Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks

Xue Li; Menglei Zhi; Tao Jiang; Rufeng Zhang; Guoqing Li

doi:10.35833/MPCE.2025.000788

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks

Original Paper | 更新时间：2026-09-28

- Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks
- Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks
- MPCE 2026年14卷第5期页码：1780-1792
- 作者机构：
  
  Department of Electrical Engineering, Northeast Electric Power University, Jilin 132012, China
- 作者简介：
  
  Xue Li received the Ph.D. degree from the University of Tennessee, Knoxville (UTK), Tennessee, USA, in 2015. She is currently a Professor with the Department of Electrical Engineering, Northeast Electric Power University, Jilin, China. Her research interests include computational method applied to power system analysis. Email:xli@neepu.edu.cn
  Menglei Zhi received the B.S. degree in electrical engineering from Northeast Electric Power University, Jilin, China, in 2022, where he is currently working toward the Ph.D. degree since September 2022. His research interests include computational method applied to power system analysis. Email:1202400011@neepu.edu.cn
  Tao Jiang received the B.S. and M.S. degrees in electrical engineering from Northeast Electric Power University, Jilin, China, in 2006 and 2011, respectively, and the Ph.D. degree in electrical engineering from Tianjin University, Tianjin, China, in 2015. He is currently a Professor with the Department of Electrical Engineering, Northeast Electric Power University. His research interests include power system stability and control, renewable energy integration, and integrated energy system. Email:tjiang@neepu.edu.cn
  Rufeng Zhang received the B.S., M.S., and Ph.D. degrees in electrical engineering from Northeast Electric Power University, Jilin, China, in 2013, 2016, and 2019, respectively. He is currently a Professor with the Department of Electrical Engineering, Northeast Electric Power University. His research interests include integrated energy system, power system operation and optimization, and renewable energy integration. Email:zhangrufeng@neepu.edu.cn
  Guoqing Li received the B.S. and M.S. degrees in electrical engineering from Northeast Electric Power University, Jilin, China, in 1984 and 1988, respectively, and the Ph.D. degree in electrical engineering from Tianjin University, Tianjin, China, in 1998. He is currently a Professor with the Department of Electrical Engineering, Northeast Electric Power University. His research interests include multi-level modular converter based high-voltage DC (MMC-HVDC) system and DC grid. Email:lgq@neepu.edu.cn
- 基金信息：
  
  the Natural Science Foundation of Jilin Province (Excellent Youth Fund Project)(20230101374JC);the National Natural Science Foundation of China(52577088)
- DOI：10.35833/MPCE.2025.000788
  中图分类号：
- 收稿：2025-08-24，
  
  修回：2025-11-12，
  
  录用：2025-12-29，
  
  网络首发：2026-04-01，
  
  纸质出版：2026-09-15
- 稿件说明：
移动端阅览
Xue Li, Menglei Zhi, Tao Jiang, 等. Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks[J]. MPCE, 2026,14(5):1780-1792.

Li Xue,Zhi Menglei,Jiang Tao,et al.Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1780-1792.
Xue Li, Menglei Zhi, Tao Jiang, 等. Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks[J]. MPCE, 2026,14(5):1780-1792. DOI： 10.35833/MPCE.2025.000788.

Li Xue,Zhi Menglei,Jiang Tao,et al.Flexible Holomorphic Embedding Solution for Power Flow Calculation in Hybrid AC/DC Active Distribution Networks[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1780-1792. DOI： 10.35833/MPCE.2025.000788.

摘要

Abstract

Holomorphic embedding (HE) method has gained increasing attention in power system analysis because of its robustness. This paper further extends the HE theories into the power flow calculation in hybrid AC/DC active distribution networks (ADNs). A flexible holomorphic embedding solution (FHES) method is proposed for the power flow calculation in AC/DC ADNs in the grid-connected and islanded modes. This paper also develops the HE models of voltage source converters (VSCs) with active and reactive power control modes. The HE models of loads in AC/DC ADNs are also formulated by taking full account of static voltage and frequency characteristics. Furthermore

the HE models of the distributed generators (DGs) under various control modes are developed. A sequential iterative method is employed to solve the developed HE models of AC/DC ADNs in the grid-connected and islanded modes. The performance of the proposed FHES method is evaluated using the modified IEEE 33-node and IEEE 123-node AC/DC ADNs. Finally

the testing results validate the accuracy and robustness of the proposed FHES method.

关键词

Keywords

references

H. Wang, C. Shao, Y. Wang et al. , “Node power injection modification model based on direct derivation for lossy power flow in hybrid AC-DC distribution networks,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 2 , pp. 500 - 513 , Mar. 2025 .

L. Xiao, K. M. Muttaqi, and A. P. Agalgaonkar, “Reliability assessment of distribution systems under influence of stochastic nature of PV and spatial-temporal distribution of EV load demand,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 4 , pp. 1287 - 1299 , Jul. 2025 .

