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

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 O(1/k) 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 O(N-L & times; n/is an element of) non-ergodic computational complexity in terms of floating-point operations for obtaining an is an element of-optimal solution measured by the KKT residual for large-scale DCOPF problems, where n represents the variable dimension, and N-L 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 & times; speedup compared with Gurobi for largescale 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.