Graphical Processing Unit Based Time-Parallel Numerical Method for Ordinary Differential Equations
Graphical Processing Unit Based Time-Parallel Numerical Method for Ordinary Differential Equations
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DOI：
10.4236/jcc.2020.82004
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Sumathi Lakshmiranganatha;S. Muknahallipatna
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文献类型：
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作者：
Sumathi Lakshmiranganatha;S. Muknahallipatna
电网的在线暂态稳定性分析对于确定电网在扰动后是否能运行到稳态稳定工作点至关重要。暂态稳定分析涉及到近实时地计算模拟电网的代数方程和模拟电网中同步发电机、励磁器、调速器等电气元件动力学的常微分方程的解。在本研究中，我们研究了时间并行方法的使用，特别是使用计算统一设备架构在图形处理单元上实现的平行算法来计算常微分方程的解。在单机无限总线测试系统上验证了并行算法在GPU上的数值解精度和计算时间。研究了单台同步发电机的两种动态模型：经典模型和详细模型。将该算法与修正欧拉法的数值解进行了比较，证明了该算法在GPU上执行的准确性。用不同的数值积分时间步长进行了仿真，证明了拟面算法在计算普通不同方程近实时解中的适用性。与序列修正欧拉法相比，采用平行面算法对同步发电机的经典动态模型和详细动态模型分别提高了25倍和31倍的速度。讨论了在每个时间步需要求解大量常微分方程时，由于顺序计算的增加以及CPU和GPU之间相关的内存传输延迟，并行算法的缩放效率较弱的问题。
On-line transient stability analysis of a power grid is crucial in determining whether the power grid will traverse to a steady state stable operating point after a disturbance. The transient stability analysis involves computing the solutions of the algebraic equations modeling the grid network and the ordinary differential equations modeling the dynamics of the electrical components like synchronous generators, exciters, governors, etc., of the grid in near real-time. In this research, we investigate the use of time-parallel approach in particular the Parareal algorithm implementation on Graphical Processing Unit using Compute Unified Device Architecture to compute solutions of ordinary differential equations. The numerical solution accuracy and computation time of the Parareal algorithm executing on the GPU are demonstrated on the single machine infinite bus test system. Two types of dynamic model of the single synchronous generator namely the classical and detailed models are studied. The numerical solutions of the ordinary differential equations computed by the Parareal algorithm are compared to that computed using the modified Euler’s method demonstrating the accuracy of the Parareal algorithm executing on GPU. Simulations are performed with varying numerical integration time steps, and the suitability of Parareal algorithm in computing near real-time solutions of ordinary different equations is presented. A speedup of 25× and 31× is achieved with the Parareal algorithm for classical and detailed dynamic models of the synchronous generator respectively compared to the sequential modified Euler’s method. The weak scaling efficiency of the Parareal algorithm when required to solve a large number of ordinary differential equations at each time step due to the increase in sequential computations and associated memory transfer latency between the CPU and GPU is discussed.