In this two-part article, 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 article, explores further implications of the results in Part I. We present a necessary and sufficient linear matrix inequality (LMI) condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition, we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semistable 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 obtained, as well as a parametrization of the boundary of the set of feasible power demands.

In this two-part article, we develop a unifying framework for the analysis of the feasibility of the power flow equations for dc power grids with constant-power loads. In Part I of this article, we present a detailed introduction to the problem of power flow feasibility of such power grids, and the associated problem of selecting a desirable operating point which satisfies the power flow equations. We introduce and identify all long-term voltage semistable operating points, and show that there exists a one-to-one correspondence between such operating points and the constant power demands for which the power flow equations are feasible. Such operating points can be found by solving an initial value problem, and a parametrization of these operating points is obtained. In addition, we give a full characterization of the set of all feasible power demands, and give a novel proof for the convexity of this set.

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