Generalized newton raphson-based augmented lagrangian algorithm for unbalanced power flow calculation of hybrid AC/DC microgrids with uncertain impedance

The feeder impedance uncertainty and droop parameters mismatch are common issues in hybrid AC/DC microgrids (HMGs), which reduces the power-sharing accuracy of voltage source converters (VSCs), and leads to errors in power flow calculation. Considering the power-sharing correction loops of VSCs in power flow equations increases the computational burden, and the convergence of the power flow solution is not guaranteed. To solve the problem mentioned above, this paper first proposes a novel modeling method for the branch, load/source, grid-forming (GFM) VSC and grid-following (GFL) VSC using an unbalanced bus injection model (UBIM). Secondly, to eliminate the computational errors caused by feeder impedance inaccuracies, a mimetic impedance loop (MIL) is proposed, which is extended to UBIM in the form of quadratic constraints by convexification. Accordingly, the Generalized Newton-Raphson Algorithm-based augmented Lagrangian method (GNR-ALM) is proposed. It deploys GNR in the inner layer to inherit the high convergence for nonlinear power flow problems, while the outer layer employs a distributed variables updating scheme, creating a convex environment for quadratic optimization. Finally, the superior accuracy and computational performance of the GNR-ALM are verified by numerical simulations.