Technical Papers
Oct 30, 2021

Two-Stage MILP Model for Optimal Skeleton-Network Reconfiguration of Power System for Grid-Resilience Enhancement

Publication: Journal of Energy Engineering
Volume 148, Issue 1

Abstract

Skeleton-network reconfiguration is an important task and plays a most important role during power system restoration (PSR) after a blackout. By determining the skeleton network, the power system can be restored as soon as possible to minimize the burden of network reconfiguration. In this paper, a resilience-based skeleton-network reconfiguration (NR) strategy, i.e., a two-stage mixed-integer linear programming (MILP)–based NR strategy for grid-resilience enhancement, is proposed to minimize the impact of emergency power outages on power systems. The start-up sequence for non-black-start generators (NBSGs) and line energization sequences are determined in the first-stage optimization model. A serial restoration constraint and a transient frequency constraint are considered to achieve the serial restoration scheme of NBSGs. Except for the generator power, all the variables attained during the first stage are assumed fixed in the second stage. The second-stage optimization model determines the optimal skeleton network by determining the target transmission lines and critical load pickup during the NR phase. Furthermore, the sets of metrics (i.e., system flexibility, power loss ratio, and recovery time resilience) are presented to determine the grid operational resilience in the skeleton-network reconfiguration. Then, two stages of skeleton-NR are formulated as MILP, and the branch-and-bound method is presented to solve both models. Finally, simulation studies are performed on the two modified power system test cases and the results validate that the proposed strategy can efficiently determine the robust skeleton network for practical and detailed PSR planning.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request:
Modified data of IEEE 30-bus power system,
Modified data of IEEE 118-bus power system, and
MATLAB code for generator start-up sequence of IEEE 30-bus power system.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (51777185).

