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


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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  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.


  1. 1.

    Anderson PM, Fouad AA (2008) Power system control and stability. Wiley, Hoboken

    Google Scholar 

  2. 2.

    Araujo ARJ, Silva RC, Kurokawa S (2014) Comparing lumped and distributed parameters models in transmission lines during transient conditions. In: 2014 IEEE PES T&D conference and exposition

  3. 3.

    Belikov J, Levron Y (2017) A sparse minimal-order dynamic model of power networks based on dq0 signals. IEEE Trans Power Syst (to be published)

  4. 4.

    Demiray T, Andersson G (2006) Comparison of the efficiency of dynamic phasor models derived from ABC and DQ0 reference frame in power system dynamic simulations. In: The 7th IET international conference on advances in power system control. Operation and Management. China, Hong Kong, pp 1–8

  5. 5.

    Dommel H (1969) Digital computer solution of electromagnetic transients in single- and multiphase networks. IEEE Trans Power Appl Syst PAS–88(4):388–399

    Article  Google Scholar 

  6. 6.

    Eid A (2014) Utility integration of PV-wind-fuel cell hybrid distributed generation systems under variable load demands. Int J Electr Power 62:689–699

    Article  Google Scholar 

  7. 7.

    Ferreira VH, Zanghi R, Fortes MZ, Sotelo GG, Silva RBM, Souza JCS, Guimarães CHC, Gomes S (2016) A survey on intelligent system application to fault diagnosis in electric power system transmission lines. Electr Power Syst Res 136:135–153

    Article  Google Scholar 

  8. 8.

    Fitzgerald AE, Kingsley C, Umans SD (2003) Electric machinery, 6th edn. McGraw-Hill, New York

    Google Scholar 

  9. 9.

    Grainger JJ, Stevenson WD (1994) Power system analysis. McGraw-Hill, New York

    Google Scholar 

  10. 10.

    Ilić M, Zaborszky J (2000) Dynamics and control of large electric power systems. Wiley, New York

    Google Scholar 

  11. 11.

    Krause PC, Wasynczuk O, Sudhoff SD, Pekarek S (2013) Analysis of electric machinery and drive systems, 3rd edn. Wiley-IEEE Press, Hoboken

  12. 12.

    Levron Y, Belikov J (2016) Toolbox for modeling and analysis of power networks in the dq0 reference frame. MATLAB Central File Exchange. Retrieved February 7, 2017

  13. 13.

    Levron Y, Belikov J (2017) DQ0 Dynamics—Software Manual. Technion—Israel Institute of Technology, Haifa, Israel.

  14. 14.

    Levron Y, Belikov J (2017) Modeling power networks using dynamic phasors in the dq0 reference frame. Electr Power Syst Res 144:233–242

    Article  Google Scholar 

  15. 15.

    Miller L, Cibulka L, Brown M, Meier AV (2013) Electric distribution system models for renewable integration: Status and research gaps analysis. Tech. rep, California Energy Commission, CA, USA

  16. 16.

    Sauer PW, Pai MA (1998) Power system dynamics and stability. Prentice Hall, Upper Saddle River

    Google Scholar 

  17. 17.

    Schiffer J, Zonetti D, Ortega R, Stanković AM, Sezi T, Raisch J (2016) A survey on modeling of microgrids–From fundamental physics to phasors and voltage sources. Automatica 74:135–150

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Stevenson WD (1982) Elements of Power system analysis, 4 edn. Electrical and Electronic Engineering Series. McGraw-Hill, New York

    Google Scholar 

  19. 19.

    Szcześniak P, Fedyczak Z, Klytta M (2008) Modelling and analysis of a matrix-reactance frequency converter based on buck-boost topology by DQ0 transformation. In: The 13th international power electronics and motion control conference, pp 165–172

  20. 20.

    Teegala SK, Singal SK (2016) Optimal costing of overhead power transmission lines using genetic algorithms. Int J Electr Power 83:298–308

    Article  Google Scholar 

  21. 21.

    Teodorescu R, Liserre M, Rodriguez P (2011) Grid converters for photovoltaic and wind power systems. Wiley, Hoboken

    Google Scholar 

  22. 22.

    Zhong Q, Hornik T (2013) Control of power inverters in renewable energy and smart grid integration. Wiley, New York

    Google Scholar 

  23. 23.

    Zhong QC, Weiss G (2011) Synchronverters: Inverters that mimic synchronous generators. IEEE Trans. Ind. Electron. 58(4):1259–1267

    Article  Google Scholar 

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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).

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