论文标题

合奏和降低场景的能量距离

The energy distance for ensemble and scenario reduction

论文作者

Ziel, Florian

论文摘要

方案降低技术被广泛用于求解复杂的动态和随机程序,尤其是在能源和电力系统中,但也用于概率预测,聚类和估计生成的对抗网络(GAN)。我们根据能量距离提出了一种新方法,以减少集合和方案,这是最大平均差异(MMD)的特殊情况。我们详细讨论了能量距离的选择,尤其是与流行的Wasserstein距离相比,该距离主导了场景减少文献。能量距离是概率度量之间的指标,可以进行强大的测试,以相等的多变量分布或独立性。多亏了后者,它是合奏和减少方案问题的合适候选人。理论特性和考虑的例子清楚地表明,相比,相比,相对于瓦斯施泰因距离的相应减少,降低的场景集倾向于在能量距离上表现出更好的统计特性。我们向Bernoulli随机步行和两个基于数据的真实数据示例展示了电力需求概况和日用电价的申请。

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial networks (GANs). We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy (MMD). We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data based examples for electricity demand profiles and day-ahead electricity prices.

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