The transition of power grids from systems based on synchronous generators to those integrating increasing shares of renewable energy sources (RES) reduces system inertia and challenges frequency stability, particularly in weak grids. Grid-forming (GFM) control has emerged as a key solution, enabling inverter-based resources to provide synthetic inertia and autonomous grid support. This paper proposes a method for assigning virtual inertia and damping coefficients to multiple GFM inverters in a microgrid or distribution feeder. The objective is to ensure that the aggregated dynamic response at the point of common coupling aligns with target values specified by the grid operator. The proposed method is validated through simulations on an IEEE test network.

Adaptive networks with time-varying connectivity provide a fundamental paradigm to model networks of neurons, whose fingerprint is synaptic plasticity. We employ the stability analysis proposed in a recent paper, based on the formulation of a master stability function, to study cluster synchronization in adaptive networks with neural plasticity. We investigate how adaptation affects multistability in the network, where each stable solution encodes an archetypal pattern for auto-associative memories. This analysis is carried out with respect to the overall coupling strength, the adaptation rule, the number of nodes of the network, and the number of coexisting stable solutions. In particular, the coupling strength can be tuned to determine the maximum cluster size and the variability in the cluster sizes.

This paper presents a black-box method for generating surrogate data from measurements taken on inductors working up to magnetic saturation. The proposed method is based on a sequential neural network architecture, optimized through the Python Tensorflow framework and the Keras API, which accurately predicts the inductor flux dynamics under varying operating conditions. The generated data can be useful to fit existing circuit models to a limited set of physical measurements (easy-to-measure quantities, i.e., inductor voltage and current), complemented by the obtained surrogate data. The proposed black-box model performs well in predicting flux across different frequencies and amplitudes. This research is a first proof of concept (we focus on zero-bias sinusoidal inputs and amorphous-core inductors at fixed temperature); anyway, it highlights the potential of combining deep learning with robust optimization and pre-processing techniques to improve predictive accuracy in circuit models of inductors working up to magnetic saturation. These models can be used for simulating and designing high-power-density switch-mode power supplies.

In this work, a nonlinear behavioral model is proposed for air-gapped ferrite-core inductors working up to magnetic saturation. The component is represented through the series connection of a nonlinear conservative inductor and a linear resistor, accounting for the instantaneous losses in both the windings and the core. The model is identified and validated through experimental measurements collected on a real buck converter. A very limited set of inductor voltages and currents is used for parameter identification. Some model coefficients depend explicitly on the air-gap length, which is useful for converter design purposes.

In this work, a nonlinear behavioral circuit model is proposed for air-gapped ferrite-core inductors working up to magnetic saturation. The model comprises a nonlinear conservative inductor, with current-dependent inductance, and two linear resistors, accounting for losses in both the winding and the core. Two representations are proposed for the nonlinear inductance, parameterized by both the number of turns and the air-gap length. The model (in both versions) is identified and validated through experimental measurements collected on a real buck converter. Inductor voltages and currents are used for parameter identification. The obtained results exhibit a good match with the experimental measurements used for validation purposes. An example of the application of the model to the design of a buck converter exploiting partially saturating inductors is also proposed.

In this paper, the derivative-free optimization algorithm MADS (mesh adaptive direct search) is adapted for implementation on field programmable gate array (FPGA) with fixed-point data representation. MADS is then exploited to solve constrained nonlinear optimization problems arising from non-linear model predictive control. The application on two examples taken from the literature shows the advantages of the proposed circuit architecture over the existing work, in terms of latency and resource occupation.

With the increasing presence of renewable energy sources in power grids, inertia estimation has become a pivotal problem in ensuring stable energy distribution. Inertia estimation during normal operating conditions of the network is still an open problem, since most algorithms rely on post-fault data or injection of probing signals in the grid. Here we extend a previously proposed algorithm for online inertia estimation to account for the presence of turbine governors in the power grid. The algorithm was tested on the IEEE 14-bus power system and it was successful in tracking the inertia of generators with and without turbine governors.

This paper is concerned with the study of the stability of the cluster-synchronous solution for directed networks of dynamical systems. Two recently proposed methods are compared by using a simple example network, thus evidencing their advantages and disadvantages, potentialities, and limitations.

A novel nonlinear behavioral model is proposed for an amorphous-core inductor working up to magnetic saturation. The model relies only on electrical quantities and represents the component as the series connection of a nonlinear conservative inductor and a nonlinear resistor, which accounts for the instantaneous losses in both the windings and the core. The model is identified and validated through measurements collected on a simple circuit, with applied unbiased sinusoidal voltage at two different frequencies.

