eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2021): 1.024
Dynamic modeling and stability analysis of power networks using dq0 transformations with a unified reference frame; pp. 368–377

Juri Belikov, Yoash Levron

The dq0 reference frame has become popular for modeling and control of traditional electric machines and small power sources. However, its widespread use for modeling and analysis of large-scale, general power systems is still a pending issue. One problem that arises when considering dq0 models is that they are typically based on local reference frames, and therefore linking different models is not straightforward. In this paper we propose to approach this problem by modeling the network and its components using a dq0 transformation that is based on a unified reference frame. We demonstrate this idea on the basis of synchronous machines and photovoltaic generators, and we also establish a dq0-based dynamic model of a transmission network. The resulting models all use a unified reference frame, and therefore can be directly linked to each other in simulation and analytically. The paper is accompanied by a free software package (Levron, Y. and Belikov, J. Toolbox for Modeling and Analysis of Power Networks in the DQ0 Reference Frame. 2016. that constructs the proposed dynamic models and provides tools for dynamic simulations and stability studies based on dq0 quantities.


1. Ilić, M. and Zaborszky, J. Dynamics and Control of Large Electric Power Systems. Wiley, New York, 2000.

2. Demiray, T. and Andersson, G. 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. Hong Kong, China, 2006, 1–8.

3. Yang, T., Bozhko, S. V., and Asher, G. M. Modeling of uncontrolled rectifiers using dynamic phasors. In Electrical System for Aircraft, Railway and Ship Propulsion (ESA RS). IEEE, 2012, 1–6.

4. Fitzgerald, A. E., Kingsley, C., and Umans, S. D. Electric Machinery. McGraw-Hill, New York, 2003.

5. Eid, A. Utility integration of PV-wind-fuel cell hybrid distributed generation systems under variable load demands. Int. J. Elec. Power, 2014, 62, 689–699.

6. Huang, B. and Handschin, E. Characteristics of the dynamics of distribution electrical networks. Int. J. Elec. Power, 2008, 30(9), 547–552.

7. Teodorescu, R., Liserre, M., and Rodriguez, P. Grid Converters for Photovoltaic and Wind Power Systems. John Wiley & Sons, 2011.

8. Sauer, P. W., Lesieutre, B. C., and Pai, M. A. Transient algebraic circuits for power system dynamic modelling. Int. J. Elec. Power, 1993, 15(5), 315–321.

9. Krause, P. C., Wasynczuk, O., Sudhoff, S. D., and Pekarek, S. Analysis of Electric Machinery and Drive Systems. Wiley-IEEE Press, 2013.

10. Schiffer, J., Zonetti, D., Ortega, R., Stankovi´c, A. M., Sezi, T., and Raisch, J. A survey on modeling of microgrids—From fundamental physics to phasors and voltage sources. Automatica, 2016, 74, 135–150.

11. Katiraei, F., Iravani, M. R., and Lehn, P. W. Small-signal dynamic model of a micro-grid including conventional and electronically interfaced distributed resources. IET Gener. Transm. Dis., 2007, 1(3), 369–378.

12. Levron, Y. and Belikov, J. Observable canonical forms of multi-machine power systems using dq0 signals. In IEEE International Conference on the Science of Electrical Engineering. Eilat, Israel, 2016, 1–6.

13. Belikov, J. and Levron, Y. A sparse minimal-order dynamic model of power networks based on dq0 signals. IEEE Trans. Power Syst., 2018, 33(1), 1059–1067.

14. Levron, Y. and Belikov, J. Modeling power networks using dynamic phasors in the dq0 reference frame. Electr. Pow. Syst. Res., 2017, 144, 233–242.

15. Zimmerman, R. D., Murillo-Sánchez, C. E., and Thomas, R. J. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst., 2011, 26(1), 12–19.

16. Levron, Y. and Belikov, J. DQ0 dynamics—Software manual. Technion—Israel Institute of Technology, Haifa, Israel, 2017.

17. Sauer, P. W. and Pai, M. A. Power System Dynamics and Stability. Prentice Hall, Upper Saddle River, New Jersey, 1998.

18. Szcześniak, P., Fedyczak, Z., and Klytta, M. 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. Poznan, Poland, 2008, 165–172.

19. Levron, Y., Canaday, S., and Erickson, R. W. Bus voltage control with zero distortion and high bandwidth for single-phase solar inverters. IEEE Trans. Power Electron., 2016, 31(1), 258–269.

20. Birchfield, A. B., Xu, T., Gegner, K. M., Shetye, K. S., and Overbye, T. J. Grid structural characteristics as validation criteria for synthetic networks. IEEE Trans. Power Syst., 2017, 32, 3258–3265.

21. Levron, Y. and Belikov, J. Open-source software for modeling and analysis of power networks in the dq0 reference frame. In IEEE PES PowerTech Conference. Manchester, UK, 2017, 1–6.


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