Reparametrization of Power Systems Models Using Manifold Boundaries

We describe a geometric approach to the question of parameter identifiability in models of power systems dynamics: whether parameters can be estimated from available measurements. When a model of a system is to be compared with measurements taken at discrete times, it can be interpreted as a mapping from parameter space into a data or prediction space. Generically, model mappings can be interpreted as manifolds with dimensionality equal to the number of structurally identifiable parameters. Empirically it is observed that model mappings often correspond to bounded manifolds. We review the concept of structural identifiability and propose a definition of practical identifiability based on the topological definition of a manifold with boundary. We numerically construct geodesics on the model manifold and use the results, combined with insights derived from the mathematical form of the equations, to identify combinations of practically identifiable and unidentifiable parameters with which to reparametrize the model. We give several examples of applications to dynamic power systems models.