arXiv subjects

Federico Milano

Publications and source records attributed to Federico Milano.

At least 37 records · Page 2Linked to original sources

arXiv2025

Transient Slack Capability

This paper introduces the concept of Transient Slack Capability (TSC), a set of three necessary device-level conditions to ensure stability under sustained power perturbations. TSC states that a device must (1) possess sufficient stored energy; (2) a controlled input power; and (3) maintain internal energy balance and synchronization. The paper shows that the relation among the time-scales of storage, control, and power perturbation is at the core of the TSC concept. Using the port-Hamiltonian (PH) framework, these conditions are formalized and validated via simulations on an adapted model of the WSCC 9-bus system. Case studies demonstrate that TSC is achievable in both Grid-Following (GFL) and Grid-Forming (GFM) converter control schemes, provided the conditions above are satisfied. Sensitivity analysis serves to identify storage and power reserve requirements to meet Conditions 1 and 2; the impact of converter current limiters on Condition 3; and inertia-less solutions able to achieve TSC.

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arXiv2025

Data Center Model for Transient Stability Analysis of Power Systems

The rising demand of computing power leads to the installation of a large number of Data Centers (DCs). Their Fault-Ride-Through (FRT) behavior and their unique power characteristics, especially for DCs catered to Artificial Intelligence (AI) workloads, pose a threat to the stability of power systems. To ensure its stability, it is required accurate models of the loads involved. Here we propose a dynamic load model that properly captures the behaviour of DCs. Its three most defining features are the use of an Uninterrupted Power Supply (UPS) which sits between the server load and the grid, the cooling load represented by an induction motor, and a pulsing load that represents the transients caused by contemporary DCs with significant AI workloads. The features of the proposed model and its impact on the dynamic performance of transmission systems are illustrated through a model of the all-island Irish transmission system and real-world data of the DCs currently connected to this system.

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arXiv2025

Impact of Power Fluctuations on Frequency Quality

This paper analyzes how power injections affect frequency quality in power systems. We first derive a general expression linking active and reactive power injections at buses to the system's frequency. This formulation explicitly considers both real and imaginary frequency components, providing a complete description of frequency behavior in power systems during transients. Next, we extend our analysis to incorporate stochastic variations of power injections. Using the frequency divider concept and power-based frequency estimation, we develop analytical relationships linking stochastic load fluctuations to frequency deviations. We discuss under which conditions the Central Limit Theorem cannot be applied to capture the frequency distribution, thereby clarifying how its hypotheses are not satisfied in power system applications. Then, we establish clear criteria for the appropriate use of statistical methods in frequency analysis. Finally, we validate our theoretical results through simulations on modified IEEE 14-bus and all-island Irish transmission test systems, highlighting the accuracy, practical utility, and limitations of our proposed formulation.

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arXiv2025

Teager Energy Operator as a Metric to Evaluate Local Synchronization of Power System Devices

This paper introduces a novel formulation to evaluate the local synchronization of power system devices, namely Synchronization Energy (SE). The formulation is derived based on the complex frequency concept and the Teager Energy Operator applied to the complex power. This formulation offers valuable insights into the relationship between complex frequency of voltage and current of the device and its stationary operating. Based on this relationship we derive the conditions for a novel definition of local synchronization of power system devices. Through various case studies, the paper demonstrates how SE can effectively assess local synchronization under diverse operating conditions.

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arXiv2025

Asymmetry of Frequency Distribution in Power Systems: Sources, Estimation, Impact and Control

This paper analyses an emerging real-world phenomena in inverter-based renewable-dominated power systems, namely, asymmetry of frequency distribution. The paper first provides a rationale on why asymmetry reduces the "quality" of the frequency control and system operation. Then it provides qualitative theoretical insights that explain asymmetry in terms of the nonlinearity of real-world power systems and associated models. In particular network losses and pitch angle-based frequency control of wind power plants are discussed. Then the paper proposes a nonlinear compensation control to reduce the asymmetry as well as a statistical metric based on the frequency probability distribution to quantify the level of asymmetry in a power system. Real-world data obtained from the Irish and Australian transmission systems serve to support the theoretical appraisal, whereas simulations based on an IEEE benchmark system show the effectiveness of the proposed nonlinear compensation. The case study also shows that, while automatic generation control reduces asymmetry, frequency control limits and droop-based frequency support provided by wind generation using a tight deadband of 15 mHz, namely active power control, leads to a significant increase in the asymmetry of the frequency probability distribution.

