2020/11/18 by Mark Jeeninga, Claudio De Persis, Jeeninga, Mark +3
Engineering · #FOS: Electrical engineering #FOS: Mathematics #Microgrid Control and Optimization #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Power System Optimization and Stability #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2011.09333
openalex publication_date 2020/11/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. In particular, we refine several results in Part I to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which is cheaper to compute than the necessary and sufficient LMI condition in Part I. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. In addition, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is also obtained, along with a parametrization of the boundary of the set of feasible power demands.