In recent years, photovoltaic energy has become one of the most implemented electricity generation options to help reduce environmental pollution suffered by the planet. Accuracy in this photovoltaic energy forecasting is essential to increase the amount of renewable energy that can be introduced to existing electrical grid systems. The objective of this work is based on developing various computational models capable of making short-term forecasting about the generation of photovoltaic energy that is generated in a solar plant. For the implementation of these models, a hybrid architecture based on recurrent neural networks (RNN) with long short-term memory (LSTM) or gated recurrent units (GRU) structure, combined with shallow artificial neural networks (ANN) with multilayer perceptron (MLP) structure, is established. RNN models have a particular configuration that makes them efficient for processing ordered data in time series. The results of this work have been obtained through controlled experiments with different configurations of its hyperparameters for hybrid RNN-ANN models. From these, the three models with the best performance are selected, and after a comparative analysis between them, the forecasting of photovoltaic energy production for the next few hours can be determined with a determination coefficient of 0.97 and root mean square error (RMSE) of 0.17. It is concluded that the proposed and implemented models are functional and capable of predicting with a high level of accuracy the photovoltaic energy production of the solar plant, based on historical data on photovoltaic energy production.