Alessandro Formisano

Lightning strikes represent a major source of risk for power systems, particularly for overhead distribution lines where indirect events can induce dangerous overvoltages through electromagnetic coupling. This work proposes a first step towards the development of a predictive lightning protection system based on the detection of Preliminary Breakdown (PB) pulses, i.e., sequences of weaker atmospherics discharges typically preceding the Return Stroke (RS) by some tens of milliseconds. Synthetic PB and RS induced voltage waveforms are generated using a dedicated simulation tool. Time domains samples of PB induced voltages from two sensors are used to train a Deep Learning (DL) model to predict the maximum RS-induced voltage and assess whether it may lead to a flashover event. The line Critical FlashOver Voltage (CFO), increased by 50%, is used as a threshold for classification between safe and dangerous conditions. The proposed model achieves promising performance, claiming for further development of a lightning preventive protection (to be combined with state-of-art methods) exploiting the PB pulses induced voltage measurements.

A new class of neural networks has been recently introduced to solve problems based on some physical model. Such networks are called “Physical-Informed Neural Networks” (PINN). PINN are trained not based on input-output data, but rather by explicitly enforcing the model physical laws. More in detail, they are trained to minimize the “equations residual” in the physical model in each point of the domain rather than the discrepancy with known data. In this contribution, we propose to formulate the equations of ElectroMagnetism (EM) embedded in a PINN by using a weak formulation approach. This helps convergence of the training process, thanks to the lower derivation order required in the error computation. In addition, the presence of different materials in the domain is easily treated. In this digest, the approach is described in its fundamentals, and a simple example is presented.

This work explores the use of Physics-Informed Neural Networks (PINNs) and a newly proposed approach, called the STacked Adaptive Residual PINN (STAR-PINN), to solve magnetic diffusion problems in the magneto quasi static regime. The study covers both one- and two-dimensional domains. The key advantage of this new architecture is the ability to refine predictions through multiple lightweight PINN blocks to achieve accurate results with lower computational cost and less architectural complexity than more advanced neural networks like Recurrent Neural Networks or Convolutional Neural Networks. The simplicity and efficiency of STAR-PINN make it a promising solution for tackling large-scale and nonlinear challenges in computational electromagnetics.

Machine Learning (ML) approaches are getting increasingly common in numerical modelling, thanks to their promptness once trained and to their capability of self‐extracting numerical models from behavioural examples. While classical numerical models have been developed for many years and presently represent a robust and well‐known solution to handle complex electromagnetic (EM) models, they still suffer from some drawbacks—the need to create a discrete version of the model from basic laws and the need for massive computational power in more complex cases. Although commercial software tools have been developed that are able to handle semi‐automatically these issues, in some applications, such as optimised design and iterative resolution of inverse problems, the cited issue may still represent a relevant limitation. We aim to balance the drawbacks and the advantages of both approaches, by investigating the performance of representative methods in each class on a simple yet relevant electrostatic problem described by Elliptic Partial Differential Equations (E‐PDE).

In this contribution the authors propose a hybrid Boundary Element Method – Physics Informed Neural Networks (BEM – PINN) approach, to be used for the resolution of partial differential equations arising when formulating boundary-value problems in electromagnetism. The approach retains both the advantages of integral methods (compact representation and no need to mesh large domains) and differential methods, where the term “differential” refers here to the Automatic Differentiation carried out during the training phase of the PINN. The method is easy to implement and adds an additional flexibility to purely PINN based solution methods.

Several electromagnetic systems and devices comprise metallic plates, acting either as structural support to other active parts of the system, or as electromagnetic shield. In the case of external anomalous or unwanted electromagnetic solicitations, the plates are interested by induced currents. These currents couple with electrically active parts of the system generating spurious effects. To correctly size the protection circuits, the computation of reaction fields and the coupling with the structures is usually done numerically. In this study, we propose a modal analysis of the plate current map to achieve a semi-analytical expression, and we attempt to relate plate modes to a suitable set of lumped elements; this allows a straightforward integration with an equivalent circuit of the system active parts and a consequent ease of calculation for the sizing of the protection system. The results indicate that the proposed approach can achieve acceptable outcomes compared to the FEM approach. Achieving the desired outcomes depends on selecting an appropriate discretization step, which is influenced by both the number of modes and the frequency.