Extreme value statistics of peak residential electricity demand: Effect of aggregation and moving-average smoothing

Abstract

Understanding the fluctuations in power demand is critical to the integration of variable renewable resources and the design of future electricity grids. We present an approach to determining the full statistical distribution of peak values of power demand based on extreme value statistics. We apply this method to characterizing the tails of the consumer demand distribution and exploring how peak electricity demand scales with aggregation over increasing numbers of consumers and moving-average smoothing at increasing timescales for two very different consumer groups. The results show evidence of fat tail distributions for some consumers. For both consumer groups, extreme values scale as an inverse power law with aggregation over increasing numbers of consumers and as a decaying exponential with the timescale of moving-average smoothing. Peak reduction by moving-average smoothing is much more sensitive to different sets of consumers than aggregation. As smoothing about a moving average is the primary effect of battery storage, this means that, in general, battery storage cannot play the same role as aggregation in reducing peak demand.