A New Convex Relaxation based OPF for Mutually Coupled Unbalanced Active Distribution Network

Increasing penetration of Distributed Generations (DGs) in Distribution Networks (DNs) for improved network reliability and efficiency has been a subject of great interest. A typical DG can be dispatchable or non-dispatchable and is generally associated with uncertain generation output. Hence, a proper setting of dispatchable DG's real power generation and voltage magnitude is necessary for Optimal Power Flow (OPF) and maintaining various network constraints. Further, DNs are complex networks due to their inherent radial and unbalanced nature with a high R/X ratio. Thus, in this paper, a first OPF problem is demonstrated for a mutually coupled unbalanced active DN. The associated optimization problem is modeled using KCL and KVL equations via a new convex relaxation for optimal settings of the DGs. The effectiveness of the proposed model is investigated for two unbalanced radial distribution feeders - IEEE 34 bus and IEEE 123 bus systems. Further, the robustness of the obtained solution is verified for load fluctuations using Monte Carlo Simulations (MCS).