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.