Vol. 22 No. 3 (2023): Revista UIS Ingenierías
Articles

Impact of Renewable Energy Sources on Voltage Stability and Assessment Techniques

Julian Mesa-Calle
Universidad de Antioquia
Walter Villa-Acevedo
Universidad de Antioquia
Jesús María López-Lezama
Universidad de Antioquia

Published 2023-09-12

Keywords

  • Voltage stability,
  • solar generation,
  • wind generation,
  • instability,
  • impact,
  • evaluation methods,
  • renewable resources,
  • security,
  • power systems,
  • distribution systems
  • ...More
    Less

How to Cite

Mesa-Calle, J. ., Villa-Acevedo, W. ., & López-Lezama, J. M. (2023). Impact of Renewable Energy Sources on Voltage Stability and Assessment Techniques. Revista UIS Ingenierías, 22(3), 151–166. https://doi.org/10.18273/revuin.v22n3-2023011

Abstract

The proliferation of renewable energy sources and their impact on power systems makes it necessary to conduct studies to ensure the proper operation of the power system. This paper investigates recent research on the impact of renewable energy sources on voltage stability and new methods used to assess this stability. The effects of solar and wind power generation both individually and collectively are studied, along with other inverter models through which renewable energy sources are connected to transmission systems or distribution networks. In addition, the results are highlighted by categorizing them into a deterministic and probabilistic approach.

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References

  1. L. Meegahapola, A. Sguarezi, J. S. Bryant, M. Gu, E. R. Conde D., R. B. A. Cunha, “Power system stability with power-electronic converter interfaced renewable power generation: Present issues and future trends,” Energies, vol. 13, no. 13, 2020, doi: https://doi.org/10.3390/en13133441
  2. R. Yan, N. Al-Masood, T. Kumar Saha, F. Bai, and H. Gu, “The anatomy of the 2016 South Australia blackout: A catastrophic event in a high renewable network,” IEEE Trans. Power Syst., vol. 33, no. 5, pp. 5374–5388, 2018, doi: https://doi.org/10.1109/TPWRS.2018.2820150
  3. M. Şahin, F. Blaabjerg, and A. Sangwongwanich, “A Comprehensive Review on Supercapacitor Applications and Developments,” Energies, vol. 15, no. 3, p. 674, 2022, doi: https://doi.org/10.3390/en15030674
  4. P. Kundur et al., “Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions,” IEEE Trans. Power Syst., vol. 19, no. 3, pp. 1387–1401, Aug. 2004, doi: https://doi.org/10.1109/TPWRS.2004.825981
  5. N. Hatziargyriou et al., “Definition and Classification of Power System Stability – Revisited & Extended,” IEEE Trans. Power Syst., vol. 36, no. 4, pp. 3271–3281, 2021, doi: https://doi.org/10.1109/TPWRS.2020.3041774
  6. J. Shair, H. Li, J. Hu, and X. Xie, “Power system stability issues, classifications and research prospects in the context of high-penetration of renewables and power electronics,” Renew. Sustain. Energy Rev., vol. 145, no. December 2020, Jul. 2021, doi: https://doi.org/10.1016/j.rser.2021.111111
  7. K. N. Hasan, R. Preece, J. V. Milanović, “Existing approaches and trends in uncertainty modelling and probabilistic stability analysis of power systems with renewable generation,” Renew. Sustain. Energy Rev., vol. 101, no. October 2018, pp. 168–180, Mar. 2019, doi: https://doi.org/10.1016/j.rser.2018.10.027
  8. N. Hosseinzadeh, A. Aziz, A. Mahmud, A. Gargoom, M. Rabbani, “Voltage Stability of Power Systems with Renewable-Energy Inverter-Based Generators: A Review,” Electronics, vol. 10, no. 2, p. 115, Jan. 2021, doi: https://doi.org/10.3390/electronics10020115
  9. M. Shafiullah, S. D. Ahmed, F. A. Al-Sulaiman, “Grid Integration Challenges and Solution Strategies for Solar PV Systems: A Review,” IEEE Access, vol. 10, pp. 52233–52257, 2022, doi: https://doi.org/10.1109/ACCESS.2022.3174555
  10. . Kamil K, “Impact of High Penetration of Solar PV Output to Line Loading, Voltage and Power Losses,” Int. J. Adv. Trends Comput. Sci. Eng., vol. 8, no. 1.6, pp. 361–367, 2019, doi: https://doi.org/10.30534/ijatcse/2019/5381.62019
  11. E. Muhammad, A. Khan, N. Arbab, and E. Zainab Huma, “Voltage Profile and Stability Analysis for High Penetration Solar Photovoltaics,” Int. J. Eng. Work. Kambohwell Publ. Enterp., vol. 5, no. May 2018, pp. 109–114, 2018.
