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.

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.

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.

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.

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 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.

Knowing solar irradiance value allows an optimized management of photovoltaic (PV) power plants in terms of produced energy. Unfortunately, although sensing temperature is easy, the measurement of solar irradiance is expensive. In this paper, two circuit architectures for the estimation of the solar irradiance based on simple measurements are proposed. They are thought to be part of a centralized system implemented on field programmable gate array (FPGA) for sensing and monitoring of solar irradiance in a whole PV plant. The FPGA centralized architecture could allow for a real-time irradiance mapping by exploiting information coming from several low-cost measuring circuits suitably allocated on the PV modules. Validations on real irradiance data collected by the U.S. Department of Energy's National Renewable Energy Laboratory are presented.

Hysteresis is a nonlinear phenomenon useful whenever memory is required, but that can become annoying in applications where linearity is desired. In these cases, a possible way to reduce the inconvenience is to compensate the undesired memory effect by pre-processing the input signal through the hysteresis inverse model. In this paper, the inverse of a recently proposed circuit modeling rate-independent hysteretic phenomena is presented and discussed. The inverse circuit model is tested through experimental data measured from a commercial piezoelectric actuator. The obtained results are compared with those obtained by resorting to the well-known Preisach model. All the circuit simulations are performed by using PSPICE.