An Efficient GPU-Based Halpern Accelerating Algorithm for Large-Scale DC Optimal Power Flow

doi:10.1109/TPWRS.2025.3635652

An Efficient GPU-Based Halpern Accelerating Algorithm for Large-Scale DC Optimal Power Flow

2025-11-21

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DOI：10.1109/TPWRS.2025.3635652

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With numerous renewable generators and energy storage systems integrated into the power grids, the security-constrained DC optimal power flow (DCOPF) is essential for power system operation. For large-scale power grids, traditional CPU-based optimization algorithms (such as the simplex and barrier methods) have saturated in computational efficiency and are inherently difficult to parallelize. To tackle these issues, by incorporating the symmetric Gauss–Seidel (sGS) decomposition, this work develops a GPU-based Halpern Peaceman-Rachford algorithm, termed the sGS-HPR, which enjoys an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(1/k)$</tex-math></inline-formula> iteration complexity in terms of the KKT residual. Moreover, the closed-form solutions for all subproblems are derived, which only consist of matrix-vector multiplications and vector operations, and thus can be easily parallelized on GPUs. As a consequence, the developed sGS-HPR algorithm enjoys a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O({N_{L} \times n} / \epsilon)$</tex-math></inline-formula> non-ergodic computational complexity in terms of floating-point operations for obtaining an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula>-optimal solution measured by the KKT residual for large-scale DCOPF problems, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> represents the variable dimension, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{L}$</tex-math></inline-formula> denotes the number of branches in the power grid. Extensive numerical tests on large-scale power grids, reaching up to the 9241-bus PEGASE system, demonstrate the scalability and superior efficiency of the developed GPU-based sGS-HPR algorithm compared to state-of-the-art methods. Notably, the proposed method achieves a 6× speedup compared with Gurobi for large-scale instances. Additionally, for ultra-large-scale cases, Gurobi throws an “out-of-memory” error, while the proposed sGS-HPR algorithm maintains its computational scalability and efficiency.

Keywords:

GPU acceleration

DC optimal power flow

Halpern iteration

Peaceman-Rachford splitting

symmetric Gauss–Seidel decomposition

convergence rate

computational complexity

An Efficient GPU-Based Halpern Accelerating Algorithm for Large-Scale DC Optimal Power Flow

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