Static Security Analysis Based On GPU Acceleration Of Linear Equations Iterative Method

In recent years, with the rapid development of modern industrial and economic growth, the development of power system presents new features. Growing scale of interconnected network has made the power system the largest human engineering. In such a case, more and more uncertainties of power system and the potential effects of the accident risks have been large threat to the safe operation of the power system. Therefore, a new static security analysis with high calculation speed is worth considering. In the static security analysis calculation, solving linear equations is accounted for 70% of the whole calculation time. Acceleration of solving linear equations will be able to greatly improve the computational efficiency of static security analysis. Utilizing parallel computing for acceleration is the current research trends, and a graphics processing unit (Graphic Processing Unit, GPU) has the advantages of floating-point calculation speed and memory access bandwidth. Combined with the power flow calculation, this paper take GPU accelerated platform for parallel iterative solving of linear equations.In this paper, preconditioning Conjugate Gradient method is used to solve the correction equation in fast decoupled load flow calculation. The incomplete LU decomposition is selected as preconditioner of conjugate gradient method, which has the best preconditioning effect among multiple preconditioners. ILUCG algorithm is implemented on GPU with cuSparse libraries and cuBlas library. In Polish2383 grid system and the extension cases from Polish2383, the parallel algorithm have made up to 2.5 times speedup compared with ILUCG algorithm on CPU.In order to make full use of GPU computing resources, this paper presents a parallel batch computing method based on GPU, and applies it to LUCG algorithm. Combined with the matrix similarity of branch breaking accident, the LU decomposition of coefficient matrix in ground state grid is seleted as preconditioner of iterative method. The batch triangular equation algorithm, batch SPMV algorithm and batch vector dot product algorithm of multiple correction equations on GPU obtain significant speedup compared with the serial algorithm on CPU respectively. In the batch method using LUCG parallel equation solver, case300, case2383wp and case9241pegase are selected for analysis of examples. With respect to the serial linear equation solver on CPU, the maximum speedup of batch LUCG parallel equation solver is respectively 248,103 and 151 times.This paper analyzes the characteristics of static security analysis after breaking fault, and according to their characteristics, a batch parallel algorithm of fast decoupled load flow calculation is developed. Case9241pegase is seleted for static security analysis, and when the number of branch break accident reaches 512, with respect to static security analysis algorithm provided by matpower on CPU, batch static security analysis algorithm on GPU gains more than 77 times speedup. The results demonstrate the effectiveness and practicality of the algorithm.