Showing papers by "Federico Milano published in 2022"

Impact of PLL Frequency Limiter on Synchronization Stability of Grid Feeding Converter

Abstract: It is well known that grid-feeding converters that synchronize to the grid through a Phase-Locked Loop (PLL) can become unstable after a fault. An often-neglected element that plays an important role in the converter synchronization stability is the PLL frequency limiter. While it slows down the phase change during the fault, the frequency limiter also constrains the error of the PLL input, thus leading to a longer settling time. This letter investigates the mechanism of the converter synchronization stability caused by the frequency limiter and provides a taxonomy to evaluate its impact on the overall system dynamic response.

Improving the Power System Dynamic Response Through a Combined Voltage-Frequency Control of Distributed Energy Resources

Abstract: The paper proposes a control scheme to improve the dynamic response of power systems through the automatic regulators of converter-based Distributed Energy Resources (DERs). In this scheme, both active and reactive power control of DERs are varied to regulate both frequency and voltage, as opposed to current practice where frequency and voltage controllers are decoupled. To assess the proposed control against the current state-of-art, the paper also defines a metric that captures the combined effect of frequency/voltage response at any given bus of the network. Results indicate that the proposed control strategy leads to a significant improvement in the stability and performance of the overall power system. These results are based on a comprehensive case study carried out by employing a modified version of the IEEE 39-bus benchmark system, where a portion of the synchronous machines is substituted by converter-interfaced DERs. The impact on the proposed control of load models, the $R/X$ ratio of network lines, as well as the level of DER penetration to the grid, are properly evaluated and conclusions are duly drawn.

Small-Signal Stability Analysis of Numerical Integration Methods

Abstract: 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.

Curvature-Based Control for Low-Inertia Systems

Abstract: This letter proposes a simple and inexpensive control of distributed energy resources aimed at improving the power system dynamic performance. The rationale behind the proposed control relies on a recent interpretation of the frequency in the differential geometry framework. A comparison with well-established controls in terms of eigensensitivity and time-domain performance is carried out to show the effectiveness of the proposed control.

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

Abstract: 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.

The Frenet Frame as a Generalization of the Park Transform

Abstract: 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.

Power system modelling as stochastic functional hybrid differential‐algebraic equations

Abstract: : This paper presents the software tools developed for the research project Advanced Modelling for Power System Analysis and Simulation (AMPSAS) funded by Science Foundation Ireland from 2016 to 2021. The main objective of AMPSAS was the development of novel analytical and computational tools to understand, efficiently design, and optimise ever-changing modern power systems and smart grids, through model-based approaches. In particular, the paper discusses: (i) stochastic differential equations for modelling power systems which are subject to large stochastic perturbations (e.g., wind and solar generation); (ii) the effect of controller and modelling imperfections, e.g., delays, discontinuities, and digital signals, on both local and area-wide regulators in power systems; and (iii) the stability analysis and dynamic performance of power systems modelled through stochastic, delay and hybrid implicit differential-algebraic equations. The software tool developed during the execution of AMPSAS integrates areas of applied mathematics, automatic control, and computer science. Several implementation features and open challenges of this software tool are also discussed in the paper. A variety of examples that illustrates the features of this software tool are based on a dynamic model of the all-island Irish transmission system.

Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency

Abstract: 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.

Voltage Stability Enhancement Through Active Power Control of Converter-Interfaced Generation

Abstract: The paper investigates the ability of Converter-Interfaced Generators (CIGs) to improve the stability margin of power systems by adjusting their active power injections at their points of connection. To this aim, a voltage magnitude-active power control scheme is examined and its effectiveness is tested considering different topology and CIG reactive power capability scenarios. The focus is on the effect on long-term voltage instabilities due to the system reaching its loadability limit, as well as on small-disturbance, short-term instabilities, arising in the form of Hopf bifurcations. Simulation results are based on a continuation power flow analysis carried out considering a modified version of the IEEE 39-bus system, where a portion of synchronous machines is replaced by CIGs.

Least Square Method for the Identification of Equivalent Inertia Constant

Abstract: This paper proposes a simple yet accurate least square method to identify the equivalent inertia constant of individual inertia providers. The proposed method requires ambient measurements and is based on the well-known classical swing equation of synchronous machines. The proposed method shows a very good accuracy for the inertia identification of the rotational and virtual inertia in different operating conditions, including stationary ones, and can also be used to quantify the inertia support effect of the time-varying adaptive inertia.

On the Impact of Probability Distributions of Stochastic Processes on Power System Dynamics

Abstract: The paper originates from the observation that, when fitting stochastic processes based on data measurements, it is often possible to fit various probability distribution functions (PDFs) to the same data. This paper evaluates the impact of modeling stochastic processes with different PDFs on the dynamic behavior of the power system. The case study uses the well-known two-area system, which is modified to include stochastic processes through wind generation. Simulation results show that modeling stochastic processes such as wind speeds through different PDFs impacts the behavior of the power system differently, despite exhibiting similar statistical properties. The case study also shows that some PDFs worsen the effects of contingencies.

On the Numerical Stability and Accuracy of One-Step Delay Approximations

Abstract: The One-Step Delay Approximation (OSDA) technique consists in delaying certain variables of a power system model with time delays of magnitude equal to the step size of the Time Domain Integration (TDI). The objective of the OSDA is to reduce the mutual coupling of the system's equations and the density of the Jacobian matrix that needs to be factorized at each step of the TDI. In turn, the OSDA leads to a simulation speedup but may worsen the accuracy of the results. This paper provides a novel matrix-pencil based approach to assess the OSDA technique in terms of its impact on the accuracy and numerical stability of the TDI of power systems. The case study illustrates the proposed approach through the WSCC 9-bus benchmark system.