R. Martínez-Parrales, C. R. Fuerte-Esquivel, B. A. Alcaide-Moreno et al. , “A VSC-based model for power flow assessment of multi-terminal VSC-HVDC transmission systems,” Journal of Modern Power Systems and Clean Energy , vol. 9 , no. 6 , pp. 1363 - 1374 , Nov. 2021 .

W. Feng, C. Yuan, Q. Shi et al. , “Graph computing based distributed parallel power flow for AC/DC systems with improved initial estimate,” Journal of Modern Power Systems and Clean Energy , vol. 9 , no. 2 , pp. 253 - 263 , Mar. 2021 .

J. Lei, T. An, Z. Du et al. , “A general unified AC/DC power flow algorithm with MTDC,” IEEE Transactions on Power Systems , vol. 32 , no. 4 , pp. 2837 - 2846 , Jul. 2017 .

J. Beerten, S. Cole, and R. Belmans, “Generalized steady-state VSC MTDC model for sequential AC/DC power flow algorithms,” IEEE Transactions on Power Systems , vol. 27 , no. 2 , pp. 821 - 829 , May 2012.

Z. Javid, T. Xue, U. Karaagac et al. , “Unified power flow solver for hybrid AC/DC distribution networks,” IEEE Transactions on Power Delivery , vol. 38 , no. 5 , pp. 3322 - 3332 , Oct. 2023 .

S. C. Tripathy, G. D. Prasad, O. P. Malik et al. , “Load-flow solutions for ill-conditioned power systems by a Newton-like method,” IEEE Transactions on Power Apparatus and Systems , vol. PAS-101, no. 10 , pp. 3648 - 3657 , Oct. 1982 .

W. Feng, C. Yuan, Q. Shi et al. , “Using virtual buses and optimal multipliers to converge the sequential AC/DC power flow under high load cases.” Electric Power Systems Research , vol. 177 , p. 106015 , Dec. 2019 .

D. Fetzer, G. Lammert, S. Gehler et al. , “Integration of voltage dependent power injections of distributed generators into the power flow by using a damped Newton method,” International Journal of Electrical Power & Energy Systems , vol. 99 , pp. 695 - 705 , Jul. 2018 .

A. A. Eajal, M. A. Abdelwahed, E. F. El-Saadany et al. , “Power flow analysis of AC/DC hybrid microgrids,” in Proceedings of IEEE Electrical Power and Energy Conference , Ottawa, Canada, Oct. 2016 , pp. 1 - 6 .

M. M. A. Abdelaziz, H. E. Farag, E. F. El-Saadany et al. , “A novel and generalized three-phase power flow algorithm for islanded microgrids using a Newton trust region method,” IEEE Transactions on Power Systems , vol. 28 , no. 1 , pp. 190 - 201 , Feb. 2013 .

A. Trias, “The holomorphic embedding load flow method,” in Proceedings of IEEE PES General Meeting , San Diego, USA, Jul. 2012 , pp. 1 - 8 .

T. Wang and H. D. Chiang, “Theoretical study of non-iterative holomorphic embedding methods for solving nonlinear power flow equations: algebraic property,” IEEE Transactions on Power Systems , vol. 36 , no. 4 , pp. 2934 - 2945 , Jul. 2021 .

S. Rao, Y. Feng, D. J. Tylavsky et al. , “The holomorphic embedding method applied to the power flow problem,” IEEE Transactions on Power Systems , vol. 31 , no. 5 , pp. 3816 - 3828 , Sept. 2016.

Y. Zhao, C. Li, T. Ding et al. , “Holomorphic embedding power flow for AC/DC hybrid power systems using Bauer’s Eta algorithm,” IEEE Transactions on Power Systems , vol. 36 , no. 4 , pp. 3595 - 3606 , Jul. 2021 .

Y. Luo and C. Liu, “A unified power flow calculation for hybrid AC/DC power systems based on holomorphic embedding method incorporating LCC-HVDC,” CSEE Journal of Power and Energy Systems , doi: 10.17775/CSEEJPES.2024.04810

Y. Luo, C. Liu, Z. He et al. , “Power flow calculation for AC/DC power systems with line-commutated converter-modular multilevel converter (LCC-MMC) hybrid high-voltage direct current (HVDC) based on the holomorphic embedding method,” Electronics , vol. 13 , no. 10 , pp. 1 - 19 , May 2024.

Y. Huang, X. Ai, J. Fang et al. , “Holomorphic embedding approach for VSC-based AC/DC power flow,” IET Generation, Transmission & Distribution , vol. 14 , no. 25 , pp. 6239 - 6249 , Dec. 2020 .

P. Tian, Y. Jin, N. Xie et al. , “Power flow calculation for VSC-based AC/DC hybrid systems based on fast and flexible holomorphic embedding,” Journal of Modern Power Systems and Clean Energy , vol. 12 , no. 5 , pp. 1370 - 1382 , Sept. 2024.

