A Method for Directly Extracting the Jacobian Matrix of the Power Flow Equations of a Power System in Polar Coordinates - Lyu, Zhongliang; Wei, Hua; Wei, Hongbo (Frontiers in Energy Research, 2022)
This paper presents a method to directly extract the Jacobian matrix of the power flow (PF) equations of a power system in polar coordinates (termed the DEJMP method). This method is designed to reduce the computational complexity of the extraction process and improve the computational efficiency of the relevant PF algorithm. Direct extraction of the Jacobian matrix from the complex power equation in polar coordinates precludes an increase in both the number of procedural steps and the computational expense, which is a problem associated with the conventional PF (C-PF) algorithm due to its requirement that the derivatives of the active and reactive bus power equations be taken in separate steps. Implementation of the program in MATLAB shows that the DEJMP-based PF algorithm method has 50% fewer lines of core code than the C-PF algorithm. In addition, simulation results obtained for IEEE-300, S-1047, S-2383, S-9241, and S-13659 bus systems validate the efficiency of the DEJMP-based PF algorithm. Compared to the C-PF algorithm, the DEJMP-based PF algorithm requires more than 15% less time to calculate the PF. This decrease in the computing time is more pronounced for large systems.