Elliptic dilogarithms and parallel lines

We prove Boyd's conjectures relating Mahler's measures and values of L-functions of elliptic curves in the cases when the corresponding elliptic curve has conductor 14

Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation

We consider the algebras eiΠλ (Q)ei , where Πλ (Q) is the deformed preprojective algebra of weight λ and i is some vertex of Q, in the case where Q is an extended Dynkin diagram and λ lies on the hyperplane orthogonal to the minimal positive imaginary root δ. We prove that the center of eiΠλ (Q)ei is isomorphic to Oλ (Q), a deformation of the coordinate ring of the Kleinian singularity that corresponds to Q. We also find a minimal k for which a standard identity of degree k holds in eiΠλ (Q)ei . We prove that the algebras AP₁,...,Pn;µ = Chx₁, . . . , xn|Pi(xi) = 0, Pn i=1 x₁ = µei make a special case of the algebras ecΠλ (Q)ec for star-like quivers Q with the origin c

The effect of manufacturing mismatch on energy production for large-scale photovoltaic plants

In the literature, the effect of the mismatch due to manufacturing tolerances on PV plant productivity has been investigated under the hypothesis of plant operation in Standard Test Conditions (STC). In this paper, mismatch impacts are evaluated in more realistic terms taking into account various possible operating conditions. Results are illustrated through the study case of a 1 MWp solar park for which module datasheets as well as flash test data are available. The plant production is evaluated assuming operating conditions that comply with the European efficiency standards. It is shown how the effect of a given mismatch on the annual productivity estimation can significantly change depending on the operating conditions

Advanced Methods for Photovoltaic Output Power Forecasting: A Review

Forecasting is a crucial task for successfully integrating photovoltaic (PV) output power into the grid. The design of accurate photovoltaic output forecasters remains a challenging issue, particularly for multistep-ahead prediction. Accurate PV output power forecasting is critical in a number of applications, such as micro-grids (MGs), energy optimization and management, PV integrated in smart buildings, and electrical vehicle chartering. Over the last decade, a vast literature has been produced on this topic, investigating numerical and probabilistic methods, physical models, and artificial intelligence (AI) techniques. This paper aims at providing a complete and critical review on the recent applications of AI techniques; we will focus particularly on machine learning (ML), deep learning (DL), and hybrid methods, as these branches of AI are becoming increasingly attractive. Special attention will be paid to the recent development of the application of DL, as well as to the future trends in this topic

A novel fault diagnosis technique for photovoltaic systems based on artificial neural networks

This work proposes a novel fault diagnostic technique for photovoltaic systems based on Artificial Neural Networks (ANN). For a given set of working conditions - solar irradiance and photovoltaic (PV) module's temperature - a number of attributes such as current, voltage, and number of peaks in the current-voltage (I-V) characteristics of the PV strings are calculated using a simulation model. The simulated attributes are then compared with the ones obtained from the field measurements, leading to the identification of possible faulty operating conditions. Two different algorithms are then developed in order to isolate and identify eight different types of faults. The method has been validated using an experimental database of climatic and electrical parameters from a PV string installed at the Renewable Energy Laboratory (REL) of the University of Jijel (Algeria). The obtained results show that the proposed technique can accurately detect and classify the different faults occurring in a PV array. This work also shows the implementation of the developed method into a Field Programmable Gate Array (FPGA) using a Xilinx System Generator (XSG) and an Integrated Software Environment (ISE)