International Conference on Renewable Energies and Power Quality (ICREPQ’15) La Coruña (Spain), 25 th to 27 th March, 2015 Renewable Energy and Power Quality Journal (RE&PQJ) ISSN 2172-038 X, No.13, April 2015 Fault detection in a three-phase system grid connected using SOGI structure to calculate vector components ROCHA, C. X. 1,2 , CAMACHO, J. R. 1 and VIAJANTE, G. P. 2 1 School of Electrical Engineering Universidade Federal de Uberlândia Campus Uberlândia – Minas Gerais (Brazil) Phone/Fax number:+0055 3432394538, e-mail: cxrocha@hotmail.com, jrcamacho@ufu.br 2 Department of Industry IFG, Instituto Federal de Goiás Campus Itumbiara – Goiás (Brazil) Phone/Fax number:+0055 6421035600, e-mail: ghunterp@gmail.com Abstract. Fault detection algorithms are very important in grid connected systems. They are used to analyze a three-phase system behavior in real time. When something wrong happens, they start some procedures to avoid the collapse. A three-phase system cannot be considered a simply sum of three independent phases, which leads us to apply some vector transform to obtain a more elegant representation of systems. A control system grid connected is based on the vector transform. In this paper we analyze a fault detection performance between some vector transform algorithms, and present a good way to accomplish these transforms using a SOGI (Second Order Generalized Integrator). Key words SOGI, grid connected, vector transform. Introduction Due to increasing global demand for energy, the depletion of natural resources of the planet (oil, coal, ...), in addition to concern over global warming, researchers worldwide are dedicated to provide clean and renewable energy (Xavier, 2013). In this context, electrical energy that can be considered one of the most important ways to distribute energy, have two main problems: Efficient generation and grid connection. A photovoltaic panel and wild turbines are today the most widely used way to generate renewable electrical energy. Thus, it’s necessary a big concern to interconnect these systems in the electrical grid. A distributed generation system, when connected with a electrical grid, need to have a synchronism and protection system, to prevent a big problems in the grid. Given the great complexity of the electrical grid systems, and a big amount of the interconnected generates system, have consider that existing controls are capable to predict unbalance phase, harmonics and even frequency changing in the power system. Thus, it requires algorithms and math tools to keep the grid under control, or simply detect disturbs in the source grid. Between the existing algorithms, the most suitable are processed using a mathematical transforms below: • Symmetrical components transform in time domain (Lyon, 1937); • αβ transform (Clarke, 1950); • dq transform (Park, 1927); • Symmetric Positive and Negative Components in αβ transform (Irani, 2003). 1. Three-Phase Transform A. Symmetrical components transform in time domain The method of decomposition into symmetric in the time domain (Lyon, 1937) components is an extension of the decomposition method in the frequency domain (Fortescue, 1918). Knowing that   é the sum of their symmetrical components, have: �   +   +   + � = 1 3 � 1   2  2 1    2 1 � �       � (1) �   −   −   − � = 1 3 � 1  2   1  2  2  1 � �       � (2) �   0   0   0 � = 1 3 � 1 1 1 1 1 1 1 1 1 � �       � (3) 1) Balanced Systems As shown in Fig. 1, in a system balanced, only the positive symmetric component (  + ) is equal system voltages (  ), and the Negative and Zero components has null value.