DC Power Flow Feasibility: Positive vs. Negative Loads

Voltage instability limits the transmission capacity of a power network. Hence, finding parametric conditions for the feasibility of the power flow equations is of theoretical as well as practical interest. Here, we take over from a recent result tailored for the case of decoupled reactive load flow. We reformulate the theory for the case of Direct Current (DC) resistive power networks and we consider the particular scenario where two different types of loads are present: classical passive loads, modeled as negative quantities, and active loads due to possible distributed generation, modeled as positive quantities. The analysis of their interaction leads us to a less conservative estimate of the injection region in parameter space with respect to a recently proposed conditioned for the solvability of the reactive power flow equations. As a byproduct of the mathematical analysis, we leverage our result into a simple yet numerical exponentially fast algorithm to compute the high-voltage load flow solution. Finally, we extensively verify our findings on standard IEEE test-beds.