Direct method for the calculation of minimal maximum voltage security margins by the smooth power flow model

• Grant number: 25/02002-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: December 31, 2025
• Field of knowledge: Engineering - Electrical Engineering - Power Systems
• Principal Investigator: Guilherme Guimarães Lage
• Grantee: Nicolas Müller Rodrigues da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This research project proposes a direct method for calculating the minimal maximum voltage security margin in electric power systems under the N-1 criterion, which is fundamental for static security analyses in short-term operation planning. The motivation stems from the need to ensure stable and robust operating margins in response to variations in scheduled active power dispatch, load forecasting, and the unpredictability of transmission line contingencies. The direct method proposed in this research project employs the minimax criterion of robust optimization and is based on mixed-integer nonlinear programming to identify the most critical contingency in transmission lines, i.e., the one that maximizes the difference between voltage security margins in the N and N-1 scenarios. To achieve this, binary variables are used to model the on and off states of transmission lines, enabling both the direct calculation of the minimal maximum voltage security margin and the identification of the respective critical contingency. Furthermore, unlike direct methods based on non-differentiable power flow models - which involve equality, inequality, and complementarity constraints to assess voltage security margins - the proposed direct method is based on the smooth power flow model, considering only differentiable equality constraints. The computational implementation of the proposed direct method will be carried out in AMPL, using the nonlinear solver Knitro, and validated through tests on benchmark systems from the IEEE Power Grid Library repository. The expected results aim to confirm the effectiveness of this proposal in the fast, accurate, and, most importantly, robust assessment of voltage security margins in electric power systems.