An Autonomous Demand Response Algorithm based on Online Convex Optimization

A price-based demand response program is a viable solution for distribution network operators (DNOs) to motivate electricity consumers toward scheduling their load demand during off-peak periods. This paper addresses the problem of load scheduling in a demand response program, while accounting for load demand uncertainty and the distribution network operational constraints. The centralized load control is a non convex optimization problem due to the ac power flow equations. We use convex relaxation techniques to transform the problem into a semidefinite program (SDP), which is solved using online convex optimization techniques to address the load demand uncertainty. To tackle the issue of computational complexity, we use proximal Jacobian alternating direction method of multipliers (PJ-ADMM) to decompose the centralized problem into the customers' load scheduling subproblems. The decentralized algorithm is executed by each customer to schedule its load demand in real-time. Via simulations on the IEEE 37-bus test feeder, we show that the proposed algorithm enables customers to approximate the optimal load profile in the benchmark scenario without load uncertainty, and the approximation is tight. Furthermore, we show a negligible gap of 2.3% between the customers' cost with the proposed algorithm and the cost in the benchmark scenario.