Optimal control of storage incorporating market impact and with energy applications
Optimal control of storage incorporating market impact and with energy applications
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发表时间：
2014-06
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通讯作者：
J. Cruise;L. Flatley;R. Gibbens;S. Zachary
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作者：
J. Cruise;L. Flatley;R. Gibbens;S. Zachary
大规模电力存储将在未来能源网络管理中发挥越来越重要的作用。这类项目经济学的一个主要方面是套利，即在便宜时购买电力，在昂贵时出售电力。我们考虑一个数学模型，它可以解释非线性|可能是随机进化的|成本函数、市场影响、输入和输出速率约束以及存储过程中的时间相关和时间无关的不确定性或损失。我们主要关心的是发展相关的强拉格朗日理论。特别是与容量限制相关的拉格朗日乘数，对于存储容量的确定具有重要的经济意义|关于其容量和其速率限制，|并证明是控制一家商店的关键。我们还开发了一种算法，它确定，按顺序在时间上，这些拉格朗日乘子和最优控制。该算法进一步简化了每个时间点的时间范围，在该时间范围之外，不必寻找以识别该点处的最优控制;此外，该时间范围是最短的。因此，该算法特别适合于在延长的时间段内的存储管理。我们给出了与现实世界系统管理相关的示例。最后，我们考虑一个务实的方法来存储在一个随机的成本环境中，这是计算上可行的，在某些理想条件下的最佳的实时管理，并在一般情况下，预计可以执行接近最优。我们的研究结果制定在一个一般的设置，允许他们的应用到其他能源管理问题，和其他商品存储问题。
Large scale electricity storage is set to play an increasingly important role in the management of future energy networks. A major aspect of the economics of such projects is captured in arbitrage, i.e. buying electricity when it is cheap and selling it when it is expensive. We consider a mathematical model which may account for nonlinear|and possibly stochastically evolving|cost functions, market impact, input and output rate constraints and both time-dependent and time-independent ineciencies or losses in the storage process. Our main concern is to develop the associated strong Lagrangian theory. The Lagrange multipliers associated with the capacity constraints in particular have important economic interpretations with regard to the dimensioning of storage|both with respect to its capacity and its rate constraints| and prove key to the ecient control of a store. We also develop an algorithm which determines, sequentially in time, both these Lagrange multipliers and the optimal control. This algorithm further identies, for each point in time, a time horizon beyond which it is not necessary to look in order to identify the optimal control at that point; this horizon is furthermore the shortest such. The algorithm is thus particularly suitable for the management of storage over extended periods of time. We give examples related to the management of real-world systems. Finally we consider a pragmatic approach to the real-time management of storage in a stochastic cost environment, which is computationally feasible, optimal under certain ideal conditions, and which may in general be expected to perform close to optimally. Our results are formulated in a general setting which permits their application to other energy management problems, and to other commodity storage problems.