Structure- and Physics-Preserving Reductions of Power Grid Models

Abstract

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 powerflow 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. The third feature allows for easy re-introduction of detailed models into the reduced, conceptual network, and makes the final reduced order model backward compatible with a sequence intermediate, partially reduced networks with varying resolution -the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms, and features of the reduced grids, are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data. Alamos, NM 87545 (backhaus@lanl.gov). arXiv:1707.03672v3 [cs.SY] 4 Oct 2018 the grid and also made issues regarding grid stability and control of paramount importance [3,43,17]. Dynamic forcing from the distribution grid has historically been much smaller than the transmission components. For example, the amount of inertia and damping in the distribution grid are limited [22]. However, rooftop solar, the internet of things [28], and other resources have cultivated the demand for decentralized resource generation and control in the distribution sub-grid [18,34,16,46,12]. With this demand comes the need for multiscale, dynamical models of the grid.Owing to the large size and dense interconnections, the control, optimization and dynamical simulation of detailed grids faces implementation issues [5,4]. Operational demands requi...

Supermodal Decomposition of the Linear Swing Equation for Multilayer Networks

“…where S is a 2m-dimensional real orthogonal matrix, and V p,∞ is the matrix of eigenvectors in the null space of A 2 (analogous to the case of M and V x,∞ ). If the system, (18), is written in the symmetric state space realization,…”

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