SECOND ORDER CONE PROGRAMMING (SOCP) BASED CONVEX OPTIMAL POWER FLOW (OPF) MODELS FOR POWER SYSTEM NETWORKS

With the modernization of power grids, high penetration of distributed energy-based resources (DERs), and modern loads, optimal power flow (OPF) analysis is one of the essential tools for reliable power system planning and operation. This research proposes novel OPF models for power distribution and transmission networks using second-order cone programming (SOCP). The advantages of SOCP-based convex OPF models are the efficient computational ability for large network systems and the global optimality. To confirm solution accuracy, the necessary conditions for the tightness of the angle and conic relaxations of power flow models are addressed in this research work for the proposed OPF models. In this dissertation, an OPF architecture is proposed to retrieve the bus voltage angle difference for radial distribution networks and thus control the reactive power flow, leading to better voltage regulation in the network and promising a globally optimal solution. This research also presents a SOCP-based AC-OPF model for unbalanced three-phase radial power distribution networks. Mutual coupling effects are generally ignored in the existing multi-phase SOCP AC-OPF models. The proposed SOCP-OPF model introduces a coupling coefficient for the mutual coupling effects on the three-phase unbalanced lines to overcome this critical issue. The derivation of the coupling coefficients has been illustrated with the required proof that the relaxation is tight and the solution from the proposed OPF model is optimal for an unbalanced multi-phase distribution network. Besides the distribution networks, this work also presents a novel SOCP-based OPF formulation for transmission system power networks. Power transmission networks generally have meshed orientation. For meshed power networks, though the conic relaxation is exact due to the cyclic angle constraints, the angle relaxation may not be exact. An OPF model is proposed for the SOCP-OPF model for power transmission networks satisfying the cyclic angle constraints. For that, the model defines a convex envelope to represent the relative bus voltage angles that satisfy the cyclic constraint criteria for a mesh in the network. This dissertation also presents an OPF formulation for AC-DC hybrid power distribution networks. The model determines the optimal modulation index for the converters for minimum network loss. In addition, this dissertation also proposes a distributed OPF (D-OPF) model for distribution networks and a time-dependent (T-OPF) model for real-time OPF analysis. All the proposed models in this research are tested in multiple and extensive networks, and the results show that the models are exact to produce globally optimal solutions for the reliable operation of the power grid.