References

Abbaszadeh, A., M. Abedi, and A. Doustmohammadi. 2018. “General stochastic Petri net approach for the estimation of power system restoration duration.” Int. Trans. Electr. Energy Syst. 28 (6): e2550. https://doi.org/10.1002/etep.2550.
Adibi, M., J. Borkoski, R. Kafka, and T. Volkmann. 1999. “Frequency response of prime movers during restoration.” IEEE Trans. Power Syst. 14 (2): 751–756. https://doi.org/10.1109/59.761908.
Akaber, P., B. Moussa, M. Debbabi, and C. Assi. 2019. “Automated post-failure service restoration in smart grid through network reconfiguration in the presence of energy storage systems.” IEEE Syst. J. 13 (3): 3358–3367. https://doi.org/10.1109/JSYST.2019.2892581.
Albert, R., I. Albert, and G. L. Nakarado. 2004. “Structural vulnerability of the North American power grid.” Phys. Rev. E 69 (2): 025103. https://doi.org/10.1103/PhysRevE.69.025103.
Anand, R., D. Aggarwal, and V. Kumar. 2017. “A comparative analysis of optimization solvers.” J. Stat. Manage. Syst. 20 (4): 623–635. https://doi.org/10.1080/09720510.2017.1395182.
Aziz, T., Z. Lin, M. Waseem, and S. Liu. 2021. “Review on optimization methodologies in transmission network reconfiguration of power systems for grid resilience.” Int. Trans. Electr. Energy Syst. 31 (3): e12704. https://doi.org/10.1002/2050-7038.12704.
Berkeley, A. R., M. Wallace, and C. COO. 2010. A framework for establishing critical infrastructure resilience goals. Washington, DC: National Infrastructure Advisory Council.
Beyza, J., E. Garcia-Paricio, H. F. Ruiz, and J. M. Yusta. 2020. “Geodesic vulnerability approach for identification of critical buses in power systems.” J. Mod. Power Syst. Clean Energy 9 (1): 37–45. https://doi.org/10.35833/MPCE.2018.000779.
Bhusal, N., M. Abdelmalak, M. Kamruzzaman, and M. Benidris. 2020. “Power system resilience: Current practices, challenges, and future directions.” IEEE Access 8: 18064–18086. https://doi.org/10.1109/ACCESS.2020.2968586.
Bie, Z., Y. Lin, G. Li, and F. Li. 2017. “Battling the extreme: A study on the power system resilience.” Proc. IEEE 105 (7): 1253–1266. https://doi.org/10.1109/JPROC.2017.2679040.
Chitra, S., and N. Devarajan. 2014. “Circuit theory approach for voltage stability assessment of reconfigured power network.” IET Circuits Devices Syst. 8 (6): 435–441. https://doi.org/10.1049/iet-cds.2013.0325.
Cotilla-Sanchez, E., P. D. H. Hines, C. Barrows, and S. Blumsack. 2012. “Comparing the topological and electrical structure of the North American electric power infrastructure.” IEEE Syst. J. 6 (4): 616–626. https://doi.org/10.1109/JSYST.2012.2183033.
Dehghanian, P., and S. Aslan. 2017. “Enhancing electric safety by improving system resiliency in face of extreme emergencies.” In Proc., 2017 IEEE IAS Electrical Safety Workshop (ESW), 1. New York: IEEE.
Dehghanian, P., S. Aslan, and P. Dehghanian. 2017. “Quantifying power system resiliency improvement using network reconfiguration.” In Proc., 2017 IEEE 60th Int. Midwest Symp. on Circuits and Systems (MWSCAS), 1364–1367. New York: IEEE.
Dehghanian, P., S. Aslan, and P. Dehghanian. 2018. “Maintaining electric system safety through an enhanced network resilience.” IEEE Trans. Ind. Appl. 54 (5): 4927–4937. https://doi.org/10.1109/TIA.2018.2828389.
Fischetti, M., and A. Lodi. 2010. “Heuristics in mixed integer programming.” In Wiley encyclopedia of operations research and management science, 1–6. Hoboken, NJ: Wiley. https://doi.org/10.1002/9780470400531.eorms0376.
Gao, H., Y. Chen, Y. Xu, and C.-C. Liu. 2016. “Resilience-oriented critical load restoration using microgrids in distribution systems.” IEEE Trans. Smart Grid 7 (6): 2837–2848. https://doi.org/10.1109/TSG.2016.2550625.
Gholami, A., T. Shekari, M. H. Amirioun, F. Aminifar, M. H. Amini, and A. Sargolzaei. 2018. “Toward a consensus on the definition and taxonomy of power system resilience.” IEEE Access 6: 32035–32053. https://doi.org/10.1109/ACCESS.2018.2845378.
Golshani, A., W. Sun, Q. Zhou, Q. P. Zheng, and J. Tong. 2017. “Two-stage adaptive restoration decision support system for a self-healing power grid.” IEEE Trans. Ind. Inf. 13 (6): 2802–2812. https://doi.org/10.1109/TII.2017.2712147.
Hvattum, L. M., A. Løkketangen, and F. Glover. 2012. “Comparisons of commercial MIP solvers and an adaptive memory (tabu search) procedure for a class of 0-1 integer programming problems.” Algorithmic Oper. Res. 7 (1): 13–20.
