Electrical Engineering

, Volume 100, Issue 2, pp 1219–1228 | Cite as

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

  • Juri BelikovEmail author
  • Yoash Levron
Original Paper


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.


Long transmission line dq0 model Dynamics Stability Small-signal 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Computer SystemsTallinn University of TechnologyTallinnEstonia
  3. 3.The Andrew and Erna Viterbi Faculty of Electrical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael

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