A Geometric Analysis of Power System Loadability Regions
For power system operators, this provides a faster way to assess system loadability without solving nonlinear problems or computing eigenvalues.
The paper proposes a geometric view of power system loadability using rectangular coordinates, enabling a linear programming framework to verify loadability boundaries, compute margins, and find boundary points. The method is computationally more efficient than existing approaches, as demonstrated on IEEE test cases.
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.