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Munoz, F. D., Hobbs, B. F., & Watson, J. P. (2016). New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints. Eur. J. Oper. Res., 248(3), 888–898.
Abstract: We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen's inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders' algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen's inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. However, the decomposition phase is required to attain optimality gaps. Use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
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Navarro, A., Favereau, M., Lorca, A., Olivares, D., & Negrete-Pincetic, M. (2024). Medium-term stochastic hydrothermal scheduling with short-term operational effects for large-scale power and water networks. Appl. Energy, 358, 122554.
Abstract: The high integration of variable renewable sources in electric power systems entails a series of challenges inherent to their intrinsic variability. A critical challenge is to correctly value the water available in reservoirs in hydrothermal systems, considering the flexibility that it provides. In this context, this paper proposes a medium -term multistage stochastic optimization model for the hydrothermal scheduling problem solved with the stochastic dual dynamic programming algorithm. The proposed model includes operational constraints and simplified mathematical expressions of relevant operational effects that allow more informed assessment of the water value by considering, among others, the flexibility necessary for the operation of the system. In addition, the hydrological uncertainty in the model is represented by a vector autoregressive process, which allows capturing spatio-temporal correlations between the different hydro inflows. A calibration method for the simplified mathematical expressions of operational effects is also proposed, which allows a detailed shortterm operational model to be correctly linked to the proposed medium -term linear model. Through extensive experiments for the Chilean power system, the results show that the difference between the expected operating costs of the proposed medium -term model, and the costs obtained through a detailed short-term operational model was only 0.1%, in contrast to the 9.3% difference obtained when a simpler base model is employed. This shows the effectiveness of the proposed approach. Further, this difference is also reflected in the estimation of the water value, which is critical in water shortage situations.
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