Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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TL;DR: In this article, a chance-constrained stochastic programming formulation with economic and reliability metrics is presented for the day-ahead scheduling, where reserve requirements and line flow limits are formulated as chance constraints in which power system reliability requirements are to be satisfied with a presumed level of high probability.
Abstract: This paper proposes a day-ahead stochastic scheduling model in electricity markets. The model considers hourly forecast errors of system loads and variable renewable sources as well as random outages of power system components. A chance-constrained stochastic programming formulation with economic and reliability metrics is presented for the day-ahead scheduling. Reserve requirements and line flow limits are formulated as chance constraints in which power system reliability requirements are to be satisfied with a presumed level of high probability. The chance-constrained stochastic programming formulation is converted into a linear deterministic problem and a decomposition-based method is utilized to solve the day-ahead scheduling problem. Numerical tests are performed and the results are analyzed for a modified 31-bus system and an IEEE 118-bus system. The results show the viability of the proposed formulation for the day-ahead stochastic scheduling. Comparative evaluations of the proposed chance-constrained method and the Monte Carlo simulation (MCS) method are presented in the paper.
222 citations
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TL;DR: In this article, a stochastic linear programming model for constructing piecewise-linear bidding curves to be submitted to Nord Pool, which is the Nordic power exchange, is proposed.
Abstract: We propose a stochastic linear programming model for constructing piecewise-linear bidding curves to be submitted to Nord Pool, which is the Nordic power exchange. We consider the case of a price-taking power marketer who supplies electricity to price-sensitive end users. The objective is to minimize the expected cost of purchasing power from the day-ahead energy market and the short-term balancing market. The model is illustrated using a case study with data from Norway.
221 citations
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TL;DR: Structural properties of and algorithms for stochastic integer programming models, mainly considering linear two‐stage models with mixed‐integer recourse (and their multi‐stage extensions) are surveyed.
Abstract: We survey structural properties of and algorithms for stochastic integer programmingmodels, mainly considering linear two‐stage models with mixed‐integer recourse (and theirmulti‐stage extensions).
221 citations
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TL;DR: In this article, the authors developed a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains.
Abstract: In a heavily congested metro line, unexpected disturbances often occur to cause the delay of the traveling passengers, infeasibility of the current timetable and reduction of the operational efficiency. Due to the uncertain and dynamic characteristics of passenger demands, the commonly used method to recover from disturbances in practice is to change the timetable and rolling stock manually based on the experiences and professional judgements. In this paper, we develop a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains. To capture the complexity of passenger traveling characteristics, the arriving ratio of passengers at each station is modeled as a non-homogeneous poisson distribution, in which the intensity function is treated as time-varying origin-to-destination passenger demand matrices. By considering the number of on-board passengers, the total energy usage is modeled as the difference between the tractive energy consumption and the regenerative energy. Then, we design an approximate dynamic programming based algorithm to solve the proposed model, which can obtain a high-quality solution in a short time. Finally, numerical examples with real-world data sets are implemented to verify the effectiveness and robustness of the proposed approaches.
221 citations
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TL;DR: It is argued that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages.
Abstract: In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.
221 citations