Admissible Region of Renewable Generation Ensuring Power Flow Solvability in Distribution Networks

The uncertainty of renewable generation makes the operating status of distribution systems more volatile, as fully controllable resource at the distribution level is rare. A dispatchable region refers to the set that consists of all admissible patterns of nodal renewable power injections under which the power flow is solvable without violating security bound constraints. This article studies the dispatchable region in distribution networks under alternating current power flow model. A rank minimization problem is proposed to test power flow solvability under a fixed nodal power injection pattern, providing basic operation to construct the exact dispatchable region. A sequential low-order semidefinite programming procedure is developed to solve the problem. Furthermore, based on a global outer approximation of the second-order conic relaxation of the distflow model, a linear programming-based polyhedral projection algorithm is developed to calculate an outer approximation of the dispatchable region. The projection algorithm is also applied to the traditional linearized distflow model. Combining the feasibility test procedure, it is shown that the intersection of the respective dispatchable regions obtained from two linearized power flow models produces a fairly accurate approximation for the true dispatchable region under the exact nonlinear distflow model. The proposed method is an extension of existing studies on security assessment for distribution systems under uncertainty.