(182c) On Representative Day Selection for Capacity Expansion Planning of Power Systems Under Extreme Events

The design of energy systems is increasingly focusing on systems that involve renewable energies. As of 2019, 64% of the electric generation capacity additions come from solar and wind [1]. The increased penetration of renewables has brought up new challenges to power systems infrastructure planning. The most important one is that renewable generations are subject to weather conditions, which makes their power output volatile. Therefore, capacity expansion planning (CEP) of power systems [2-4] has to capture the hourly variations of renewable generator outputs and load demand.

Since the CEP problem typically involves a planning horizon of several years, some “representative days" are usually selected as a surrogate to the fullspace model where the operating decisions corresponding to all the days in the dataset are considered. Several mixed-integer linear programming (MILP) models that include “representative days” in the capacity expansion planning problem have been proposed [4,5]. One of the key questions in formulation these models is how the “representative days” can be selected. Several works [5-7] have been done on solving this issue. Typically, a dataset is given that consists of the historical load data, and capacity factor data for solar and wind generators. The historical data is then scaled to account for load growth. Based on this scaled dataset, k representative days are selected in each year of the planning problem to represent the whole planning horizon where k<<365. A clustering algorithm, such as k-means clustering or k-medoids clustering, is used to divide the whole historical dataset into k clusters based on some of the characteristics of the historical days. The centroid or the medoid of each cluster is selected as the representative day.

In this presentation, we present an input-based and a cost-based approach in combination with the k-means and the k-medoids clustering algorithms for representative day selection. The mathematical properties of the proposed algorithms are analyzed including an approach to calculate the “optimality gap" of the investment decisions obtained from the representative day model to the fullspace model, and the relationship between the clustering error and the optimality gap. To capture the extreme events, two novel approaches, i.e., a “load shedding cost" approach and a “highest cost" approach, are proposed to identify the “extreme days". A case study based on the Electric Reliability Council of Texas (ERCOT) region is presented to compare the different approaches and the effects of adding the extreme days on the large-scale MILP model.

[1] U.S. Energy Information Administration. New electric generating capacity in 2019 will come from renewables and natural gas. URL= eia.gov/todayinenergy/detail.php?id=37952

[2] Koltsaklis, N.E., Dagoumas, A.S.: State-of-the-art generation expansion planning: A review. Applied Energy230, 563–589 (2018)

[3] Krishnan, V., Ho, J., Hobbs, B.F., Liu, A.L., McCalley, J.D., Shahideh-pour, M., Zheng, Q.P.: Co-optimization of electricity transmission and generation resources for planning and policy analysis: review of concepts and modeling approaches. Energy Systems7(2), 297–332 (2016).

[4] Lara, C.L., Mallapragada, D.S., Papageorgiou, D.J., Venkatesh, A., Grossmann, I.E.: Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm. European Journal of Operational Research271(3), 1037–1054 (2018)

[5] D. S. Mallapragada, D. J. Papageorgiou, A. Venkatesh, C. L. Lara, I. E.Grossmann, Impact of model resolution on scenario outcomes for electricity sector system expansion, Energy 163 (2018) 1231–1244

[6] H. Teichgraeber, A. R. Brandt, Clustering methods to find representative periods for the optimization of energy systems: An initial framework and comparison, Applied Energy 239 (2019) 1283–1293

[7] W. W. Tso, C. D. Demirhan, C. F. Heuberger, J. B. Powell, E. N. Pistikopoulos, A hierarchical clustering decomposition algorithm for optimizing renewable power systems with storage, Applied Energy 270 (2020)115190