  The integration of renewables into electrical grids calls for
optimization-based control schemes requiring reliable grid models. Classically,
parameter estimation and optimization-based control is often decoupled, which
leads to high system operation cost in the estimation procedure. The present
work proposes a method for simultaneously minimizing grid operation cost and
optimally estimating line parameters based on methods for the optimal design of
experiments. This method leads to a substantial reduction in cost for optimal
estimation and in higher accuracy in the parameters compared with standard
Optimal Power Flow and maximum-likelihood estimation. We illustrate the
performance of the proposed method on a benchmark system.
