ETBR: Extended Truncated Balanced Realization Method for On-Chip Power Grid Network Analysis

Abstract

In this paper, we present a novel simulation approach for power grid network analysis. The new approach, called ETBR for extended truncated balanced realization, is based on model order reduction techniques to reduce the circuit matrices before the simulation. Different from the (improved) extended Krylov subspace methods EKS/IEKS [15,2], ETBR performs fast truncated balanced realization on response Grammian to reduce the original system with the similar computation costs of EKS. ETBR also avoids the adverse explicit moment representation of the input signals. Instead, it uses spectrum representation of input signals by fast Fourier transformation. As a result, ETBR is more flexible for different types of input sources and can better capture the high frequency contents than EKS, and this leads to more accurate results especially for fast changing input signals. Experimental results on a number of large networks (up to one million nodes) show that, given the same order of the reduced model, ETBR is indeed more accurate than the EKS method especially for input sources rich in high-frequency components. ETBR also shows similar computation costs of EKS and less memory consumption than EKS.

Transient analysis of large linear dynamic networks on hybrid GPU-multicore platforms

“…To retrieve the original waveforms, a left multiplication of the basis matrix V on the reduced circuit statex(t) is required, i.e., x(t) = Vx(t). The stability and passivity properties of ETBR can be promised if proper operations are applied during the reduction [5].…”

“…In this project, we use ETBR method [5], because it is more amenable for parallel computing as each frequency domain response can be computed independently. Algorithm 1 summarizes the flow of ETBR, which reduces the original system in Eq.…”

“…Various algorithms have been proposed to improve scalability in computing time and to reduce memory footprints [2], [3], [4], [5]. But most of those techniques are based on the homogeneous single-core architectures.…”

Scalable power grid transient analysis via MOR-assisted time-domain simulations

“…In practice, frequency domain [22], [8], model order reduction (MOR) [15], [10], [11], and matrix exponential [16] methods have been studied as alternatives to time domain simulations for power grid transient analysis and show promises of scalability as they do not depend on the time steps explicitly. However, these methods are still quite costly if similar accuracy as time domain simulations is desired due to the difficulty in handling current excitations.…”

Deterministic random walk preconditioning for power grid analysis

“…The efforts of the first group lead to efficient algorithms that can obtain approximated solutions by exploiting structures of the power grid, e.g. hierarchical analysis [34], multigrid [24,16,30,38,39,7], random walks [26,19], Poisson solver [28], frequency domain methods [35,13], and model order reduction techniques [31,17,18]. The second group [2,37,27,8,33,32,4,36], which attracts a lot of interests recently due to the demand to accurately characterize the static and dynamic behaviors of power grids [20,21], utilize iterative solvers, especially preconditioned conjugate gradient (PCG), to further improve the solution accuracy.…”