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arXiv2025

Smooth Rate Limiter Model for Power System Stability Analysis and Control

The letter proposes a smooth Rate Limiter (RL) model for power system stability analysis and control. The proposed model enables the effects of derivative bounds to be incorporated into system eigenvalue analysis, while replicating the behavior of conventional non-smooth RLs with high fidelity. In addition, it can be duly modified to enhance the system's dynamic control performance. The behavior of the proposed model is demonstrated through illustrative examples as well as through a simulation of the New York/New England 16-machine 68-bus system.

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arXiv2024

Local Synchronization of Power System Devices

This paper introduces a novel concept of local synchronization of power systems devices based on the difference between the complex frequency of the voltage and current injected at terminals. Formal definitions are provided to account for bounded and asymptotic local synchronization. The definitions are suitable for modern power systems as they remove classical assumptions limiting the application of the concept of synchronization to synchronous machines and omitting voltage dynamics. The paper also provides a systematic analytical description of the synchronization mechanisms of common power system devices. Finally, a variety of examples is included to illustrate the theoretical value and practical application of the proposed definitions to power systems modeling and stability analysis.

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arXiv2024

Dual Grid-Forming Converter

This letter proposes a dual model for grid-forming (GFM) controlled converters. The model is inspired from the observation that the structures of the active and reactive power equations of lossy synchronous machine models are almost symmetrical in terms of armature resistance and transient reactance. The proposed device is able to compensate grid power unbalance without requiring a frequency signal. In fact, the active power control is based on the rate of change of the voltage magnitude. On the other hand, synchronization and frequency control is obtained through the reactive power support. The letter shows that the proposed dual-GFM control is robust and capable of recovering a normal operating condition following large contingencies, such as load outages and three-phase faults.

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arXiv2024

Equivalence between Geometric Frequency and Lagrange Derivative

The paper shows the equivalence between the geometric frequency of an electric quantity, namely, voltage and current, and the Lagrange derivative of a stream-line of a fluid. The geometric frequency is a concept recently proposed by the author and is a generalization of the instantaneous frequency, a quantity that is particularly important for the analysis and the control of electric power systems. On the other hand, the Lagrange derivative is mostly utilized in fluid dynamics and helps decomposing the time derivative into various components. The paper shows how these components relate to the elements of the geometric frequency. The paper also shows, through a variety of numerical examples, how the decomposition of the Lagrange derivative helps identifying the distortion of the waveform of a measured electric quantity and how this information can be utilized to classify system operating conditions.

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arXiv2024

Instantaneous Frequency Estimation in Unbalanced Systems Using Affine Differential Geometry

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on this link, a new instantaneous frequency estimation formula is proposed, which is particularly suited for unbalanced and single-phase systems. Several examples as well as measurements based on two real-world events illustrate the findings of the paper.

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arXiv2024

Dynamic Slack Bus

This letter proposes a general dynamic formulation of slack bus. With this aim, the angle constraint imposed by the slack bus is redefined as a set of differential equations and an energy source. The existence and role of the transient component of this source is also discussed in the letter. Based on this framework, the letter shows that the swing equations of synchronous machines can be interpreted as distributed, dynamic, multi-variable, local slack buses. Other relevant cases, including primary and secondary frequency regulation, passive loads as well as grid following and grid forming converters are discussed.