  12. S. Rahman et al., “Analysis of Power Grid Voltage Stability With High Penetration of Solar PV Systems,” IEEE Trans. Ind. Appl., vol. 57, no. 3, pp. 2245–2257, 2021, doi: https://doi.org/10.1109/TIA.2021.3066326
  13. E. Munkhchuluun, L. Meegahapola, and A. Vahidnia, “Long-term voltage stability with large-scale solar-photovoltaic (PV) generation,” Int. J. Electr. Power Energy Syst., vol. 117, no. May 2019, p. 105663, May 2020, doi: https://doi.org/10.1016/j.ijepes.2019.105663
  14. S. S. Refaat, H. Abu‐Rub, A. P. Sanfilippo, and A. Mohamed, “Impact of grid‐tied large‐scale photovoltaic system on dynamic voltage stability of electric power grids,” IET Renew. Power Gener., vol. 12, no. 2, pp. 157–164, Feb. 2018, doi: https://doi.org/10.1049/iet-rpg.2017.0219
  15. H. Sultan, A. Diab, O. Kuznetsov, Z. Ali, and O. Abdalla, “Evaluation of the Impact of High Penetration Levels of PV Power Plants on the Capacity, Frequency and Voltage Stability of Egypt’s Unified Grid,” Energies, vol. 12, no. 3, p. 552, Feb. 2019, doi: https://doi.org/10.3390/en12030552
  16. C. Dondariya and D. K. Sakravdia, “Voltage Stability Assessment and Improvement in Power Systems with Solar Photovoltaic Penetration,” in 2021 IEEE 2nd International Conference On Electrical Power and Energy Systems (ICEPES), 2021, pp. 1–4. doi: https://doi.org/10.1109/ICEPES52894.2021.9699827
  17. G. Lammert, D. Premm, L. D. P. Ospina, J. C. Boemer, M. Braun, T. Van Cutsem, “Control of Photovoltaic Systems for Enhanced Short-Term Voltage Stability and Recovery,” IEEE Trans. Energy Convers., vol. 34, no. 1, pp. 243–254, Mar. 2019, doi: https://doi.org/10.1109/TEC.2018.2875303
  18. A. S. Saidi, “Impact of large photovoltaic power penetration on the voltage regulation and dynamic performance of the Tunisian power system,” Energy Explor. Exploit., vol. 38, no. 5, pp. 1774–1809, Sep. 2020, doi: https://doi.org/10.1177/0144598720940864
  19. S. M. Al-jubouri, “Influence of Photovoltaic System on Voltage Stability,” Int. J. Adv. Eng. Manag. Res., vol. 3, no. 6, pp. 77–85, 2018.
