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This paper presents a fundamental study of voltage collapses that occur on a post-fault trajectory of a stressed power system in seconds after large disturbances. The focus of the study are voltage collapses that are induced by certain load models. Using an n-machine-N-bus power system model, the paper explicitly shows that the voltage collapse is caused by the non-existence of a real, positive solution for a load voltage magnitude in different areas of a relative rotor angle space when the load is of non-linear type. These “areas without voltage solution” are denoted as Voltage Impasse Regions (VIR) and are mathematically characterized as trigonometric functions of (n -1) relative rotor angles. Once the post-fault trajectory enters a VIR, voltage magnitude solutions become complex or negative, the algebraic Jacobian becomes singular, and the behaviour of a system becomes undefined. The case study has been carried out using a simple 3-machine-1-load system with static load models. In the study, VIR appeared and enlarged as the non-linear (constant power and constant current) load increased. Furthermore, the non-convergence of time-domain solution occurred exactly at VIR, thereby confirming that the problem is of structural nature. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient methodology to assess rotor angle stability (RAS) in parameter space has been proposed. This methodology maps deformations of the power system RAS region under operational changes to a security region in parameter space that can be assessed online. In order to choose the proper parametrization, security boundaries have been constructed using polynomial regression models with coefficients obtained from ordinary least squares. The identification of suitable parametrization has been carried out, and the newly introduced sensitivity of a single machine equivalent (SIME) has been employed to describe the behavior of a power system along different parameter-space directions. For the chosen parametrization, constrained least squares optimization set up as a quadratic programming problem has been used in order to keep the estimates inside the security region. The case study has been carried out using small test systems in two- and three-dimensional parameter-spaces. [ABSTRACT FROM AUTHOR]