Virtual load damping is a valid alternative to virtual inertia to ensure frequency support in low-inertia power systems. We show that virtual load damping can be provided by multiple small power/capacity inverter-based resources. This can be obtained by exploiting inverter-based resources installed at domestic utilities in distribution feeders, which integrate renewable energy sources. Assessing the impact of these units on frequency requires changing the paradigm used to study power grid stability, since feeders need to be simulated in detail and cannot be represented with equivalent load models anymore, as was done in the past. Time-domain analyses of modified versions of the IEEE 14-BUS and MINIWECC power system benchmarks, obtained by the addition of several feeders in different virtual load damping scenarios, are included to support our claims.

A challenge posed by the increasing penetration of inverter-based resources (IBRs) in distribution networks is how to efficiently simulate a transmission system with a large number of them, since this leads to an "explosion" in system complexity. This paper presents a two-step reduction method for IBR-dominated distribution networks. In the first step, the approach synthesizes a distribution network as a multi-port: one port at the substation connecting it to the transmission system and the others for each IBR connected to the feeder. Then, in the second step, IBRs at the connecting ports are possibly clustered, thus reducing their number. The method differs from others in the literature since it is numerical and can handle clusters of IBRs with different power ratings and set-points. Simulation results of a distribution network with IBRs show the effectiveness of the method.

Some (very) large circuits have the peculiar feature of being composed of numerous repetitions of sub-circuits identical in terms of topology and components. If a traditional simulation paradigm is adopted, such a structure poses a high computational burden. In this paper we describe a general approach based on isomorphism that greatly improves simulation efficiency by exploiting the repetitive structure of these sub-circuits. After describing the core aspects of the approach, we show its potentiality by simulating a battery energy storage system (BESS) at battery cell level in different conditions.

An adequate level of power system inertia and load damping is essential to ensure frequency stability following power imbalances. Prior to that, however, it is first necessary to be capable of estimating these parameters. In this paper, we propose an original method to estimate the global inertia and damping of a power system comprising conventional synchronous generators, as well as modern generation units based on grid forming and following converters, which can provide virtual inertia and load damping. The effectiveness of our approach is tested on a modified version of the IEEE39 power system with ambient noise.

Stability analysis of conventional power systems relies on established modelling practices and tools. Among them, a popular approach exploits the impedances at given buses computed after deriving the power flow solution of the grid typically modelled in the dq-frame. However, in modern grids, this approach is hindered by the presence of elements formulated in the abc-frame, such as inverter-based resources, which make the grid a hybrid system. This paper proposes a novel efficient and versatile tool, directly implemented at simulator level, that allows computing impedances even in these cases.

Modular multilevel converters, used in AC/DC power systems, are characterized by complex (trans-)impedances with a frequency dependence never seen before in electro-mechanical power devices. Since these impedances may severely influence the stability of the entire power system, adequate design actions are needed to ensure safety margins. A straightforward derivation of these complex (trans-)impedances requires making suitable numerical tools available to designers. In this paper, we compute these impedances with the periodic small-signal analysis, a novel numerical approach in the power system realm. After commenting on some impedances computed with this approach, we exploit them to understand how a modular multilevel converter can impact the stability of the AC or DC grids connected to it. Stability issues highlighted through periodic small-signal analysis are verified by detailed transient stability simulations.

Load forecasting plays a crucial role in the day-to-day operations of electric utilities, especially in modern power systems, where a significant share of power generation is attributable to renewable sources. Over the years, several algorithms have been developed to tackle this problem, on time scales ranging from a few hours to several months. Most recent solutions have employed machine learning techniques such as deep learning to increase the granularity of the prediction, down to the single-building level. Here, we employ a framework based on long short-term memory networks to estimate the average power consumption of a single building equipped with solar panels. We show which measurements are more important for an accurate forecast and test several prediction horizons in order to find the best trade-off between training speed and prediction accuracy. Our results reinforce the notion that long short-term memory networks can be successfully used for short-to medium-term load forecasting.

Instability and oscillation issues originating in high-voltage direct current (HVDC) systems comprising modular multilevel converters (MMCs) are gaining increasing interest in the research community. To detect such phenomena in advance, considerable effort has been devoted recently to developing MMC models for small-signal analysis. The derivation of such models is a challenging task due to the topology and complex control structure of MMCs, which results in them having a multi-frequency response. To address this issue, scholars developed methods based on dynamic phasors and harmonic state-space modelling, which, however, require extensive pen-and-paper computations. In this paper, the periodic small-signal analysis (PAC) is adopted to determine numerically several MMCs transfer functions. Such functions can be computed between any electrical circuit node or input/output port, without the need to recast the three-phase average MMC model to derive a linear equivalent one, possibly in the DQ-frame. We show how vector fitting allows converting these functions to equivalent algebraic representations, which can be profitably used to design MMCs and study their stability following some parameter changes. To showcase this feature, we exploit one of these transfer functions to detect DC-side instability in a point-to-point HVDC system.

