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

TL;DR

This work tackles secure operation under high REG uncertainty by constructing a geometric, polyhedral representation of the operational security region (GOSR) via a linearized AC model. It introduces the Point-Hyperplane Geometry (PHG) framework, combining a boundary-point solver (BPS), orthogonal basis generation (OBG), and a point-hyperplane iteration (PHI) algorithm to progressively build the GOSR as a polytope defined by $H: c^T w + d = 0$ and $Cw + D \le 0$. Key contributions include a rigorous uniqueness condition for boundary hyperplanes, a dynamic exterior-point adjustment mechanism, progressive geometric expansion to mitigate combinatorial explosion, and a tunable maximum tolerated angle $\phi$ to balance accuracy and computational cost. Case studies on IEEE 30-bus and IEEE 118-bus networks demonstrate high geometric and approximation accuracy, with substantial efficiency gains over benchmark approaches, confirming the method’s practical applicability for hosting capacity and REG accommodation analysis in power systems.

Abstract

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 studies verify the effectiveness and superiority of the PHG method.

Figures (5)

• Figure 1: Schematic diagram of proposed OBG method
• Figure 2: Schematic diagram of DEPA method
• Figure 3: Visualization results of PHG method and verified by MCS: 2D
• Figure 4: Visualization results of PHG method and verified by MCS: 3D
• Figure 5: Errors of PHG method under different values of $\phi$.