On Convexity of Power Flow Feasibility Boundary

Power flow feasibility boundaries are constraints limiting the operating transmission capability and the available stability (security) margin of the system. The convexity properties of this boundary are important to the analytical description of its shape (including the needs of approximation) and for the calculation of security margins. These analyses are significantly simplified if the boundary is convex. The conjecture that the boundary is convex in the space of system parameters has been used over a long time. However, some alarming experimental counterexamples already exist which show that this boundary is not always convex. In this letter, an analytical approach is presented to analyze the convexity properties of the power flow feasibility boundary. In particular, the approach helps to identify nonconvex parts of the boundary. Numerical case studies illustrate the effectiveness of the approach.