Load flow solvers for DC and hybrid AC/DC grids

Abstract

The main objective of this dissertation is the establishment of fast and robust power flow (PF) solvers for DC and hybrid AC/DC distribution networks. The developed PF solvers can employ all types of converters and handle any arbitrary DC and hybrid AC/DC network configurations. All PF solvers are tested on various test systems for different loading conditions and R/X ratios of the AC lines. The accuracy of the PF solutions is validated with Electromagnetic Transient (EMT) simulations. First the DC/DC converter models are developed for DC PF solution and integrated into DC PF solvers. The Laplacian Matrix (LM) based DC PF solvers offer the widest convergence range. The convergence and PF solution uniqueness of LM based DC PF solvers are demonstrated with the Banach Fixed Point Theorem (BFPT) using contraction mapping. However, they are non-derivative PF solvers and their computational speeds are well below then the DC PF solver which uses modified augmented nodal analysis (MANA) formulation and Newton Raphson (NR) algorithm (MANA-DC). The uniqueness of solution and the conditions for guaranteed convergence of MANA-DC are derived using the Kantorovich’s theorem. The calculated guaranteed convergence range of MANA-DC PF solver for the test networks is also well above the practical loading conditions. The Holomorphic Embedding PF (HE-PF) solver is the slowest one. This thesis also developed AC/DC converter models and applied the MANA formulation to obtain a unified PF solver for hybrid AC/DC networks. The proposed PF solver does not need the existence of a DC slack bus, nor does it have network topology constraints. The superior convergence characteristics of the MANA with NR (MANA-NR) over the classical nodal analysis (NA) with NR (NA-NR) is illustrated through simulations and explained by inspecting the condition number of the Jacobian matrix. The formulation is further extended to include solid-state transformer (SST) model (MANA-SST) and the accuracy is validated with OpenDSS model available in literature.