  20. A. Sonawane, A. Umarikar, “Small-Signal Stability Analysis of PV-Based Synchronverter Including PV Operating Modes and DC-Link Voltage Controller,” IEEE Trans. Ind. Electron., vol. 69, no. 8, pp. 8028–8039, 2022, doi: https://doi.org/10.1109/TIE.2021.3109506
  21. D. S. Kumar, A. Sharma, D. Srinivasan, and T. Reindl, “Stability implications of bulk power networks with large scale PVs,” Energy, vol. 187, p. 115927, Nov. 2019, doi: https://doi.org/10.1016/j.energy.2019.115927
  22. O. B. Adewuyi, M. E. Lotfy, B. O. Akinloye, H. O. Rashid Howlader, T. Senjyu, and K. Narayanan, “Security-constrained optimal utility-scale solar PV investment planning for weak grids: Short reviews and techno-economic analysis,” Appl. Energy, vol. 245, no. January, pp. 16–30, 2019, doi: https://doi.org/10.1016/j.apenergy.2019.04.008
  23. J.-K. Kim, B. Lee, J. Ma, G. Verbic, S. Nam, and K. Hur, “Understanding and Evaluating Systemwide Impacts of Uncertain Parameters in the Dynamic Load Model on Short-Term Voltage Stability,” IEEE Trans. Power Syst., vol. 36, no. 3, pp. 2093–2102, 2021, doi: https://doi.org/10.1109/TPWRS.2020.3027692
  24. S. Li, Z. Wei, and Y. Ma, “Fuzzy Load-Shedding Strategy Considering Photovoltaic Output Fluctuation Characteristics and Static Voltage Stability,” Energies, vol. 11, no. 4, p. 779, Mar. 2018, doi: https://doi.org/10.3390/en11040779
  25. T. Lund, H. Wu, H. Soltani, J. G. Nielsen, G. K. Andersen, and X. Wang, “Operating Wind Power Plants Under Weak Grid Conditions Considering Voltage Stability Constraints,” IEEE Trans. Power Electron., vol. 37, no. 12, pp. 15482–15492, Dec. 2022, doi: https://doi.org/10.1109/TPEL.2022.3197308
  26. T. V. C. and C. Vournas, “Voltage Stability of Electrical Power Systems,” J. Al-Azhar Univ. Eng. Sect., vol. 15, no. 55, pp. 538–545, 1998.
  27. B. B. Adetokun, C. M. Muriithi, and J. O. Ojo, “Voltage stability assessment and enhancement of power grid with increasing wind energy penetration,” Int. J. Electr. Power Energy Syst., vol. 120, no. January 2020, p. 105988, Sep. 2020, doi: https://doi.org/10.1016/j.ijepes.2020.105988
  28. B. B. Adetokun and C. M. Muriithi, “Impact of integrating large-scale DFIG-based wind energy conversion system on the voltage stability of weak national grids: A case study of the Nigerian power grid,” Energy Reports, vol. 7, pp. 654–666, Nov. 2021, doi: https://doi.org/10.1016/j.egyr.2021.01.025
  29. J. N. da Costa, J. A. Passos Filho, and R. Mota Henriques, “Loading margin sensitivity analysis in systems with significant wind power generation penetration,” Electr. Power Syst. Res., vol. 175, no. June, p. 105900, Oct. 2019, doi: https://doi.org/10.1016/j.epsr.2019.105900
  30. K. Ren, H. Li, S. Li, and H. Dong, “Voltage Stability Analysis of Front-End Speed Controlled Wind Turbine Integrated into Regional Power Grid Based on Bifurcation Theory,” Complexity, vol. 2020, pp. 1–11, Oct. 2020, doi: https://doi.org/10.1155/2020/8816334
  31. T. Souxes, I.-M. Granitsas, and C. Vournas, “Effect of stochasticity on voltage stability support provided by wind farms: Application to the Hellenic interconnected system,” Electr. Power Syst. Res., vol. 170, no. January, pp. 48–56, 2019, doi: https://doi.org/10.1016/j.epsr.2019.01.007
  32. E. A. Feilat, S. Azzam, and A. Al-Salaymeh, “Impact of large PV and wind power plants on voltage and frequency stability of Jordan’s national grid,” Sustain. Cities Soc., vol. 36, no. October 2017, pp. 257–271, 2018, doi: https://doi.org/10.1016/j.scs.2017.10.035
  33. G. Pierrou and X. Wang, “Analytical Study of the Impacts of Stochastic Load Fluctuation on the Dynamic Voltage Stability Margin Using Bifurcation Theory,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 67, no. 4, pp. 1286–1295, Apr. 2020, doi: https://doi.org/10.1109/TCSI.2019.2943509
