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A major benefit of the smart grid is that it can provide real-time pricing, which enables residential electricity customers to reduce their electricity expenses by scheduling their appliance use. A commonly utilized technique is to operate electrical appliances when the price of electricity is low. Although this technique is simple in principle and easy to apply, there are several issues that need to be addressed: Studies have shown that residents do not know how, or have the time to take advantage of real-time price information; residents seek to save money by delaying device usage but do not want the inconvenience of long wait times; and a lack of automated energy management systems - industry trials of real-time pricing programs requiring manual user intervention have performed poorly. In this work, we address these issues by the means of an optimal stopping approach, which can balance electricity expense and waiting time. We formulate the problem of deciding when to start home appliances as an optimal stopping problem, and combine optimal stopping rules with appliance energy usage profiles. Our result is an automated residential energy management and scheduling platform, which can reduce energy bills and minimize peak loads. Reduced peak loads result in lower usage rates of dirty coal-based peaker plants, reducing carbon emissions. Additional benefits include lower domestic energy use by controlling vampire loads. Simulation results show that our approach can reduce energy costs by about 10-50 percent depending on the appliance type, and demonstrate the usefulness of our approach in managing residential energy costs.