GPU-Accelerated Sparse Matrices Parallel Inversion Algorithm for Large-Scale Power Systems


State-of-the-art Graphics Processing Unit (GPU) has superior performances on float-pointing calculation and memory bandwidth, and therefore has great potential in many computationally intensive power system applications, one of which is the inversion of large-scale sparse matrix. It is a fundamental component for many power system analyses which requires to solve massive number of forward and backward substitution (F&B) subtasks and seems to be a good GPU-accelerated candidate application. By means of solving multiple F&B subtasks concurrently and a serial of performance tunings in compliance with GPU's architectures, we successfully develop a batch F&B algorithm on GPUs, which not only extracts the intra-level and intra-level parallelisms inside single F&B subtask but also explores a more regular parallelism among massive F&B subtasks, called inter-task parallelism. Case study on a 9241-dimension case shows that the proposed batch F&B solver consumes 2.92 μs per forward substitution (FS) subtask when the batch size is equal to 3072, achieving 65 times speedup relative to KLU library. And on the basis the complete design process of GPU-based inversion algorithm is proposed. By offloading the tremendous computational burden to GPU, the inversion of 9241-dimension case consumes only 97 ms, which can achieve 8.1 times speedup relative to the 12-core CPU inversion solver based on KLU library. The proposed batch F&B solver is practically very promising in many other power system applications requiring solving massive F&B subtasks, such as probabilistic power flow analysis.


Electrical and Computer Engineering

Research Center/Lab(s)

Center for Research in Energy and Environment (CREE)


This study was supported by the National Natural Science Foundation of China (Grant No. 51877038 ) and the Science and Technology Foundation of State Grid Corporation of China : High-Performance Computing Technology for Analysis and Service on Entire Network of STATE GRID Corporation of China (Grant No. DZB17201800023 ).

Keywords and Phrases

Computer graphics; Computer graphics equipment; Electric load flow; Electric power systems; Matrix algebra; Program processors; Accelerated; Inversion; Large scale sparse matrix; Large-scale power systems; Parallelism; Power flows; Power system applications; Probabilistic power flow; Graphics processing unit; Backward substitution; Forward substitution; GPU; Spares matrix

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Article - Journal

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© 2019 Elsevier, All rights reserved.

Publication Date

01 Oct 2019