Detecção, identificação e correção de erros grosseiros de medição em redes de distribuição desequilibradas utilizando multiplicadores de Lagrange

Abstract

This work addresses detecting, identifying, and correcting gross errors (EG) in unbalanced three-phase electrical systems. Unbalanced three-phase electrical systems are standard in power distribution networks, where unbalanced loads, connection issues, and component failures can lead to imbalances in electrical quantities such as voltages and currents. A method is proposed that applies state estimation (E-OPFT) to detect, identify, and correct these gross errors in unbalanced electrical systems. The method utilizes Lagrange multipliers (ML) related to the lower and upper bounds of the measured variables, thereby calculating error indices related to these bounds. Initially, the developed method implements gross error detection algorithms that identify inconsistent patterns in the measurements. Subsequently, identification algorithms are applied to determine the buses that have gross errors. This step is performed through Modified E-OPFT (E-OPFT-m). At the end of E-OPFT-m, the ML values corresponding to the lower and upper margins are found, and with them, the respective error indices (IND) of the measurements are calculated, and when non-zero values are encountered, it indicates that the measurement contains an error. The correction step uses the mean error, which depends on the identified error and the meter uncertainty, to determine pseudo-measurements, which are considered as the new measurements for estimation, and finally applies it to Final E-OPFT (E-OPFT-f). This technique allows correcting the incorrect measurements and re-estimating the system states, aiming to provide more accurate and reliable estimates of the electrical quantities. The dissertation also presents case studies and simulations in modified 4-bus and 33-bus systems to validate the effectiveness and robustness of the proposed method. The results show that the method is capable of accurately detecting and correcting gross errors in unbalanced three-phase electrical systems, contributing to the performance and safety of these systems. In summary, this work contributes to the advancement of the detection, identification, and correction of gross errors in unbalanced three-phase electrical systems, offering a new method based on state estimation and Lagrange multipliers. The obtained results demonstrate the feasibility and efficiency of the proposed method, providing significant benefits to the electrical sector in terms of safety and operational efficiency.