Power system Huber M-estimation with equality and inequality constraints

The solution to the power system state estimation problem using the Huber M-estimator has been previously discussed. In earlier methods, the state estimation problem has been formulated as an unconstrained nonlinear program. The power systems literature reports solution to this problem using an iteratively re-weighted least squares technique. In this paper, the Huber M-estimator is formulated as a constrained nonlinear programming problem in which all functions are twice continuously differentiable. Such a formulation entails two advantages. Firstly, it enables accurate modelling of both zero bus injections and realistic system limits via equality and inequality constraints. Secondly, the differentiability property allows the system state to be conveniently computed via a primal-dual interior-point approach. Simulations on standard power systems show that even in the presence of bad data, the equality constraints in the Huber M-estimator effectively model the zero bus injections. Moreover, the numerical results reveal that the enforcement of practical system limits via inequality constraints can be useful in the absence of complete system observability.