Random effects mixture models for clustering electrical load series

For purposes such as rate setting and long-term capacity planning, electrical utility companies are interested in dividing their customers into homogeneous groups or clusters in terms of the customers' electricity demand profiles. Such demand profiles are typically represented by load series, long time series of daily or even hourly rates of energy consumption of individual customers. The high dimension and time series nature inherent in the load series render existing methods of clustering analysis ineffective. To handle the high dimension and to take advantage of the time-series nature of load series, we introduce a class of mixture models for time series, the random effects mixture models, which are particularly useful for clustering the load series. The random effects mixture models are based on a hierarchical model for individual components. They employ highly flexible antedependence models to effectively capture the time-series characteristics of the covariance of the load series. We present details on the construction of such mixture models and discuss a special Expectation-maximization (EM) algorithm for their computation. We also apply these models to cluster the data set which had motivated this research, a set of 923 load series from BC Hydro, a crown utility company in British Columbia, Canada.

出于费率设定和长期容量规划等目的，电力公用事业公司有兴趣根据客户的电力需求曲线将其客户划分为同质的群体或集群。这种需求曲线通常由负荷序列来表示，即单个客户每日甚至每小时的能源消耗率的长时间序列。负荷序列固有的高维度和时间序列性质使得现有的聚类分析方法失效。为了处理高维度问题并利用负荷序列的时间序列性质，我们引入了一类时间序列混合模型，即随机效应混合模型，它对于负荷序列的聚类特别有用。随机效应混合模型基于单个组件的分层模型。它们采用高度灵活的先行依赖模型来有效捕捉负荷序列协方差的时间序列特征。我们详细介绍了此类混合模型的构建，并讨论了一种用于其计算的特殊期望最大化（EM）算法。我们还将这些模型应用于对激发这项研究的数据集进行聚类，该数据集是来自加拿大不列颠哥伦比亚省的一家皇家公用事业公司——不列颠哥伦比亚水电公司的923个负荷序列。