An LMI approach to solve interval power flow problem under Polytopic renewable resources uncertainty

Integrating renewable energy sources into a power system imposes uncertainty in the power generation, rendering traditional power flow methods ineffective. By calculating uncertain power flow, we can obtain more realistic and reliable estimates of the system state. Interval methods have been recognized as a powerful tool for analyzing uncertain power systems and increasing their overall reliability. In this paper, an approach is proposed to formulate the uncertain power flow with interval uncertainties, called Interval Power Flow (IPF), as a convex feasibility problem. To attain this goal, the IPF problem is written in the form of Bilinear Matrix Inequalities. Then, the polytopic model of IPF is derived and 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 polytopic uncertain space. Then, the 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 prove its efficacy compared to the existing method.