Comparing Different Approaches for Solving Large Scale Power-Flow Problems With the Newton-Raphson Method

Abstract

This paper focuses on using the Newton-Raphson method to solve the power-flow problems. Since the most computationally demanding part of the Newton-Raphson method is to solve the linear equations at each iteration, this study investigates different approaches to solve the linear equations on both central processing unit (CPU) and graphical processing unit (GPU). Six different approaches have been developed and evaluated in this paper: two approaches of these run entirely on CPU while other two of these run entirely on GPU, and the remaining two are hybrid approaches that run on both CPU and GPU. All six direct linear solvers use either $LU$ or $QR$ factorization to solve the linear equations. Two different hardware platforms have been used to conduct the experiments. The performance results show that the CPU version with $LU$ factorization gives better performance compared to the GPU version using standard library called cuSOLVER even for the larger power-flow problems. Moreover, it has been proven that the best performance is achieved using a hybrid method where the Jacobian matrix is assembled on GPU, the preprocessing with a sparse high performance linear solver called KLU is performed on the CPU in the first iteration, and the linear equation is factorized on the GPU and solved on the CPU. Maximum speed up in this study is obtained on the largest case with 25000 buses. The hybrid version shows a speedup factor of 9.6 with a NVIDIA P100 GPU while 13.1 with a NVIDIA V100 GPU in comparison with baseline CPU version on an Intel Xeon Gold 6132 CPU.

Keywords

• High performance computing
• Newton method
• parallel algorithms
• power engineering computing
• power-flow
• direct solver