Robust scheduling of smart appliances with uncertain electricity prices in a heterogeneous population

Majority of the research conducted in the field of optimal scheduling of smart appliances does not consider the inherent uncertainties in this problem. Besides, the ones that count for the uncertainty usually assume full knowledge about the exact form of the probability distribution of the uncertain parameters. This assumption is hardly fulfilled in reality. In this paper, we seek to find solutions that are robust with respect to the probability distribution of the uncertain parameters while making no explicit assumptions about their exact forms. Accordingly, we define a chance-constrained model to find the optimal schedule and use robust optimization to characterize its solution and the associated uncertain parameters. We also consider the effect of heterogeneous populations on the optimal solution while simultaneously determining the most appropriate classification for accurate predictions. In the process, we investigate the effect of delays in information sharing on computed optimal conditions and we develop a new classification for in-house appliances. We explore features of our model using price data from the "Olympic Peninsula" project. We anticipate that by pursuing optimal options, a typical customer can save up to 33% in her electricity bills while sacrificing 19% of her comfort level. Moreover, in a heterogeneous population, while the results suggest no direct dependency between savings and income level, a meaningful correlation is detected between savings and employment status. (C) 2014 Elsevier B.V. All rights reserved.