  34. B. Qi, K. N. Hasan, and J. V. Milanovic, “Identification of Critical Parameters Affecting Voltage and Angular Stability Considering Load-Renewable Generation Correlations,” IEEE Trans. Power Syst., vol. 34, no. 4, pp. 2859–2869, 2019, doi: https://doi.org/10.1109/TPWRS.2019.2891840
  35. W. Huang, D. J. Hill, and X. Zhang, “Small-Disturbance Voltage Stability of Power Systems: Dependence on Network Structure,” IEEE Trans. Power Syst., vol. 35, no. 4, pp. 2609–2618, Jul. 2020, doi: https://doi.org/10.1109/TPWRS.2019.2962555
  36. W. Huang and D. J. Hill, “Network-based analysis of long-term voltage stability considering loads with recovery dynamics,” Int. J. Electr. Power Energy Syst., vol. 119, p. 105891, 2020, doi: https://doi.org/10.1016/j.ijepes.2020.105891
  37. Z. Zhong, H. Zhang, J. Wang, G. Ma, W. Qiu, and Y. Wang, “Study on Voltage Characteristics of Distributed Power Supply Connected to Distribution Network,” Am. J. Electr. Electron. Eng., vol. 7, no. 4, pp. 99–104, Oct. 2019, doi: https://doi.org/10.12691/ajeee-7-4-3
  38. M. Ghaffarianfar and A. Hajizadeh, “Voltage Stability of Low-Voltage Distribution Grid with High Penetration of Photovoltaic Power Units,” Energies, vol. 11, no. 8, p. 1960, Jul. 2018, doi: https://doi.org/10.3390/en11081960
  39. N. B. G. Brinkel et al., “Impact of rapid PV fluctuations on power quality in the low-voltage grid and mitigation strategies using electric vehicles,” Int. J. Electr. Power Energy Syst., vol. 118, no. June 2019, p. 105741, Jun. 2020, doi: https://doi.org/10.1016/j.ijepes.2019.105741
  40. M. S. Rawat and S. Vadhera, “Impact of Photovoltaic Penetration on Static Voltage Stability of Distribution Networks: A Probabilistic Approach,” Asian J. Water, Environ. Pollut., vol. 15, no. 3, pp. 51–62, Aug. 2018, doi: https://doi.org/10.3233/AJW-180043
  41. A. S. Saidi, M. Ben Slimene, M. A. Khlifi, M. Fazle Azeem, S. Al Ahmadi, and A. Draou, “Analysis and study of two-dimensional parameter bifurcation of wind power farms and composite loads,” Wind Energy, vol. 22, no. 9, pp. 1243–1259, 2019, doi: https://doi.org/10.1002/we.2353
  42. V. Behravesh, R. Keypour, and A. A. Foroud, “Stochastic analysis of solar and wind hybrid rooftop generation systems and their impact on voltage behavior in low voltage distribution systems,” Sol. Energy, vol. 166, no. June 2017, pp. 317–333, May 2018, doi: https://doi.org/10.1016/j.solener.2018.03.063
  43. B. Abdelkader and L. Djamel, “Contribution of DGs in the stability and voltage drop reduction for future MV network in desert regions,” Int. J. Power Electron. Drive Syst., vol. 11, no. 2, p. 977, 2020, doi: https://doi.org/10.11591/ijpeds.v11.i2.pp977-987
  44. S. Li, Z. Zhou, Q. Shan, and J. An, “Analysis of Transient Voltage Stability in a Low Voltage Distribution Network Using SST for the Integration of Distributed Generations,” J. Electr. Comput. Eng., vol. 2018, pp. 1–9, 2018, doi: https://doi.org/10.1155/2018/3498491
  45. I. Alvarez-Fernandez et al., “Impact analysis of DERs on bulk power system stability through the parameterization of aggregated DER_a model for real feeders,” Electr. Power Syst. Res., vol. 189, no. July, p. 106822, 2020, doi: https://doi.org/10.1016/j.epsr.2020.106822
  46. O. B. Adewuyi, R. Shigenobu, T. Senjyu, M. E. Lotfy, and A. M. Howlader, “Multiobjective mix generation planning considering utility-scale solar PV system and voltage stability: Nigerian case study,” Electr. Power Syst. Res., vol. 168, no. May 2018, pp. 269–282, 2019, doi: https://doi.org/10.1016/j.epsr.2018.12.010
  47. R. Karthikeyan, “Investigation On Voltage Stability of Wind Integrated Power System,” Int. J. Progress. Res. Sci. Eng., no. 6, pp. 102–105, 2020.
