2-D Convolutional Deep Neural Network for the Multivariate Prediction of Photovoltaic Time Series

The transition toward increasingly distributed and sustainable energy systems has turned renewable energy forecasting into a central component of modern energy engineering. In the case of photovoltaic plants, the ability to accurately anticipate how much energy will be produced in the coming hours becomes crucial for power grid management, energy market optimisation, and the coordination of distributed resources. The work addresses this challenge by introducing a new deep learning scheme designed for multivariate energy time series forecasting. The central idea is to exploit information coming simultaneously from multiple physical variables, not only the power produced by a photovoltaic plant, but also correlated meteorological measurements, in order to improve prediction accuracy over time.

Traditionally, many energy forecasting techniques rely on univariate approaches, where a model predicts the future behaviour of a variable based solely on its past values. In the renewable energy domain, however, this approach presents clear limitations, since energy production depends on a complex network of environmental phenomena. To overcome this limitation, a multivariate paradigm is adopted in which several time series are considered simultaneously. In addition to the power generated by a photovoltaic plant, the model incorporates meteorological variables such as temperature, wind speed and direction, atmospheric pressure, humidity, and turbulence-related indicators. These quantities contain indirect but relevant information about solar radiation behaviour and atmospheric conditions that influence energy production. The goal therefore, becomes identifying the temporal and physical relationships that connect these variables, transforming a heterogeneous set of environmental measurements into a representation suitable for forecasting.

The most original methodological contribution concerns how the data are represented inside the neural network. Instead of treating time series as independent sequences, samples from different variables and different time instants are organised into a two-dimensional structure that resembles an image. This transformation makes it possible to apply convolutional techniques typically used in computer vision. Convolutional filters analyse simultaneously the relationships among different variables and the dependencies over time, generating feature maps that capture the most relevant correlations among the observed phenomena. Through this process, the network automatically builds a richer representation of the data compared to traditional time series embedding methods. The result is a set of features that describe not only the temporal evolution of energy production, but also the interactions among multiple environmental variables.

The proposed architecture integrates two fundamental components of modern deep learning. The first consists of a bidimensional convolutional layer responsible for automatically extracting informative features from multivariate sequences. The second is an LSTM network, a specialised type of recurrent neural network designed to capture long-term temporal dependencies. The features produced by the convolutional stage are converted into sequences that feed the LSTM network, which performs the actual prediction task. Thanks to its memory cell structure, the LSTM can retain relevant information across multiple time steps and model complex temporal dynamics in the data. The entire system can therefore be interpreted as a deep architecture composed of specialised layers: some dedicated to extracting structured representations from the data, and others focused on modelling the temporal dynamics that govern energy production.

To evaluate the effectiveness of the method, the system is tested using real-world data collected from a photovoltaic power plant located in the United States. The dataset includes two years of hourly observations related to both energy production and several meteorological variables, including temperature, wind speed, wind direction, humidity, and atmospheric pressure. The performance of the proposed model is compared with architectures based solely on traditional LSTM networks. Experiments are conducted across different months of the year and under various forecasting horizons, considering both short-term predictions over a few days and more demanding extended forecasting scenarios. The results show that the integration of bidimensional convolution and LSTM enables the model to better exploit the information contained in multivariate datasets. In many experimental configurations, the proposed scheme achieves lower prediction errors than traditional approaches, demonstrating a stronger capability to capture correlations between meteorological phenomena and energy production.

The value of this approach extends beyond photovoltaic forecasting alone. The methodology illustrates how artificial intelligence can integrate heterogeneous sources of information to improve the understanding of complex energy systems. In the future, models of this kind may become key components of advanced energy management systems, intelligent microgrids, and virtual power plants that coordinate multiple renewable sources. Improving the ability to forecast energy production means increasing the stability of the entire energy ecosystem and facilitating the large-scale integration of renewable resources. The evolution of deep learning techniques applied to energy time series, therefore, points toward a clear direction: not merely observing data, but building models capable of interpreting the physical relationships that govern the system. In this perspective, artificial intelligence becomes a tool to transform the complexity of environmental data into actionable knowledge for managing the energy systems of the future.