Estimation of Nodal Voltage Angles in Electrical Power Systems Using Artificial Neural Networks and Sensitivity Analysis of Input Variables

The estimation of nodal voltage angles is essential for the efficient and secure operation of electrical power systems. Traditionally, this estimation depends on the prior solution of the power flow problem, a procedure that may become computationally expensive in studies involving multiple operating scenarios. The present research demonstrates relevant potential impact by employing artificial neural networks for the direct estimation of nodal voltage angles. Although the power flow is used during the database generation stage, it is no longer required during the model application phase, resulting in a significant reduction in computational effort of approximately 80%. The proposed model was trained using the error backpropagation algorithm, achieving a mean squared error (MSE) on the order of 10−3 in only four iterations, with a training time of approximately 3 s and a correlation coefficient (R) of 0.99. Validation using unseen samples (10% of the samples) also demonstrated high accuracy, with an error on the order of 10−3 between the estimated and expected values. Furthermore, the P–θ curves were successfully obtained for the IEEE 14-, 30-, and 57-bus systems, enabling the identification of the maximum loading point with low estimation error. These results confirm the neural network’s ability to generalize and operate as a reliable estimator under different system loading conditions. Another relevant aspect of this work was the sensitivity analysis of the input variables, which made it possible to identify the variables that exerted the greatest influence on the neural network response. In addition, a normalization step was proposed to overcome distortions associated with the magnitudes of the input data, demonstrating the efficiency and robustness of the proposed method.