Implementing nonquadratic objective functions for state estimation and bad data rejection

Using a nonquadratic objective function for network state estimation can combine several estimation and bad data rejection techniques into one algorithm: e.g. the benefits of maximum likelihood least squares estimation can be coupled with the bad data rejection properties of least absolute value estimation. For such estimators, we describe an efficient implementation, one that builds naturally on existing least squares software, that is based on an iterative Gauss-Newton solution of the KKT optimality conditions. We illustrate the behavior of a quadratic-linear and a quadratic-constant objective function on a set of test networks. The former is closely related to the Huber M-estimator. The latter shows somewhat better bad data rejection properties, perhaps because it arises from a natural model of meter failure.