New angles for monitoring areas

We define the voltage angle across an area of a power system to measure the area stress. The voltage angle across the area is a weighted combination of the voltage angles at all the buses along the border of an area. The area angle can be divided into two parts; one part is internal stress caused by power injections inside the area and the other part is external stress caused by power flows from other areas. The area angle can be monitored using voltage synchrophasor measurements at the border buses. If the currents or powers owing into the area at the border buses are also measured, then the internal stress angle can also be monitored. The internal stress angle changes when lines inside the area outage or when there is redispatch of power within the area. The internal stress angle does not change when lines outage outside the area or power is redispatched outside the area. This makes the internal stress angle useful for detecting and monitoring changes inside the area. If it is known which line inside the area is outaged, the angle across the line after the outage can be computed from the change in the internal stress angle. The analysis uses a DC load flow model of the power system and exploits the recently discovered cutset angle.