Frequency Divider as a Continuum

Abstract: The letter describes a novel, continuum-based approach, to capture the evolution of electromechanical dynamics in a power network following a disturbance. Such approach is based on the frequency divider formula (FDF), which was recently proposed by the third author. A key point in obtaining the frequency divider formula (FDF) as a consequence of a continuum, is to show that the spatial rate of change, at a given time, of the frequency along a lossless line is constant. The proposed derivation is then compared with the electromechanical wave approach (EWA), which has been discussed in the literature in a variety of hues and is aimed at modeling the propagation in a power system of frequency oscillations following a disturbance. The discussion illustrates similarities and differences between FDF and electromechanical wave approach (EWA).

Effect of Uniformly Distributed Parameter Line Models on the Evaluation of PV Curves and of the Maximum Loading Condition

Abstract: PV curves are generally obtained by considering lumped models of transmission lines. This approximated model can yield an inaccurate estimation of the maximum loading condition of the system. This letter shows that accuracy can be improved by considering line models with uniformly distributed parameters. Analytical evaluations of the PV curve and of the voltage collapse point of a two-bus system are obtained by applying the Ossanna's theorem. Then the impact of different line models on large-scale systems is evaluated through a continuation power flow analysis of a real-world model of the Sicilian transmission system including the Sicily-Malta 120 km cable connection.

On the Impact of Discrete Secondary Controllers on Power System Dynamics

Abstract: This paper discusses the impact of discrete secondary controllers on the dynamic response of power systems. The idea of the paper originates from the observation that there is a range of values, from few tens of seconds to few minutes, of the execution cycles of conventional automatic generation control (AGC) that leads to a limit cycle. Below and above this range the system is stable. This is certainly not a problem in practice as the AGC updates the power set points of generating units every few seconds. However, this phenomenon has interesting consequences if one considers real-time electricity markets with short dispatch periods (i.e., 5 minutes) as these markets can be modeled as a sort of AGC. The paper first provides a formal analogy between conventional AGC and real-time electricity markets. Then it shows that the discretization-driven instability exists if the system includes a real-time electricity market modeled as secondary frequency controller. Finally, the paper discusses the impact of the combined effect of high wind generation shares and discrete secondary controllers on power system dynamics.

Real-Time Estimation of VPP Equivalent Inertia and Fast Frequency Control

Abstract: The paper proposes a method to estimate, in transient conditions, the equivalent inertia constant and fast frequency control droop gain of Virtual Power Plants (VPPs). The estimations are obtained based on the frequency and active power variations at the point of connection of the VPP with the power grid. The accuracy of the estimator is enhanced by a novel technique employed to approximate the VPP's equivalent internal reactance, based on the voltage and reactive power variations at the point of connection. The performance of the proposed method is illustrated through a case study based on a modified version of the WSCC 9-bus system.

Robust Nonlinear Controller to Damp Drivetrain Torsional Oscillation of Wind Turbine Generators

Abstract: This article develops a novel nonlinear controller for the mitigation of drivetrain torsional oscillations of wind turbine generators following large disturbances. The key idea is to integrate differential geometry theory with an extended state observer. Differential geometry allows transforming the wind turbine generator nonlinear model into a simple second-order Brunovsky system, whereas the extended state observer can accurately estimate the states of the transformed Brunovsky system and compensate unknown disturbances. Simulation results show that, under various conditions in different test systems, the proposed controller achieves significant enhancements with respect to conventional approximate linearization-based controller and nonlinear sliding mode control-based method.

Frequency control and regulating reserves by VPPs

Abstract: The virtual power plant (VPP) is a paradigm that aggregates widely dispersed resources over an electrical grid or part of it thereof and aspires to emulate the behavior of conventional generators. In this sense, VPPs are expected to contribute to system services. One of the most typical and important system services is frequency control. Frequency control ensures the continuous balance of generation and demand and acts so to preserve it in real-time as imbalances occur. To realize this service, proper reserves, defined as regulating reserves, must be procured and retained to respond to any imbalance during a given planning time-frame. As VPPs comprise multiple different resources, which are dispersed over potentially vast areas, procuring regulating reserves and realizing frequency control is a challenging task. This chapter defines frequency control as a service offered by VPPs, and also illustrates the ways this service may be planned and realized.

Taxonomy of Power Converter Control Schemes based on the Complex Frequency Concept

Abstract: This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of complex frequency. This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased.

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

Abstract: Virtual inertia controllers (VICs) for wind turbine generators(WTGs)have been recently developed to compensate the reduction of inertia in power systems. However, VICs can induce drivetrain torsional oscillations of WTGs. This paper addresses this issue and develops a novel nonlinear VIC based on objective holographic feedback theory and the definition of a completely controllable system of Brunovsky type. Simulation results under various scenarios demonstrate that the proposed technique outperforms existing VICs in terms of enhancement of system frequency nadir, suppression of WTG drivetrain torsional oscillations, fast and smooth recovery ofWTGrotor speed to the originalmaximum power point (MPP) before the disturbance as well as preventing secondary frequency dip caused by traditional VIC. The proposed technique is also able to adaptively coordinate multiple WTGs to enhance the frequency support and the dynamic performance of each WTG.

Inertia Estimation through Covariance Matrix

Abstract: —This work presents a technique to estimate on-line the inertia of a power system based on environment measure- ments. The proposed approach 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 damping of the machines. This feature is exploited to estimate the droop of grid-following converters. The technique is comprehensively tested on a modified version of the IEEE 39-bus system.

Complex Frequency

Abstract: 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 the usual approximations of the models utilized for the transient stability analysis of power systems. A variety of analytical and numerical examples show the applications and potentials of the proposed concept.