# Bug traps in electric power networks.

Monitoring the well-being of their extensive electric power networks presents utilities with a formidable task. Using a limited number of power-level measurements at various points scattered throughout a network, power engineers at a central control facility must have access to sufficient data to pinpoint problems and reach appropriately.

But these elaborate networks, stretching from generating stations to distribution centers, substations and individual factories, businesses and homes, are often so large that engineers sometimes have trouble quickly locating faults, such as overloads or interruptions of electrical current in certain branches. Minor but frequent in the links between various parts of the network exacerbate the problem.

Mathematician Paul W. Davis and electrical engineer kevin A. Clements of the Worcester (Mass.) Polytechnic Institute have now developed a mathematical tool, based on linear algebra, that allows power engineers to readily identify vulnerable links in their networks and blind spots in their monitoring programs. The researchers look at a set of equations representing the relationship between measured power levels and calculated voltages at various points in an electric power network. Expressed in the form of a grid of numbers, or matrix, these equations also include information on the network's connections. The idea is to use these equations, or equivalent matrix, to identify problems in the network.

Davis and Clements established a mathematical theorem involving these matrices, which enables them to propose a convenient method of identifying situations in which a failure in a certain branch or group of branches may not show up in a given set of power measurements, thereby making the fault undetectable at the control center. "We could immediately pinpoint vulnerable branches," Davis says.

Moreover, careful examination of the network geometry leads to useful ideas as to where within a given network to measure power levels to detect certain types of problems, Davis contends. It suggests how a utility could alter its measurement pattern -- perhaps simply by shifting the locations of a few measuring devices -- to detect more problems in more branches.

"This work is ready for implementation by power engineers," he adds. "What we've got to do now is run some test cases."