Comparação de métodos de armazenamento de matrizes esparsas para contribuição à simulação em tempo real de redes elétricas

Abstract

Real-time digital simulation (RTDS) of electrical networks is an important analysis tool, with applications in the operation, design, planning, and expansion of electrical systems. Among the simulators, the Real-Time Digital Simulator (RTDS®), developed by RTDS Technologies, and the HYPERSIM and eMEGASIM, produced by OPAL-RT Technologies stand out. To make SDTR viable, it is necessary the computational modeling of the components of the electrical networks and their characteristics, from the generation of energy and distribution and transmission circuits to the loads. This modeling represents a major obstacle for RTDS since it consists of solving systems of large linear equations, arising from the high number of bars that make up the networks. Invariably, the matrices that describe the behavior of the passive network are sparse and, in this work, emphasis is given to the storage techniques of these matrices, to optimize the processing, operating only with values other than zero. Through the collection of processing time and computational memory use, the performance of five of these techniques is compared: Compressed Sparse Row (CSR), Compressed Sparse Column (CSC), Compressed Sparse Vector (CSV), Skyline, and DFA2, which are associated with the iterative methods of Jacobi and Gauss-Seidel to obtain the solutions of the system of equations that describes the behavior of the electrical network. As a reference for this comparison, OpenDSS, through the OpenDSSDirect.py, was also submitted to the proposed analyses. The results obtained show that the CSR and CSC storage methods, associated with the Gauss-Seidel method, demonstrate the ability to collaborate with the simulation in real-time.