Journal of Power Electronics

The Korean Institute of Power Electronics (전력전자학회)
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Advanced Small-Signal Model of Multi-Terminal Modular Multilevel Converters for Power Systems Based on Dynamic Phasors

  • Hu, Pan (School of Electrical Engineering, Wuhan University) ;
  • Chen, Hongkun (School of Electrical Engineering, Wuhan University) ;
  • Chen, Lei (School of Electrical Engineering, Wuhan University) ;
  • Zhu, Xiaohang (School of Electrical Engineering, Wuhan University) ;
  • Wang, Xuechun (School of Electrical Engineering, Wuhan University)
  • Received : 2017.06.14
  • Accepted : 2017.11.27
  • Published : 2018.03.20
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Abstract

Modular multilevel converter (MMC)-based high-voltage direct current (HVDC) presents attractive technical advantages and contributes to enhanced system operation and reduced oscillation damping in dynamic MMC-HVDC systems. We propose an advanced small-signal multi-terminal MMC-HVDC based on dynamic phasors and state space for power system stability analysis to enhance computational accuracy and reduce simulation time. In accordance with active and passive network control strategies for multi-terminal MMC-HVDC, the matchable small-signal stability models containing high harmonics and dynamics of internal variables are conducted, and a related theoretical derivation is carried out. The proposed advanced small-signal model is then compared with electromagnetic-transient and traditional small-signal state-space models by adopting a typical multi-terminal MMC-HVDC network with offshore wind generation. Simulation indicates that the advanced small-signal model can successfully follow the electromechanical transient response with small errors and can predict the damped oscillations. The validity and applicability of the proposed model are effectively confirmed.

Keywords

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Fig. 1. Four-terminal MMC？HVCD test system.

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Fig. 2. Topology of MMC？HVDC. (a) Structure of the converter and active network. (b) Averaged EMT model of MMC？HVDC.

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Fig. 3. Control block diagrams of dual-loop and circulating？suppressing controllers. (a) Dual-loop controller. (b) 2ndharmonic circulating？suppressing controller.

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Fig. 4. DC network model. (a) DC node model. (b) Equivalentmodel of DC line.

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Fig. 5. Methodology used to obtain the complete small-signal model of a multi-terminal MMC？HVDC.

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Fig. 6. Response of the MMC1 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 7. Response of the MMC2 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 8. Response of the MMC3 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 9. Response of the MMC4 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 10. Response of the MMC1 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 11. Response of the MMC2 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 12. Response of the MMC3 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 13. Response of the MMC4 converter. (a) D-axis AC current. (b) Q-axis AC current. (c) Direct voltage. (d) Direct current.

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Fig. 14. Frequency response for state-space and dyn.phasor models.