The dynamics of modern hybrid power systems are characterized by behaviors at different timescales, typically separated by several orders of magnitude. In this paper we apply the envelope-following method to hybrid power systems simulations, in which single-phase and three-phase representations of a power system co-occur. This simulation method is well suited for handling coexisting behaviors occurring at different timescales. Compared to the simulation approaches present in the literature, the envelope-following method does not need to continuously switch between two separate simulation engines, but rather automatically handles instantaneous variations in the dynamics of the system, such as faults or topology changes. Additionally, given the vast penetration of power electronic components in modern electricity networks, employing the envelope-following method allows using a vast array of numerical algorithms that have been developed over the years to simulate electrical and electronic circuits. The proposed approach is validated by means of power systems case studies of increasing complexity.

Approximate stability boundaries for Constant on- Time buck converters are derived and verified against numerical results obtained by bifurcation analysis. These boundaries are given as analytical expressions involving the main Constant on- Time (cot) buck converter parameters. They allow the designer to avoid the appearance of the pulse bursting phenomenon. A case study is proposed having in mind automotive applications, which are characterized by a wide input-voltage range. The input- voltage and the output-capacitor equivalent series resistance, that is typically poorly controlled for many types of capacitors, were chosen as bifurcation parameters.

Modular multilevel converters (mmcs) are the basic building blocks of multi-terminal direct current systems (mtdcs). The current rapid growth of such systems makes it imperative to develop methods to analyse their dc-side stability, thereby ensuring a correct overall operation. In this paper, starting from a simplified mmc model, general conditions for dc-side stability are derived. These conditions have been validated by simulating a point-to-point high voltage direct current system and an mtdc network. mmc models of different degrees of accuracy have been adopted to show that the conditions derived in the paper hold with a good degree of approximation even when more detailed representations are considered.

In recent years, a novel approach based on multi-objective optimization has been developed to automatically tune biophysically realistic, multi-compartmental neuron models starting from electrophysiological recordings. Here, we apply this methodology to the optimization of model neurons capable of reproducing the reduced excitability observed in experiments carried out in cortical pyramidal cells in a rodent model of fetal alcohol spectrum disorder. We find that both control and ethanol-exposed model cells present an excellent match with the experiments in terms of membrane voltage dynamics, with the latter group displaying a small but significant rightward shift of their current-frequency relationship. We identify a possible interplay between model parameters and cellular morphology and suggest future improvements to better capture the features of dendritic voltage dynamics.

In this paper, a study of the nonlinear dynamics of a boost converter performing maximum power point tracking from a PV source and charging a battery is presented. Numerical simulations shows that the system can exhibit subharmonic oscillations under the variation of suitable parameters such as those related to weather conditions (irradiance) and those related to the controller and the pulse width modulator. A state space switched model was developed for simulating the dynamic behavior and validating the desired working regime of the system in terms of the different parameters taking into account the nonlinearity of the PV source and the inductor. Analog-mixed-signal circuit simulation performed by the MATLAB-PAN (MP) simulation environment is used to explore the dynamical behavior that the system can exhibit. Stability boundaries are determined revealing the effect of the parameters on the system behavior by doing harmonic analysis of the circuit through simulations.

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 follow up with recent proposals of using inductors working in weak and deep-saturation region to improve the features of switching mode power supplies. To this aim, we use a constant on-time (COT) converter including a saturable inductor as a test vehicle. The inductor model takes into account both hysteresis and dependence on the working temperature of the core and windings. The digital controller of the COT converter is considered too. Electro-thermal simulations are performed to analyse the performances of the overall analog mixed-signal circuit. It is shown that using a proper saturable inductor positively impacts on the design of the converter by mitigating its main drawback of having a working frequency largely dependent on the load conditions and input supply voltage. Some weak points of proposed design are also identified.

The black box model by Josef Urbanek of electric-arc, in air-blast circuit breakers or in circuit breakers characterized by an electro-negative gas (e.g. SF6) as quenching medium, is adopted to simulate DC current interruption in HVDC applications. In particular, it is used to model the electric arc phenomenon in passive resonance circuit breakers. Owing to its formulation, the Urbanek model (UM) allows both to easily verify design rules proposed in the literature and to provide more accurate ones. Numerical bifurcation analysis and basin of attraction calculation are used to this aim.

