A Full Characterization of the Power Flow Feasibility for DC Power Grids with Constant-Power Loads

We give an overview of the main contributions of [1], [2], which study the power flow feasibility of DC power grids with constant-power loads. We give a necessary and sufficient LMI condition for the feasibility of the power flow problem, and give a geometric description of the constant power demands for which this power flow problem is feasible. Moreover, we show that there is a one-to-one correspondence between the feasible power demands and the so-called long-term voltage semi-stable operating points. Such an operating point can be found by solving an initial value problem. This operating point is shown to element-wise strictly dominate all other operating points, and is shown to minimize the dissipation in the lines among all operating points.