TABLE I MMC CONVERTER PARAMETERS

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TABLE II RUNNING TIME OF SIMULATION UNDER THE THREE MODELS

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References

  1. European Network of Transmission System, "Operators for Electricity: Ten-year network development plan," 2014. Final Report, 2014.
  2. A. Bayo-Salas, J. Beerten, J. Rimez, and D. Van Hertem "Analysis of control interactions in multi-infeed VSC HVDC connections," IET Gener, Transm. Dis., Vol. 10, No. 6, pp. 1336-1344, Apr. 2016. https://doi.org/10.1049/iet-gtd.2015.0876
  3. S. J. Shao and V.G. Agelidis, "Review of DC system technologies for large scale integration of wind energy systems with electricity grids," Energies, Vol. 3, No. 6, pp. 1303-1319, Jun. 2010. https://doi.org/10.3390/en3061303
  4. J. Dorn, H. Huang, and D. Retzmann, "A new multilevel voltage sourced converter topology for HVDC applications," In Proc. 2008 of CIGRE, pp. 1-8.
  5. M. P. Bahrman and B. Johnson, "The ABCs of HVDC transmission technologies," IEEE Power Energy Mag., Vol. 5, No. 2, pp. 32-44, Apr. 2007. https://doi.org/10.1109/MPAE.2007.329194
  6. S. Cole, J. Beerten, and R. Belmans, "Generalized dynamic VSC-MTDC model for power system stability studies," IEEE Trans. Power Syst., Vol. 25, No. 3, pp. 1655-1662, Sep. 2010. https://doi.org/10.1109/TPWRS.2010.2040846
  7. J. Beerten, S. D'Arco, and J. A. Suul, "Frequency-dependent cable modelling for small-signal stability analysis of VSC- HVDC systems," IET Gener., Transm. Dis., Vol. 10, No. 6, pp. 1370-1381, Feb. 2016. https://doi.org/10.1049/iet-gtd.2015.0868
  8. G. O. Kalcon, G. P. Adam, O. Anaya-Lara, S. Lo, and K. Uhlen, "Small-signal stability analysis of multi-terminal VSC-based DC transmission systems," IEEE Trans. Power Syst., Vol. 27, No. 4, pp. 1818-1830, Nov. 2012. https://doi.org/10.1109/TPWRS.2012.2190531
  9. L. M. Castro and E. Acha, "A unified modeling approach of multi-terminal VSC-HVDC links for dynamic simulations of large-scale power systems," IEEE Trans. Power Syst., Vol. 31, No. 6, pp. 1-10, Feb. 2016. https://doi.org/10.1109/TPWRD.2016.2642498
  10. T. Ngoc-Tuan, Z. Marcus, W. Klaus, and E. István, "Generic model of MMC-VSC-HVDC for interaction study with AC power system," IEEE Trans. Power Syst., Vol. 31, No. 1, pp. 27-34, Feb. 2015. https://doi.org/10.1109/TPWRS.2015.2390416
  11. J. Xu, A. M. Gole, and C. Zhao, "The use of averaged-value model of modular multilevel converter in DC grid," IEEE Trans. Power Del., Vol. 30, No. 2, pp. 519-528, Apr. 2015. https://doi.org/10.1109/TPWRD.2014.2332557
  12. S. Liu, Z. Xu, W. Hua, G. Tang, and Y. L. Xue, "Electromechanical transient modelling of modular multilevel converter based multiterminal HVDC systems," IEEE Trans. Power Syst., Vol. 29, No. 1, pp. 72-83, Jul. 2014. https://doi.org/10.1109/TPWRS.2013.2278402
  13. L. Zhou, S. Liu, W. Lu, and S. Hu, "Quasi-steady-state large-signal modelling of DC-DC switching converter: justification and application for varying operating conditions," IET Power Electron., Vol. 7, No. 10, pp. 2455- 2464, Oct. 2014. https://doi.org/10.1049/iet-pel.2013.0487
  14. S. Chiniforoosh, J. Jatskevich, A. Yazdani, V. Sood, V. Dinavahi, J. A. Martinez, and A. Ramirez, "Definitions and applications of dynamic average models for analysis of power systems," IEEE Trans. Power Del., Vol. 25, No. 4, pp. 2655-2669, Nov. 2010. https://doi.org/10.1109/TPWRD.2010.2043859