Jiang, Y., S. Chen, C.-C. Liu, W. Sun, X. Luo, S. Liu, N. Bhatt, S. Uppalapati, and D. Forcum. 2017. “Blackstart capability planning for power system restoration.” Int. J. Electr. Power Energy Syst. 86 (Mar): 127–137. https://doi.org/10.1016/j.ijepes.2016.10.008.
Jufri, F. H., V. Widiputra, and J. Jung. 2019. “State-of-the-art review on power grid resilience to extreme weather events: Definitions, frameworks, quantitative assessment methodologies, and enhancement strategies.” Appl. Energy 239 (Apr): 1049–1065. https://doi.org/10.1016/j.apenergy.2019.02.017.
Ketabi, A., A. Karimizadeh, and M. Shahidehpour. 2019. “Optimal generation units start-up sequence during restoration of power system considering network reliability using bi-level optimization.” Int. J. Electr. Power Energy Syst. 104 (Jan): 772–783. https://doi.org/10.1016/j.ijepes.2018.07.045.
Liang, H. 2015. “An improved optimization algorithm for network skeleton reconfiguration after power system blackout.” Tehnički Vjesnik 22 (6): 1359–1363.
Lima, R. 2010. “IBM ILOG CPLEX—What is inside of the box.” In Proc., 2010 EWO Seminar, 1–72. Pittsburgh: Carnegie Mellon Univ.
Lin, Y., Z. Bie, and A. Qiu. 2018. “A review of key strategies in realizing power system resilience.” Global Energy Interconnect. 1 (1): 70–78. https://doi.org/10.14171/j.2096-5117.gei.2018.01.009.
Lin, Z., F. Wen, H. Wang, G. Lin, T. Mo, and X. Ye. 2017. “CRITIC-based node importance evaluation in skeleton-network reconfiguration of power grids.” IEEE Trans. Circuits Syst. II Express Briefs 65 (2): 206–210. https://doi.org/10.1109/TCSII.2017.2703989.
Lin, Z., F. Wen, and Y. Xue. 2016. “A restorative self-healing algorithm for transmission systems based on complex network theory.” IEEE Trans. Smart Grid 7 (4): 2154–2162. https://doi.org/10.1109/TSG.2016.2539199.
Liu, C.-C. 2015. “Distribution systems: Reliable but not resilient?” IEEE Power Energy Mag. 13 (3): 93–96. https://doi.org/10.1109/MPE.2015.2397332.
Liu, S., Z. Lin, Y. Zhao, Y. Liu, Y. Ding, B. Zhang, Q. Wang, L. Yang, and S. E. White. 2020a. “Robust system separation strategy considering online wide-area coherency identification and uncertainties of renewable energy sources.” IEEE Trans. Power Syst. 35 (5): 3574–3587. https://doi.org/10.1109/TPWRS.2020.2971966.
Liu, S., S. You, H. Yin, Z. Lin, Y. Liu, W. Yao, and L. Sundaresh. 2020b. “Model-free data authentication for cyber security in power systems.” IEEE Trans. Smart Grid 11 (5): 4565–4568. https://doi.org/10.1109/TSG.2020.2986704.
Liu, S., Y. Zhao, Z. Lin, Y. Liu, Y. Ding, L. Yang, and S. Yi. 2019a. “Data-driven event detection of power systems based on unequal-interval reduction of PMU data and local outlier factor.” IEEE Trans. Smart Grid 11 (2): 1630–1643. https://doi.org/10.1109/TSG.2019.2941565.
Liu, W., L. Sun, Z. Lin, F. Wen, and Y. Xue. 2016a. “Multi-objective restoration optimisation of power systems with battery energy storage systems.” IET Gener. Transm. Distrib. 10 (7): 1749–1757. https://doi.org/10.1049/iet-gtd.2015.0434.
Liu, W., J. Zhan, C. Chung, and L. Sun. 2019b. “Availability assessment based case-sensitive power system restoration strategy.” IEEE Trans. Power Syst. 35 (2): 1432–1445. https://doi.org/10.1109/TPWRS.2019.2940379.
Liu, Y., R. Fan, and V. Terzija. 2016b. “Power system restoration: A literature review from 2006 to 2016.” J. Mod. Power Syst. Clean Energy 4 (3): 332–341. https://doi.org/10.1007/s40565-016-0219-2.
Liu, Y., and X. Gu. 2007. “Skeleton-network reconfiguration based on topological characteristics of scale-free networks and discrete particle swarm optimization.” IEEE Trans. Power Syst. 22 (3): 1267–1274. https://doi.org/10.1109/TPWRS.2007.901486.
Liu, Y., P. Sun, and C. Wang. 2015. “Group decision support system for backbone-network reconfiguration.” Int. J. Electr. Power Energy Syst. 71 (Oct): 391–402. https://doi.org/10.1016/j.ijepes.2015.03.006.
Oboudi, M. H., R.-A. Hooshmand, and S. Rahimi. 2020. “Stochastic operation framework of microgrid under uncertainties of load, generation, and contingency.” J. Energy Eng. 146 (1): 04019037. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000639.
Oboudi, M. H., M. Mohammadi, and M. Rastegar. 2019. “Resilience-oriented intentional islanding of reconfigurable distribution power systems.” J. Mod. Power Syst. Clean Energy 7 (4): 741–752. https://doi.org/10.1007/s40565-019-0567-9.
Pal, S., S. Sen, and S. Sengupta. 2015. “Power network reconfiguration for congestion management and loss minimization using genetic algorithm.” In Proc., 2015 Michael Faraday IET International Summit, 291–296. New York: IEEE.
