2019/10/18 by Zhou, Fengyu, Chen, Yue, Low, Steven H.
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1910.08258
This paper proves that in an unbalanced multi-phase network with a tree topology, the semidefinite programming relaxation of optimal power flow problems is exact when critical buses are not adjacent to each other. Here a critical bus either contributes directly to the cost function or is where an injection constraint is tight at optimality. Our result generalizes a sufficient condition for exact relaxation in single-phase tree networks to tree networks with arbitrary number of phases.