Solving the Hydro Unit Commitment Problem via Dual Decomposition and Sequential Quadratic Programming

Finardi, Erlon Cristian; Silva, E.L. da

doi:10.1109/tpwrs.2006.873121

Cited by 139 publications

(106 citation statements)

References 24 publications

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“…A very standard approach is to value the differential between the initial and end volume of a reservoir against a volumedependent water value; we refer to van Ackooij et al (2011) and Cerjan et al (2011) for details on various other modeling choices. A particular difficulty appears when we wish to integrate the water head effect on turbining efficiency (e.g., Finardi and Silva 2006;Ramos et al 2012), since this is typically a nonlinear and nonconvex relationship.…”

Section: The Objective Functionmentioning

confidence: 99%

Large-scale Unit Commitment under uncertainty

Ackooij²,

et al. 2015

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The Unit Commitment problem in energy management aims at finding the optimal productions schedule of a set of generation units while meeting various system-wide constraints. It has always been a large-scale, non-convex difficult problem, especially in view of the fact that operational requirements imply that it has to be solved in an unreasonably small time for its size. Recently, the ever increasing capacity for renewable generation has strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex, uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focusing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, also providing entry points to the relevant literature on optimization under uncertainty

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Section: The Objective Functionmentioning

confidence: 99%

Large-scale Unit Commitment under uncertainty

Ackooij²,

et al. 2015

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“…For unit-commitment scheduling, for instance, thermal subproblems are mixed-0-1 problems, often solved by dynamic programming, [42,76]. Hydro subproblems are generally large scale programs, sometimes involving 0-1 variables and/or nonlinear relations, [12,38].…”

Section: Lagrangian Relaxation Examplesmentioning

confidence: 99%

Divide to conquer: decomposition methods for energy optimization

Sagastizábal

2012

Math. Program.

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Modern electricity systems provide a plethora of challenging issues in optimization. The increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting. The liberalization of the electricity sector brought the need of designing sound markets, ensuring capacity investments while properly reflecting strategic interactions. In all these problems, hedging risk, possibly in a dynamic manner, is also a concern. The fact of representing uncertainty and/or competition of different companies in a multi-settlement power market considerably increases the number of variables and constraints. For this reason, usually a trade-off needs to be found between modeling and numerical tractability: the more details are brought into the model, the harder becomes the optimization problem. For structured optimization and generalized equilibrium problems, we explore some variants of solution methods based on Lagrangian relaxation and on Benders decomposition. Throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems.

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“…The first group takes advantage of the special features of stochastic problems to improve data structures and solution strategies [18]. The second group uses 3 There are two ways of writing DEs: the implicit and the explicit [15]. The difference is the way in which the constraints (nonanticipativity) are handled.…”

Section: Multistage Stochastic Optimization Problemsmentioning

confidence: 99%

Comparing stochastic optimization methods to solve the medium-term operation planning problem

Gonçalves¹,

Finardi²,

Silva³

et al. 2011

Comput. Appl. Math.

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Abstract. The Medium-Term Operation Planning (MTOP) of hydrothermal systems aimsto define the generation for each power plant, minimizing the expected operating cost over the planning horizon. Mathematically, this task can be characterized as a linear, stochastic, large-scale problem which requires the application of suitable optimization tools. To solve this problem, this paper proposes to use the Nested Decomposition, frequently used to solve similar problems (as in Brazilian case), and Progressive Hedging, an alternative method, which has interesting features that make it promising to address this problem. To make a comparative analysis between these two methods with respect to the quality of the solution and the computational burden, a benchmark is established, which is obtained by solving a single Linear Programming problem (the Deterministic Equivalent Problem). An application considering a hydrothermal system is carried out.Mathematical subject classification: Primary: 06B10; Secondary: 06D05.

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Solving the Hydro Unit Commitment Problem via Dual Decomposition and Sequential Quadratic Programming

Cited by 139 publications

References 24 publications

Large-scale Unit Commitment under uncertainty

Large-scale Unit Commitment under uncertainty

Divide to conquer: decomposition methods for energy optimization

Comparing stochastic optimization methods to solve the medium-term operation planning problem

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