Optimizing Mean-field Dynamics for Distributed Control of Flexible Loads

Since the 1980s, mean-field models have been used as a tool for analysis of distributed control of flexible loads. This talk surveys recent work on the optimization of mean-field dynamics. The focus is on a Kullback-Leibler-Quadradic (KLQ) optimal control formulation for the Demand Dispatch problem, i.e. creating virtual energy storage from flexible electric loads. The grid balancing authority simply broadcasts the desired aggregate power consumption target signal, and the heterogeneous population of loads ramps power consumption up and down to accurately track the signal. Analysis of the Lagrangian dual of the KLQ optimization problem leads to a menu of solution options, and expressions of the gradient and Hessian suitable for Monte-Carlo-based optimization.