M. Y. Morgan, M. F. Shaaban, H. F. Sindi et al. , “A holomorphic embedding power flow algorithm for islanded hybrid AC/DC microgrids,” IEEE Transactions on Smart Grid , vol. 13 , no. 3 , pp. 1813 - 1825 , May 2022.

Y. Huang, X. Ai, J. Fang et al ., “Holomorphic embedding power flow modeling of autonomous AC/DC hybrid microgrids,” International Journal of Electrical Power & Energy Systems , vol. 145 , p. 108549 , Feb. 2023 .

Q. Sun, Y. Zhang, Y. Zhou et al. , “Multi-dimensional holomorphic embedding three-phase power flow for AC-DC hybrid distribution systems,” IEEE Transactions on Power Systems , vol. 39 , no. 3 , pp. 5310 - 5323 , May 2024.

S. Mousavizadeh, M. R. Haghifam, and M. H. Shariatkhah, “A new approach for load flow calculation in AC/DC distribution networks considering the control strategies of different converters,” International Transactions on Electrical Energy Systems , vol. 26 , no. 11 , pp. 2479 - 2493 , May 2016.

M. Mousavizadeh, M. H. Shariatkhah, and M. R. Haghifam, “Load flow analysis for AC/DC distribution systems with distributed generations,” Electric Power Components and Systems , vol. 45 , no. 10 , pp. 1057 - 1067 , Jul. 2017 .

A. A. Hamad, M. A. Azzou z, and E. F. E. Saadany, “A sequential power flow algorithm for islanded hybrid AC/DC microgrids,” IEEE Transactions on Power Systems , vol. 31 , no. 5 , pp. 3961 - 3970 , Sept. 2016.

A. A. Eajal, M. A. Abdelwahed, E. F. El-Saadany et al. , “A unified approach to the power flow analysis of AC/DC hybrid microgrids,” IEEE Transactions on Sustainable Energy , vol. 7 , no. 3 , pp. 1145 - 1158 , Jul. 2016 .

K. Murari and N. P. Padhy, “A network-topology-based approach for the load-flow solution of AC-DC distribution system with distributed generations,” IEEE Transactions on Industrial Informatics , vol. 15 , no. 3 , pp. 1508 - 1520 , Mar. 2019 .

H. M. A. Ahmed, A. B. Eltantawy, and M. Salama, “A generalized approach to the load flow analysis of AC-DC hybrid distribution systems,” IEEE Transactions on Power Systems , vol. 33 , no. 2 , pp. 2117 - 2127 , Mar. 2018 .

Z. S. Molaee, E. Rokrok, and M. Doostizadeh, “A unified power flow approach using VSC-efficiency for AC-DC distribution systems operating at grid connected and islanded modes,” International Journal of Electrical Power & Energy Systems , vol. 130 , p. 106906 , Feb. 2021 .

P. Kundur, N. J. Balu, and M. G. Lauby, Power System Stability and Control. New York, USA: McGraw-Hill, 1994.

W. W. Price, H. D. Chiang, H. K. Clark et al. , “Load representation for dynamic performance analysis,” IEEE Transactions on Power Systems , vol. 8 , no. 2 , pp. 472 - 482 , May 1993.

V. C. Cunha, T. Kim, N. Barry et al. , “Generalized formulation of steady-state equivalent circuit models of grid-forming inverters,” IEEE Open Access Journal of Power and Energy , vol. 8 , pp. 352 - 364 , Sept. 2021.

P. C. Loh, D. Li, Y. K. Chai et al. , “Autonomous operation of hybrid microgrid with AC and DC subgrids,” IEEE Transactions on Power Electronics , vol. 28 , no. 5 , pp. 2214 - 2223 , May 2013.

H. Khodr, F. Olsina, P. D. O.-D. Jesus et al. , “Maximum savings approach for location and sizing of capacitors in distribution systems,” Electric Power Systems Research , vol. 78 , no. 7 , pp. 1192 - 1203 , Jul. 2008 .

B. Wang, C. Liu, and K. Sun, “Multi-stage holomorphic embedding method for calculating the power-voltage curve,” IEEE Transactions on Power Systems , vol. 33 , no. 1 , pp. 1127 - 1129 , Jan. 2018 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

Adaptive Robust Optimization for Operation of Active Distribution Networks in Real-time Energy Markets

Polytope-based Aggregation Method for User-side Flexible Energy Resources to Improve Flexibility of Active Distribution Networks

Multi-region and Multi-stage Coordinated Control Method for Resilience Enhancement of Dynamic AC/DC Microgrids

Active and Reactive Power Coordination Control for Voltage Control in Active Distribution Networks Based on LCCIN-SAC Algorithm

Robust Scheduling of Integrated Electricity-heat-hydrogen System Considering Bidirectional Heat Exchange Between Alkaline Electrolyzers and District Heating Networks