  Linearized models of power systems are often desirable to formulate tractable
control and optimization problems that still reflect real-world physics
adequately under various operating conditions. In this paper, we propose an
approach that can make use of known data concerning the distribution of demand,
and/or intermittent supply, to minimize expected model inconsistency with
respect to the original non-linear model. The optimal linearization is obtained
by approximating a generalized moment problem with a hierarchy of sparse
semi-definite relaxations. The output is a linearization point that minimizes
the expected absolute constraint violation with respect to the uncertain supply
and demand. Numerical results for different power systems networks demonstrate
the accuracy and scalability of our linearization method.