  48. X. Liang, M. N. S. K. Shabbir, N. Khan, and X. Yan, “Measurement-Based Characteristic Curves for Voltage Stability and Control at the Point of Interconnection of Wind Power Plants,” Can. J. Electr. Comput. Eng., vol. 42, no. 3, pp. 163–172, 2019, doi: https://doi.org/10.1109/CJECE.2019.2906007
  49. A. Rabiee, S. Nikkhah, and A. Soroudi, “Information gap decision theory to deal with long-term wind energy planning considering voltage stability,” Energy, vol. 147, pp. 451–463, 2018, doi: https://doi.org/10.1016/j.energy.2018.01.061
  50. B. Qin, H. Li, X. Zhang, T. Ding, K. Ma, and S. Mei, “Quantitative short‐term voltage stability analysis of power systems integrated with DFIG‐based wind farms,” IET Gener. Transm. Distrib., vol. 14, no. 19, pp. 4264–4272, 2020, doi: https://doi.org/10.1049/iet-gtd.2019.1701
  51. M. Baa Wafaa and L. Dessaint, “Approach to dynamic voltage stability analysis for DFIG wind parks integration,” IET Renew. Power Gener., vol. 12, no. 2, pp. 190–197, Feb. 2018, doi: https://doi.org/10.1049/iet-rpg.2016.0482
  52. M. R. Monteiro, Y. R. Rodrigues, M. Abdelaziz, A. C. Z. de Souza, and L. Wang, “New technique for area-based voltage stability support using flexible resources,” Electr. Power Syst. Res., vol. 186, no. April, p. 106384, Sep. 2020, doi: https://doi.org/10.1016/j.epsr.2020.106384
  53. B. B. Adetokun, J. O. Ojo, and C. M. Muriithi, “Reactive Power-Voltage-Based Voltage Instability Sensitivity Indices for Power Grid With Increasing Renewable Energy Penetration,” IEEE Access, vol. 8, pp. 85401–85410, 2020, doi: https://doi.org/10.1109/ACCESS.2020.2992194
  54. H. Marzooghi, M. Garmroodi, G. Verbic, A. S. Ahmadyar, R. Liu, and D. J. Hill, “Scenario and Sensitivity Based Stability Analysis of the High Renewable Future Grid,” IEEE Trans. Power Syst., vol. 37, no. 4, pp. 3238–3248, Jul. 2022, doi: https://doi.org/10.1109/TPWRS.2020.2999070
  55. M. S. Rawat and S. Vadhera, “Probabilistic Steady State Voltage Stability Assessment Method for Correlated Wind Energy and Solar Photovoltaic Integrated Power Systems,” Energy Technol., vol. 9, no. 2, p. 2000732, Feb. 2021, doi: https://doi.org/10.1002/ente.202000732
  56. L. Van Dai, N. Minh Khoa, and L. Cao Quyen, “An Innovatory Method Based on Continuation Power Flow to Analyze Power System Voltage Stability with Distributed Generation Penetration,” Complexity, vol. 2020, pp. 1–15, Sep. 2020, doi: https://doi.org/10.1155/2020/8037837
  57. S. Lin, Y. Lu, M. Liu, Y. Yang, S. He, H. Jiang, “SVSM calculation of power system with high wind‐power penetration,” IET Renew. Power Gener., vol. 13, no. 8, pp. 1391–1401, Jun. 2019, doi: https://doi.org/10.1049/iet-rpg.2018.6144
  58. A. Sajadi, K. Clark, and K. A. Loparo, “Statistical Steady-State Stability Analysis for Transmission System Planning for Offshore Wind Power Plant Integration,” Clean Technol., vol. 2, no. 3, pp. 311–332, Aug. 2020, doi: https://doi.org/10.3390/cleantechnol2030020
  59. R. Ma, X. Li, W. Gao, P. Lu, and T. Wang, “Random-Fuzzy Chance-Constrained Programming Optimal Power Flow of Wind Integrated Power Considering Voltage Stability,” IEEE Access, vol. 8, pp. 217957–217966, 2020, doi: https://doi.org/10.1109/ACCESS.2020.3040382
