A Robust Solution to the Load Curtailment Problem

Operations planning in smart grids is likely to become a more complex and demanding task in the next decades. In this paper we show how to formulate the problem of planning short-term load curtailment in a dense urban area, in the presence of uncertainty in electricity demand and in the state of the distribution grid, as a stochastic mixed-integer optimization problem. We propose three rolling-horizon look-ahead policies to approximately solve the optimization problem: a deterministic one and two based on approximate dynamic programming (ADP) techniques. We demonstrate through numerical experiments that the ADP-based policies yield curtailment plans that are more robust on average than the deterministic policy, but at the expense of the additional computational burden needed to calibrate the ADP-based policies. We also show how the worst case performance of the three approximation policies compares with a baseline policy where all curtailable loads are curtailed to the maximum amount possible.