Parameterized potential functions for equality constraints

Abstract

Prior methods of state estimation, based on a constrained optimization problem with equality and/or inequality constraints, rely on penalty-based heuristics which can produce very large weight values, resulting in ill-conditioning of the gain matrix. Disclosed embodiments of state estimation convert the constrained optimization problem into an unconstrained convex optimization problem in which violated equality and/or inequality constraints are represented as parameterized potential functions, each comprising a center-of-attraction parameter. This unconstrained convex optimization problem can be iteratively formed, using successively updated values for the center-of-attraction parameters, and solved, until no equality and/or inequality constraints are violated, to produce a final estimated state. This final estimated state may then be used to control the system being monitored, such as a power system.