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The choice of the factorization rank of a matrix is critical, e.g., in dimensionality reduction, filtering, clustering, deconvolution, etc., because selecting a rank that is too high amounts to adjusting the noise, while selecting a rank that is too low results in the oversimplification of the signal. Numerous methods for selecting the factorization rank of a non-negative matrix have been proposed. One of them is the cophenetic correlation coefficient (ccc), widely used in data science to evaluate the number of clusters in a hierarchical clustering. In previous work, it was shown that ccc performs better than other methods for rank selection in non-negative matrix factorization (NMF) when the underlying structure of the matrix consists of orthogonal clusters. In this article, we show that using the ratio of ccc to the approximation error significantly improves the accuracy of the rank selection. We also propose a new criterion, concordance, which, like ccc, benefits from the stochastic nature of NMF; its accuracy is also improved by using its ratio-to-error form. Using real and simulated data, we show that concordance, with a CUSUM-based automatic detection algorithm for its original or ratio-to-error forms, significantly outperforms ccc. It is important to note that the new criterion works for a broader class of matrices, where the underlying clusters are not assumed to be orthogonal.

As the energy transition is upon us, the replacement of combustion engines by electrical ones will imply a greater stress on the electrical grid of different countries. Therefore, it is of paramount importance to simulate a great number of hypothetical multi-variant scenarios to correctly plan the roll-out of new grids. In this paper, we deploy Generative Adversarial Networks (GANs) to swiftly reproduce the non-Gaussian and multimodal distribution of real energy-related samples, making GANs a valuable tool for data generation in the field. In particular, we propose an original dataset deriving from the aggregation of two European providers including hourly electric inland generation from several European countries. This dataset also comes along with the corresponding season, day of the week, hour of the day and macro-economic variables aiming at unequivocally describing the country’s energetic profile. Finally, we evaluate the performance of our model via dedicated metrics capable of grasping the non-Gaussian nature of the data and compare it with the state-of-the-art model for tabular data generation.

With the increasing constraints on energy and resource markets and the non-decreasing trend in energy demand, the need for relevant clean energy generation and storage solutions is growing and is gradually reaching the individual home. However, small-scale energy storage is still an expensive investment in 2022 and the risk/reward ratio is not yet attractive enough for individual homeowners. One solution is for homeowners not to store excess clean energy individually but to produce hydrogen for mutual use. In this paper, a collective production of hydrogen for a daily filling of a bus is considered. Following our previous work on the subject, the investigation consists of finding an optimal buy/sell rule to the grid, and the use of the energy with an additional objective: mobility. The dominant technique in the energy community is reinforcement learning, which however is difficult to use when the learning data is limited, as in our study. We chose a less data-intensive and yet technically well-documented approach. Our results show that rulebooks, different but more interesting than the usual robust rule, exist and can be cost-effective. In some cases, they even show that it is worth punctually missing the H2 production requirement in exchange for higher economic performance. However, they require fine-tuning as to not deteriorate the system performance.

Hydrogen has been identified as a very promising vector for energy storage, especially for heavy mobility applications. For this reason, France is making significant investments in this field, and use cases need to be evaluated as they are sprouting. In this paper, the relevance of H2 in two storage applications is studied: a domestic renewable electricity production system connected to the grid and a collective hydrogen production for the daily bus refill. The investigation consists of the sizing of the system and then the evaluation of its performance according to several criteria depending on case. Optimizations are made using Bayesian and gradient-based methods. Several variations around a central case are explored for both cases to give insights on the impact of the different parameters (location, pricing, objective, etc.) on the performance of the system.Our results show that domestic power-to-power applications (case 1) do not seem to be competitive with electrochemical storage. Meanwhile, without any subsidies or incentives, such configuration does not allow prosumers to save money (+16% spendings compared to non-equipped dwelling). It remains interesting when self-sufficiency is the main objective (up to 68% of energy is not exchanged). The power-to-gas application (case 2, central case), with a direct use of hydrogen for mobility, seems to be more relevant according to our case study, we could reach a production cost of green H2 around 5 €/kg, similar to the 3–10 $/kg found in literature, for 182 houses involved. In both cases, H2 follows a yearly cycle, charging in summer and discharging in winter (long term storage) due to low conversion efficiency.