IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2224-d1436401.html
   My bibliography  Save this article

Optimization of Interconnected Natural Gas and Power Systems Using Mathematical Programs with Complementarity Constraints

Author

Listed:
  • Cristian Alejandro Blanco-Martínez

    (Automatics Research Group, Universidad Tecnológica de Pereira (UTP), Pereira 660003, Colombia)

  • Andrés Marino Álvarez-Meza

    (Signal Processing and Recognition Group, Universidad Nacional de Colombia, Manizales 170003, Colombia)

  • Germán Castellanos-Dominguez

    (Signal Processing and Recognition Group, Universidad Nacional de Colombia, Manizales 170003, Colombia)

  • David Augusto Cárdenas-Peña

    (Automatics Research Group, Universidad Tecnológica de Pereira (UTP), Pereira 660003, Colombia)

  • Álvaro Angel Orozco-Gutiérrez

    (Automatics Research Group, Universidad Tecnológica de Pereira (UTP), Pereira 660003, Colombia)

Abstract

The demand for thermal power generation from natural gas has increased globally due to its cleaner burning properties compared to other fossil fuels. Optimizing the gas flow through the network to meet this demand is challenging due to the nonconvex Weymouth equation constraining gas flow and nodal pressures in pipelines. Traditional methods for addressing this nonconvexity lead to significant approximation errors or high operational costs. This study poses the Weymouth constraint as a Mathematical Programming with Complementarity Constraints (MPCC) for an optimal gas flow problem. The complementarity constraints reformulate the discontinuous sign function using binary-behaving continuous variables. This MPCC-based approach avoids solving mixed-integer programming problems while enhancing the accuracy of conventional linear and second-order approximations. Testing the approach on various interconnected systems, including Colombia’s national gas transportation grid, demonstrated significant reductions in Weymouth approximation errors, thereby supporting effective optimization for interconnected networks.