Pang, K., C. Wang, F. Wen, I. Palu, C. Feng, Z. Yang, M. Chen, H. Zhao, and H. Shang. 2020. “Two-stage self-healing restoration strategy considering operating performance.” J. Energy Eng. 146 (4): 04020036. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000683.
Qiu, F., and P. Li. 2017. “An integrated approach for power system restoration planning.” Proc. IEEE 105 (7): 1234–1252. https://doi.org/10.1109/JPROC.2017.2696564.
Rajaraman, P., N. Sundaravaradan, B. Mallikarjuna, and D. Mohanta. 2018. “Robust fault analysis in transmission lines using Synchrophasor measurements.” Prot. Control Mod. Power Syst. 3 (1): 14. https://doi.org/10.1186/s41601-018-0082-4.
Rothberg, E. 2007. “An evolutionary algorithm for polishing mixed integer programming solutions.” INFORMS J. Comput. 19 (4): 534–541. https://doi.org/10.1287/ijoc.1060.0189.
Sun, L., Z. Lin, Y. Xu, F. Wen, C. Zhang, and Y. Xue. 2018. “Optimal skeleton-network restoration considering generator start-up sequence and load pickup.” IEEE Trans. Smart Grid 10 (3): 3174–3185. https://doi.org/10.1109/TSG.2018.2820012.
Sun, P., Y. Liu, X. Qiu, and L. Wang. 2015. “Hybrid multiple attribute group decision-making for power system restoration.” Expert Syst. Appl. 42 (19): 6795–6805. https://doi.org/10.1016/j.eswa.2015.05.001.
Sun, R., and Y. Liu. 2018. “An on-line generator start-up strategy based on deep learning and tree search.” In Proc., 2018 IEEE Power & Energy Society General Meeting (PESGM), 1–5. New York: IEEE.
Sun, W., C.-C. Liu, and R. F. Chu. 2009. “Optimal generator start-up strategy for power system restoration. In Proc., 2009 15th Int. Conf. on Intelligent System Applications to Power Systems, 1–7. New York: IEEE.
Sun, W., C.-C. Liu, and L. Zhang. 2010. “Optimal generator start-up strategy for bulk power system restoration.” IEEE Trans. Power Syst. 26 (3): 1357–1366. https://doi.org/10.1109/TPWRS.2010.2089646.
Wang, J., L. Mu, F. Zhang, and X. Zhang. 2018. “A parallel restoration for black start of microgrids considering characteristics of distributed generations.” Energies 11 (1): 1–18. https://doi.org/10.3390/en11010001.
Wang, Y., C. Chen, J. Wang, and R. Baldick. 2015. “Research on resilience of power systems under natural disasters—A review.” IEEE Trans. Power Syst. 31 (2): 1604–1613. https://doi.org/10.1109/TPWRS.2015.2429656.
Waseem, M., Z. Lin, Y. Ding, F. Wen, S. Liu, and I. Palu. 2020a. “Technologies and practical implementations of air-conditioner based demand response.” J. Mod. Power Syst. Clean Energy 1–19. https://doi.org/10.35833/MPCE.2019.000449.
Waseem, M., Z. Lin, S. Liu, I. A. Sajjad, and T. Aziz. 2020b. “Optimal GWCSO-based home appliances scheduling for demand response considering end-users comfort.” Electr. Power Syst. Res. 187 (Oct): 106477. https://doi.org/10.1016/j.epsr.2020.106477.
Waseem, M., Z. Lin, S. Liu, Z. Zhang, T. Aziz, and D. Khan. 2021. “Fuzzy compromised solution-based novel home appliances scheduling and demand response with optimal dispatch of distributed energy resources.” Appl. Energy 290 (May): 116761. https://doi.org/10.1016/j.apenergy.2021.116761.
Xie, Y., D. Li, Y. Xu, Q. Wu, and M. Yin. 2020. “A MILP-based restoration planning method for generator start-up considering flexible re-energizing times of transmission lines.” Int. J. Electr. Power Energy Syst. 124 (Jan): 106357. https://doi.org/10.1016/j.ijepes.2020.106357.
Xu, Y. 2020. “A review of cyber security risks of power systems: From static to dynamic false data attacks.” Prot. Control Mod. Power Syst. 5 (1): 1–12. https://doi.org/10.1186/s41601-020-00164-w.
Zhang, B., P. Dehghanian, and M. Kezunovic. 2017. “Optimal allocation of PV generation and battery storage for enhanced resilience.” IEEE Trans. Smart Grid 10 (1): 535–545. https://doi.org/10.1109/TSG.2017.2747136.
Zhang, C., Z. Lin, F. Wen, G. Ledwich, and Y. Xue. 2014. “Two-stage power network reconfiguration strategy considering node importance and restored generation capacity.” IET Gener. Transm. Distrib. 8 (1): 91–103. https://doi.org/10.1049/iet-gtd.2013.0065.
Zhang, C., L. Sun, F. Wen, Z. Lin, G. Ledwich, and Y. Xue. 2015. “An interpretative structural modeling based network reconfiguration strategy for power systems.” Int. J. Electr. Power Energy Syst. 65 (Feb): 83–93. https://doi.org/10.1016/j.ijepes.2014.09.030.
Zhao, J., H. Wang, Q. Wu, N. D. Hatziargyriou, and F. Shen. 2020. “Optimal generator start-up sequence for bulk system restoration with active distribution networks.” IEEE Trans. Power Syst. 36 (3): 2046–2057. https://doi.org/10.1109/TPWRS.2020.3040130.

