非精确牛顿法与基于GPU加速的迭代线性求解法在电力系统计算中的应用研究

With the enlargement of modern power grid and the extensive integration of high-penetration renewable energy, the scale and complexity of power flow computations are increased significantly accordingly. The power flow computation based on traditional LU decomposition can hardly satisfy those aforementioned computational needs because of its lack of scalability and parallel potentials. In order to solve such issues, this project will discuss following topics. A two-level iterative architecture is used to perform power flow computations. The inner iterative model is to solve the Jacobian equations with iterative linear solvers, which are scalable and parallel friendly for large-scale linear systems. Additionally, these linear solvers will be accelerated by GPU (Graphic Processing Unit) for the parallel implementation. Preconditioners will be integrated to the inner level as well, aiming at improving the convergence rate of the corresponding linear solvers. The outer level is incorporated with inexact Newton method to reduce the number of iterations of the inner iterative solvers, which ultimately improves the holistic efficiency of the linear solution yet no influence to the accuracy of the power flow. This project will discuss the extension of such two-level iterative model to the solution of many other non-linear equations in power system analysis, and further generalize it to other realms, thus provide theoretic basis and practical experiences for the acceleration of solving non-linear equations from different fields of study.

随区域电网互联规模的扩大与高渗透率可再生能源大幅并网，电力系统潮流计算规模和复杂度急剧上升。传统基于LU分解的潮流计算方法因伸缩性和并行性的缺陷，已难满足这样的计算需求。针对此问题，本项目拟在如下领域取得突破：构建电力系统潮流求解的双层迭代模型，在内层迭代模型中采用迭代求解法求解修正方程组，满足大规模潮流修正方程组求解的可伸缩性和并行性需求；设计基于GPU加速的迭代线性求解法，实现修正方程组求解并行化，提高其求解效率；并在内层模型中引入预处理器以提高内层迭代算法的收敛速度。在外层迭代模型中，引入非精确牛顿法求解电力系统的潮流方程，在不影响最终潮流解精度的条件下，减少内循环迭代次数，以提升整个潮流方程的求解效率。本项目也将讨论将此双层迭代求解模型推广至电力系统分析中大量其他非线性方程组的求解，并进一步扩展至其他学科方向，为多领域的基本非线性求解问题的并行加速提供理论基础和实践经验。

随区域电网互联规模的扩大与高渗透率可再生能源大幅并网，电力系统潮流计算规模和复杂度急剧上升，急需对潮流计算的新方法进行探索，提高潮流计算效率。本项目的主要研究内容和完成情况如下。1）基于GPU的迭代线性求解法的研究方面，根据潮流计算、PQ解耦潮流计算中雅可比矩阵的性质，分别采用双共轭梯度稳定法和共轭梯度法基于GPU进行求解。2）基于非精确牛顿法和迭代线性求解法的潮流计算性能研究和改善上，结合迭代线性求解法的性质，引入多种二阶预处理方法，结合非精确牛顿法对潮流计算效率进行提高。3）基于非精确牛顿法和迭代线性求解法对通用非线性方程求解的推广方面，上述运算架构以及运算方法已成功应用到电力系统负荷裕度的计算当中，有效提高了负荷裕度的计算效率。本项目在执行过程中获得的重要结果如下。经预处理的迭代求解法和非精确牛顿法相结合的方法及其GPU并行化实现有效改善了PQ解耦潮流、常规潮流的计算效率，在满足相应的计算精度和收敛性的条件下，可完成超大规模系统的计算，加速比分别最高可达2.86倍和7.11倍。上述运算架构结合负荷裕度的直接求解法可推广至电力系统负荷裕度的求解，不但改善了负荷裕度求解的收敛情况，亦大幅提高了大规模至超大规模系统负荷裕度的计算效率，加速比最高可达42.8倍。本项目积极探索了大规模及超大规模系统潮流计算的效率改善问题，针对潮流计算中雅可比矩阵的特点，研究了多种迭代线性求解法及其所对应的预处理方法，并完成了基于GPU的并行实现，该方法亦已推广至电力系统负荷裕度的计算。本项目为超大规模复杂潮流及其他大规模非线性方程的快速求解及并行实现提供了理论支撑与实践经验。