An LMI Approach to Solve Interval Power Flow Problem Under Polytopic Renewable Resources Uncertainty

Adding renewable energies to a power system, results in an uncertain system where the usual power flow approaches cannot be exploited. In the literature, uncertain power flow with interval uncertainties called Interval Power Flow (IPF) is mostly solved using Monte Carlo Simulation (MCS). However, MCS is too time-consuming and does not solve the problem for the whole domain of uncertainty. In this paper, an approach is proposed to formulate the IPF as a convex feasibility problem. To attain this goal, the PF problem is written in the form of Bilinear Matrix Inequalities. Then, it is proved that to guarantee the validity of IPF for the whole range of renewable energy changes, it is enough to solve the matrix inequalities in the corner points of the uncertain space. Then, Inside-Ellipsoids Outside-Sphere model is applied to the IPF model resulting in a convex feasibility problem plus a non-convex quadratic constraint which is later relaxed to achieve an LMI problem. The final problem is solved by one of the off-the-shelf solvers and a robust operating point for the IPF problem is obtained. The approach is tested for various case studies and the results approve its efficacy compared to the existing method.