Abstract
We consider a capacity planning problem for networks including storage. Given a graph and a time series of demands and supplies, we seek for integer link and storage capacities that permit a single commodity flow with valid storage in- and outtakes over all time steps. This problem arises, for example, in power systems planning, where storage can be used to buffer peaks of varying supplies and demands. For typical time series spanning a full year at hourly resolution, this leads to huge optimization models. To reduce the model size, time series aggregation is commonly used. The time horizon is sliced into fixed size periods, e.g. days or weeks, a small set of representative periods is chosen via clustering methods, and a much smaller model involving only the chosen periods is solved. Representative periods, however, typically do not contain the situations with the most extreme demands and supplies and the strongest effects on storage. In this paper, we show how to identify such critical periods using principal component analysis (PCA) and convex hull computations and we compare the quality and solution time of the reduced models to the original ones for benchmark instances derived from power systems planning.
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References
Bley, A., & Hahn, P. (2021). Identifying critical demand scenarios for the robust capacitated network design problem using principal component analysis. Technical report. Institute for Mathematics, University of Kassel.
Bukenberger, J. P., & Webster, M. D. (2020). Approximate latent factor algorithm for scenario selection and weighting in transmission expansion planning. IEEE Transactions on Power Systems, 35(2), 1099–1108.
Gurobi Optimization, LLC. (2022). Gurobi optimizer reference manual. https://www.gurobi.com
Hoffmann, M., Kotzur, L., Stolten, D., & Robinius, M. (2020). A review on time series aggregation methods for energy system models. Energies, 13, 641.
IBM Ilog CPLEX. (2020). User’s manual for CPLEX (Vol. 12, p. 9).
Mahdavi, M., Antunez, C. S., Ajalli, M., & Romero, R. (2019). Transmission expansion planning: Literature review and classification. IEEE Systems Journal, 13(3), 3129–3140.
Mende, D., Harms, Y., Härtel, P., Frischmuth, F., Stock, D. S., Braun, M., Herrmann, M., Hofmann, L., Valois, M., Bley, A., Hahn, P., Jurczyk, J., & Rathke, C. (2020). NSON II: Next steps in economical connection and international integration of offshore wind energy in the north seas. In Proceedings of the 19th Wind Integration Workshop, Ljubljana, Slovenia.
Miltenberger, M., Oberdieck, R., Siefen, K., Aramon, M., & Bowly, S. grblogtools. https://github.com/Gurobi/grblogtools
Plotly Technologies Inc. (2015). Collaborative data science. https://plot.ly
Saxena, A., Prasad, M., Gupta, A., Bharill, N., Patel, O. P., Tiwari, A., Er, M. J., Ding, W., & Lin, C. T. (2017). A review of clustering techniques and developments. Neurocomputing, 267, 664–681.
Acknowledgements
This work was supported by the German Federal Ministry for Economic Affairs and Energy (BMWi), Project NSON II, [7].
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Bley, A., Hahn, P. (2023). Identifying Critical Demand Periods in Capacity Planning for Networks Including Storage. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_27
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DOI: https://doi.org/10.1007/978-3-031-24907-5_27
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