  With increasing smart grid direct current (DC) deployments in distribution
feeders, microgrids, buildings, and high-voltage transmission, there is a need
for better understanding the landscape of power flow (PF) solutions as well as
for efficient PF solvers with performance guarantees. This work puts forth
three approaches with complementary strengths towards coping with the PF task
in DC power systems. We consider a possibly meshed network hosting ZIP loads
and constant-voltage/power generators. The first approach relies on a monotone
mapping. In the absence of constant-power generation, the related iterates
converge to the high-voltage solution, if one exists. To handle generators
operating in constant-power mode at any time, an alternative Z-bus method is
studied. For bounded constant-power generation and demand, the analysis
establishes the existence and uniqueness of a PF solution within a predefined
ball. Moreover, the Z-bus updates converge to this solution. Third, an energy
function approach shows that under limited constant-power demand, all PF
solutions are local minima of a function. The derived conditions can be checked
without knowing the system state. The applicability of the conditions and the
performance of the algorithms are numerically validated on a radial
distribution feeder and two meshed transmission systems under varying loading
conditions.
