Deterministic random walk preconditioning for power grid analysis

Wang, Jia

doi:10.1145/2429384.2429467

Cited by 9 publications

(4 citation statements)

References 48 publications

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“…On the other hand, iterative solvers, which mainly depend on simple operations such as matrixvector multiplication and inner product of vectors, are more amicable for parallelization, especially on GPU platforms. There are some newly published papers, such as [14,10,37,40,39], which confirm the practicality and effectiveness of iterative solvers in solving large linear dynamic networks like power grid networks.…”

Section: Introductionmentioning

confidence: 81%

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Tan

Zhao

et al. 2016

Integration

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a b s t r a c tIn this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large linear dynamic systems such as large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU-GPU platforms. The new solver is very robust and can be applied to power grids with different structures as well as for general analysis problems for large linear dynamic systems with asymmetric matrices. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and convergence rate can be achieved for the best overall performance. Such tunable feature can make this algorithm very adaptive to different problems. GPU-GMRES solver properly partitions the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPUs to enhance performance of the proposed method. Furthermore, we propose a new fast parallel sparse matrix-vector (SpMV) multiplication algorithm to further accelerate the GPU-GMRES solver. The new algorithm, called segSpMV, can enjoy full coalesced memory access compared to existing approaches. To further improve the scalability and efficiency, segSpMV method is further extended to multi-GPU platforms, which leads to more scalable and faster multi-GPU GMRES solver. Experimental results on the set of the published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver, UMFPACK. The resulting multi-GPU-GMRES can also deliver 3-12 Â speedup over the CPU implementation of the same GMRES method on transient analysis.

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Section: Introductionmentioning

confidence: 81%

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Tan

Zhao

et al. 2016

Integration

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“…Wang provides a deterministic random walk based pre-processing and graph reduction algorithm also aimed at solving the DC power-flow problem [44]; Chen & Chen present Krylov-subspace iterative methods for preconditioning [7].…”

Section: Contributionmentioning

confidence: 99%

Structure- and Physics-Preserving Reductions of Power Grid Models

Grudzien¹,

Deka²,

Chertkov³

et al. 2018

Multiscale Model. Simul.

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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...

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“…Markov metrics have proved to be a powerful tool for analyzing and solving a variety of problems [1,2,3,4]. Hitting time, for instance, as the most well-known Markov metric has been exploited vastly in different network analysis applications.…”

Section: Introductionmentioning

confidence: 99%

Avoidance Markov Metrics and Node Pivotality Ranking

Golnari¹,

Boley²

2018

Preprint

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We introduce the avoidance Markov metrics and theories which provide more flexibility in the design of random walk and impose new conditions on the walk to avoid (or transit) a specific node (or a set of nodes) before the stopping criteria. These theories help with applications that cannot be modeled by classical Markov chains and require more flexibility and intricacy in their modeling. Specifically, we use them for the pivotality ranking of the nodes in a network reachabilities. More often than not, it is not sufficient simply to know whether a source node s can reach a target node t in the network and additional information associated with reachability, such as how long or how many possible ways node s may take to reach node t, is required. In this paper, we analyze the pivotality of the nodes which capture how pivotal a role that a node k or a subset of nodes S may play in the reachability from node s to node t in a given network. Through some synthetic and real-world network examples, we show that these metrics build a powerful ranking tool for the nodes based on their pivotality in the reachability.

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Deterministic random walk preconditioning for power grid analysis

Cited by 9 publications

References 48 publications

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

Structure- and Physics-Preserving Reductions of Power Grid Models

Avoidance Markov Metrics and Node Pivotality Ranking

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