Loop Analysis and Angle Recovery Based Reactive Power Optimization for Three-Phase Unbalanced Weakly-Meshed Active Distribution Networks

This paper presents a loop analysis and angle recovery (LAAR) based reactive power optimization for three-phase unbalanced and weakly-meshed active distribution networks (ADNs). For each loop, the width first search (WFS) method is used to find the breakpoint bus of each tie line, and then all loops are broken up at these breakpoint buses by disconnecting tie lines, placing added buses, and adding compensation powers, so that the original weakly-meshed ADN can be precisely converted into an equivalent radial ADN. Furthermore, the traditional second-order cone programming can be employed for the equivalent radial networks to find the global optimal solution. However, the compensation powers are not constant values but related to the bus voltages, which are unknown before opening the loops. To address this problem, we design an iterative method to dynamically update the values of compensation powers until the convergence criterion is met. Moreover, the voltage angles are recovered for all loops at each iteration. The effectiveness of the proposed LAAR method is demonstrated by 9 cases, and the results show that the LAAR method can achieve a better convergence performance than the traditional method.