**1. Introduction**

Power flow (PF) analysis is popularly employed to analyze electrical power systems by estimating the voltage and phase angle of buses inside the power system. Power flow computation is designed to repeatedly apply several numerical methods for solving nonlinear equations of such electric power systems; the calculations thus require a considerable amount of computational execution time. Furthermore, due to a general increase in the demand for electric power, the introduction of emerging renewable energy sources, and the spread of electric vehicles (EVs), modern power systems are continually expanding and display rapidly increasing complexity. The adoption of smart grids and advanced electronic devices creates a need for more electrical power of higher quality, and the spread of EVs is expected to lead to increased power consumption in the near future. Hence, recently, there has been greater demand for more accurate power flow analysis. In addition, because power flow analysis involves a large amount of contingency analysis for all probable accident conditions in power systems, the computational resources and time required for such analyses have increased dramatically.

Numerous studies have been undertaken to significantly reduce the computation time of complex numerical analysis by applying parallel and distributed processing with massive computing resources. In particular, the use of high-performance computing (HPC) machines to reduce computational times in power flow computation has long been studied [1–5]. After D. M. Falcao et al. [1] and V. Ramesh et al. [2] introduced the application of HPC to power system problems, several studies have been conducted in earnest into the use of HPC for accelerating power system analysis. R. Baldick et al. [3] and F. Li et al. [4] proposed rapid power flow computation using distributed computing, which uses multiple computers connected via an Ethernet network. Currently, because HPC technologies such as multi-core processors, clusters, and GPUs have made significant strides, many more studies have

been undertaken into accelerating power system analysis by using parallel and cloud computing and adopting HPC technologies [5].

Attempts to reduce the analysis time of power systems by using GPU-based parallel computing have recently increased. Of course, the use of GPU is not confined to power flow studies. One example is the visualization part of power systems. Some studies into the visualization of power systems have been undertaken [6]. Real-time visualization of power systems is necessary for the simulation, state estimation, and prediction of power systems, and many studies have been performed investigating the speedup using HPC [7]. The parallel processing is also valuable in the electric railway system because it requires a lot of computation and data processing in various fields such as scheduling optimizations, signal processing, finite element analysis, train dynamics, and power network simulation [8]. A variety of parallel processing techniques can be applied to the electric railways, and some studies using GPU have been conducted in this area [9–11]

The rest of the paper is organized as follows: In Section 2, we describe the background of our review, such as GPU, power flow computation, and matrix handling methods, briefly. In Section 3, we present GPU application trends in power flow computation. For the sake of understanding, we introduce the previous PF studies with parallel processing and describe the recent trend of GPU-based power flow studies. In Section 4, we provide a detailed description of some representative studies that apply GPU-based parallel computing to power flow analysis and summarize their performance using a comparative analysis table. Finally, the conclusion is made in Section 5.
