Monitoring voltage collapse margin by measuring the area voltage across several transmission lines with synchrophasors

We consider the fast monitoring of voltage collapse margin using synchrophasor measurements at both ends of transmission lines that transfer power from two generators to two loads. This shows a way to extend the monitoring of a radial transmission line to multiple transmission lines. The synchrophasor voltages are combined into a single complex voltage difference across an area containing the transmission lines that can be monitored in the same way as a single transmission line. We identify ideal conditions under which this reduction to the single line case perfectly preserves the margin to voltage collapse, and give an example that shows that the error under practical non-ideal conditions is reasonably small.