Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis
Abstract
The repeated assembly of the sparse Jacobian matrix constitutes a primary computational bottleneck in the Newton-Raphson power-flow analysis. Through an algebraic equivariance analysis of the Jacobian matrix, this paper proposes a direct sparse Jacobian assembly method based on symbolic permutation. By pre-applying the permutation to the admittance matrix during a one-time symbolic phase, the runtime bus-type projection overhead is entirely eliminated. Consequently, complex Jacobian differentiation and global matrix assembly fuse into a single operation, yielding a single-pass, branchless algorithm that streams values directly into contiguous memory. The framework is realized in the open-source RustPower solver. Benchmarks on IEEE test systems and PEGASE 9241 demonstrate that the proposed assembly is 24.4-30.1x faster than the MATPOWER- style baseline and 6.0-7.8x faster than the Schafer-Braun optimized assembly. End-to-end, the grid-level solve time is 11.7x-154.3x faster than pandapower 3.5.4 with Numba, while leaving numerical results and convergence behavior unchanged. Compared with the native C++ LightSim2Grid 1.0.0, grid-level performance is comparable on IEEE 39 and 1.3x-1.8x faster on IEEE 118 and the PEGASE systems. The method extends directly to general problems where a sparse Jacobian inherits its structure from a static network operator, including transient stability analysis, EMT simulation, and OPF Hessian assembly.
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BibTeX
@misc{cheng2026symbolicpermutationbased,
title = {{Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis}},
author = {Tianshi Cheng and Venkata Dinavahi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12654},
eprint = {2610.12654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12654},
}
RIS
TY - UNPB
TI - Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis
AU - Tianshi Cheng
AU - Venkata Dinavahi
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12654
UR - https://arxiv.org/abs/2610.12654
AB - The repeated assembly of the sparse Jacobian matrix constitutes a primary computational bottleneck in the Newton-Raphson power-flow analysis. Through an algebraic equivariance analysis of the Jacobian matrix, this paper proposes a direct sparse Jacobian assembly method based on symbolic permutation. By pre-applying the permutation to the admittance matrix during a one-time symbolic phase, the runtime bus-type projection overhead is entirely eliminated. Consequently, complex Jacobian differentiation and global matrix assembly fuse into a single operation, yielding a single-pass, branchless algorithm that streams values directly into contiguous memory. The framework is realized in the open-source RustPower solver. Benchmarks on IEEE test systems and PEGASE 9241 demonstrate that the proposed assembly is 24.4-30.1x faster than the MATPOWER- style baseline and 6.0-7.8x faster than the Schafer-Braun optimized assembly. End-to-end, the grid-level solve time is 11.7x-154.3x faster than pandapower 3.5.4 with Numba, while leaving numerical results and convergence behavior unchanged. Compared with the native C++ LightSim2Grid 1.0.0, grid-level performance is comparable on IEEE 39 and 1.3x-1.8x faster on IEEE 118 and the PEGASE systems. The method extends directly to general problems where a sparse Jacobian inherits its structure from a static network operator, including transient stability analysis, EMT simulation, and OPF Hessian assembly.
ER -