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Stochastic dynamic programming approach to managing power system uncertainty with distributed storage

Author

Listed:
  • Luckny Zéphyr

    (Cornell University)

  • C. Lindsay Anderson

    (Cornell University)

Abstract

Wind integration in power grids is challenging because of the uncertain nature of wind speed. Forecasting errors may have costly consequences. Indeed, power might be purchased at highest prices to meet the load, and in case of surplus, power may be wasted. Energy storage may provide some recourse against the uncertainty of wind generation. Because of their sequential nature, in theory, power scheduling problems may be solved via stochastic dynamic programming. However, this scheme is limited to small networks by the so-called curse of dimensionality. This paper analyzes the management of a network composed of conventional power units and wind turbines through approximate dynamic programming, more precisely stochastic dual dynamic programming. A general power network model with ramping constraints on the conventional generators is considered. The approximate method is tested on several networks of different sizes. The numerical experiments also include comparisons with classical dynamic programming on a small network. The results show that the combination of approximation techniques enables to solve the problem in reasonable time.

Suggested Citation

  • Luckny Zéphyr & C. Lindsay Anderson, 2018. "Stochastic dynamic programming approach to managing power system uncertainty with distributed storage," Computational Management Science, Springer, vol. 15(1), pages 87-110, January.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:1:d:10.1007_s10287-017-0297-2
    DOI: 10.1007/s10287-017-0297-2
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    References listed on IDEAS

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    1. Zéphyr, Luckny & Lang, Pascal & Lamond, Bernard F. & Côté, Pascal, 2017. "Approximate stochastic dynamic programming for hydroelectric production planning," European Journal of Operational Research, Elsevier, vol. 262(2), pages 586-601.
    2. Shapiro, Alexander & Tekaya, Wajdi & da Costa, Joari Paulo & Soares, Murilo Pereira, 2013. "Risk neutral and risk averse Stochastic Dual Dynamic Programming method," European Journal of Operational Research, Elsevier, vol. 224(2), pages 375-391.
    3. Nils Löhndorf & David Wozabal & Stefan Minner, 2013. "Optimizing Trading Decisions for Hydro Storage Systems Using Approximate Dual Dynamic Programming," Operations Research, INFORMS, vol. 61(4), pages 810-823, August.
    4. Anthony Papavasiliou & Shmuel S. Oren, 2013. "Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network," Operations Research, INFORMS, vol. 61(3), pages 578-592, June.
    5. Yekini Suberu, Mohammed & Wazir Mustafa, Mohd & Bashir, Nouruddeen, 2014. "Energy storage systems for renewable energy power sector integration and mitigation of intermittency," Renewable and Sustainable Energy Reviews, Elsevier, vol. 35(C), pages 499-514.
    6. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    7. C. Russell Philbrick & Peter K. Kitanidis, 2001. "Improved Dynamic Programming Methods for Optimal Control of Lumped-Parameter Stochastic Systems," Operations Research, INFORMS, vol. 49(3), pages 398-412, June.
    8. Succar, Samir & Denkenberger, David C. & Williams, Robert H., 2012. "Optimization of specific rating for wind turbine arrays coupled to compressed air energy storage," Applied Energy, Elsevier, vol. 96(C), pages 222-234.
    9. Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-672, November.
    10. PAPAVASILIOU, Anthony & OREN, Schmuel S., 2013. "Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network," LIDAM Reprints CORE 2500, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    12. Sharon A. Johnson & Jery R. Stedinger & Christine A. Shoemaker & Ying Li & José Alberto Tejada-Guibert, 1993. "Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation," Operations Research, INFORMS, vol. 41(3), pages 484-500, June.
    13. Moura, Pedro S. & de Almeida, Aníbal T., 2010. "The role of demand-side management in the grid integration of wind power," Applied Energy, Elsevier, vol. 87(8), pages 2581-2588, August.
    14. Bradbury, Kyle & Pratson, Lincoln & Patiño-Echeverri, Dalia, 2014. "Economic viability of energy storage systems based on price arbitrage potential in real-time U.S. electricity markets," Applied Energy, Elsevier, vol. 114(C), pages 512-519.
    15. Luckny Zéphyr & Pascal Lang & Bernard Lamond, 2015. "Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems," Computational Management Science, Springer, vol. 12(4), pages 539-557, October.
    16. Wee, Jung-Ho, 2013. "A review on carbon dioxide capture and storage technology using coal fly ash," Applied Energy, Elsevier, vol. 106(C), pages 143-151.
    17. Huseyin Topaloglu & Warren B. Powell, 2006. "Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 31-42, February.
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    2. Fang, Xin & Hodge, Bri-Mathias & Jiang, Huaiguang & Zhang, Yingchen, 2019. "Decentralized wind uncertainty management: Alternating direction method of multipliers based distributionally-robust chance constrained optimal power flow," Applied Energy, Elsevier, vol. 239(C), pages 938-947.

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