arXiv subjects

Federico Milano

Publications and source records attributed to Federico Milano.

50 records · Page 3Linked to original sources

arXiv2023

Analysis of Wind Energy Curtailment in the Ireland and Northern Ireland Power Systems

The All-Island power system (AIPS) of Ireland and Northern Ireland currently accommodates up to 75% of system non-synchronous penetration (SNSP) (e.g., wind). These unprecedented levels of renewable penetration challenge the operation of the power system. The AIPS is not always able to accommodate all of the available renewable generation due to binding operational and technical constraints. In this context, this paper analyses wind energy curtailment in the AIPS using actual data. It is found that there is a positive correlation between the installed wind capacity and curtailment levels, and that the trend is that these levels increase. The paper also shows that the main driver for curtailment in AIPS during 2020-2021 was the operational constraint that imposes a minimum number of conventional units online (MUON) (80% of the time), with the SNSP limit accounting for less than 20%. Other system-wide limits, such as rate of change of frequency (RoCoF) and inertia are found to have a negligible impact on wind curtailment.

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arXiv2023

Frequency Quality in Low-Inertia Power Systems

This paper analyses the issue of frequency quality in low-inertia power systems. The analysis is based on a real-world large-scale low-inertia power system namely, the All-Island transmission system (AITS) of Ireland and Northern Ireland currently accommodating up to 75% of non-synchronous generation. The paper is motivated by a recent trend of some frequency quality parameters such as the standard frequency deviation and the slow frequency restoration. The paper first discusses the frequency control services currently in place to ensure frequency quality in the AITS. An analysis of the frequency quality parameters of the AITS is then presented based on actual data. The paper also discusses, through an illustrative example, the effectiveness of automatic generation control as a potential approach to keep frequency within the operational range.

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arXiv2023

Inertia Estimation Through Covariance Matrix

This work presents a technique to estimate on-line the inertia of a power system based on ambient measurements. The proposed technique utilizes the covariance matrix of these measurements and solves an optimization problem that fits such measurements to the synchronous machine classical model. We show that the proposed technique is adequate to accurately estimate the actual inertia of synchronous machines and also the virtual inertia provided by the controllers of converter-interfaced generators that emulate the behavior of synchronous machines. We also show that the proposed approach is able to estimate the equivalent damping of the classical synchronous machine model. This feature is exploited to estimate the droop of grid-following converters, which has a similar effect of the swing equation equivalent damping. The technique is comprehensively tested on a modified version of the IEEE 39-bus system as well as on a dynamic 1479-bus model of the all-island Irish transmission system.

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arXiv2022

On the Calculation of the Variance of Algebraic Variables in Power System Dynamic Models with Stochastic Processes

This letter presents a technique to calculate the variance of algebraic variables of power system models represented as a set of stochastic differential-algebraic equations. The technique utilizes the solution of a Lyapunov equation and requires the calculation of the state matrix of the system. The IEEE 14-bus system serves to demonstrate the accuracy of the proposed technique over a wide range of variances of stochastic processes. The accuracy is evaluated by comparing the results with those obtained with Monte Carlo time domain simulations. Finally, a case study based on a 1479-bus dynamic model of the all-island Irish transmission system shows the computational efficiency of the proposed approach compared to the Monte Carlo method.

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arXiv2022

The Frenet Frame as a Generalization of the Park Transform

The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three dimensions, which correspond to the common three-phase circuits. Then, the expression of the time derivative of the proposed transform is discussed and the Frenet-Serret formulas and the Darboux vector are introduced. The change of reference frame and its differentiation based on Cartan's moving frames and attitude matrices are also described. Finally, the extension to circuits with more than three phases is presented. The features of the Frenet frame are illustrated through a variety of examples, including a case study based on the IEEE 39-bus system.

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arXiv2022

Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency

This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system.

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arXiv2022

Small-Signal Stability Analysis of Numerical Integration Methods

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1, 479-bus dynamic model of the All-Island Irish Transmission System.

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arXiv2021

Applications of the Frenet Frame to Electric Circuits

The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of "torsional frequency." Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper.

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arXiv2021

Complex Frequency

The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for constant elements of the network admittance matrix. A variety of analytical and numerical examples show the applications and potentials of the proposed concept.

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arXiv2021

A Geometrical Interpretation of Frequency

The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of frequency is shown to be a special case of the proposed theoretical framework. Several examples serve to show the features, generality as well as practical aspects of the proposed approach.

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arXiv2020

Nonlinear Virtual Inertia Control of WTGs for Enhancing Primary Frequency Response and Suppressing Drive-Train Torsional Oscillations

Virtual inertia controllers (VICs) for wind turbine generators (WTGs) have been recently developed to compensate for the reduction of inertia in power systems. However, VICs can induce low-frequency torsional oscillations of the drive train of WTGs. This paper addresses this issue and develops a new nonlinear VIC based on objective holographic feedbacks theory. This approach allows transforming the objectives that require improvement into a completely controllable system of Brunovsky's type. Simulation results under various scenarios demonstrate that the proposed method outperforms existing VICs in terms of suppression of WTG low-frequency drive-train torsional oscillations, enhancement of system frequency nadir as well as fast and smooth recovery of WTG rotor speed to the original MPP before the disturbance. The proposed method is also able to coordinate multiple WTGs.

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arXiv2020

On the Modeling and Simulation of Anti-Windup Proportional-Integral Controller

This paper investigates the chattering and deadlock behaviors of the proportional-integral (PI) controller with an anti-windup (AW) limiter recommended by the IEEE Standard 421.5-2016. Depending on the simulation method, the controller may enter a chattering or deadlock state in some combinations of parameters and inputs. Chattering and deadlock are analyzed in the context of three numerical integration approaches: explicit partitioned method (EPM), execution-list based method (ELM), and implicit trapezoidal method (ITM). This paper derives the chattering stop condition for EPM and ELP, and analyzes the impacts of step size and convergence tolerance for simultaneous method. The deduced chattering stop conditions and deadlock behavior is verified with numerical simulations.

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arXiv2015

Construction of SDE-based wind speed models with exponential autocorrelation

This paper provides a systematic method to build wind speed models based on stochastic differential equations (SDEs). The resulting models produce stochastic processes with a given probability distribution and exponential decaying autocorrelation function. The only information needed to build the models is the probability density function of the wind speed and its autocorrelation coefficient. Unlike other methods previously proposed in the literature, the proposed method leads to models able to reproduce an exact exponential autocorrelation even if the probability distribution is not Gaussian. A sufficient condition for the property above is provided. The paper includes the explicit formulation of SDE-based wind speed models obtained from several probability distributions used in the literature to describe different wind speed behaviors.

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arXiv2015

Generalized Model of VSC-based Energy Storage Systems for Transient Stability Analysis

This paper presents a generalized energy storage system model for voltage and angle stability analysis. The proposed solution allows modeling most common energy storage technologies through a given set of linear differential algebraic equations (DAEs). In particular, the paper considers, but is not limited to, compressed air, superconducting magnetic, electrochemical capacitor and battery energy storage devices. While able to cope with a variety of different technologies, the proposed generalized model proves to be accurate for angle and voltage stability analysis, as it includes a balanced, fundamental-frequency model of the voltage source converter (VSC) and the dynamics of the dc link. Regulators with inclusion of hard limits are also taken into account. The transient behavior of the generalized model is compared with detailed fundamental-frequency balanced models as well as commonly-used simplified models of energy storage devices. A comprehensive case study based on the WSCC 9-bus test system is presented and discussed.

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