Optimal Distributed Generation Placement in Distribution Systems via Semidefinite Relaxation

An optimal distributed generation (DG) placement and sizing problem is formulated in this paper, for existing three-phase feeders and future microgrids. Similar to various optimal DG placement and sizing formulations, nonlinear AC power flow relations and binary selection variables representing presence (or absence) of DG units render the proposed optimization problem NP-hard. Nevertheless, a relaxed convex re-formulation is obtained by leveraging semidefinite relaxation techniques, and sparsity-promoting regularization approaches. It is shown that by adjusting a sparsity-tuning parameter, one can trade off attainable system operation efficiency for DG deployment cost. The proposed scheme is tested on the IEEE 37-node test feeder.