship.

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Belikov, J., Levron, Y. Integration of long transmission lines in large-scale dq0 dynamic models. Electr Eng 100, 1219–1228 (2018). https://doi.org/10.1007/s00202-017-0582-7

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Keywords

  • Long transmission line
  • dq0 model
  • Dynamics
  • Stability
  • Small-signal