Abstract
Optimization problems under uncertainty arise in many application areas and their solution is very challenging. We propose here methods that merge off-line and on-line decision stages: we start with a two stage off-line approach coupled with an on-line heuristic. We improve this baseline in two directions: (1) by replacing the on-line heuristics with a simple anticipatory method; (2) by making the off-line component aware of the on-line heuristic. Our approach is grounded on a virtual power plant management system, where the load shifts can be planned off-line and the energy balance should be maintained on-line. The overall goal is to find the minimum cost energy flows at each point in time considering (partially shiftable) electric loads, renewable and non-renewable energy generators, and electric storages. We compare our models with an oracle operating under perfect information and we show that both our improved models achieve a high solution quality, while striking different trade-offs in terms of computation time and complexity of the off-line and on-line optimization techniques.
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Notes
- 1.
Available at http://www.gurobi.com.
- 2.
Available at https://www.gams.com/latest/docs/S_BARON.html.
- 3.
Available at http://www.neos-server.org/neos/.
- 4.
Available at https://data.lab.fiware.org/dataset/.
References
Bai, H., Miao, S., Ran, X., Ye, C.: Optimal dispatch strategy of a virtual power plant containing battery switch stations in a unified electricity market. Energies 8(3), 2268–2289 (2015)
Bent, R.W., Van Hentenryck, P.: Scenario-based planning for partially dynamic vehicle routing with stochastic customers. Oper. Res. 52(6), 977–987 (2004)
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Series in Operations Research and Financial Engineering. Springer, New York (1997). https://doi.org/10.1007/978-1-4614-0237-4
Bordin, C., Anuta, H.O., Crossland, A., Gutierrez, I.L., Dent, C.J., Vigo, D.: A linear programming approach for battery degradation analysis and optimization in offgrid power systems with solar energy integration. Renew. Energy 101, 417–430 (2017)
Bracewell, R.N.: The Fourier Transform and its Applications, vol. 31999. McGraw-Hill, New York (1986)
De Filippo, A., Lombardi, M., Milano, M., Borghetti, A.: Robust optimization for virtual power plants. In: Esposito, F., Basili, R., Ferilli, S., Lisi, F. (eds.) AI*IA 2017. LNCS, vol. 10640, pp. 17–30. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70169-1_2
Espinosa, A.N., Ochoa, L.N.: Dissemination document “low voltage networks models and low carbon technology profiles”. Technical report, University of Manchester, June 2015
Gamou, S., Yokoyama, R., Ito, K.: Optimal unit sizing of cogeneration systems in consideration of uncertain energy demands as continuous random variables. Energy Convers. Manag. 43(9), 1349–1361 (2002)
Van Hentenryck, P., Bent, R.: Online Stochastic Combinatorial Optimization. The MIT Press, Cambridge (2009)
Hodge, B.-M., Lew, D., Milligan, M., Holttinen, H., Sillanpää, S., Gómez-Lázaro, E., Scharff, R., Söder, L., Larsén, X.G., Giebel, G., et al.: Wind power forecasting error distributions: an international comparison. In: 11th Annual International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Power Plants Conference (2012)
Jurković, K., Pandšić, H., Kuzle, I.: Review on unit commitment under uncertainty approaches. In: 2015 38th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), pP. 1093–1097. IEEE (2015)
Kall, P., Wallace, S.W.: Stochastic Programming. Springer, Heidelberg (1994). ISBN 9780471951087
Kaut, M., Wallace, S.W.: Evaluation of scenario-generation methods for stochastic programming. Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik (2003)
Laporte, G., Louveaux, F.V.: The integer l-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett. 13(3), 133–142 (1993)
Mercier, L., Van Hentenryck, P.: Amsaa: a multistep anticipatory algorithm for online stochastic combinatorial optimization. In: Perron, L., Trick, M.A. (eds.) CPAIOR 2008. LNCS, vol. 5015, pp. 173–187. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68155-7_15
Morales, J.M., Conejo, A.J., Madsen, H., Pinson, P., Zugno, M.: Integrating Renewables in Electricity Markets: Operational Problems, vol. 205. Springer, Boston (2013). https://doi.org/10.1007/978-1-4614-9411-9
Powell, W.B.: A unified framework for optimization under uncertainty. In: Optimization Challenges in Complex, Networked and Risky Systems, pp. 45–83. INFORMS (2016). https://doi.org/10.1287/educ.2016.0149
Palma-Behnke, R., Benavides, C., Aranda, E., Llanos, J., Sez, D.: Energy management system for a renewable based microgrid with a demand side management mechanism. In: 2011 IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG), pp. 1–8, April 2011
Reddy, S.S., Sandeep, V., Jung, C.-M.: Review of stochastic optimization methods for smart grid. Front. Energy 11(2), 197–209 (2017)
Kaplanis, S., Kaplani, E.: A model to predict expected mean and stochastic hourly global solar radiation i(h; nj) values. Renew. Energy 32(8), 1414–1425 (2007)
Sahinidis, N.V.: Optimization under uncertainty: state-of-the-art and opportunities. Comput. Chem. Eng. 28(6), 971–983 (2004). FOCAPO 2003 Special issue
Shapiro, A.: Sample average approximation. In: Gass, S.I., Fu, M.C. (eds.) Encyclopedia of Operations Research and Management Science, pp. 1350–1355. Springer, Boston (2013). https://doi.org/10.1007/978-1-4419-1153-7
Shapiro, A., Philpott, A.: A tutorial on stochastic programming. Manuscript (2007). www2.isye.gatech.edu/~ashapiro/publications.html
Wallace, S.W., Fleten, S.-E.: Stochastic programming models in energy. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 637–677. Elsevier (2003)
Winston, W.L., Goldberg, J.B.: Operations Research: Applications and Algorithms, vol. 3. Thomson Brooks/Cole, Belmont (2004)
Zhou, Z., Zhang, J., Liu, P., Li, Z., Georgiadis, M.C., Pistikopoulos, E.N.: A two-stage stochastic programming model for the optimal design of distributed energy systems. Appl. Energy 103, 135–144 (2013)
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De Filippo, A., Lombardi, M., Milano, M. (2018). Off-Line and On-Line Optimization Under Uncertainty: A Case Study on Energy Management. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_8
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