Suggested Citation

  • Cristian Alejandro Blanco-Martínez & Andrés Marino Álvarez-Meza & Germán Castellanos-Dominguez & David Augusto Cárdenas-Peña & Álvaro Angel Orozco-Gutiérrez, 2024. "Optimization of Interconnected Natural Gas and Power Systems Using Mathematical Programs with Complementarity Constraints," Mathematics, MDPI, vol. 12(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2224-:d:1436401
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2224/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2224/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Cheng & Wei, Wei & Wang, Jianhui & Bi, Tianshu, 2019. "Convex optimization based adjustable robust dispatch for integrated electric-gas systems considering gas delivery priority," Applied Energy, Elsevier, vol. 239(C), pages 70-82.
    2. Wang, Yongli & Wang, Yudong & Huang, Yujing & Yang, Jiale & Ma, Yuze & Yu, Haiyang & Zeng, Ming & Zhang, Fuwei & Zhang, Yanfu, 2019. "Operation optimization of regional integrated energy system based on the modeling of electricity-thermal-natural gas network," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    3. Ordoudis, Christos & Pinson, Pierre & Morales, Juan M., 2019. "An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers," European Journal of Operational Research, Elsevier, vol. 272(2), pages 642-654.
    4. Rao, Amar & Lucey, Brian & Kumar, Satish, 2023. "Climate risk and carbon emissions: Examining their impact on key energy markets through asymmetric spillovers," Energy Economics, Elsevier, vol. 126(C).
    5. Villa-Loaiza, Carlos & Taype-Huaman, Irvin & Benavides-Franco, Julián & Buenaventura-Vera, Guillermo & Carabalí-Mosquera, Jaime, 2023. "Does climate impact the relationship between the energy price and the stock market? The Colombian case," Applied Energy, Elsevier, vol. 336(C).
    6. Obringer, Renee & Mukherjee, Sayanti & Nateghi, Roshanak, 2020. "Evaluating the climate sensitivity of coupled electricity-natural gas demand using a multivariate framework," Applied Energy, Elsevier, vol. 262(C).
    7. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    8. Zhou, Li & Liao, Zuwei & Wang, Jingdai & Jiang, Binbo & Yang, Yongrong, 2014. "MPEC strategies for efficient and stable scheduling of hydrogen pipeline network operation," Applied Energy, Elsevier, vol. 119(C), pages 296-305.
    9. Aydin, Mucahit, 2018. "Natural gas consumption and economic growth nexus for top 10 natural Gas–Consuming countries: A granger causality analysis in the frequency domain," Energy, Elsevier, vol. 165(PB), pages 179-186.
    10. Duan, Jiandong & Liu, Fan & Yang, Yao, 2022. "Optimal operation for integrated electricity and natural gas systems considering demand response uncertainties," Applied Energy, Elsevier, vol. 323(C).
    11. Gemayqzel Bouza & Georg Still, 2007. "Mathematical Programs with Complementarity Constraints: Convergence Properties of a Smoothing Method," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 467-483, May.
    12. J. Restrepo-Trujillo & Ricardo Moreno-Chuquen & Francy Nelly Jim nez-Garc a, 2020. "Strategies of Expansion for Electric Power Systems Based on Hydroelectric Plants in the Context of Climate Change: Case of Analysis of Colombia," International Journal of Energy Economics and Policy, Econjournals, vol. 10(6), pages 66-74.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Baining & Qian, Tong & Li, Weiwei & Xin, Yanli & Zhao, Wei & Lin, Zekang & Tang, Wenhu & Jin, Xin & Cao, Wangzhang & Pan, Tingzhe, 2024. "Fast distributed co-optimization of electricity and natural gas systems hedging against wind fluctuation and uncertainty," Energy, Elsevier, vol. 298(C).
    2. H. Z. Luo & X. L. Sun & Y. F. Xu, 2010. "Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 489-506, June.
    3. Meng Xu & Guangmin Wang & Susan Grant-Muller & Ziyou Gao, 2017. "Joint road toll pricing and capacity development in discrete transport network design problem," Transportation, Springer, vol. 44(4), pages 731-752, July.
    4. Lei Guo & Gaoxi Li, 2024. "Approximation Methods for a Class of Non-Lipschitz Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1421-1445, September.
    5. Z Fang & D Ding & C Guan, 2024. "Does Methodology Matter? Revisiting the Energy-growth Nexus in Asia Pacific Economies," Economic Issues Journal Articles, Economic Issues, vol. 29(1), pages 5-34, March.
    6. Yang, Dechang & Wang, Ming & Yang, Ruiqi & Zheng, Yingying & Pandzic, Hrvoje, 2021. "Optimal dispatching of an energy system with integrated compressed air energy storage and demand response," Energy, Elsevier, vol. 234(C).
    7. Minhui Qian & Jiachen Wang & Dejian Yang & Hongqiao Yin & Jiansheng Zhang, 2024. "An Optimization Strategy for Unit Commitment in High Wind Power Penetration Power Systems Considering Demand Response and Frequency Stability Constraints," Energies, MDPI, vol. 17(22), pages 1-15, November.
    8. Christos N. Dimitriadis & Evangelos G. Tsimopoulos & Michael C. Georgiadis, 2021. "A Review on the Complementarity Modelling in Competitive Electricity Markets," Energies, MDPI, vol. 14(21), pages 1-27, November.
    9. Magazzino, Cosimo & Mele, Marco & Schneider, Nicolas, 2021. "A D2C algorithm on the natural gas consumption and economic growth: Challenges faced by Germany and Japan," Energy, Elsevier, vol. 219(C).
    10. Stefan Scholtes, 2004. "Nonconvex Structures in Nonlinear Programming," Operations Research, INFORMS, vol. 52(3), pages 368-383, June.
    11. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    12. Xu, Jing & Wang, Xiaoying & Gu, Yujiong & Ma, Suxia, 2023. "A data-based day-ahead scheduling optimization approach for regional integrated energy systems with varying operating conditions," Energy, Elsevier, vol. 283(C).
    13. Lan, Puzhe & Han, Dong & Xu, Xiaoyuan & Yan, Zheng & Ren, Xijun & Xia, Shiwei, 2022. "Data-driven state estimation of integrated electric-gas energy system," Energy, Elsevier, vol. 252(C).
    14. Xu, Xiao & Hu, Weihao & Cao, Di & Liu, Wen & Huang, Qi & Hu, Yanting & Chen, Zhe, 2021. "Enhanced design of an offgrid PV-battery-methanation hybrid energy system for power/gas supply," Renewable Energy, Elsevier, vol. 167(C), pages 440-456.
    15. Pang, Simian & Xu, Qingshan & Yang, Yongbiao & Cheng, Aoxue & Shi, Zhengkun & Shi, Yun, 2024. "Robust decomposition and tracking strategy for demand response enhanced virtual power plants," Applied Energy, Elsevier, vol. 373(C).
    16. Horobet, Alexandra & Boubaker, Sabri & Belascu, Lucian & Negreanu, Cristina Carmencita & Dinca, Zeno, 2024. "Technology-driven advancements: Mapping the landscape of algorithmic trading literature," Technological Forecasting and Social Change, Elsevier, vol. 209(C).
    17. Nader Trabelsi & Aviral Kumar Tiwari & Buhari Dogan, 2024. "Water and Emerging Energy Markets Nexus: Fresh Evidence from Advanced Causality and Correlation Approaches," Energies, MDPI, vol. 17(13), pages 1-22, June.
    18. Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G.J., 2003. "Equilibrium Constrained Optimization Problems," Econometric Institute Research Papers ERS-2003-085-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    20. Andreas Ehrenmann & Karsten Neuhoff, 2009. "A Comparison of Electricity Market Designs in Networks," Operations Research, INFORMS, vol. 57(2), pages 274-286, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2224-:d:1436401. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.