Information & Authors

Information

Published In

Go to Journal of Energy Engineering
Journal of Energy Engineering
Volume 148Issue 1February 2022

History

Received: Apr 1, 2021
Accepted: Sep 22, 2021
Published online: Oct 30, 2021
Published in print: Feb 1, 2022
Discussion open until: Mar 30, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Student, School of Electrical Engineering, Zhejiang Univ., Hangzhou 310027, China. ORCID: https://orcid.org/0000-0002-4767-0154. Email: [email protected]
Ph.D. Student, School of Electrical Engineering, Zhejiang Univ., Hangzhou 310027, China. ORCID: https://orcid.org/0000-0002-0923-1476. Email: [email protected]
Shengyuan Liu [email protected]
Ph.D. Student, School of Electrical Engineering, Zhejiang Univ., Hangzhou 310027, China. Email: [email protected]
Professor, School of Electrical Engineering, Zhejiang Univ., Hangzhou 310027, China; Professor, School of Electrical Engineering, Shandong Univ., Jinan 250061, China (corresponding author). ORCID: https://orcid.org/0000-0003-2125-9604. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • A Risk-Based Framework to Improve a Distribution System’s Resilience against Earthquakes, Journal of Energy Engineering, 10.1061/JLEED9.EYENG-4586, 149, 1, (2023).
  • Digital twin application for reinforcement learning based optimal scheduling and reliability management enhancement of systems, Solar Energy, 10.1016/j.solener.2023.01.042, 252, (29-38), (2023).
  • Review of restoration technology for renewable‐dominated electric power systems, Energy Conversion and Economics, 10.1049/enc2.12064, 3, 5, (287-303), (2022).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share