The increasing presence of renewable energy sources (RES) in a power grid tends to reduce its inertia constant, which quantifies the grid's ability to contrast the frequency changes due to external disturbances. This led to the development of control strategies that interface the RES to the grid providing synthetic inertia, but these strategies cannot avoid oscillations of the overall system inertia, thus requiring algorithms for the online inertia constant estimation under normal operating conditions of the power grid. In this paper, we consider one of these algorithms, which exploits the data measured online through phasor measurement units, and critically analyze it, in order to efficiently apply it to the estimation of the inertia constant in the IEEE-14-bus power system, also with the addition of a PV power plant. The obtained results point out an increased efficiency of the online estimation of the network inertia.

A nonlinear inductor model has been recently proposed, which takes into account the magnetic saturation and the dependence of the inductance on the temperature. The model depends on seven parameters, which are identified based on experimental measurements of the inductor current in a switch-mode power supply. In this paper we show how the accuracy of each parameter affects the overall modeling accuracy in reproducing the inductor current.

This paper is concerned with the analysis of multi-layer networks consisting of different kinds of oscillators and couplings. In particular, we propose an algorithm for finding equitable clusters in this general class of networks, thus generalizing an existing algorithm specific for networks with identical nodes and one kind of connections. The algorithm is suitable to analyze complex networks of particular interest for the scientific community, such as neuron networks and electrical networks. The algorithm is tested on a random heterogeneous network with 40 oscillators of two different kinds and couplings of two different kinds. The stability of the obtained clusters is checked in a two-dimensional parameter space by using brute-force simulations.

This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.

More compact Switched-Mode Power Supplies (SMPSs) satisfying the overall design specifications can be obtained by exploiting ferrite core inductors working in partial saturation. In this case, the inductance is no longer a constant parameter, since it exhibits a sharp drop as the inductor current increases. A behavioral model has been recently proposed, which provides the inductance at steady state. In this paper, a generalization of this model is presented, in order to capture the inductance behavior also during the thermal transient. The model inputs are the the inductor current and the SMPS load current, both measurable quantities. The model fitting to experimental measurements relies on accurate SMPS simulations performed with the envelope analysis method, particularly suitable for fast-slow systems. The simulations are also used to validate the model reliability, through comparisons with the experimental results on a boost converter.

We propose and discuss a digital architecture suitable for hardware implementation of multifunctional neural networks to regulate several gaits for quadruped locomotion. These circuits have a far-reaching application for various bio-inspired robotics and synthetic prosthetics. The circuit is tested by implementing an 8-cell network proposed and analyzed here for the first time, whose robustness is checked with respect to parameter mismatching.

Any Atomic Force Microscope (AFM) scanner based on piezoelectric ceramics is affected by nonlinear distortions, mainly due to rate-independent hysteresis and rate-dependent creep, two different phenomena often referred to, collectively, as rate-dependent hysteresis. To compensate for these distortions, especially in old or cheap instruments, empirical open-loop compensation techniques are frequently adopted. In this paper, a complete hardware/software toolchain is proposed, for data acquisition, identification of hysteresis and creep models, and real-time open-loop compensation of rate-dependent hysteresis in AFM scanners.

This paper discusses practical approaches for designing reduced synthetic circuits of central pattern generators (CPGs) for quadruped locomotion using our newly developed bifurcation toolkit. Specifically, two CPGs containing only four elements (cells) are proposed that can reliably generate natural gaits of typical quadrupeds more effectively than large dedicated complex networks do. In addition, we analyze an enhanced locomotion system that incorporates a neuromechanical model for each leg and includes mechanisms of sensory feedback. We demonstrate how the proposed CPGs produce the desired gaits, which remain robust with respect to external perturbations.

This paper describes the MATLAB toolbox HysTool for the identification from experimental measurements and the simulation of four different hysteresis and creep models (Preisach, Prandtl-Ishlinskii, Kuhnen and power-law). The toolbox can automatically generate the inverse models (compensators) and also provide (for three out of four models) the C files for their microcontroller implementation. Tests on two different datasets are provided.

This paper is focused on a new object-oriented toolbox, called CEPAGE, devoted to simulation and analysis of Central Pattern Generators (CPGs). A CPG is a little group of neurons producing periodical patterns, which control rhythmic activities of animals. CEPAGE is conceived to carry out brute-force bifurcation analysis, but can also generate data for subsequent continuation analysis through other widely-used packages, such as AUTO or MATCONT. Two case studies are considered, with three and four neurons, with the twofold purpose of illustrating the main CEPAGE functionalities and provide new analysis results.