Microelectromechanical systems contain mechanical elements coupled with conditioning electronics that control and process the signal generated by the mechanical component. These systems are miniature and can be easily integrated on one chip, which explains the enormous popularity of MEMS. The applications of MEMS began with environmental sensors and have grown to encompass RF and optical applications along with energy harvesting. Because of their mixed-domain nature, the design of conditioning electronics relies on accurate models of the mechanical component. As an additional requirement, the model must be simple enough and be compatible with common circuit simulation tools. The latter requirement may be particularly difficult to achieve due to the fact that most of modern MEMS structures are quite complex and often nonlinear. In this conference contribution, we describe the methodology of building a model of a nonlinear MEMS resonator using the conventional modelling approach and then using an improved model together with an optimisation technique on the basis of the circuit simulator PAN.

An electro-mechanical model of a SF6circuit breaker for medium voltage applications, i.e. for voltages up to 36 kV and short circuit currents up 50 kA is presented. The model is developed by starting from the well known Schwarz-Advonin arc model with the addition of the mechanical effects on the arc geometry and of the “puffer”. The puffer can blow the arc during its full duration and mainly during current zero crossing to extinguish it. This action is carefully exploited by breaker designers and often is the key aspect to obtain arc extinction in high current conditions.

The constant-time discontinuity map is presented and used to compute the nonlinear effects of quantization noise injected in fractional-N phase locked loops by ΔΣ modulators. The effects of quantization noise are studied through sensitivity analysis of the nominal trajectory of a noiseless integer-N phase locked loop with respect to a small additive perturbation. It is shown that, to accurately measure the effects of quantisation noise injection, a simple linearized model is not sufficient. A nonlinear constant-time discontinuity map across the switching points of the vector field allows the sensitivity analysis to be significantly improved, at a small computational cost.

In the near future Electrical Vehicless (EVs) will most likely replace conventional combustion-engine based ones. This and the increase in the use of renewable energy sources will have an important positive impact on our ecosystem. At the same time it will require a serious reanalysis and possibly redesign of the structure of our distribution network. In this paper we propose a model that, at a relatively fine level, describes the behavior of communities in terms of transport requirements, derives statistic driving behavior patterns and determines the corresponding induced Electric Vehicle Charging habits. The energy consumption of every simulated EV is computed taking into account the features of the trip and the vehicle itself. The model has been tailored to data extracted from a portion of the Milan (Italy) metropolitan area, but is trivially adaptable to any area for which a similar set of data is available. The obtained results are compared to data from similar works, showing good agreement. The outputs of the model, i.e. the energy consumption of the vehicles and their time-spatial distribution within a specific area (and consequently the loads on the distribution network nodes due to charging operations), have been (and will be) used to perform impact analyses on network performances and on personal mobility.

Quantization errors often produce the dominant phase noise component in wide-band fractional-N phase locked loops (PLLs). Recently, a few techniques have been proposed to alleviate the issue, at the cost of extra components. This work illustrates the possibility to significantly reduce the impact of quantization errors without additional building blocks, only relying on an optimal design of the noise shaping features of the ΔΣ modulator driving the PLL divider. In a representative design example the reduction in the peak noise density appreciated via linearized models can be better than 18 dB.

This paper is concerned with the time-domain simulation of circuits including noise sources. In general, when a circuit admits a steady-state solution, small signal analyses are used to determine noise effects. There is a class of circuits (e.g., fractional PLLs based on ΔΣ modulators and forced oscillators) not admitting a steady-state solution with a period reasonable low multiple of the characteristic time scales of the circuit. In commercial analog simulators, time domain noise analyses have been implemented by “extending” linear multi-step integration methods or by introducing sampled versions of noise generators. Through a set of basic benchmark circuits, we show that these extensions are often affected by a relevant numerical noise floor hiding the effects of noise sources and drastically limiting the applicability of time domain noise analysis.

Probe insertion is traditionally used in the frequency domain to increase robustness of the harmonic balance method and avoid the DC degenerate solution. This technique evidences several good properties, for instance when simulating oscillators that are based on high quality factor resonators or AC coupled ones. In this paper the probe insertion technique is extended to the time domain, allowing the application of the shooting method to a wider class of circuits including for example crystal oscillators. Time domain methods, such as shooting, are superior in the simulation of strongly nonlinear, and, thanks to a recent extention, mixed analog/digital circuits. Moreover, time domain probe insertion can be used to find multiple steady state solutions and check their stability properties, without the need to compute the eigenvalues of the monodromy matrix.

