The paper presents selected results of research on the design of artificial neural networks and training them using the electrical power system development model (EPS or EP system) based on IEEE RTS 96 test data, i.a. creation of training and test files, development of architecture of the artificial neural network, selection of parameters of the network, selection of appropriate training and testing method, etc. As a result of the development and training an ANN, the following EP system development models were obtained, which were examined for sensitivity to changes of the number of hidden layers, number of neurons in a layer, activation function, training method, etc. Subsequently, simulation models for studying fitness of the obtained models to the real systems. Interesting results were obtained, e.g. the method of the neural modelling of the system, the optimal architecture of the ANN that is a model of the system, possibilities and directions to improve a neural model of the system, etc.