January 27, 2012, ESB 2001

I define the voltage across an area of a resistive network by suitably combining voltages at nodes (buses) on the border of the area. The new voltage across the area satisfies circuit laws. In applications to power grids, the same concept works to define the voltage angle difference across an area of a DC load flow network and the complex voltage difference across an area of an AC load flow network. I first define the voltage across a cutset of lines, and then derive and explain the voltages across areas, including generalizations to several voltages across an area and multiple areas. The new voltages across areas seem promising for both power system monitoring and network reduction, and I describe their application to monitoring the stress of areas of the power system with synchrophasor measurements.

Ian Dobson was educated at Cambridge and Cornell, and previously worked for the University of Wisconsin-Madison. He is currently Sandbulte professor of Electrical and Computer Engineering at Iowa State University. Ian has worked on avoiding voltage collapse blackouts and various other engineering applications of nonlinear dynamics and chaos. His current interests include avoiding blackouts caused by cascading failure, monitoring the smart transmission grid, and complex systems aspects of reliability and risk analysis.