An Online Convex Optimization Approach to Real-Time Energy Pricing for Demand Response

Real-time price setting strategies are investigated for use by demand response programs in future power grids. The major challenge is that consumers have varying degrees of responsiveness to price adjustments at different time instants, which must be learned and accounted for by demand response initiatives. To this end, an online learning approach is developed here offering strong performance guarantees with minimal assumptions on the dynamics of load levels and consumer elasticity, even when consumers are adversarial and take actions strategically. The developed algorithms can determine electricity prices sequentially so as to elicit desirable usage behavior and flatten load curves, while implicitly learning individual consumers' price elasticity based on available feedback information. Two feedback structures are considered: 1) a full information setup, where aggregate load levels as well as individual price elasticity parameters are directly available, and 2) a partial information (bandit) case, where only the aggregate load levels are revealed. Fairness and sparsity constraints are also incorporated via appropriate regularizers. Numerical tests verify the effectiveness of the proposed approach.