  60. A. Gholizadeh, A. Rabiee, and R. Fadaeinedjad, “A scenario-based voltage stability constrained planning model for integration of large-scale wind farms,” Int. J. Electr. Power Energy Syst., vol. 105, 2018, pp. 564–580, Feb. 2019, doi: https://doi.org/10.1016/j.ijepes.2018.09.002
  61. M. Jadidbonab, M. J. Vahid-Pakdel, H. Seyedi, and B. Mohammadi-ivatloo, “Stochastic assessment and enhancement of voltage stability in multi carrier energy systems considering wind power,” Int. J. Electr. Power Energy Syst., vol. 106, no. May 2018, pp. 572–584, 2019, doi: https://doi.org/10.1016/j.ijepes.2018.10.028
  62. M. Ghaljehei, A. Ahmadian, M. A. Golkar, T. Amraee, and A. Elkamel, “Stochastic SCUC considering compressed air energy storage and wind power generation: A techno-economic approach with static voltage stability analysis,” Int. J. Electr. Power Energy Syst., vol. 100, no. March, pp. 489–507, Sep. 2018, doi: https://doi.org/10.1016/j.ijepes.2018.02.046
  63. X. He, H. Geng, and G. Mu, “Modeling of wind turbine generators for power system stability studies: A review,” Renew. Sustain. Energy Rev., vol. 143, no. January, p. 110865, Jun. 2021, doi: https://doi.org/10.1016/j.rser.2021.110865
  64. J. Zhang et al., “A Probabilistic Assessment Method for Voltage Stability Considering Large Scale Correlated Stochastic Variables,” IEEE Access, vol. 8, pp. 5407–5415, 2020, doi: https://doi.org/10.1109/ACCESS.2019.2963280
  65. X. Xu, Z. Yan, M. Shahidehpour, H. Wang, and S. Chen, “Power System Voltage Stability Evaluation Considering Renewable Energy With Correlated Variabilities,” IEEE Trans. Power Syst., vol. 33, no. 3, pp. 3236–3245, May 2018, doi: https://doi.org/10.1109/TPWRS.2017.2784812
  66. J. Shukla, B. K. Panigrahi, and P. K. Ray, “Stochastic reconfiguration of distribution system considering stability, correlated loads and renewable energy based DGs with varying penetration,” Sustain. Energy, Grids Networks, vol. 23, p. 100366, Sep. 2020, doi: https://doi.org/10.1016/j.segan.2020.100366
  67. C. Shuai, Y. Deyou, G. Weichun, L. Chuang, C. Guowei, and K. Lei, “Global sensitivity analysis of voltage stability in the power system with correlated renewable energy,” Electr. Power Syst. Res., vol. 192, no. October 2020, p. 106916, Mar. 2021, doi: https://doi.org/10.1016/j.epsr.2020.106916
  68. F. Alsokhiry, G. P. Adam, and Y. Al-Turki, “Limitations of voltage source converter in weak ac networks from voltage stability point of view,” Int. J. Electr. Power Energy Syst., vol. 119, no. September 2019, p. 105899, Jul. 2020, doi: https://doi.org/10.1016/j.ijepes.2020.105899
  69. C. Li, Y. Yang, Y. Cao, L. Wang, and F. Blaabjerg, “Frequency and Voltage Stability Analysis of Grid-Forming Virtual Synchronous Generator Attached to Weak Grid,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 10, no. 3, pp. 2662–2671, Jun. 2022, doi: https://doi.org/10.1109/JESTPE.2020.3041698
  70. A. S. Saidi, “Investigation of Structural Voltage Stability in Tunisian Distribution Networks Integrating Large-Scale Solar Photovoltaic Power Plant,” Int. J. Bifurc. Chaos, vol. 30, no. 13, p. 2050259, Oct. 2020, doi: https://doi.org/10.1142/S0218127420502594
  71. J. H. Braslavsky, L. D. Collins, and J. K. Ward, “Voltage Stability in a Grid-Connected Inverter With Automatic Volt-Watt and Volt-VAR Functions,” IEEE Trans. Smart Grid, vol. 10, no. 1, pp. 84–94, Jan. 2019, doi: https://doi.org/10.1109/TSG.2017.2732000