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arXiv2024

Instantaneous Power Theory Revisited with Classical Mechanics

The paper revisits the concepts of instantaneous active and reactive powers and provides a novel definition for basic circuit elements based on quantities utilized in classical mechanics, such as absolute and relative velocity, momentum density, angular momentum and apparent forces. The discussion leverages from recent publications by the authors that interpret the voltage and current as velocities in generalized Lagrangian coordinates. The main result of the paper is a general and compact expression for the instantaneous active and reactive power of inductances, capacitances and resistances as a multivector proportional to the generalized kinetic energy and the geometric frequency multivector. Several numerical examples considering stationary and transient sinusoidal and non-sinusoidal conditions are discussed in the case study.

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arXiv2024

Emerging Challenges of Integrating Solar PV in the Ireland and Northern Ireland Power Systems

This paper discusses emerging operational challenges associated with the integration of solar photovoltaic (PV) in the All-Island power system (AIPS) of Ireland and Northern Ireland. These include the impact of solar PV on: (i) dispatch down levels; (ii) long-term frequency deviations; (iii) voltage magnitude variations; and (iv) operational demand variations. A case study based on actual data from the AIPS is used to analyze the above challenges. It is shown that despite its (still) relatively low penetration compared to wind power penetration, solar PV is challenging the real-time operation of the AIPS, e.g., maintaining frequency within operational limits. EirGrid and SONI, the transmission system operators (TSOs) of the AIPS, are working toward addressing all the above challenges.

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arXiv2024

Stability Assessment of Low-Inertia Power Systems: A System Operator Perspective

This paper discusses the stability assessment of low-inertia power systems through a real-world large-scale low-inertia system, namely, the All-Island power system (AIPS) of Ireland and Northern Ireland. This system currently accommodates world-record levels of system non-synchronous penetration namely 75% (planning to increase to 80% next year). The paper discusses one-month results obtained with the state-of-the-art stability tool called look-ahead security assessment (LSAT). This tool carries out rotor-angle, frequency and voltage stability analyses and is implemented in the control centres of the transmission system operators (TSOs). The paper shows that, at the time of writing, the main binding stability constraint of the AIPS is related to the limits on the rate of change of frequency (RoCoF).

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arXiv2023

Modeling Hybrid AC/DC Power Systems with the Complex Frequency Concept

The concept of complex frequency has been recently introduced on the IEEE Transactions on Power Systems to study bus voltage variations in magnitude and frequency and their link with complex power injections of a power system. In this paper, the complex frequency is applied to time-varying series connections, namely, RLC dynamic branches, regulating transformers and AC/DC converters. The proposed modeling approach allows deriving an explicit expression for the complex frequency of the voltage of a certain bus as a linear combination of three elements: net current injected by the devices connected to the bus, adjacent voltages, and time-varying series branches. The proposed formulation unifies the link between voltage and frequency dynamics in AC, DC, as well as hybrid AC/DC power systems. A variety of static and dynamic examples are presented to show the potential of the proposed formulation. Relevant applications of the proposed modeling approach are outlined.

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arXiv2023

Enhancing Frequency Control through Rate of Change of Voltage Feedback

This letter proposes a simple and inexpensive technique to improve the frequency control of distributed energy resources. The proposed control consists in modifying the conventional estimated bus frequency signal with an additional feedback signal that utilizes the rate of change of the voltage magnitude measured at the same bus. The case study showcases the benefits of the proposed control and compares its performance with standard frequency control schemes through time-domain simulations.

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arXiv2023

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

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.

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arXiv2023

On the Emulation of Synchronous Machine Dynamics by Converter-Interfaced Generators

This paper discusses the conditions that a device needs to satisfy to replicate the behavior of a conventional synchronous machine (SM) connected to a power network. The conditions pertain to the device's stored energy, time scale of response, oscillation damping, and behavior during short-circuits. Relevant remarks for devices that do/don't satisfy these conditions are discussed through an illustrative numerical example as well as through simulation results based on a modified version of the well-known WSCC 9-bus test system.

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