In order to address the convergence issue in fuzzy power flow calculations, this paper proposes an analytical approach based on the Levenberg–Marquardt method, aiming to improve the convergence of the fuzzy Newton power flow method. Firstly, a detailed analysis is conducted on the convergence theorem and convergence behavior of the fuzzy Newton method, revealing its poor convergence when the initial values are not properly selected. The Levenberg–Marquardt method is then selected as a means to enhance the convergence of the fuzzy Newton power flow calculations, specifically to tackle the problem of initial value deviation. Since the Jacobian matrix has a significant impact on the convergence region of the power flow, this paper reconstructs the Jacobian matrix based on the Levenberg–Marquardt method, effectively enlarging the convergence region. Through validation experiments on the IEEE 118 standard nodes and simulation comparative analysis, the results confirm the method’s effectiveness in resolving the problem of initial value deviation and notably enlarging the convergence region, thereby improving the convergence of power flow calculations.

Modern power systems include synchronous generators (SGs) and inverter-based resources (IBRs) that provide fast frequency support (FFS) to the system. To evaluate the FFS ability of both SGs and IBRs under a unified framework, this paper proposes a method that evaluates the FFS ability of each generation unit via its dynamic trajectories of the active power output and the frequency following a contingency. The proposed method quantified FFS ability via two indexes, namely, the equivalent inertia constant and the equivalent droop, of each generation unit. The Tikhonov regularization algorithm is employed to estimate the FFS ability indexes. The New England 10-machine system serves to validate the feasibility and accuracy of the proposed method and illustrate the different FFS ability of the grid−forming and grid−following IBRs.