Neumann Series based Linear Bus Injection Model of Three-Phase AC Power Flow for Active Distribution Network

Linearization of AC power flow is crucial for simplifying the analysis and optimization of power systems, enabling more efficient and scalable computation for network operation and control. In this paper, a Neumann series expansion based linear bus injection model (NS-BIM) of three-phase AC power flow of active distribution network (ADN) is proposed. First, the full-nonlinear three-phase BIM is built based on AC power flow equations. Then, the mathematical derivation of the proposed NS-BIM is provided. Moreover, the approximation error analysis is given which guarantee the robustness of the NS-BIM. Finally, numerical case studies on different benchmark ADN systems are carried out to verify the accuracy of the NS-BIM in comparing with other representative linear BIMs.