Sensitivity Based Thevenin Index With Systematic Inclusion of Reactive Power Limits

This paper presents proof for the relation between the Local Thevenin Index (LTI), measured at a Phasor Measurement Unit (PMU), that is used as an indicator of voltage stability, and the system operating condition. The derivation establishes that there is a direct connection between the sensitivity and the LTI and provides a mathematically rigorous justification to use LTI as a static long-term voltage stability indicator of the entire system. A Sensitivity based Thevenin Index, calculated using wide area measurements, is proposed and it can be used at the control center to authenticate the LTI being received from PMUs, to safeguard against malicious and spurious data. The association between the sensitivity and the LTI can also be used to predict the effect of various what-if scenarios on the LTI. As a demonstration, the impact of generator limits on the LTI is predicted, enabling the operator to anticipate the abrupt change in LTI before the limits are reached. Results are described in detail for a 5-bus system, and verified on larger systems up to 300 buses, establishing the connection between the LTI and the sensitivities, and validating the prediction of impact of the generator reactive limits on the LTI.