General Three-Phase Linear Power Flow for Active Distribution Networks With Good Adaptability Under a Polar Coordinate System

Linear power flow (LPF) is necessary for robust and fast centralized control of active distribution networks (ADNs). With penetration of distributed generators (DGs) into ADN, voltage-controlled nodes are becoming more common, to maintain a normal voltage profile in the distribution network. Existing three-phase LPF formulations under a rectangular coordinate system cannot cope with local voltage-controlled nodes, and does not consider multi-slack-node features of three-phase distribution network, detailed control characteristics and loss participation features of DGs. Here, a general three-phase LPF under a polar coordinate system is presented to address these issues. The proposed method can account for various connection ZIP loads, transformers, and single-phase or three-phase DGs. The detailed control model of the DGs and the distributed slack bus are taken into account. The effectiveness and advantages of the proposed method are validated with balanced 33, 70, 84, 119, and 874-node networks and modified IEEE 13, 34, 37, and 123 unbalanced networks.