2021/02/27 by Mazhar Ali, Ali, Mazhar, Elena Gryazina +5
Engineering · #FOS: Mathematics #Numerical Analysis (math.NA) #Optimal Power Flow Distribution #Power System Optimization and Stability #Smart Grid Security and Resilience
paper · pdf · doi:10.48550/arxiv.2103.00168
openalex publication_date 2021/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment is directly connected to the robustness of the operating condition and is evaluated by analyzing proximity to the power flow solution space's boundary. Calculating location of such a boundary is a computationally challenging task, linked to the power flow equations' non-linear nature, presence of technological constraints, and complicated network topology. In this paper we introduce a general framework to characterize points on the power flow solution space boundary in terms of auxiliary variables subject to algebraic constraints. Then we develop an adaptive continuation algorithm to trace 1-dimensional sections of boundary curves which exhibits robust performance and computational tractability. Implementation of the algorithm is described in detail, and its performance is validated on different test networks.