A Point-Hyperplane Geometry Method for Operational Security Region of Renewable Energy Generation in Power Systems

The rapid growth of renewable energy generation challenges the secure operation of power systems. It becomes crucial to quantify the critical security boundaries and hosting capability of renewable generation at the system operation level. This paper proposes a novel point-hyperplane geometry (PHG) method to accurately obtain the geometric expression of the operational security region of renewable energy generation for power systems. Firstly, the geometric expression of the operational security region is defined as a polytope of boundary hyperplanes in the form of inequalities satisfying the system operation constraints. Then, an orthogonal basis generation method is proposed to solve a single boundary hyperplane of the polytope based on intersecting and orthogonal geometric principles. Next, a point-hyperplane iteration algorithm is developed to progressively obtain the overall geometric polytope of the operational security region of renewable energy generation in power systems. Besides, the flexible performance trade-off can be achieved by modifying the proposed maximum tolerated angle between adjacent hyperplanes. Finally, comprehensive case stydies verify the effectiveness and superiority of the PHG method.