  We propose an approach based on neural networks and the AC power flow
equations to identify single- and double-line outages in a power grid using the
information from phasor measurement unit sensors (PMUs) placed on only a subset
of the buses. Rather than inferring the outage from the sensor data by
inverting the physical model, our approach uses the AC model to simulate sensor
responses to all outages of interest under multiple demand and seasonal
conditions, and uses the resulting data to train a neural network classifier to
recognize and discriminate between different outage events directly from sensor
data. After training, real-time deployment of the classifier requires just a
few matrix-vector products and simple vector operations. These operations can
be executed much more rapidly than inversion of a model based on AC power flow,
which consists of nonlinear equations and possibly integer / binary variables
representing line outages, as well as the variables representing voltages and
power flows. We are motivated to use neural network by its successful
application to such areas as computer vision and natural language processing.
Neural networks automatically find nonlinear transformations of the raw data
that highlight useful features that make the classification task easier. We
describe a principled way to choose sensor locations and show that accurate
classification of line outages can be achieved from a restricted set of
measurements, even over a wide range of demand profiles.
