Analysis of Fast Decoupled Power Flow Via Multiple Axis Rotations

The Fast Decoupled Power Flow (FDPF) method has been widely adopted due to its computational speed advantages relative to the Newton-Raphson method for many practically relevant power flow problems. The FDPF method relies on the assumption that the lines are highly inductive, i.e., have small R/X ratios. When this assumption does not hold (e.g., for distribution systems and some subtransmission systems), the FDPF method may exhibit slow convergence or fail to converge entirely. To address such cases, previous work has proposed an axis rotation method which rescales the complex power injections and the bus admittances by a unit-magnitude complex scalar parameter. Since this complex parameter adjusts the lines' R/X ratios, an appropriate choice for this parameter can improve the FDPF method's performance. In contrast to previous work that only introduces one complex parameter for the entire system (or one complex parameter per large subsystem), we propose and analyze an axis rotation method that introduces different complex parameters at each bus. The additional degrees of freedom provided in this more granular approach are particularly valuable for systems where the lines have wider ranges of R/X ratios. To obtain appropriate values for the complex parameters, we propose to minimize the sum of the squared errors associated with the FDPF approximations. This method can also be adapted for cases with large voltage angle differences. Our simulation results demonstrate the effectiveness of the proposed method.