Scenario-Based Hybrid Robust-Stochastic Programming for Coordinated Scheduling of Electricity & Natural Gas Supply Systems

Document Type : Research Paper

Authors

1 Niroo Research Institute (NRI)

2 Sharif University of Technology

10.22059/aie.2023.349439.1849

Abstract

Stochastic and robust optimizations have been considered as two different views of stochastic problems. While robust optimization takes optimization in the worst case, stochastic optimization regards no conservative view and merely focuses on expected value. However, a unilateral view of stochastic problems does not apply to most real problems. In this article, a hybrid robust and stochastic approach is proposed for optimization problems under uncertainty. Our major contribution is presenting different conservative levels in solving an optimization problem using a Hybrid Robust and Stochastic Optimization approach. To this end, we cluster uncertain parameters into different clusters using Latin Hypercube Sampling and k-Means clustering tools; having established various numbers of clusters of uncertain parameters, different clustering criteria and a Multi-Criteria Decision Making (MCDM) tool is employed to determine the optimal number of clusters of uncertain parameters. Then, a hybrid energy optimization model under uncertainty is applied to coordinate the scheduling of natural gas-fired electricity generation units and gas supply units (gas refinery) under natural gas and electricity demand uncertainty, with known probability distribution and uncertain parameters having different levels of conservatism. The results indicate that while no special trend is evident in the execution time as the number of clusters increases, the optimal value is decreased.

