Authors

Zhen Tian, Yingjie Tang, Xiaoming Zha, Jianjun Sun, Meng Huang, Xikun Fu, Fei Liu

Abstract

As the crucial interface of renewable energy integration, the stable operation of power converters under grid faults and external disturbances has become much more important. However, synchronization instability of grid-tied inverters has been found caused by the phase-locked loop (PLL) under some critical operating conditions, such as the grid voltage sag, current surge, and transmission line faults. Due to the strong nonlinearity, transient stability analysis of inverters with PLL becomes much more complicated under large-signal perturbations and weak grid conditions. In this article, the large-signal synchronization stability of grid-tied inverters is investigated from the energy perspective. Based on the structural resemblance between the PLL and synchronous generator, the energy function is constructed to establish a port-Hamiltonian model for the grid-tied inverter. For the nonlinear inverter system, an explicit Hamilton-based stability criterion is developed for grid-tied converters according to the concept of dissipativity and LaSalle’s theorem. Moreover, the analytical stability boundary is acquired based on the proposed stability criterion and attraction region estimation, covering both controller parameters and grid parameters. To verify the effectiveness of the proposed analysis approach, extensive simulation and experimental results are presented. Compared with the conventional large-signal methods, the proposed Hamilton-based approach has explicit physical meaning and high accuracy.

Citation

  • Journal: IEEE Journal of Emerging and Selected Topics in Power Electronics
  • Year: 2022
  • Volume: 10
  • Issue: 1
  • Pages: 413–423
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/jestpe.2021.3076189

BibTeX

@article{Tian_2022,
  title={{Hamilton-Based Stability Criterion and Attraction Region Estimation for Grid-Tied Inverters Under Large-Signal Disturbances}},
  volume={10},
  ISSN={2168-6785},
  DOI={10.1109/jestpe.2021.3076189},
  number={1},
  journal={IEEE Journal of Emerging and Selected Topics in Power Electronics},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Tian, Zhen and Tang, Yingjie and Zha, Xiaoming and Sun, Jianjun and Huang, Meng and Fu, Xikun and Liu, Fei},
  year={2022},
  pages={413--423}
}

