Calculating the long term voltage stability margin using a linear index

Monitoring the long term voltage stability of the power grid is necessary to ensure its secure operation. In this paper, a voltage stability index that is linear with the power demand, called the M-index, based only on angles is proposed. The linearity of the M-index can be utilized to estimate the load margin directly. The linearity of the M-index is proved for the two-bus system and a method to apply this to a multi-nodal system by using the multi-port equivalent is described. The M-index can estimate voltage stability margin and identify weak buses in a system based on the SCADA and PMU data at the EMS. The M-index is tested on the IEEE-30 Bus system using the multi-port equivalent methodology under several scenarios - different load increase direction & a line outage. The results demonstrate that the M-index is indeed linear with the load increase for all these cases and successfully estimated the load margin.