Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production 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, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and 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, focussing 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, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Network Methods for Head-dependent Hydro Power Scheduling

. We study short-term planning of hydro power with a nonlinear objective function. Given prices on the power one seeks to maximize the value of the production over a time-horizon. By assuming a bilinear dependency on head and discharged water we prove that the objective varies concavely when one sends flow along cycles. It follows that in each set of points of equal value containing a local optimum, there is an extreme point of the feasible set. This suggests computing stationary points by using a modified minimum cost network flow code. The model also allows us to derive explicit convex lower bounding functions of the objective. We present computational results for a real-sized hydro-power system. 1 Introduction Hydro power is an important source of electricity in many countries. In Sweden it accounts for around 50% of the electricity produced. Other countries with high share of hydro power are e.g. Canada, Norway, and Switzerland. An important benefit of hydro power is that it does ..

Leukotriene B-4 plays a pivotal role in CD40-dependent activation of chronic B lymphocytic leukemia cells

Blosynthesis of leukotrienes (LTs) occurs in human myeloid cells and B lymphocytes. However, the function of leukotrienes in B lymphocytes is unclear. Here, we report that B-cell chronic lymphocytic leukemia (B-CLL) cells produce leukotriene B-4, and that specific leukotriene biosynthesis inhibitors counteracted CD40-dependent activation of B-CLL cells. Studies on the expression of the high-affinity receptor for LTB4 (BLT1) by flow cytometry analysis showed that the receptor was expressed, to a varying degree, in all investigated B-CLL clones. At a concentration of 100 nM, the drugs BWA4C (a specific 5-lipoxygenase inhibitor) and MK-886 (a specific 5-lipoxygenase activating protein inhibitor) markedly inhibited CD40-induced DNA synthesis (45% and 38%, respectively) and CD40-induced expression of CD23, CD54, and CD150. Addition of exogenous LTB4 (150 nM) almost completely reversed the effect of the inhibitors on DNA synthesis and antigen expression. Taken together, the results of the present study suggest that leukotriene biosynthesis inhibitors may have a therapeutic role in B-CLL

Solving the unit commitment problem in power generation by primal and dual methods

The unit commitment problem in power plant operation planning is addressed. For a real power system comprising coal- and gas- red thermal and pumped-storage hydro plants a large-scale mixed integer optimization model for unit commitment is developed. Then primal and dual approaches to solving the optimization problem are presented and results of test runs are reported

Solving Unit Commitment Problems in Power Production Planning

Unit commitment in production planning of power systems involves dynamic, mixed-integer programming problems. We show that specialized bundle methods applied to Lagrangian relaxations provide not only lower bounds on the optimal value (as do subgradient methods), but also certain relaxed primal solutions. These solutions can be used for constructing good primal feasible solutions. We present computational experience for large-scale examples. 1 Introduction The unit commitment (UC) problem in the daily operation of power systems determines on/off schedules and power outputs of the generators, so as to minimize the system operating cost over a planning horizon of 24 to 168 hours. It is a large-scale mixed integer programming problem. Many solution methodologies [ShF94] have been proposed for the UC problem. Among the most promising is Lagrangian relaxation [MuK77, MoR94, LPRS96], in which a dual function is formed by minimizing the cost augmented with coupling constraints weighted by La..

Multi-Tree Decomposition Methods for Large-Scale Mixed Integer Nonlinear Optimization

Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. Decomposition methods solve a block-separable MINLP by alternately solving master problems and sub-problems. In practice, decomposition methods are sometimes the only possibility to compute high-quality solutions of large-scale optimization problems. However, efficient implementations may require expert knowledge and problem-specific features. Recently, there is renewed interest in making these methods accessible to general users by developing generic decomposition frameworks and modelling support. The focus of this chapter is on so-called multi-tree decomposition methods, which iteratively approximate the feasible area without using a single (global) branch-and-bound tree, i.e. branch-and-bound is only used for solving sub-problems. After an introduction, we describe first outer approximation (OA) decomposition methods, including the adaptive, multivariate partitioning (AMP) and the novel decomposition-based outer approximation (DECOA) algorithm . This is followed by a description of multi-tree methods using a reduced master problem for solving large-scale industrial optimization problems. The first method to be described applies parallel column generation (CG) and iterative fixing for solving nonconvex transport optimization problems with several hundred millions of variables and constraints. The second method is based on a novel approach combining CG and compact outer approximation. The last methodology to be discussed is the general Benders decomposition method for globally solving large nonconvex stochastic programs using a reduced mixed-integer programming (MIP) master problem