Dynamic price optimization models for managing time-of-day electricity usage

We present a day-ahead price-optimization based approach for an electric utility to proactively manage the intra-day residential electricity load profile, using dynamic-pricing incentives within a smart grid framework. A novel aspect of our approach is the ability to predict the customer response to price incentives that are designed to induce shifts in the electricity usage from the peak to the off-peak time periods of the daily residential load cycle. A Multinomial Logit (MNL) consumer-choice model is used for estimating the magnitudes of these intra-day hourly loads. The resulting nonlinear optimization problem for the specified profit and capacity-utilization objectives is solved using a series of transformations, which include the reformulation-linearization technique (RLT), to obtain a Mixed-Integer Programming (MIP) model. Using a piecewise-linear cost structure for satisfying electricity demand, we subsequently derive a set of valid inequalities to effectively tighten the underlying relaxation of this MIP. The proposed optimization methodology can also incorporate various regulatory and customer bill-protection constraints. Our model calibration and computational analysis using a real-world data set indicates that the proposed predictive-control methodology can be incorporated into a practical decision support tool to manage the time-of-day electricity demand in order to achieve the desired objectives.