The large-scale penetration of renewable energy sources is forcing the transition towards the future electricity networks modeled on the smart grid paradigm, where energy clusters call for new methodologies for the dynamic energy management of distributed energy resources and foster to form partnerships and overcome integration barriers. The prediction of energy production of renewable energy sources, in particular photovoltaic plants that suffer from being highly intermittent, is a fundamental tool in the modern management of electrical grids shifting from reactive to proactive, with also the help of advanced monitoring systems, data analytics and advanced demand side management programs. The gradual move towards a smart grid environment impacts not only the operating control/management of the grid, but also the electricity market. The focus of this article is on advanced methods for predicting photovoltaic energy output that prove, through their accuracy and robustness, to be useful tools for an efficient system management, even at prosumer's level and for improving the resilience of smart grids. Four different deep neural models for the multivariate prediction of energy time series are proposed; all of them are based on the Long Short-Term Memory network, which is a type of recurrent neural network able to deal with long-term dependencies. Additionally, two of these models also use Convolutional Neural Networks to obtain higher levels of abstraction, since they allow to combine and filter different time series considering all the available information. The proposed models are applied to real-world energy problems to assess their performance and they are compared with respect to the classic univariate approach that is used as a reference benchmark. The significance of this work is to show that, once trained, the proposed deep neural networks ensure their applicability in real online scenarios characterized by high variability of data, without requiring retraining and end-user's tricks.