報告書番号

R06

タイトル（和文）

確率計画法の電気事業への応用

タイトル（英文）

Applications of Stochastic Programming to Optimization Problems in Electric Power Industry

概要 （図表や脚注は「報告書全文」に掲載しております）

従来、電気事業における設計、計画、運用などの問題に対しては、確定的な数理計画法が用いられてきたが、現実の数理計画問題には、目的関数および制約条件に不確実要素を伴う場合が多い。不確実な状況下での意思決定にはリスクが含まれるため、現実システムの不確実性をモデル化し、確率的変動要素を考慮することが必要となる。そのため、確率計画法の理論、手法のより一層の進展が求められている。本報告では、電気事業で現れる実問題に適用可能な、確率計画法に基づく効率的な解法を開発することを目的とする。確率計画法を応用することにより、ネットワーク設計問題と発電機起動停止問題に対しては、需要変動から生じるリスクを回避することが可能となり、補修計画と電力供給計画に対しては、供給に支障が生じるリスクを管理することが可能となる。

概要 （英文）

Mathematical programming has been applied to various fields in everyday life. However for many actual problems, the assumption that the parameters involved in the problem are deterministic known data is often unjustified. These data contain uncertainty and are thus represented as random variables, since they represent information about the future. In this paper, we consider a mathematical programming problem in which some parameters are uncertain. Decision-making under conditions of uncertainty involves potential risk. For example, setting up too few new electric power plants may result in a shortage of capacity for future electricity demand. On the other hand, excessive investment will cause an excess of capacity. Our problem is thus a strategic decision problem under uncertainty, and can be viewed as a stochastic programming problem. The approach to stochastic programming is classified into two approaches: stochastic programming with recourse and chance-constrained programming. The electric power industry is undergoing restructuring and deregulation, and it is necessary to incorporate uncertainties such as the level of electric power demand and availability of power generators into the optimization problem in the electric power industry. The purpose of this paper is to develop algorithms to solve stochastic programming problems and their applications to optimization problems in the electric power industry. In this paper, we consider four optimization problems in the electric power industy. The stocchastic programming model with recourse is applied to the topological design of centralized communication networks andthe unit commitment problem. As for the maintenance scheduling problem of power plants and the electric power capacity expansion problem, the chace-constrained programming model is developed. Our studies clearly show stochastic programming to be very valuable for solving the optimization problem in the electric power industry.

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