Download the bib file

References

  • Kroposki, B. et al. Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy. IEEE Power and Energy Magazine vol. 15 61–73 (2017) – 10.1109/mpe.2016.2637122
  • Zhou, Q. et al. Optimal Consensus-Based Distributed Control Strategy for Coordinated Operation of Networked Microgrids. IEEE Transactions on Power Systems vol. 35 2452–2462 (2020) – 10.1109/tpwrs.2019.2954582
  • Subotic, I., Gros, D., Colombino, M. & Dorfler, F. A Lyapunov Framework for Nested Dynamical Systems on Multiple Time Scales With Application to Converter-Based Power Systems. IEEE Transactions on Automatic Control vol. 66 5909–5924 (2021) – 10.1109/tac.2020.3047368
  • Xin, H., Huang, L., Zhang, L., Wang, Z. & Hu, J. Synchronous Instability Mechanism of P-f Droop-Controlled Voltage Source Converter Caused by Current Saturation. IEEE Transactions on Power Systems vol. 31 5206–5207 (2016) – 10.1109/tpwrs.2016.2521325
  • Markovic, U. et al. Understanding Small-Signal Stability of Low-Inertia Systems. IEEE Transactions on Power Systems vol. 36 3997–4017 (2021) – 10.1109/tpwrs.2021.3061434
  • Samanta, S. & Chaudhuri, N. R. On Stability Analysis of Power Grids with Synchronous Generators and Grid-Forming Converters under DC-side Current Limitation. 2021 American Control Conference (ACC) 1817–1823 (2021) doi:10.23919/acc50511.2021.9483299 – 10.23919/acc50511.2021.9483299
  • Gao. arXiv:2009.05759 (2020)
  • Tayyebi. arXiv:2008.07661 (2020)
  • Tayyebi, A., Gross, D., Anta, A., Kupzog, F. & Dorfler, F. Frequency Stability of Synchronous Machines and Grid-Forming Power Converters. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 8 1004–1018 (2020) – 10.1109/jestpe.2020.2966524
  • Pattabiraman, D., Lasseter, R. H. & Jahns, T. M. Impact of Phase-Locked Loop Control on the Stability of a High Inverter Penetration Power System. 2019 IEEE Power & Energy Society General Meeting (PESGM) 1–5 (2019) doi:10.1109/pesgm40551.2019.8973657 – 10.1109/pesgm40551.2019.8973657
  • Goksu, O., Teodorescu, R., Bak, C. L., Iov, F. & Kjaer, P. C. Instability of Wind Turbine Converters During Current Injection to Low Voltage Grid Faults and PLL Frequency Based Stability Solution. IEEE Transactions on Power Systems vol. 29 1683–1691 (2014) – 10.1109/tpwrs.2013.2295261
  • Hu, Q., Fu, L., Ma, F. & Ji, F. Large Signal Synchronizing Instability of PLL-Based VSC Connected to Weak AC Grid. IEEE Transactions on Power Systems vol. 34 3220–3229 (2019) – 10.1109/tpwrs.2019.2892224
  • Taul, M. G., Wang, X., Davari, P. & Blaabjerg, F. An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters Under Severe Symmetrical Grid Faults. IEEE Transactions on Power Electronics vol. 34 9655–9670 (2019) – 10.1109/tpel.2019.2892142
  • Wu, H. & Wang, X. Design-Oriented Transient Stability Analysis of PLL-Synchronized Voltage-Source Converters. IEEE Transactions on Power Electronics vol. 35 3573–3589 (2020) – 10.1109/tpel.2019.2937942
  • Amin, M. & Molinas, M. Small-Signal Stability Assessment of Power Electronics Based Power Systems: A Discussion of Impedance- and Eigenvalue-Based Methods. IEEE Transactions on Industry Applications vol. 53 5014–5030 (2017) – 10.1109/tia.2017.2712692
  • Dong, D., Wen, B., Boroyevich, D., Mattavelli, P. & Xue, Y. Analysis of Phase-Locked Loop Low-Frequency Stability in Three-Phase Grid-Connected Power Converters Considering Impedance Interactions. IEEE Transactions on Industrial Electronics vol. 62 310–321 (2015) – 10.1109/tie.2014.2334665
  • Yang, D. et al. Symmetrical PLL for SISO Impedance Modeling and Enhanced Stability in Weak Grids. IEEE Transactions on Power Electronics vol. 35 1473–1483 (2020) – 10.1109/tpel.2019.2917945
  • Wang, X., Harnefors, L. & Blaabjerg, F. Unified Impedance Model of Grid-Connected Voltage-Source Converters. IEEE Transactions on Power Electronics vol. 33 1775–1787 (2018) – 10.1109/tpel.2017.2684906
  • Zhou, J. Z., Ding, H., Fan, S., Zhang, Y. & Gole, A. M. Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter. IEEE Transactions on Power Delivery vol. 29 2287–2296 (2014) – 10.1109/tpwrd.2014.2330518
  • Hans, F., Schumacher, W., Chou, S.-F. & Wang, X. Passivation of Current-Controlled Grid-Connected VSCs Using Passivity Indices. IEEE Transactions on Industrial Electronics vol. 66 8971–8980 (2019) – 10.1109/tie.2018.2883261
  • Harnefors, L., Wang, X., Yepes, A. G. & Blaabjerg, F. Passivity-Based Stability Assessment of Grid-Connected VSCs—An Overview. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 4 116–125 (2016) – 10.1109/jestpe.2015.2490549
  • He, X., Geng, H., Xi, J. & Guerrero, J. M. Resynchronization Analysis and Improvement of Grid-Connected VSCs During Grid Faults. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 9 438–450 (2021) – 10.1109/jestpe.2019.2954555
  • Geng, H., Liu, L. & Li, R. Synchronization and Reactive Current Support of PMSG-Based Wind Farm During Severe Grid Fault. IEEE Transactions on Sustainable Energy vol. 9 1596–1604 (2018) – 10.1109/tste.2018.2799197
  • Pan, D., Wang, X., Liu, F. & Shi, R. Transient Stability of Voltage-Source Converters With Grid-Forming Control: A Design-Oriented Study. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 8 1019–1033 (2020) – 10.1109/jestpe.2019.2946310
  • Rantzer, A. Almost global stability of phase-locked loops. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) vol. 1 899–900 – 10.1109/cdc.2001.980221
  • Fu, X. et al. Large-Signal Stability of Grid-Forming and Grid-Following Controls in Voltage Source Converter: A Comparative Study. IEEE Transactions on Power Electronics vol. 36 7832–7840 (2021) – 10.1109/tpel.2020.3047480
  • Zhao, J., Huang, M., Yan, H., Tse, C. K. & Zha, X. Nonlinear and Transient Stability Analysis of Phase-Locked Loops in Grid-Connected Converters. IEEE Transactions on Power Electronics vol. 36 1018–1029 (2021) – 10.1109/tpel.2020.3000516
  • Kabalan, M., Singh, P. & Niebur, D. Large Signal Lyapunov-Based Stability Studies in Microgrids: A Review. IEEE Transactions on Smart Grid vol. 8 2287–2295 (2017) – 10.1109/tsg.2016.2521652
  • Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
  • Zonetti. arXiv:2101.05047 (2021)
  • Weaver, W. W., Robinett, R. D., Wilson, D. G. & Matthews, R. C. Metastability of Pulse Power Loads Using the Hamiltonian Surface Shaping Method. IEEE Transactions on Energy Conversion vol. 32 820–828 (2017) – 10.1109/tec.2017.2652980
  • Bravo, M., Garces, A., Montoya, O. D. & Baier, C. R. Nonlinear Analysis for the Three-Phase PLL: A New Look for a Classical Problem. 2018 IEEE 19th Workshop on Control and Modeling for Power Electronics (COMPEL) 1–6 (2018) doi:10.1109/compel.2018.8460081 – 10.1109/compel.2018.8460081
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. (2014) doi:10.1561/9781601987877 – 10.1561/9781601987877
  • Golestan, S., Guerrero, J. M. & Vasquez, J. C. Three-Phase PLLs: A Review of Recent Advances. IEEE Transactions on Power Electronics vol. 32 1894–1907 (2017) – 10.1109/tpel.2016.2565642
  • Khalil. Noninear System (1996)
  • Khan, O., Acharya, S., Al Hosani, M. & El Moursi, M. S. Hill Climbing Power Flow Algorithm for Hybrid DC/AC Microgrids. IEEE Transactions on Power Electronics vol. 33 5532–5537 (2018) – 10.1109/tpel.2017.2779238