  The large size of multiscale, distribution and transmission, power grids
hinder fast system-wide estimation and real-time control and optimization of
operations. This paper studies graph reduction methods of power grids that are
favorable for fast simulations and follow-up applications. While the classical
Kron reduction has been successful in reduced order modeling of power grids
with traditional, hierarchical design, the selection of reference nodes for the
reduced model in a multiscale, distribution and transmission, network becomes
ambiguous. In this work we extend the use of the iterative Kron reduction by
utilizing the electric grid's graph topology for the selection of reference
nodes, consistent with the design features of multiscale networks.
Additionally, we propose further reductions by aggregation of coherent
subnetworks of triangular meshes, based on the graph topology and network
characteristics, in order to preserve currents and build another power-flow
equivalent network.
  Our reductions are achieved through the use of iterative aggregation of
sub-graphs that include general tree structures, lines, and triangles.
Important features of our reduction algorithms include that: (i) the reductions
are, either, equivalent to the Kron reduction, or otherwise produce a
power-flow equivalent network; (ii) due to the former mentioned power-flow
equivalence, the reduced network can model the dynamic of the swing equations
for a lossless, inductive, steady state network; (iii) the algorithms
efficiently utilize hash-tables to store the sequential reduction steps.
