This research considers the dataset of the IEEE 14 bus system, generated from Modelica Dymola, to correctly classify the power system stability using deep neural networks and classical machine learning algorithms. The ground truth is set from the damping ratio metric of the system eigenvalues. The size of the dataset decreases the efficiency of the neural network slightly, but the efficiency of the classical machine learning algorithms drops drastically. Different architecture and activation functions are used for neural network design. Increasing the number of hidden layers increases prediction precision, however, increasing more than two hidden layers does not further improve the classification efficiency. This research will help in further research on the stability classification of power systems using damping ratio or eigenvalue as the base and using deep learning and machine learning algorithms for the prediction.