Keywords

References

  1. He, C., et al., Robust coordination of interdependent electricity and natural gas systems in day-ahead scheduling for facilitating volatile renewable generations via power-to-gas technology. Journal of Modern Power Systems and Clean Energy, 2017. 5(3): p. 375-388.
  2. He, C., et al., Coordination of interdependent electricity grid and natural gas network—a review. Current Sustainable/Renewable Energy Reports, 2018. 5(1): p. 23-36.
  3. Zhang, X., L. Che, and M. Shahidehpour. Impact of natural gas system on short-term scheduling with volatile renewable energy. in 2015 IEEE Power & Energy Society General Meeting. 2015. IEEE.
  4. Alabdulwahab, A., et al., Coordination of interdependent natural gas and electricity infrastructures for firming the variability of wind energy in stochastic day-ahead scheduling. IEEE Transactions on Sustainable Energy, 2015. 6(2): p. 606-615.
  5. Zheng, J., Q. Wu, and Z. Jing, Coordinated scheduling strategy to optimize conflicting benefits for daily operation of integrated electricity and gas networks. Applied energy, 2017. 192: p. 370-381.
  6. Li, T., M. Eremia, and M. Shahidehpour, Interdependency of natural gas network and power system security. IEEE transactions on power systems, 2008. 23(4): p. 1817-1824.
  7. Raheli, E., et al., Optimal coordinated operation of integrated natural gas and electric power systems: A review of modeling and solution methods. Renewable and Sustainable Energy Reviews, 2021. 145: p. 111134.
  8. Rahimian, H. and S. Mehrotra, Distributionally robust optimization: A review. arXiv preprint arXiv:1908.05659, 2019.
  9. Ordoudis, C., P. Pinson, and J.M. Morales, An integrated market for electricity and natural gas systems with stochastic power producers. European Journal of Operational Research, 2019. 272(2): p. 642-654.
  10. Bertsimas, D., et al., Adaptive robust optimization for the security constrained unit commitment problem. IEEE transactions on power systems, 2012. 28(1): p. 52-63.
  11. Liu, G. and K. Tomsovic, Robust unit commitment considering uncertain demand response. Electric Power Systems Research, 2015. 119: p. 126-137.
  12. Bertsimas, D., D.B. Brown, and C. Caramanis, Theory and applications of robust optimization. SIAM review, 2011. 53(3): p. 464-501.
  13. Wang, C., et al., Robust defense strategy for gas–electric systems against malicious attacks. IEEE Transactions on Power Systems, 2016. 32(4): p. 2953-2965.
  14. He, Y., et al., Robust constrained operation of integrated electricity-natural gas system considering distributed natural gas storage. IEEE Transactions on Sustainable Energy, 2017. 9(3): p. 1061-1071.
  15. Blanco, I. and J.M. Morales, An efficient robust solution to the two-stage stochastic unit commitment problem. IEEE Transactions on Power Systems, 2017. 32(6): p. 4477-4488.
  16. Rahimian, H., Risk-Averse and Distributionally Robust Optimization: Methodology and Applications. 2018, The Ohio State University.
  17. Gao, R. and A.J. Kleywegt, Distributionally robust stochastic optimization with dependence structure. arXiv preprint arXiv:1701.04200, 2017.
  18. Noyan, N., G. Rudolf, and M. Lejeune, Distributionally robust optimization with decision-dependent ambiguity set. Optimization Online, 2018.
  19. Xiao, X., et al. A two-stage distributionally robust coordinated dispatch for integrated electricity and natural-gas energy systems considering uncertainty of wind power. in IOP Conference Series: Materials Science and Engineering. 2018. IOP Publishing.
  20. Zhang, Y., et al., Two-stage distributionally robust coordinated scheduling for gas-electricity integrated energy system considering wind power uncertainty and reserve capacity configuration. Renewable energy, 2019. 135: p. 122-135.
  21. Yao, L., et al., Robust day-ahead scheduling of electricity and natural gas systems via a risk-averse adjustable uncertainty set approach. Sustainability, 2018. 10(11): p. 3848.
  22. Fang, X., et al., Distributionally-robust chance constrained and interval optimization for integrated electricity and natural gas systems optimal power flow with wind uncertainties. Applied Energy, 2019. 252: p. 113420.
  23. He, C., et al., Distributionally robust scheduling of integrated gas-electricity systems with demand response. IEEE Transactions on Power Systems, 2019. 34(5): p. 3791-3803.
  24. Wang, C., et al., Risk-based distributionally robust optimal gas-power flow with wasserstein distance. IEEE Transactions on Power Systems, 2018. 34(3): p. 2190-2204.
  25. Hou, G. and X. Jian, Distributionally robust chance-constrained economic dispatch of multi-area electricity–gas–heat integrated energy systems. Electric Power Systems Research, 2023. 217: p. 109090.
  26. Liu, H., et al., Distributionally Robust Joint Chance-Constrained Dispatch for Electricity–Gas–Heat Integrated Energy System Considering Wind Uncertainty. Energies, 2022. 15(5): p. 1796.
  27. Song, G. and H. Wei, Distributionally Robust Multi-Energy Dynamic Optimal Power Flow Considering Water Spillage with Wasserstein Metric. Energies, 2022. 15(11): p. 3886.
  28. Yang, L., et al., Distributionally Robust Frequency Constrained Scheduling for an Integrated Electricity-Gas System. IEEE Transactions on Smart Grid, 2022.
  29. Hu, Y., et al. The Study of Distributionally Robust Optimization for Integrated Electric-Gas Distribution System with Demand Response Uncertainty. in 2022 4th Asia Energy and Electrical Engineering Symposium (AEEES). 2022. IEEE.
  30. Mobaraki, A.H., et al., A hybrid Robust-Stochastic optimization model for planned outage based Day-Ahead scheduling of a Plug-in electric vehicles parking lot. Sustainable Energy Technologies and Assessments, 2022. 54: p. 102831.
  31. Zhong, Z., N. Fan, and L. Wu, A hybrid robust-stochastic optimization approach for day-ahead scheduling of cascaded hydroelectric system in restructured electricity market. European Journal of Operational Research, 2023. 306(2): p. 909-926.
  32. Nasiri, N., M.R. Banaei, and S. Zeynali, A hybrid robust-stochastic approach for unit commitment scheduling in integrated thermal electrical systems considering high penetration of solar power. Sustainable Energy Technologies and Assessments, 2022. 49: p. 101756.
  33. Liu, G., et al., Low carbon economic dispatch of biogas-wind-solar renewable energy system based on robust stochastic optimization. International Journal of Electrical Power & Energy Systems, 2022. 139: p. 108069.
  34. Nourollahi, R., et al., A two-stage hybrid robust-stochastic day-ahead scheduling of transactive microgrids considering the possibility of main grid disconnection. International Journal of Electrical Power & Energy Systems, 2022. 136: p. 107701.
  35. Najafi, A., et al., A hybrid decentralized stochastic-robust model for optimal coordination of electric vehicle aggregator and energy hub entities. Applied Energy, 2021. 304: p. 117708.
  36. Nazari-Heris, M., et al., A hybrid robust-stochastic optimization framework for optimal energy management of electric vehicles parking lots. Sustainable Energy Technologies and Assessments, 2021. 47: p. 101467.
  37. Liu, Y., et al., A hybrid stochastic/robust-based multi-period investment planning model for island microgrid. International Journal of Electrical Power & Energy Systems, 2021. 130: p. 106998.
  38. Dehghan, S., et al., A new hybrid stochastic‐robust optimization approach for self‐scheduling of generation companies. International Transactions on Electrical Energy Systems, 2016. 26(6): p. 1244-1259.
  39. Sanjani, K., et al., A robust-stochastic approach for energy transaction in energy hub under uncertainty, in Robust optimal planning and operation of electrical energy systems. 2019, Springer. p. 219-232.
  40. Nikpayam, H. and M. Rafiee, Coordinated Planning and Scheduling of Electricity and Natural Gas Systems. Journal of Operational Research In Its Applications (Applied Mathematics)-Lahijan Azad University, 2019. 16(4): p. 37-54.
  41. Helton, J.C. and F.J. Davis, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety, 2003. 81(1): p. 23-69.
  42. Heitsch, H. and W. Römisch, Scenario tree reduction for multistage stochastic programs. Computational Management Science, 2009. 6(2): p. 117-133.
  43. Madhulatha, T.S., An overview on clustering methods. arXiv preprint arXiv:1205.1117, 2012.
  44. Mary, S.A.L., A. Sivagami, and M.U. Rani, Cluster validity measures dynamic clustering algorithms. ARPN Journal of Engineering and Applied Sciences, 2015. 10(9): p. 4009-4012.
  45. Mittal, M., R. Sharma, and V. Singh, Validation of k-means and threshold based clustering method. International Journal of Advancements in Technology, 2014. 5(2): p. 153-160.
  46. Jain, A.K., Data clustering: 50 years beyond K-means. Pattern recognition letters, 2010. 31(8): p. 651-666.
  47. Lai, Y.-J., T.-Y. Liu, and C.-L. Hwang, Topsis for MODM. European journal of operational research, 1994. 76(3): p. 486-500.
  48. Liu, C., et al., Security-constrained unit commitment with natural gas transmission constraints. IEEE Transactions on Power Systems, 2009. 24(3): p. 1523-1536.
Advances in Industrial Engineering
Volume 57, Issue 2
December 2023
Pages 137-154

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