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The economic dispatch problem is considered for unbalanced three-phase powerdistribution networks entailing both non-deferrable and elastic loads, anddistributed generation (DG) units. The objective is to minimize the costs ofpower drawn from the main grid and supplied by the DG units over a given timehorizon, while meeting the overall load demand and effecting voltageregulation. Similar to optimal power flow counterparts for balanced systems,the resultant optimization problem is nonconvex. Nevertheless, a semidefiniteprogramming (SDP) relaxation technique is advocated to obtain a (relaxed)convex problem solvable in polynomial-time complexity. To promote a reliableyet efficient feeder operation, SDP-compliant constraints on line and neutralcurrent magnitudes are accommodated in the optimization formulated, along withconstraints on the power factor at the substation and at nodes equipped withcapacitor banks. Tests on the IEEE 13-node radial feeder demonstrate theability of the proposed method to attain the globally optimal solution of theoriginal nonconvex problem.

Economic Dispatch in Unbalanced Distribution Networks via Semidefinite Relaxation