  Understanding the feasible power flow region is of central importance to
power system analysis. In this paper, we propose a geometric view of the power
system loadability problem. By using rectangular coordinates for complex
voltages, we provide an integrated geometric understanding of active and
reactive power flow equations on loadability boundaries. Based on such an
understanding, we develop a linear programming framework to 1) verify if an
operating point is on the loadability boundary, 2) compute the margin of an
operating point to the loadability boundary, and 3) calculate a loadability
boundary point of any direction. The proposed method is computationally more
efficient than existing methods since it does not require solving nonlinear
optimization problems or calculating the eigenvalues of the power flow
Jacobian. Standard IEEE test cases demonstrate the capability of the new method
compared to the current state-of-the-art methods.