  15. S. Chandrasekar and R. Gokaraju, "Dynamic phasor modeling of type 3 DFIG wind generators (including SSCI phenomenon) for short-circuit calculations," IEEE Trans. Power Del., Vol. 30, No. 2, pp. 887-897, Apr. 2015. https://doi.org/10.1109/TPWRD.2014.2365587
  16. A. Emadi, "Modeling of power electronics loads in AC distribution systems using the generalized state-space averaging method," IEEE Trans. Ind. Electron., Vol. 51, No. 5, pp. 992-1000, Nov. 2004. https://doi.org/10.1109/TIE.2004.834950
  17. A. M. Stankovic, R. Seth, and T. Aydin, "Dynamic phasors in modelling and analysis of unbalanced polyphase AC Machines," IEEE Trans. Energy Convers., Vol.17, No. 1, pp. 107-113, Apr. 2002. https://doi.org/10.1109/60.986446
  18. P. C. Stefanov and A. M. Stankovic, "Modeling of UPFC operation under unbalanced conditions with dynamic phasors," IEEE Trans. Power Syst., Vol. 17, No. 2, pp. 395-403, Apr. 2002.
  19. X. Guo, Z. Lu, B. Wang, X. Sun, L. Wang, and J. M. Guerrero, "Dynamic phasors-based modeling and stability analysis of droop-controlled inverters for microgrid applications," IEEE Trans. Smart Grid, Vol. 5, No. 6, pp. 2980-2987, Nov. 2014. https://doi.org/10.1109/TSG.2014.2331280
  20. L. Tan, A. M. Gole, and C. Zhao, "Harmonic instability in MMC-HVDC converters resulting from internal dynamics," IEEE Trans. Power Del., Vol. 31, No. 4, pp. 1738-1747, Aug. 2016 https://doi.org/10.1109/TPWRD.2016.2542188
  21. D. Jovcic and F. A. Jamshidi, "Phasor model of modular multilevel converter with circulating current suppression control," IEEE Trans. Power Del., Vol. 30, No. 4, pp. 1889-1897, Aug. 2015. https://doi.org/10.1109/TPWRD.2014.2372780
  22. M. Daryabak, S. Filizadeh, J. Jatskevich, A. Davoudi, M. Saeedifard, V. Sood, Juan. Martinez, D. Aliprantis, J. Cano, and A. Mehrizi-Sani, "Modeling of LCC-HVDC systems using dynamic phasors," IEEE Trans. Power Del., Vol. 29, No. 4, pp. 1989-1998, Aug. 2014. https://doi.org/10.1109/TPWRD.2014.2308431
  23. M. Saeedifard and R. Iravani, "Dynamic performance of a modular multilevel back-to-back HVDC system," IEEE Trans. Power Del., Vol. 25, No. 4, pp. 2903-2912, Nov. 2010. https://doi.org/10.1109/TPWRD.2010.2050787
  24. Q. Song, W. Liu, and X. Li, "A steady-state analysis method for a modular multilevel converter," IEEE Trans. Power Electron., Vol. 28, No. 8, pp. 3702-3713, Aug. 2013. https://doi.org/10.1109/TPEL.2012.2227818
  25. L. Zhang, L. Harnefors, and H. P. Nee, "Interconnection of two very weak AC systems by VSC-HVDC links using power-synchronization control," IEEE Trans. Power Syst., Vol. 26, No. 1, pp. 344-355, Mar. 2011. https://doi.org/10.1109/TPWRS.2010.2047875
  26. J. Zhou, H. Ding, S. Fan, Y. Zhang, and A. M. Gole, "Impact of short-circuit ratio and phase-locked loop parameters on the small-signal behavior of a VSC-HVDC Converter," IEEE Trans. Power Del., Vol. 29, No. 5, pp. 2287-2296, Oct. 2014. https://doi.org/10.1109/TPWRD.2014.2330518
  27. S. R. Sanders, J. M. Noworolski, X. Z. Liu, and G. C. Verghese, "Generalized averaging method for power conversion circuits," IEEE Trans. Power Electron., Vol. 6, No. 2, pp. 251-259, Apr. 1991. https://doi.org/10.1109/63.76811
  28. F. Wu, X. Zhang, K. Godfrey, and P. Ju, "Small signal stability analysis and optimal control of a wind turbine with doubly fed induction generator," IET Gener., Transm. Dis., Vol. 1, No. 5, pp. 751-760, Sep. 2007. https://doi.org/10.1049/iet-gtd:20060395
  29. P. Kundur, Power System Stability and Control, 2nd ed., McGraw-Hill, pp. 700-706, 2001.