Authors

Sai Sowmya Nagam, Bikash C. Pal, Heng Wu, Frede Blaabjerg

Abstract

This article proposes port-Hamiltonian (pH) stability analysis of synchronous reference frame-phase-locked loop (SRF-PLL) and double second-order generalized integrator-PLL (DSOGI-PLL) while accounting for the overlapping converter dynamics under low-inertia and weak-grid scenarios. The main aim is to highlight the risk of PLL interactions with the converter controllers under nonideal operating conditions. The nonlinear pH models of SRF-PLL and DSOGI-PLL are used to derive analytical stability criteria, which help monitor the effect of PLL interactions on synchronization stability. The stability criteria are substantiated through MATLAB/Simulink simulations on a 400-V Converter-Grid test system. It is shown that the stability criteria derived based on time-scale separation is inexact. In comparison, the proposed criteria, accounting for converter dynamics, offer better stability predictions and match closely with the simulation results.

Citation

  • Journal: IEEE Transactions on Control Systems Technology
  • Year: 2025
  • Volume: 33
  • Issue: 3
  • Pages: 952–962
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/tcst.2024.3523711

BibTeX

Download the bib file

References

  • 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
  • Zhang, L., Harnefors, L. & Nee, H.-P. Power-Synchronization Control of Grid-Connected Voltage-Source Converters. IEEE Transactions on Power Systems vol. 25 809–820 (2010) – 10.1109/tpwrs.2009.2032231
  • Erlich, I. et al. Effect of wind turbine output current during faults on grid voltage and the transient stability of wind parks. 2009 IEEE Power & Energy Society General Meeting 1–8 (2009) doi:10.1109/pes.2009.5275626 – 10.1109/pes.2009.5275626
  • Ma, S., Geng, H., Liu, L., Yang, G. & Pal, B. C. Grid-Synchronization Stability Improvement of Large Scale Wind Farm During Severe Grid Fault. IEEE Transactions on Power Systems vol. 33 216–226 (2018) – 10.1109/tpwrs.2017.2700050
  • 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
  • Qi, Y., Deng, H., Wang, J. & Tang, Y. Passivity-Based Synchronization Stability Analysis for Power-Electronic-Interfaced Distributed Generations. IEEE Transactions on Sustainable Energy vol. 12 1141–1150 (2021) – 10.1109/tste.2020.3035261
  • Wang, X. et al. Grid-Synchronization Stability of Converter-Based Resources—An Overview. IEEE Open Journal of Industry Applications vol. 1 115–134 (2020) – 10.1109/ojia.2020.3020392
  • He, X., Geng, H. & Yang, G. Synchronization Stability Analysis of Grid-Tied Power Converters under Severe Grid Voltage Sags. 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC) 1–6 (2018) doi:10.1109/peac.2018.8590280 – 10.1109/peac.2018.8590280
  • 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
  • Hu, Q., Hu, J., Yuan, H., Tang, H. & Li, Y. Synchronizing stability of DFIG-based wind turbines attached to weak AC grid. 2014 17th International Conference on Electrical Machines and Systems (ICEMS) (2014) doi:10.1109/icems.2014.7013943 – 10.1109/icems.2014.7013943
  • Andrade, F., Kampouropoulos, K., Romeral, L., Vasquez, J. C. & Guerrero, J. M. Study of large-signal stability of an inverter-based generator using a Lyapunov function. IECON 2014 - 40th Annual Conference of the IEEE Industrial Electronics Society 1840–1846 (2014) doi:10.1109/iecon.2014.7048752 – 10.1109/iecon.2014.7048752
  • Zarif Mansour, M. et al. Nonlinear Transient Stability Analysis of Phased-Locked Loop-Based Grid-Following Voltage-Source Converters Using Lyapunov’s Direct Method. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 10 2699–2709 (2022) – 10.1109/jestpe.2021.3057639
  • Zhang, Y., Zhang, C. & Cai, X. Large-Signal Grid-Synchronization Stability Analysis of PLL-Based VSCs Using Lyapunov’s Direct Method. IEEE Transactions on Power Systems vol. 37 788–791 (2022) – 10.1109/tpwrs.2021.3089025
  • Zhang, Z. et al. Domain of Attraction’s Estimation for Grid Connected Converters With Phase-Locked Loop. IEEE Transactions on Power Systems vol. 37 1351–1362 (2022) – 10.1109/tpwrs.2021.3098960
  • Dai, Z. et al. Global Stability Analysis for Synchronous Reference Frame Phase-Locked Loops. IEEE Transactions on Industrial Electronics vol. 69 10182–10191 (2022) – 10.1109/tie.2021.3125655
  • Tang, Y. & Li, Y. Common Lyapunov Function Based Stability Analysis of VSC With Limits of Phase Locked Loop. IEEE Transactions on Power Systems vol. 38 1759–1762 (2023) – 10.1109/tpwrs.2022.3233762
  • Tian, Z. et al. Hamilton-Based Stability Criterion and Attraction Region Estimation for Grid-Tied Inverters Under Large-Signal Disturbances. IEEE Journal of Emerging and Selected Topics in Power Electronics vol. 10 413–423 (2022) – 10.1109/jestpe.2021.3076189
  • Sun, Y. et al. The Impact of PLL Dynamics on the Low Inertia Power Grid: A Case Study of Bonaire Island Power System. Energies vol. 12 1259 (2019) – 10.3390/en12071259
  • Gong, H., Wang, X. & Harnefors, L. Rethinking Current Controller Design for PLL-Synchronized VSCs in Weak Grids. IEEE Transactions on Power Electronics 1–1 (2021) doi:10.1109/tpel.2021.3105549 – 10.1109/tpel.2021.3105549
  • 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
  • Kundur, Power System Stability and Control (2022)
  • Ilic, M. D. From Hierarchical to Open Access Electric Power Systems. Proceedings of the IEEE vol. 95 1060–1084 (2007) – 10.1109/jproc.2007.894711
  • Hatziargyriou, N. et al. Definition and Classification of Power System Stability – Revisited & Extended. IEEE Transactions on Power Systems vol. 36 3271–3281 (2021) – 10.1109/tpwrs.2020.3041774
  • Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
  • Zhang, Transient stability analysis of wind turbines with full-scale voltage source converter. Proc. CSEE (2017)
  • Khalil, Nonlinear Control (2015)
  • Teodorescu, R., Liserre, M. & Rodríguez, P. Grid Converters for Photovoltaic and Wind Power Systems. (2010) doi:10.1002/9780470667057 – 10.1002/9780470667057
  • Milano, F., Dorfler, F., Hug, G., Hill, D. J. & Verbic, G. Foundations and Challenges of Low-Inertia Systems (Invited Paper). 2018 Power Systems Computation Conference (PSCC) (2018) doi:10.23919/pscc.2018.8450880 – 10.23919/pscc.2018.8450880
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002