Robust Steady State Analysis of the Power Grid

A robust framework for steady-state analysis (power flow and three-phase power flow problem) of the transmission as well as distribution networks is essential for operation and planning of the electric power grid. The critical nature of this analysis has led to this problem being one of the most actively researched topics in the field of energy in the last few decades. This has produced significant advances in the related technologies; however, the present state-of-the-art methods still lack the general robustness needed to securely and reliably operate as well as plan for the ever-changing power grid. The reasons for this are manifold, but the most important ones are: lack of general assurance toward convergence of power flow and three-phase power flow problems to the correct physical solution when a good initial state is not available; the use of disparate formulation and modeling frameworks for transmission and distribution steady-state analyses that has led to the two analyses being modeled and simulated separately.This thesis addresses the existing limitations in steady-state analysis of power grids to enable a more secure and reliable environment for power grid operation and planning. To that effect, we develop a generic framework based on equivalent circuit formulation that can model both the positive sequence network of the transmission grid and the three-phase network of the distribution grid without loss of generality. Furthermore, we demonstrate that when combined with novel as well as adapted circuit simulation techniques, the framework can robustly solve for the steady-state solution for both these network models (positive sequence and three-phase) by constraining the developed models in their physical space, independent of the choice of initial conditions. Importantly, the developed framework treats the transmission grid no differently than the distribution grid and, therefore, allows for any further advances in the field to be directly applicable to the analysis of both. One of which is the ability to robustly simulate the “combined” positive sequence network of the transmission grid and three-phase network of the distribution grid. To validate the applicability of the proposed equivalent circuit formulation to realistic industry sized systems as well to demonstrate the robustness of the developed methods, we simulate large positive-sequence and three-phase networks individually and jointly from arbitrary initial conditions and show convergence to correct physical solution. Examples for positive sequence transmission networks include 75k+ nodes test cases representing the U.S. Eastern Interconnection high-voltage grid and for three-phase networks include 8k+ nodes taxonomy feeders.