  72. M. Katsanevakis, R. A. Stewart, and L. Junwei, “A novel voltage stability and quality index demonstrated on a low voltage distribution network with multifunctional energy storage systems,” Electr. Power Syst. Res., vol. 171, no. January, pp. 264–282, Jun. 2019, doi: https://doi.org/10.1016/j.epsr.2019.01.043
  73. M. Islam, M. Nadarajah, and M. J. Hossain, “Dynamic voltage stability of unbalanced DNs with high penetration of roof-top PV units,” Int. Trans. Electr. Energy Syst., vol. 30, no. 12, pp. 1–26, Dec. 2020, doi: https://doi.org/10.1002/2050-7038.12631
  74. J. Yaghoobi, M. Islam, and N. Mithulananthan, “Analytical approach to assess the loadability of unbalanced distribution grid with rooftop PV units,” Appl. Energy, vol. 211, no. December 2015, pp. 358–367, Feb. 2018, doi: https://doi.org/10.1016/j.apenergy.2017.11.030
  75. A. Traupmann, M. Greiml, and T. Kienberger, “Reduction method for planning cross-energy carrier networks in the cellular approach applicable for stability assessment in low-voltage networks,” e i Elektrotechnik und Informationstechnik, vol. 137, no. 8, pp. 509–514, Dec. 2020, doi: https://doi.org/10.1007/s00502-020-00851-4
  76. M. Sarkar, A. D. Hansen, and P. E. Sørensen, “Quantifying robustness of Type 4 wind power plant as reactive power source,” Int. J. Electr. Power Energy Syst., vol. 122, no. April, p. 106181, Nov. 2020, doi: https://doi.org/10.1016/j.ijepes.2020.106181
  77. M. T. Kenari, M. S. Sepasian, and M. S. Nazar, “Probabilistic assessment of static voltage stability in distribution systems considering wind generation using catastrophe theory,” IET Gener. Transm. Distrib., vol. 13, no. 13, pp. 2856–2865, 2019, doi: https://doi.org/10.1049/iet-gtd.2018.5497
  78. M. Tourandaz Kenari, M. S. Sepasian, and M. Setayesh Nazar, “Probabilistic voltage stability assessment of distribution networks with wind generation using combined cumulants and maximum entropy method,” Int. J. Electr. Power Energy Syst., vol. 95, pp. 96–107, 2018, doi: https://doi.org/10.1016/j.ijepes.2017.08.011
  79. H. Lotfi, A. A. Shojaei, V. Kouhdaragh, and I. Sadegh Amiri, “The impact of feeder reconfiguration on automated distribution network with respect to resilience concept,” SN Appl. Sci., vol. 2, no. 9, p. 1590, 2020, doi: https://doi.org/10.1007/s42452-020-03429-z
  80. Y. Song, D. J. Hill, T. Liu, “Static Voltage Stability Analysis of Distribution Systems Based on Network-Load Admittance Ratio,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2270–2280, 2019, doi: https://doi.org/10.1109/TPWRS.2018.2886636
  81. H. Wu, P. Dong, and M. Liu, “Distribution Network Reconfiguration for Loss Reduction and Voltage Stability With Random Fuzzy Uncertainties of Renewable Energy Generation and Load,” IEEE Trans. Ind. Informatics, vol. 16, no. 9, pp. 5655–5666, 2020, doi: https://doi.org/10.1109/TII.2018.2871551
  82. M. S. Rawat and S. Vadhera, “Probabilistic Approach to Determine Penetration of Hybrid Renewable DGs in Distribution Network Based on Voltage Stability Index,” Arab. J. Sci. Eng., vol. 45, no. 3, pp. 1473–1498, 2020, doi: https://doi.org/10.1007/s13369-019-04023-1
  83. H. Sheng and X. Wang, “Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks With Renewables,” IEEE Trans. Power Syst., vol. 33, no. 6, pp. 6726–6735, 2018.