Thévenin equivalents are used by a range of power system stability indicators, such as the L-index for voltage stability and the aperiodic small signal rotor angle stability indicator. This paper investigates the effect of using different factorization methods for computing coefficients for wide-area Thévenin equivalents. Direct and incomplete factorization methods are compared with respect to runtime, accuracy and amount of fill-in. The paper introduces a proof that the block triangular form of bus admittance matrices will have no non-zero entries in the off-diagonal. KLU factorization is found to perform almost twice as fast as the standard LU factorization with no cost of accuracy. It is, however, shown that the largest computational workload is associated with dense matrix multiplications. An incomplete method reduces the fill-in of coefficient matrices at the cost of accuracy in Thévenin voltages. It is shown, that inaccuracies are amplified as the L-index approaches the stability limit.

This paper identifies weakness of existing method for voltage stability assessment and proposes new approach for determining point of maximum deliverable power to a given load that accounts for the variations in the Thevenin voltage magnitude. The approach uses Thevenin equivalents seen from nodes of constant voltage magnitude and load nodes in order to determine a distance to instability. A simple five-bus system together with IEEE 14 bus system were used in order to perform dynamic simulation in PSS/E. The simulation data were used to create synthetic Phasor Measurement Unit (PMU) snapshots, which served as input to the proposed approach. The new approach is demonstrated on the two test systems, where improved accuracy in determining the point of maximum deliverable power is demonstrated. The results show that the point of maximum deliverable power to the load occurs well before the Thevenin impedance matching criteria.

In this paper, wind speed models are used to consider its variability in real-time voltage stability assessment using Thévenin equivalent methods. A stochastic differential equation was used to produce a set of wind speeds required for the simulation scenarios together with a very short-term forecast based on a probabilistic method, which provides the means for including anticipation in the stability assessment. This is achieved by representing the variation in the wind as an uncertainty in the Thévenin equivalent parameters, which are used for wide-area assessment, and studying corresponding changes in the stability boundary for a specific time horizon. The methodology was tested with time domain simulation a cigré benchmark system for network integrations of renewables, where the approach successfully represented the final Thévenin Equivalent parameters with a maximum error of 2.5% of the estimated variables, for a time horizon of 1 minute in the used forecast.

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