Angle stability predictive indices

The variance of phase angle differences over the grid is a good indicator of overall stress and angle stability. The integral square generator angle (ISGA) difference had previously been proposed to judge the severity of stable and unstable transient events in simulation. This paper proposes its extension to bus voltage angles (ISBA) which could be measured over a wide area using synchronized phasor measurement units (PMUs). The discontinuity of bus angles at plus and minus 180 degrees is handled by reconstructing continuous trajectories that go outside the range between plus and minus 180 degrees before calculating the index. The paper also addresses the issue of finding the best threshold for an angle stability index using simulation data. This task is complicated by the fact that large databases are somewhat likely to contain a few events that experience loss of synchronism around the end of the simulation window.