Optimal Net Load Flattening in Unbalanced Distribution Systems via Rank-Penalized Semidefinite Programming

A formidable challenge that hinders the widespread adoption of renewable energy sources is potential mismatch between their intermittent supply and fluctuating demand. This necessitates proper coordination to moderate temporal net load variations while reducing costly curtailment production. By capturing physical security constraints unbalanced distribution systems, this paper formulates a problem manage various fleets commercial- residential-scale distributed resources (DERs), i.e., photovoltaics (PVs), deferrable loads (DLs), electric vehicles (EVs), thermostatically-controlled (TCLs). multi-phase system expanded on relaxed power flow considered account for network awareness. The proposed objective minimize hour-to-hour fluctuations variable, reduce solar curtailment, prioritize preferred EV state charge indoor temperature. objective, however, renders convex relaxation inexact, wherein positive-semidefinite (PSD) matrices are higher than rank-1. To overcome issue therefore enhance reliability solution, we propose tighten via appending trace PSD function. Multiple case studies IEEE 13-bus feeder demonstrate effectiveness optimize profile yield exact solutions.