Voltage Stability Analysis in HVDC Systems Using Jacobian Singularity and Saddle-Node Bifurcations

This paper introduces a methodology for evaluating the voltage stability margin in high-voltage direct-current (HVDC) systems, which analyzes the singularity of the power flow Jacobian matrix—computed via the Newton—Raphson method—and identifies saddle-node bifurcations. The continuation power flow method is employed to model progressive load increases, enabling the continuous tracking of power flow solutions and the determination of voltage collapse points. Within this framework, the system’s behavior is analyzed under contingency conditions, particularly transmission line outages, assessing its capability to maintain secure operating conditions under increasing demand scenarios. The main objective is to identify the most critical line in the system, defined as that which leads to the greatest reduction in loadability when unavailable, prior to voltage collapse. This approach allows for the early identification of structural vulnerabilities, supporting decision-making processes aimed at risk mitigation and operating cost optimization. The proposed methodology is validated using two systems: the six-terminal CIGRE-B4 HVDC system and an 11-node HVDC test feeder.