This paper proposes a novel electrical power system architecture capable to efficiently transfer energy from a solar generator to high power electric thrusters of a spacecraft. The architecture is based on a maximum power point tracker that acts on a DC/DC converter connected between a subsection of the solar generator and the thrusters. The other sections of the solar generator, that deliver most of the total power, are directly connected to the thrusters. The novelty of the proposed architecture is that the maximum power point tracker is always operating and, while conditioning only a fraction of the total power, is able to transfer to the thrusters an amount of power greater than the handled one.

Periodic circuits driven by multitone signals are still a challenging simulation problem despite several numerical methods being presented in the literature. In this paper, a mixed time-frequency method for the solution of this problem and suitable for both autonomous and nonautonomous circuits is presented. The method is based on an extension of the envelope following method, which allows us to reduce the number of unknowns involved in the steady-state problem with respect to previous mixed time-frequency approaches, and a suitable reformulation of the periodicity constraint that allows us to obtain a significant acceleration in the determination of the solution by reducing the time interval along which the envelope analysis must be performed. The method is first presented for nonautonomous circuits and then extended to autonomous ones.

The probe-based harmonic balance (HB) method is a well-known and largely used tool to compute the steady state behavior of autonomous circuits (oscillators). In this paper, the method is extended to analyze coupled oscillators, where the working frequencies and conditions, i.e., pulling and locking modes, have great relevance. It is shown that probe insertion can be considered as a specific matrix-bordering technique applied to the Jacobian matrix of the HB method. It transforms the original coupled autonomous system in a non-autonomous one, forcing the circuit to lock to the probes themselves. In this context, a novel approach to find the steady state solution is introduced. This approach exploits the properties of the power exchanged among the probes and the coupled oscillators. Possibly, more than one steady state solution with the oscillators working in pulling or locking modes can be found.

The shooting method is largely employed to determine the steady-state working condition of both autonomous and nonautonomous circuits. In general, the conventional shooting method employs the Newton algorithm to estimate a better approximation of the steady-state working condition. The Newton algorithm requires the computation of the Jacobian matrix and this seriously limits the use of the conventional shooting method to solve medium/large scale circuits. In this paper, an approach to efficiently determine the shooting matrix is presented. It is shown that the approach is also adequate to deal with mixed analog/digital circuits.

In this paper we present a design for reliability methodology, with the goal of reducing the impact of transistor VTHdegradation due for example to phenomena such as NBTI. It uses infrastructure IPs (I-IPs) featuring a self compensation scheme that automatically detects transistor aging effects and illustrates the design for test infrastructure used to make the SoC/System aware of the NBTI effects. This scheme is conceptually validated by using multi-level simulation and models. The discussion of possible exploitation models completes the paper.

This paper describes an approach to determine the Floquet exponents and the related eigenfunctions of linear time-varying circuits, that represent a vehicle to implement the variational model of periodic nonlinear circuits. The Floquet exponents and eigenfunctions allow us to exploit the structure of the analytical solution of the linear time-varying circuit and, as shown, yield an efficient solution. The proposed approach allows the calculation of the Floquet exponents directly and is developed from the harmonic-balance formulation adopted to find the steady-state solution of the nonlinear periodic circuit.

Some algorithmic aspects in RF circuit simulation are reviewed, emphasizing the problems related to the contributions included in this Special Session. Recent achievements as well as open problems are pointed out

In deep-submicrometer layouts, the determination of the signal delay due to interconnects is a main aspect of the design. Usually, on-chip interconnects are modeled by a distributed resistance-capacitance (RC) line. Key aspects of the interconnect modeling are the extraction of parasitic capacitances and the determination of reduced lumped models suited for electrical simulation. This paper addresses both these aspects. The parasitic capacitance extraction problem of layouts is efficiently carried out by means of the floating random walk (FRW) algorithm. It is shown how the employment of the Monte Carlo integration jointly to an extended version of the FRW algorithm allows to directly synthesize an accurate reduced-order RC equivalent net. The new method can deal with very complex geometries in an efficient way and needs neither fracturing of the original layout into subregions nor discretization of interconnects.

Computer simulation of periodically switched power circuits is an important step of the design; however it is an heavy task that takes a lot of cpu time. This paper presents an algorithm that reduces the cpu time required and improves simulation efficiency.

A numerical model of a three-junction device is presented. It allows the simulation of the external characteristics of the PNPN family devices, and in this work the simulation of the gate turn-off thyristor is particularly considered. The reasons that led to the realization of this model are explained by reviewing previous works in this area. The model is based on the Ebers-Moll equations extended to include the three-junction devices, and it is implemented (built-up) in the source code of the SPICE2 circuit simulator. A detailed description of the implementation of the model equations and different tests are reported and discussed. The results are in accordance with the measurements from the devices reported on data sheets and the computation time is sufficiently short.>