Novel insights into lossless AC and DC power flow

A central question in the analysis and operation of power networks is feasibility of the power flow equations subject to security constraints. For large-scale networks the solution of the nonlinear AC power flow equations can be constructed only numerically or approximated through the linear DC power flow. The latter serves as well-used approximation to obtain the phase angle differences near an acceptable operating point, but the accuracy of the DC approximation drops in a stressed grid. Here, we propose a modified DC approximation that applies to lossless networks with parametric uncertainties and with voltage magnitudes bounded within security constraints. We show that the phase angle differences can be well approximated by the solution to a set of linear and interval-valued equations reminiscent of the DC power flow equations. Our proposed approximation improves upon the standard DC approximation, is computationally attractive and provably exact for a broad range of network topologies and parameters. We validate the accuracy of our approximation through standard power network test cases with randomized power demand at the loads.