  For fast timescales or long prediction horizons, the AC optimal power flow
(OPF) problem becomes a computational challenge for large-scale, realistic AC
networks. To overcome this challenge, this paper presents a novel network
reduction methodology that leverages an efficient mixed-integer linear
programming (MILP) formulation of a Kron-based reduction that is optimal in the
sense that it balances the degree of the reduction with resulting modeling
errors in the reduced network. The method takes as inputs the full AC network
and a pre-computed library of AC load flow data and uses the graph Laplacian to
constraint nodal reductions to only be feasible for neighbors of non-reduced
nodes. This results in a highly effective MILP formulation which is embedded
within an iterative scheme to successively improve the Kron-based network
reduction until convergence. The resulting optimal network reduction is, thus,
grounded in the physics of the full network. The accuracy of the network
reduction methodology is then explored for a 100+ node medium-voltage radial
distribution feeder example across a wide range of operating conditions. It is
finally shown that a network reduction of 25-85% can be achieved within seconds
and with worst-case voltage magnitude deviation errors within any super node
cluster of less than 0.01pu. These results illustrate that the proposed
optimization-based approach to Kron reduction of networks is viable for larger
networks and suitable for use within various power system applications.
