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

Scenario Reduction in Stochastic Programming: An Approach Using Probability Metrics

Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50 % reduction of the scenario tree the optimal reduced tree still has about 90 % relative accuracy

Scenario Reduction in Stochastic Programming: An Approach Using Probability Metrics

Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after a 50% reduction of the scenario tree the optimal reduced tree still has about 90% of relative accuracy

Mean-risk optimization of electricity portfolios

We present a mathematical model with stochastic input data for mean-risk optimization of electricity portfolios containing several physical components and energy derivative products. The model is designed for the optimization horizon of one year in hourly discretization. The aim consists in maximizing the mean book value of the portfolio at the end of the optimization horizon and, at the same time, in minimizing the risk of the portfolio decisions. The risk is measured by the conditional value-at-risk and by some multiperiod extension of CVaR, respectively. We present numerical results for a large-scale realistic problem adapted to a municipal power utility and study the effects of varying weighting of risk

Hydropower with Financial Information

The paper considers a single utility company's long- and medium-term hydropower planning. The uncertainties are from the electricity forward curve and a random inflow. A simple and intuitive parameterization is given for the optimal production strategy. The accuracy of the parameterization is analysed by comparing its expected cash flows with the corresponding upper bound. In a test case the proposed method is compared with the realized production strategy of a Norwegian hydropower producer during winters 1997-2003. The parameterization gives earnings that are within 2.6% from the theoretical upper bound. Further, the results illustrate that during some years, part of the realized production strategy can be explained with the method, suggesting that during these years the forward curve information has already been incorporated in the production planning. However, even during the years when the correlation between the proposed strategy and the realized production is low, the strategy would have increased the realized earnings. This suggests that the information from the derivative markets would improve the production strategy.Electricity forward curve, hydropower production,

Gibran Araujo de Souza, guitar

Radames GnatalliJohann Sebastian BachFernando SorIsaac AlbenizJoaquin Rodrig

Stochastic programming for power production and trading under uncertainty

Accepted versio