Receding-Horizon Optimization of Unbalanced Distribution Systems with Time-Scale Separation for Discrete and Continuous Control Devices

This paper presents a method for the optimal control of discrete and continuous devices in an unbalanced three-phase distribution network with significant renewable generation. A hierarchical control scheme is presented where the discrete mechanical assets are dispatched at a slow time-scale as a mixed-integer program (MIP) and the continuous DERs are controlled at a fast time-scale as a convex program. The optimization programs are operated at two time scales as they manage controllable grid resources with different levels of responsiveness and flexibility. The MIP optimizes slow mechanical assets to position voltage robustly against uncertain net-load and a three-phase SOCP program is used to solve the fast loss-minimization optimization for the continuously operated DERs while providing corrective control against the intermittent and variable renewable net-load generation. The scheme is presented on the IEEE-13 node test feeder.