A framework for computing power consumption scheduling functions under uncertainty

One of the goals of this paper is to make a step further towards knowing how an electrical appliance should exploit the available information to schedule its power consumption; mainly, this information corresponds here to an imperfect forecast of the non-controllable (exogenous) load or electricity price. Reaching this goal led us to three key results which can be used for other settings which involve multiple agents with partial information: 1. In terms of modeling, we exploit the principal component analysis to approximate the exogenous load and show its full relevance; 2. Under some reasonable but improvable assumptions, this work provides a full characterization of the set of feasible payoffs which can be reached by a set of appliances having partial information; 3. A distributed algorithm is provided to compute good power consumption scheduling functions. These results are exploited in the numerical analysis, which provides several new insights into the power consumption scheduling problem. We provide first results for the standard cost functions, transformer aging in particular, where we compare our method with iterative water filling algorithm (IWFA). We test our proposed algorithm on real data and show that it is more robust with respect to noise in the signals received. We also observe that our proposed method becomes even more relevant when the proportion of appliances with smart counters increase.