Periodic Steady State of Power Networks Using Limit Cycle Extrapolation, Spline Interpolation and Parallel Processing Based on GPUs

Abstract

This paper details a fast and efficient algorithm for the simulation of the steady state response of power networks under non-sinusoidal conditions in the time domain. The algorithm uses the Fourth-Order Runge-Kutta (RK4) to integrate the systems of ordinary differential equations (ODEs), generated by the power system. The Numerical Differentiation method (ND) is used to accelerate the process of convergence of the state variables to the limit cycle. The Cubic Spline Interpolation (CSI) to increase the efficiency of the conventional RK4 method to obtain the time domain waveform using the fewest number of possible time steps, and parallel processing techniques based on Graphic Processing Units (GPUs). It is shown that the implementation on a GPU-based platform becomes an efficient computational resource to find the steady state solution since floating-point operations and repetitive calculations increase in proportion to the size of the network; related with the computer effort.