A dynamic interpretation of the load-flow Jacobian singularity for voltage stability analysis

In voltage stability analysis, both static and dynamic approaches are used to evaluate the system critical conditions. The static approach is based on the standard load-flow equations. For small-disturbance analysis, the dynamic approach is based on the eigenvalue computation of the linearized system, while for large-disturbance analysis a complete time-domain simulation is required. However, both the equilibrium point around which linearization is performed and the initial conditions for the simulation are computed by a procedure which uses the standard load-flow equations. The standard load-flow equations make some implicit assumptions on the steady-state behaviour of dynamic components (generator control systems, loads). These assumptions are not satisfied by the usual dynamic models, and this discrepancy leads to different results in the voltage stability assessment using static and dynamic methods. In the framework of bifurcation theory, this paper discusses the relationships between static and small-disturbance dynamic approaches to find the voltage stability critical condition, with emphasis on system component modelling. A set of hypotheses on generator control systems and load models is given for a multimachine system, according to which the same critical conditions are obtained both from the load-flow equations and from the full eigenvalue analysis. These hypotheses are less restrictive than those previously proposed in the literature and make it possible to obtain equivalence between the singularity of the load-flow Jacobian and a null eigenvalue of the linearized dynamic system. Following a dynamic argumentation based on small-disturbance analysis, this result may justify the use of simple and fast static methods for voltage stability assessment and shows that the small-disturbance voltage stability limit depends only on the steady-state characteristics of the dynamic components of the system.